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1. 2 843 1130 8 136 0 6633 Inlet pressure controlled variable 144 142 Setpoint OLGA Measurement 2 j 500 1000 1500 2000 2500 Valve position manipulated variable X 2476 Y 0 6634 N 0 5 1000 2000 2500 time sec 1500 Figure 5 36 Simulation result of control using gain scheduling between PI controllers tuned for the initial choke valve position of Z 40 94 5 4 Comparison of experimental and simulated results The simulations in this thesis have been matched with the experimental models from valve1 Slow valve Therefore in case of numerical comparison it is reasonable to compare simulated results with experimental results from valve1 But generally in case of comparison of different tuning methods and finding the best tuning approach for the slugging system the simulated results do agree with the experimental results from the both valves In this section each tuning method would be discussed separately and the result of control from simulations and experiments will be compared Finally a comparison of all tuning methods used in the thesis based on the simulations and both valves experiments will be presented 5 4 1 Open loop bifurcation diagrams A comparison of the simulated open loop results from the OLGA case and the experimental results
2. Measurement 200 400 600 800 1000 1200 1400 1600 1800 Valve position manipulated variable a aw X 1742 Y 0 5461 0 0 200 400 600 800 1000 1200 1400 1600 1800 time sec Figure 5 32 Simulation result of control using the IMC based PID controller tuned at the initial choke valve position of Z 40 Inlet pressure controlled variable 146 144 Setpoint _ Measurement 142 L a 140 RE ee Re eT a 500 1000 1500 2000 Valve position manipulated variable N 0 4 X 1929 Y 0 5101 0 2 0 0 500 1000 1500 2000 time sec Figure 5 33 Simulation result of control using the IMC based PI controller tuned at the initial choke valve position of Z 40 88 5 3 3 3 Tuning using simple online method with gain scheduling Simple PI tuning rules based on identified MATLAB static model of nonlinear part of the system was used as the last tuning method in the simulations The method has been proposed by Jahanshahi Jahanshahi and Skogestad 2013 and described in section 2 9 3 5 3 3 3 1 Modifying MATLAB model As the first step in implementing this method the simple static MATLAB model of the system which tuning rules are based on needed to
3. 1 riser AP of SS2 corresponding to U 0 10ms andU co 2 00ms m iguid Co Gas 1 Blockage of the riser base 2 Slug growth 3 Liquid production 4 Fast liquid production 5 Gas blowdown a Riser AP bar i i 0 50 100 150 200 Time s b Figure 2 7 Stages for SS1 a a graphical illustartion b marked on a cycle of an experimental riser APtrace u 0 20ms andU 1 00ms Malekzadeh Henkes et al 2012 e Liquid CI Gas Riser Pipeline t mm 1 Blockage of the riser base 2 Slug growth 3 Fast liquid production 4 Gas blowdown a 50 100 150 200 Time s b Figure 2 8 Stages for SS2 a a graphical illustartion b marked on a cycle of an experimental riser APtrace u 0 10ms andu 2 00ms Malekzadeh Henkes et al 2012 10 2 5 Anti slug operations As the fields become more mature the more advanced technology is demanded The reason is that the energy of reservoir decreases due to its aging This leads to lower pressure and temperatures in reservoir The lower pressure of reservoir causes limited driving force to the flow and thereby lower phase velocities in result and finally more probable riser slugging formation Low temperatures also increase the probability of solid formation Changing the design of pipe riser system to avoid slugging cannot be economically feasible The most common methods for avoiding slugging are presented
4. mse 155 f F Mi V i l set point 150 lt 4 Exp data Filtered identified 145 250 300 350 400 450 500 550 600 650 700 time sec Figure 5 5 Presentation of identified closed loop step response The dashed black line shows the identified closed loop transfer function obtained from IMC design Then the open loop unstable system has been back calculated by using the procedure proposed by Jahanshahi Jahanshahi and Skogestad 2013 The open loop unstable system has the form of 0 0005538 S 2 858e 05 P s a S 0 008984S 0 004088 Equation 5 2 Then the IMC controller C is designed by using the method explained in section 2 9 2 2 The time constant of the closed loop system is an important manipulated parameter and has been selected as 20 This number was obtained by trial and error and experiencing different results The designed IMC controller is 287 0673 S 0 02146S 0 0007862 po ee ee Equation 5 3 S S 0 05161 The IMC controller is a second order transfer function which can be written in form of a PIDF controller PIDF is a PID controller which a low pass filter has been applied on its derivative action It will be mentioned as PID controller 53 A PI controller was also obtained by reducing the order of IMC controller to 1 The related tuning parameters have been obtained and are shown in table 5 3 Table 5 3 IMC based PID and PI tuning parameter E
5. Setpoint Measurement Filtered 150 148 0 100 200 300 400 500 600 time sec Figure 5 9 Set point step change for a closed loop feedback experiment with a P_only controller using inlet buffer pressure as control variable A low pass filter with a smoothing factor of 0 25 was used to remove the noise effect from the response 5 1 2 3 Tuning the controller Three different methods explained in section 2 9 have been used to tune the controller using buffer inlet pressure as the control variable and fast choke valve as the actuator The tuning procedure and the related results will be presented below 5 1 2 3 1 Tuning by Shams s closed loop method Shams s tuning method developed by Shamsuzzoha Shamsuzzoha and Skogestad 2010 was used as the first tuning method Table 5 4 shows the resulted tuning parameters by Shams s method The system has been considered as a first order plus delay model The information from the closed loop step test See figure 5 9 was used to find the tuning parameters Table 5 4 Tuning parameters from Sham s method for the slugging system 250 1 5738 1 3823 331 0775 246 7640 59 As expected according to results of valve 1 the PI controller with these tuning parameters couldn t stabilize the system meaning that Shams s method is not a suitable method to tune the slugging system controller 5 1 2 3 2 Tuning based on IMC design I
6. atan 1 72 2 z tp sgrt 12 72 Tau E sqrt 1 Z7 2 Tau Dl DO exp z tp Tau sin E tp Phi tauz 2 lau BOr z 27 Tau 2 lau 2 1l p1 2 lz 2 5 S Ci Ss disp The identified closed loop model GZ K2 llauz Ss exp 0 6 7 Tau 24s 2 2 2 Tau S 1 u zeros l round t_init dt dy_ s ones 1 round 3600 t _init dt t1l t 0 dt 3600 yl lsim G2 u t plot t yl y init k Linenidth 2 25 37 legend Setpoint OLGA measurement Identified model 3 o O o O BACK CALCULATION OF THE OPEN LOOP UNSTABLE SYSTEM AO 1 Tau 2 Al 2 z Tau BO K2 Tau 2 Bl K2 Tauz Tau 2 gt Kp dy_inf KcO abs dy_s dy_inf a0 AO 1 Kc0 Kp bO Kp ao bl B1 Kc0 al Al KcO b1 s tf s disp Identified model Ge b1 s b0 s 2 al s a0 gcl feedback Kc0 Ge 1 113 C 3 Design of Internal Model Controller 66 Internal Model Controller IMC Plant Information Zero Pole Gain Ts zpkdata Ge v indRHPzero real Zero gt 0 indices of open RHP Zeros indRHPpole real Pole gt 0 indices of open RHP poles RHPpoles Pole indRHPpole RHP poles NumRHP zeros sum indRHPzero number of open RHP Zeros NumRHPpoles sum indRHPpole number of open RHP poles Tauc 10 Tuning parameter time constant of the closed loop system for MP systems q tilde zpk Pole Zero 1 Gain k NumR
7. Ke taul K 2 Tetha taul min taul 8 Tetha Tau_c Tetha C 2 Model identification based on IMC design cle clear all close all load z30_148_150 Kev 14 dys 2 t init 200 dt 0 1 t z30_148_150 y z330 146 150s re z300 146 150 u z30_ 148 _150 e r Sr S Nr e o o figure 1 plot t r 2 Linewidch 2 25 hold on pLOoU t y D LineWwidth 2 25 xlabel time sec ylabel Inlet pressure kPa xlim 170 300 title Closed loop step response from OLGA simulations grid on hold on o o i_init find t t_init y_ plant y 1_init end t_plant t i_init end u_plant u i_init end YAN y i init 100 3 u ainit u i antac 100 ypl max y_plant dy pl abs ypl y init i_yp1 find y_plant yp1 t_pl mean t_plant i_ypl Vu min y plant 1 yol 10 1 ypl dy_u abs yu y_init i_yu find y_plant yu t_u mean t_plant i_yu E 112 yp2 max y_plant 1_yu 2 1i_yu dy p2 abs ypz Yoinit yini y_plant end dy int aba yini y init DO day pl dy inf l dy inf deltar s t u tpl vli dy_inf dy_u dy_p1 dy_inf z log v1 sgrt pi 2 l1og V1L 2 3 Tau deltaT pi sgrt 1 z 2 K dy ant dy ini dy s K2 K K 1 alpha K t1 K 1 Taul 2 2 Tau h L sqrt 4 2 2 Tau 2m Rael 2 Kel K 11 Tau 2 Lo tpl ciate Phi
8. Technology NTNU Date and signature 26 06 2 013 A Abstract One of the best suggested solutions for prevention of severe slugging flow conditions at offshore oilfields is the active control of the production choke valve This thesis is a study of robust control solutions for stabilizing multiphase flow inside the riser systems through S riser experiments and OLGA simulations Nonlinearity as the important characteristic of slugging system poses some challenges for control Focus of this thesis is on online tuning rules that take into account nonlinearity of the slugging system The main objective has been to increase the stability of riser systems at higher levels of valve openings with more production rates Similar research has been done previously but is repeated in this thesis using new systematic tuning methods Three different tuning methods have been applied in this thesis One is Shams s set point overshoot method developed by Shamsozzhoha Shamsuzzoha and Skogestad 2010 The other is IMC Internal Model Control based tuning method with respect to the identified model of the system from closed loop step test The last tuning method is simple PI tuning rules with gain scheduling for the whole Operating range of the system considering the nonlinearity of the static gain The two latter methods have been developed very recently by Jahanshahi and Skogestad Jahanshahi and Skogestad 2013 Two series of experiments have be
9. parameters by Shams s method K is the initial gain used in the step test K is the calculated proportional gain and 7 is the integral tuning parameter The system has been considered as a first order plus delay model Table 5 2 Tuning parameters from Sham s method for the slugging system 220 0 3846 0 6501 121 5189 224 3679 It was tried to control the system by the related tuning parameters seen in table 5 2 Yet the mentioned tuning parameters couldn t work meaning that the PI controller with these parameters was not able to stabilize the system and severe slugging was not eliminated We may say that the Sham s tuning method is not a suitable approach for the slugging system 5 1 1 3 2 Tuning based on IMC design Next method applied in tuning of controller in experiments was the IMC based tuning described in section 2 9 2 To do this it was tried to identify the closed loop stable system with respect to the data from step test and according to the method proposed by Jahanshahi Jahanshahi and Skogestad 2013 explained in section 2 9 2 1 The identified model of closed loop system was in the form of 11 74 S 0 606 G S _ als 96 3857 10 885 1 Equation 5 1 The identified closed loop transfer function is shown by the black line in figure 5 5 52 Closed loop step response 175 l 170 r i I I I F 165 ah e9 5 l a 160 ab I Sum i 1
10. was mounted at top of the S riser It was used as the control actuator for controlling the inlet pressure top pressure and outlet flow density as the control variables It was also possible to adjust it manually while running the system in open loop position Pressure transmitters PT1 and PT2 and the conductance probe as the density meter C were installed at various places in the setup and were used to construct a number of different control structures After the S riser air and water were entered into an overflow tank T4 then moved into a small separator T5 through a large flexible pipe made of hoses and were separated there The water is then returned from the test section back to the water large storage tank in the basement The air is vented out without further treatment The dimensions of the experimental setup are illustrated in figure 3 4 The length scale is given in meters 28 Centrifugal Figure 3 3 Medium scale Test Rig Layout with more details NTNU z N ap z 5 k S ai z m N 3 7 039 m 2 883 m 2 632 m 1 410 m e S a eee Figure 3 4 Configuration of the S shaped riser test section Lilleby 2003 29 3 2 Equipment In this section properties and purpose of the main equipment are given All the pipes bends and other connections are made of acid proof steel AISI 316L This is the case for the entire piping up to the test sections The valves are made of treated brass and are quite r
11. was used to smooth the signal as well as required 1 means no filtering Figure 5 4 illustrates the step response used in the tuning methods 175 170 T I l l w 165 i A 2 aD 5 a 160 aB i Au p O I E 155 H I l o i Setpoint a Data Filtered 145 0 100 200 300 400 500 600 700 800 900 time sec Figure 5 4 Set point step change for a closed loop feedback experiment with a P_only controller using inlet buffer pressure as control variable A low pass filter with a smoothing factor of 0 001 was used to remove the noise effect from the response 5 1 1 3 Tuning the controller The tuning methods explained in section 2 9 have been used to tune the controller using buffer inlet pressure as the control variable and slow choke valve as the actuator The tuning procedure and the related results are explained in the following 51 5 1 1 3 1 Tuning by Shams s closed loop method The first method to be used for tuning of the controller was Shams s method developed by Shamsuzzoha Shamsuzzoha and Skogestad 2010 In order to tune by Shams s method explained in section 2 9 1 the information from the step test explained in previous section See figure 5 4 were used Then the overshoot was calculated and the appropriate tuning parameters were found Table 5 2 shows the resulted tuning
12. 2 P min Openloop 3 P_ss Openloop 4 figure 1 plot z o0lca P_ss b LineWidrth 2 5 hold on legend Simple static MATLAB model OLGA case 2 plot z_oOlga P max b Linewicthn 2 5 3 hold on plot z2 olga min b binewidch 2 5 grid on 121
13. 5 13 compares simple static MATLAB model to the experimental model As clear in the figure there is a good match between the two models The MATLAB model is attached in Appendix C 5 The black midline in the figure presents the steady state values of the inlet pressure and the red midline is the values of inlet pressure from the MATLAB model The top and bottom black lines show the maximum and minimum values of pressure oscillations at each operating point in the open loop system 64 220 Simple static MATLAB model Experimental 200 Fj A gt 180 a 7 Wn A lt P gt 160 140 120 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 Figure 5 13 Simple static MATLAB model compared to the experimental model The black midline in the figure presents the steady state values of the inlet pressure and the red midline is the values of inlet pressure from the MATLAB model The top and bottom black lines show the maximum and minimum values of pressure oscillations at each operating point in the open loop system In order to find the appropriate tuning parameters based on the identified MATLAB model a closed loop test with step change of set point is required See section 2 9 3 2 Data from the step test explained in section 5 1 2 2 was used See figure 5 9 and the parameter f was found from the equation 2 41 as 2 0 038 The period of slugging oscilla
14. 75 2 K A 5 17 518 Q o 5 1 65 5 A 2 1 6 1 6 d 1 55 Setpoint d 1 4 Setpoint Data Data 1 5 0 100 200 300 0 200 400 600 Test 3 Test 4 1 75 1 8 T Fy 8 17 A i7 P 16s a ads gl p ao 7 N N 4 1 6 4 1 6 E 1 55 Mi AL Setpoint E Setpoint z ol Fb Hf p E 15 Data Data 1 5 i 0 200 400 600 0 200 400 600 800 time sec time sec Figure 5 3 Presentation of different tests of set point step change for a closed loop feedback experiment with a P_only controller using inlet buffer pressure as control variable Test 4 shows the best characteristics in case of desired overshoot and steady State gain required for tuning the controller After evaluating data from step tests it seemed that the last one test_4 has better characteristics compared to the others with respect to the point that a unit step test was going to be used for all tuning methods It was decided to use test_4 in the tuning of controller by different methods Some important considerations in selecting the best step test were 1 For the step test to be used in Shams s method the recommended 0 3 overshoot was desired 50 2 The steady state gain of the system must be smaller than one lt 1 to be S used in IMC based tuning method Since the response was noisy a low pass filter in MATLAB from the type of Simple infinite impulse response filter was used to reduce the noise effect A smoothing factor of 0 00
15. FAST valve 1 ees me 30 7 W S y N 207 WwWhasc Ma vaiu i 10 0 0 500 1000 1500 time sec 73 Figure 5 19 Comparison of IMC based control results from slow valve with those of fast valve With the slow valve it has been able to decrease set point in a wider range to a lower level With the fast valve the open loop system switched to slugging at P 170 kpa while with the slow valve the instability started at P 180 kpa in the open loop system These are the initial points respectively to start control The minimum achievable set point has been P 154 kpa for the slow valve and P 158 kpa for the fast valve This means that the slow valve has shown a better performance for the slugging system and has been already fast enough as well 5 3 Simulated results from OLGA model In this chapter simulation of the experimental cases in OLGA are presented The simulations have been matched with the experimental models from valve1 Slow valve The open loop simulations are discussed in section 5 3 1 In section 5 3 2 results of control simulations by trial and error would be explained Section 5 3 3 deals with finding the appropriate tuning rules based on the methods explained in section 2 9 Results of control by applying the calculated tuning parameters are also discussed in this section 5 3 1 Open loop simulations The first step before implementing the controller is running simulations for different valve openings with fixed liquid and
16. PI controllers tuned for the initial choke valve position of Z 30 92 Inlet pressure controlled variable 150 Setpoint 145 OLGA Measurement A 140 135 500 1000 1500 2000 2500 3000 3500 4000 Valve position manipulated variable 0 8 7 E E X 3881 ila Y 0 7554 0 4 ao 0 500 1000 1500 2000 2500 3000 3500 4000 time sec Figure 5 35 Simulation result of control using gain scheduling between PI controllers tuned for the initial choke valve position of Z 30 5 3 3 3 4 Results of tuning using initial valve position of Zo 0 4 Everything has been done in the same way as explained in previous section for Zo 0 3 except for the step test that has been run for Zo 0 4 With respect to the information extracted from the step test the parameter fhas been found as f 0 8183 In order to do gain scheduling with multiple controllers in the simulations eight PI controllers were implemented in OLGA with the related found tuning parameters The controllers could stabilize the flow up to Z 66 34 of valve opening Table 5 14 and Figure 5 36 describe the result of tuning and control using control using gain scheduling between eight PI controllers tuned for the initial choke valve position of Z 40 93 Table 5 14 PI tuning values in OLGA simulation with initial choke valve position of Z 40
17. Pa T 15 273 15 par r2 0 025 par A2 pix par r2 2 6Initial valve position in step test 6gain used for the step test Step change is positive 6The operating point S Gravity m s2 SInlet mass flow rate of gas Kg se ec S6Inlet mass flow rate of liquid SInlet mass flow rate Kg sec Scas constant J K Kmol SMolecular weight of Gas kg kmol sseperator pressure pa Sminimum Pressure drop over the valve Riser temprature K SRadius of riser m SCross section area of riser m2 117 rho_g p_st p_vmin M_g R T outlet Kg m3 rho_1 1000 alpha_g Wg_in Wg_in Wl_in volume fraction rio alpha 1 rho 1 l alpha_i rho L_r 5 30 z_star 0 26 cd 0 31 k po sgrt 2 par A2 a 1 rho W K_pc 2 p star rho_l g L_r o_s p vmin fz star z_star cd sgrt 1 z_star 2 cd 2 delta_p_star a fz_star 2 pfo p_star delta_p_star position of the valve at z 1 pa fz g Cd sort 1 7 2 cd Z K z 2Z a 2 3 cd 2 K z0 2 8 z20 s3 cd Z 666PI tuning parameters T osc 140 6Liguid density SsAverage gas density at the Kg m3 SAverage gas mass fraction alpha_l 1 alpha_g rho_g 1 alpha_g rho_gtalpha_g rho_1 lt liguid sAverage mixture density 6Length of riser SpLeuUrCacion pole Discharge coefficient of valve SValve constant m2 Constant parameter Sinlet pressure at fully open 6static gain of the system pa speriod of s
18. The same as the one for P only controller happened for the PI controllers with the gain values of K 0 0land K 1 The simulator could not converge for any values of Set point meaning that it was impossible to control the system with the tuning parameters filled with dash 78 Inlet Pressure Controlled variable 180 Set point Measurement bm oO P Kpa z 120 0 500 1000 1500 2000 2500 3000 Valve position Manipulated variable 1 N 0 5 X 2951 Y 0 6415 D 0 500 1000 1500 2000 2500 3000 time sec Figure 5 23 simulation results of control by PI controller for K 0 5 and7 800 5 3 3 Tuning the controller Three tuning methods explained in section 2 9 were used in simulations The aim has been to compare the tuning methods based on simulations as well as experiments 5 3 3 1 Tuning using Shams s closed loop method In order to tune the controller with Shams s method a closed loop step test was required As explained in section 2 9 1 a P only control is required to determine the optimal tuning parameters The P only controllers described in section 5 3 2 1 were used to achieve a step response close to the recommend 0 3 overshoot First the system was set with the choke opening at Z 30 where it is unstable in open loop position and stable in closed loop position It was at steady state initially and then a st
19. be modified to be similar to the OLGA case used in the simulations of the thesis As explained before the OLGA case was the pipeline S shaped riser setup located at multiphase laboratory of NTNU As described in section 2 9 3 the simple model is based on the valve equation w K S CNW PAP Equation 5 17 For the valve used in OLGA simulations the valve characteristic is defined as z cd f z ee Equation 5 18 Here cd is the discharge coefficient of the valve and had an important role in fitting the MATLAB model to the simulations K was considered as K J2A Equation 5 19 A is the cross sectional area of the pipe and finally the model was found as the following for the simulations 2 3 2 2 p z cd K The model is a function of valve opening and therefor the value of inlet pressure k z Equation 5 20 and the static gain achieved at a specified operating point valve opening was different from the one in another operating point Since the tuning parameters are found based on this model it is very important that the model to be realistic meaning that the values of inlet pressure and the static gain obtained by the model needed to be true values In order to make a good match between the model and the OLGA case the geometry was changed to suit the experimental setup However it soon became clear that the model needed to be manipulated to achieve the desired results As the manipulated 89 parameters length of rise
20. below 2 5 1 Choking Schmidt et al 1979 first suggested choking decreasing the opening Z of the valve at the riser top as an elimination way of severe slugging The theory behind this suggestion is that the steady flow is gained if the acceleration of the gas above the riser is stabilized before reaching the choke valve Jansen Shoham et al 1996 This increases the back pressure and the velocity at the choke thereupon The mechanism is explained as a positive perturbation in the liquid holdup in a pipeline riser system with a Stable flow will increase weight and will cause the liquid to fall down The result of this is an increased pressure drop over the riser The increased pressure drop will increase the gas flow and push the liquid back up the riser resulting in more liquid at the top of the riser than prior to the perturbation With a valve opening larger than a certain critical value Zcrit too much liquid will leave the system resulting in a negative deviation in the liquid holdup that is larger than the original positive perturbation Thus we have an unstable situation where the oscillations grow resulting in slug flow For a valve opening less than the critical value Zerit the resulting decrease in the liquid holdup is smaller than the original perturbation and we have a stable system that will return to its original non slugging state Storkaas 2005 2 5 2 Gas lift Gas lift has been suggested as another method of eli
21. different sections of system The model has been then linearized around an unstable operating point and a fourth order linear model with two unstable poles two stable poles and two zeros is produced Since a model with two unstable poles is enough for control design the model order is reduced by using balanced model truncation via square root method This identified model of the system is then used for an IMC Internal Model Control design and finding new IMC based tuning rules Jahanshahi and Skogestad 2013 Moreover a simple model for the static nonlinearity of the system is proposed by Jahanshahi and based on this static model simple PI tuning rules considering nonlinearity of the system are given Jahanshahi and Skogestad 2013 These tuning rules have been used in the simulations and experiments of this thesis and a clear comparison of the results have been presented Zl Bifurcation diagrams Bifurcation diagrams have been used in this thesis in order to plot the values of pressure versus the values of valve opening for the slugging system either in open loop position or in closed loop position with different controllers Bifurcation diagrams are the simplest way to illustrate the stability of the system In the stable regions the plot consists of a unit curve showing the exact value of the pressure in simulations or the average of very small pressure oscillations in experiments while in the unstable regions the plot consists of three cur
22. disp FEED TO OLGA AND CLOSE THE LOOP C3 Ko Pie 1417 e Tt Pi L3 C3 Ge allmargin L3 C 5 Simple static model fitted to experiments o 666Simple Static Model le clear all Q g gpI S Gravity m s2 Wg_in 0 0024 SInlet mass flow rate of gas Kg sec WL 17 0 39298 S Inlet mass flow rate of liquid Kg sec W Wg_in Wl_in S Inlet mass flow rate Kg sec R 8314 Gas constant J K Kmol1 M g 29 Molecular weight of Gas kg kmol p_s 101325 Separator pressure pa p_vmin 0 Sminimum Pressure drop over the valve T 15 273 15 gt Riser temperature K parta 0 025 SRadius of riser m Par A2 pipar t2 Cross section area of riser m2 rho g p_st tp_vmin M_g R T SAverage gas density at the outlet Kg m3 115 rho_1 1000 alpha_g Wg_in Wg_in Wl_in fraction rho alpha L rhoe 1 l aloha ly rno g dig ES 5 15 zZ Star 0 26 od 0 31 K pe sgri 2 par AZ a 1 rho W K_pc 2 star rho l g L r tp s p vmin fz star 2 ster cd sqrt 1l z_star 2 cd 2 delta_p_star a fz_star 2 p_fo p_star delta_p_star position of the valve at z 1 pa zt 0227502001 1 n length z_t Pin zeros 1 n K_z_t zeros 1l n ror i ben fz 2 a cd sgrt l1 z2 t1 2rcd 2 i Pin i a fz 2 p_fo 1000 K z c i 2 a za t 1 3 cda 2 71000 end figure 1 clf SaDPELOTC 2 1 1 plou zZ_t Pin k Lanentieth 2 3 xlabel
23. er z a k a las a r li dTi EFA E A HER Oy yA Yt At IN F rd Z m 0 i0 20 30 40 50 60 70 80 90 100 Valve opening 7 Figure 5 17 Characteristic curves for slow linear and fast quick opening valves There is a lower level of valve opening for the fast valve at a specific flow rate for instance 50 meaning that the fast valve can produce the same flow rate as the slow valve even at lower levels of valve opening Open loop Bifurcation Diagrams 220 Slow valve Fast valve 200 S Se Ke 160 180 140 Inlet Pressure Kpa 120 100 0 2 0 4 0 6 0 8 1 Valve opening Z Figure 5 18 Comparison of inlet pressure between the slow valve and the fast valve at their different operating points for the open loop system At a certain level of valve opening the slow valve gives a lower inlet pressure 71 Based on the previous descriptions it was decided to compare the minimum achievable set points in the closed loop responses Figure 5 19 present the control results with IMC based PI and IMC based PID controllers The valve opening is also presented just in case and is not a point of interest to compare the results From the figures it can be said that the slow valve has had a better performance compared to the fast valve This means that the slow valv
24. leakage from the connection during the work This could affect the accuracy of the experiments since the flow meters were located before this connection 102 However the flow meters themselves were not of the best quality and their numbers may be also inaccurate One way to overcome this occasional leakage is to make a multiple connection between the pipeline and all risers with the manual valves for each connection Then the valves can be manipulated to change flow directions instead of the time consuming change of the connections by mechanical work 103 7 Conclusion This chapter is organized based on the tasks defined in the thesis description These tasks have been followed and the desired results have been obtained mostly 7 1 Stabilizing control experiments using bottom pressure Stabilization control experiments using the medium scale S riser setup proved that the severe slugging phenomena can be delayed to a large extent by active control of production choke valve and using the bottom pressure buffer tank pressure as the control variable Two sets of experiments with two different choke valves showed that the anti slug control structure using bottom pressure as measurement and a good tuning method as well the stability region could be extended widely 7 2 Testing online tuning rules on S riser experiments Three different tuning methods for anti slug control were tested online and their robustness was compared with respec
25. on the experimental result of valve 1 and also fit the steady state OLGA values with the steady state values from experiments and models The diagram comparing steady state values from OLGA with that of the model will be presented in section 5 3 3 As clear in the figure the critical stability point was found to be at approximately choke valve opening of Z 26 Open loop Bifurcation Diagram OLGA model 220 e Steady state 200 180 160 N 140 Inlet Pressure Kpa 120 100 Figure 5 20 Open loop bifurcation diagram from OLGA simulations The bifurcation point occurs at valve opening of Z 0 26 The top and bottom line illustrate the maximum and minimum values of oscillations for inlet pressure respectively at each operating point The mid black line is the shows the average values of pressure 5 3 2 Control by trial and error As the first work after implementing PID controller in OLGA it was tried to stabilize the flow by trial and error Two types of controller including P only controller and PI controller were tried to be tuned by trying many different values as the related tuning parameters 75 5 3 2 1 P only controller As the first try a P only controller was used to stabilize the system P only controller has been designed by inserting t 0 and r 10 o A point in unstable region with Z 0 3 was selected and different valu
26. tank and back to the separator and maintain a constant liquid level inside the tank The pressure at the overflow tank will be constant equal to the hydrostatic pressure of the liquid column from the tank This will simulate a constant reservoir pressure and make the inflow to the test section dependent on the inlet pressure The supply pipes for the plastic overflow tank are small so it will only work properly if the flow through it is very low Figure 3 8 Over flow tank at top of riser 3 2 5 Pressure transmitters Pressure transducers PT1 and PT2 made by Siemens were installed on the buffer tank and riser to measure the buffer pressure and top pressure respectively They have a working range of 0 4 bars 33 3 2 6 Small separator The flow from the overflow tank T5 is moved into a small separator located down the hoses pipe A picture of the separator is shown underneath in figure 3 9 The air from the riser is released from the top outlet The bottom outlet is used for the water recycle and returns the water to the water storage tank Mb pbb ha APLLALLLL TTT ARAL j j j Figure 3 9 Small separator 3 2 7 Centrifugal water pump A large centrifugal water pump P1 of the type DN100 flange made by Wilo Norge AS was used to push the water into the system In order to prevent water flow oscillations the centrifugal water pump was run in a very high level of power 80 of the maximum However to get the desired fl
27. the flow from the reservoir It also increases the mechanical wear of the pipeline due to large oscillations in pressure The capital and maintenance costs of a slug catcher are relatively large Olsen 2006 2 5 4 Active control Riser slugging can be prevented using stabilizing feedback control An approach based on feedback control was first proposed by Shmidt Shmidt et al 1978 The idea of paper was to suppress terrain slugging by using the top side choke valve and a simple feedback loop measuring pressure at the inlet and upstream the riser or the top pressure before the choke valve as inputs With feedback control the stability of the flow regimes can be changed to enhance operation In fact the boundaries can be moved via feedback control thereby stabilizing a desirable flow regime where riser slugging naturally occurs Storkaas 2005 Anti slug control can move the boundaries in flow regime map resulting in increased stable region It sounds to be one of the best solutions for prevention of severe slugging Several models have been suggested by researchers to describe the system dynamics and several controllers have been designed The models are meant to aid tuning of controllers which use the production choke valve as the actuator and try to stabilize the system with a more production rate in a higher valve opening The objective could be defined as obtaining the most robustness for the system against large inflow disturbances No
28. was repeating the first series of tests with a new fast valve as the actuator A new method of tuning has been used here in addition to the tuning methods of previous section 5 1 2 1 Open loop experiments The loop was run in manual mode with fixed flow rates of w 0 3927 kg sec for water and w 0 0024 kg sec for air These flow rates are the same values used for the slow valve The related inflow conditions have been fully described in section 5 1 1 1 The tests were run in different valve openings with fixed liquid and gas flow rates without applying control The system behavior in natural conditions was then presented with the related bifurcation diagram as seen in figure 5 8 5 1 2 1 1 Bifurcation diagram The starting point was the valve opening of Z 0 1 Then the valve was open stepwise until it was fully open The results of buffer inlet pressure were logged and the related bifurcation diagram was plotted The critical stability point the bifurcation point is the maximum choke valve opening the system can have while being stable and is located at Z 0 16 for the system with valve 2 In the presented bifurcation diagram the top line tracks the maximum values of pressure at each operating point the bottom line presents the minimum values of pressure and the middle line shows the average values of the buffer pressure at different valve openings Small pressure oscillations before the bifurcation point are due to hydrodynamic s
29. 2 ylabel Inlet Pressure hold on grid pn kFa l subplot Ly 2 DlLOt zZ t K z t K Linewidch 2 Xxlabel Z ylabel K z hold on grid on 116 6Ligquid density KG ms SAverage gas mass fraction alpha_l 1l alpha_g rho_g l alpha_g rho_gtalpha_g rho_1 6liquid volume sAverage mixture density 6Length of riser Bifurcation point 6Discharge coefficient of valve SValve constant m2 s6Constant parameter Sinlet pressure at fully open 6Different valve openings 6Inlet Pressure 6Static gain of the system pa C 6 Online tuning based on simple static model and a closed loop step test cle clear all load z40_141_142 ZO 0 4 Keus 0 15 dy_s 1 t init 300 dt 0 1 t z40_141_ 142 1 y z240_141_142 2 r zZz40_141_ 142 3 u z40_141_142 4 i init Lind t t_init y_plant y i_init end t_plant t i_init end u_plant u i_init end y init Via anata init u i _init 10 yp max y_plant dy p abs yp y_init i yp 1ind y plant yp t_pl mean t_plant i_yp yu min y_ plant 1_ypo 10 1_yp dy u abs yu y_init i_yu find y_plant yu t_u mean t_plant i_yu y_inf y_plant end d _inf abs y _i nf yo init to Col tO Ini J401 Wg_in 0 0024 Wl_in 0 39298 Kg sec W Wg_intWl_in R 8314 Mg 29 Q N p_s 101325 p_vmin 0
30. 45 0 0 500 1000 1500 2000 time sec Figure 5 27 Simulation result of control by Shams s method for the initial choke valve position of 40 The values of Z 0 395 and P 142 kpa have been the maximum achieved valve opening and the minimum achieved set point respectively 82 5 3 3 2 Tuning based on IMC design Next method used in tuning of controller in simulations was the IMC based tuning described in section 2 9 2 As explained before the open loop system switches to slugging flow at valve opening of Z 26 and it is unstable at Z 30 or 40 Tuning by this method was done for two different operating points of the system Z 30 and Z 40 Both simulations as well as their results are presented in this section 5 3 3 2 1 IMC based tuning at Z 30 as the initial valve position The loop was closed by a P only controller with an initial gain K 0 1 and set point was changed by 2 kPa at Z 30 Then with respect to the data from step test and according to the method proposed by Jahanshahi Jahanshahi and Skogestad 2013 explained in section 2 9 2 1 closed loop stable system was identified as the following 8 105 S 0 919 CG jae als 17 738 3 765S 1 Equation 5 11 Figure 5 28 illustrates the implemented step change and the identified closed loop transfer function shown by the black line Then the open loop unstable system has been back calculated by using the procedure proposed by Jahanshahi The open loop unst
31. D is approximately 30 Figure 2 10 shows a graphical illustration and equation 2 4 finds the overshoot 15 0 8 Ayu 0 54 ee EEEETETTETT L ETTI TTTTT Aal j i i i 0 1 2 4 6 8 Figure 2 10 closed loop set point response with P only controller Skogestad and Grimholt 2011 Extract information from the graphical step response Time to first peak t Maximum output change Ay Relative steady state output change Ay Alternatively Ay can be estimated from equation 2 6 using the output change at first undershoot Ay Ay 0 45 Ay Ay Equation 2 3 Overshoot n Ay Ay Equation 2 4 Ay Steady state offset Ay Ay Equation 2 5 Sa lI Ay 16 e The parameter A A 1 152D 1 607D 1 Equation 2 6 e The parameter r 2A r gt Equation 2 7 The first order plus delay model parameters e Steady state gain k Equation 2 8 K B e Delay 0 t 0 309 0 209e Equation 2 9 e Time constant T r0 Equation 2 10 Now a first order plus delay model is found and with respect to this model the tuning parameters are Equation 2 11 Equation 2 12 min 7 4 c 0 In the paper by Skogestad Skogestad 2003 it was recommended to use T as a good compromise between performance and robustness 2 9 2 Method 2 Tuning based on IMC design The Internal Model Control IMC method was developed by Morari et al Morari and Za
32. E a aa tad lnarnneladiayl 41 A21 Fow path geometry anakna a a aiaiai 42 M22 FIM PrODeEIUleS cxiacitonsensians daalesnsniinindaeminwie E E GSN 43 4 2 3 Boundary and initial conditionS ss ssesssssssrsssrresrressnessnresrensnensneennrennnnnnnnnnnesnnnsnnnnnnnnns 43 ADA Numerical settini sssaaa na Gta rte et toler 44 4 3 Implementing PID controller in OLGA ssssssssssessssessresnsrnensrnsnnnnsnnnnnnnnsnnnnsnnnnnnnnennnnsnnnnsnnnnenns 44 3 Results anddiscusslo esegi E 46 5 1 Experimental results assrsssssssnrssranaransnunoranoaninanvnnnananasnnnnonnonnnnnnananananannnnanaronadnnnaninanonannnansananaan 46 5 1 1 Series of experiments with valve1 slow choke valve sssssssssssesssressressressresssees 47 5 1 2 Series of experiments with valve 2 fast choke Valve ssssssssssssssrssrrssressressresssees 57 5 1 3 Cascade Control using top pressure combined with density uu 68 5 2 Comparison of Slow valve and Fast valve s sssesssessersssrensrenrrenrnesrnensnsesneesnensnennnenenennnrnnns 70 5 3 Simulated results from OLGA Mel cesseesseeseeseeeeseseeneseesseeneaeeneneeeeneseeneaeeneeeneaeetens 74 S3 OpenslOOp SIMUlALIONS mizanda a E 74 S3 Control bpy trialand 6rrOFnansspsemeinamnnnunaniai 75 93 3 Tuning the controle i esernonnnaane en ea ae tre EA 79 5 4 Comparison of experimental and simulated results ccsssssseesesesesesessseseeeeeseeeeees 95 5 4 1 Open loop bifurcation diagramS s ss ssrsssrsesrresrnensrrssrenrne
33. HPpolest l since Vm always contains an pole at origin for step input m max length zero q tilde length pole q tilde 1 make sure q q_tilde f is proper FilterOrder m tk 1 oS Calculate filter as sum a k s k 7 tCau s 1 filter rder coefficients ones 1 k if NumRHPpoles gt 0O A zeros NumRHPpoles NumRHPpoles for ctRHPpole 1 length RHPpoles A ctRHPpole RHPpoles ctRHPpole 1 NumRHPpoles end b Tauc RHPpolestl1 filterOrder coefficients 1 coefficients Z2 end real A b end lt Computing iL num fliplr coefficients den fliplr poly repmat Tauc 1 filterOrder tf num den q minreal q tilde f C feedback q Ge 1 disp The IMC controller C minreal C Ll C Ge allmargin L1 114 C 4 Finding PID PI tuning rules based on IMC design disp IMC based PID tunings KO PID Ki _PiID Kad PID TEPID piddata c Ti PID Kc PID Ki_ PID Td PID Kd_PID Kc_PID disp Kp num2str Kc_PID disp Ti num2str Ti_PID disp Ta numZzstr Td_PIpD disp Tf num2str T _PID disp FEED TO OLGA AND CLOSE THE LOOP C2 Ke _PID 1 1 Ti_PID s Td _PID s Tf f_PID s 1 L2 C2 Ge allmargin L2 o O o O SReduce to PI Controller C3 balancmr C 1 Ke PI Ki_Pl piddata C3 Ti_PI Kc_PI Ki_PTI disp IMC based PI tuning disp Kp num2str Kc_PI disp Ti num2str Ti_PlI
34. MC based tuning method described in section 2 9 2 was applied as the next method to tune the system with fast valve Data from step test See figure 5 9 were used and The model of closed loop system was identified as explained in section 2 9 2 1 G 5 9 076 S 0 7406 T A Equation 5 4 64 76S 4 635S 1 The identified closed loop transfer function is shown by the black line in figure 5 10 Closed loop step response 166 164 i rT 162 tT II l 160 if A l x i 2 158 gt I 3 l 156 Hl _ Z asa A MANALI S 154p A rata i 152 set point Measurement 150 Filtered identified 148 0 100 300 400 500 600 time sec Figure 5 10 Presentation of identified closed loop step response The dashed black line shows the identified closed loop transfer function obtained from IMC design The open loop unstable system was then calculated as the form of equation 5 5 by using the procedure proposed by Jahanshahi Jahanshahi and Skogestad 2013 60 0 0005606 S 4 574e 05 P s T Equation 5 5 0 068585 0 004006 The IMC controller C was obtained then as the equation 5 6 See section 2 9 2 2 A value of 2 24 5 was used for the time constant of the closed loop system This value was manipulated by trial and error until a satisfying gain phase a
35. NTNU Trondheim Norwegian University of Science and Technology Robust control solutions for stabilizing flow from the reservoir S Riser experiments Mahnaz Esmaeilpour Abardeh Chemical Engineering Submission date June 2013 Supervisor Sigurd Skogestad IKP Co supervisor Ole J rgen Nydal EPT Esmaeil Jahanshahi IKP Norwegian University of Science and Technology Department of Chemical Engineering Robust control solutions for stabilizing flow from the reservoir S Riser experiments and simulations Mahnaz Esmaeilpour Abardeh June 26 2013 Preface This thesis is written as the final part of my Master degree in Chemical Engineering at the Norwegian University of Science and Technology NTNU class of 2013 I would like to express my greatest gratitude to my highly knowledgeable supervisor professor Sigurd Skogestad for all his helps his good guidance and encouragements I am also grateful to my co supervisors professor Ole Jorgen Nydal and PhD student Esmaeil Jahanshahi who helped and supported me throughout my thesis It has been a great opportunity and honor for me to be part of your team in generating new ideas and I am confident what I have learned through this thesis will be surely used in practice in my professional career Declaration of Compliance I Mahnaz Esmaeilpour Abardeh hereby declare that this is an independent work according to the exam regulations of the Norwegian University of Science and
36. R PI 287 0673 65 6371 The approach of implementing the low pass filter in the experiments is described in appendix A To find the control results all related tuning parameters were implemented in LabVIEW and the loop was run in the stable region with an average valve opening of Z 25 Then it was tried to decrease the set point value in a stepwise manner At each step it was waited until the steady state was reached and then a new step of reduction was done Figures 5 6and 5 7 describe the results of control using the IMC based PID and PI controllers respectively The experimental slugging system could be stabilized up to Z 40 with IMC based PID controller and up to Z 38 4 with IMC based PI controller even though the controllers have been designed at valve opening of Z 28 54 IMC based PID Controller __ 190 Setpoint a AAAA L i Mn Measurement 5 170 TAY Y Puna 2 160 Wainy AN A di LUTER AAM aa N i l t HAA Ha Ana MN f AV 150 ai 140 0 200 400 600 800 1000 1200 1400 50 X 1363 ss Y 40 2 40 B 30 y N 20 10 0 0 200 400 600 800 1000 1200 1400 time sec Figure 5 6 Result of control using the IMC based PID controller The controller has been able to move the bifurcation point from Z 26 up to Z 40 2 190 180 170 160 150 Inlet Pressure Kpa 140 0 IMC based PI Co
37. RCO 0215 6gain used for the step test dy s 1 t_init 300 de Oo Le t z240_141_ 142 1 y z240_141_142 2 r 240_141_142 3 u z240_141_142 4 1 init find t t_init y_plant y i_init end t_plant t i_init end u_plant u i_init end 119 y init yt init 10 j u_init u i_init 10 yp max y_plant dy p abs yp y init i yp Cindy plan yp t_pl mean t_plant i_yp yu dy u abs yu y_init i_yu find y_plant yu t_u mean t_plant i_yu y_inf y_plant end dy inf abs y_i nf y init to tpl Init deltat t u t_pl 6555 S6MODELS S z dea g 9 81 Wg_in 0 0024 Wl in 0 39296 Kg sec W Wg_int Wl_in R 8314 Mg 29 p s 101329 p_vmin 0 Pa T 1572 735153 par r2 0 025 Dar AZ pipar r2 rho_g p_st p_vmin M_g R T outlet Kg m3 rho_1 1000 alpha_g Wg_in Wg_in Wl_in alpha J l alphag rho g 1 alpha_g rho_ gtalpha_ g rho_l volume fraction 6Step change is positive minty plant 1 yor 10 i yo 6The operating point S Gravity m s2 SInlet mass flow rate of gas Kg s c S6Inlet mass flow rate of liquid S Inlet mass flow rate Kg sec Gas constant J K Kmol1 SMolecular weight of Gas kg kmol sseperator pressure pa Sminimum Pressure drop over the valve Riser temprature K SRadius of riser m SCross section area of riser m2 SsAverage g
38. able system has the form of 4 572 s 0 5184 o s 0 2448s 0 00457 Then the IMC controller C is then designed by using the method explained in Equation 5 12 section 2 9 2 2 The time constant of the closed loop system has been selected as 4 10 This number was obtained by trial and error and experiencing different results The designed IMC controller is 0 11916 S 0 04668S 0 001835 Ce eee Equation 5 13 S S 0 1134 83 Closed loop step response from OLGA simulations 151 5 151 150 5 150 r o ee L aaRS RR 149 5 149 a Inlet pressure kPa 148 5 Setpoint OLGA measurement Identified model 148 180 200 220 240 260 280 300 time sec 147 5 Figure 5 28 Closed loop response of step change at initial valve opening Z 0 3 The dashed black line shows the transfer function of the IMC based identified model The IMC controller is a second order transfer function and can be written in form of a PIDF controller PIDF is a PID controller which a low pass filter has been applied on its derivative action It will be mentioned as PID controller A PI controller has been also obtained by reducing the order of IMC controller to one The related PID and PI tuning parameters have been calculated as described in section 2 9 2 3 and are shown in table 5 11 Table 5 11 IMC based PID and PI
39. alpy or entropy were filled with dummy numbers 4 2 3 Boundary and initial conditions The types of the air and water sources as inlet nods were defined as inlet mass flow The flow rates were fixed for all simulations The volume fractions were established to 1 for both nodes since only water or air was injecting through the node The outlet nod type was selected to pressure type and it has been set to atmospheric pressure 43 4 2 4 Numerical setting The numerical setting specifications such as simulation time and time step were adjusted in different numbers from case to case This is due to the diversity of phase velocity in different cases 4 3 Implementing PID controller in OLGA In order to implement a PID controller in OLGA first a positive check valve was placed right after the water source in pipe 2 section 1 of the case The reason was to make sure that the flow will move only in the defined direction Then a pressure transmitter was located in pipe 2 section 2 that is the inlet of the riser right after the buffer tank It was aimed to measure the buffer pressure and send the pressure signal into the PID controller The PID controller was used in a way that it received the measurement signal from the pressure transmitter and sent the output signal into the choke valve located at top of the riser Pipe 8 section 3 Choke valves can be simulated by selecting the Hydrovalve for the valve model in OLGA PID P Buffer Pressu
40. and trying different values for K andz The aim as the previous part was to tune the controller to create stable flow with the highest production rate the highest level of valve opening Z Stepwise reduction of the Set point was implemented as the one for P only controller Table 5 9 shows different values of tuning parameters that have been tried and the corresponding minimum value of Set point and maximum value of Z Table 5 9 Simulation Results of different tried tuning parameters for PI controller 0 01 0 05 0 1 0 5 Ti naar 1368 E oaie T365 osa 80 po Sp oon a ots oer wo par ose isss oasr rez cas w pps e esa a 800 _ 141 3 0 397 139 4 0 463 136 2 0 646 As it is observed in the table the best tuning parameters are K 0 5 and T 800 Higher values of 800 were also tried for the parameter T and no difference was made in result Result of control by PI controller with the best tuning parameters is presented in figure 5 23 Increasing the parameter 7 decreased the system oscillations very well and even eliminated it in some cases However it caused a longer time to be required for the output to track the Set point in each step of Set point reduction This important effect of applying integral time constant could be verified by comparing figures 5 23 and 5 22 As it is observed a less oscillatory system with longer simulation time is the result of PI controller compared with P only controller
41. as density at the S Liguid density Kg m3 SAverage gas mass fraction eLiguid SAverage mixture density Length of riser 2oLLUrCaL Lon Polit Discharge coefficient of SValve constant m2 s6Constant parameter rho alpha_l rho_1 l alpha 1 rhog Lr 5 30 z_star 0 26 cd 0 31 valve K po sgrt 2 par AZ a 1 rho W K_pc 2 p star rho l o L r tpo_ s p_vmin fz star 2 star cd sqrt l z _ star 2 cda 2 delta_p_star a fz_star 2 p_fo p_star delta_p_star position of the valve at z 1 fz 2 Cd sqru l 2 2 cd 2 Koa 2 a 2 3 Ced Z K z0 2 a z0 3 cd Z Sinlet pressure at fully open pa 6static gain of the system pa 120 666PI tuning parameters T_osc 140 period of slugging oscillations in sec in the open loop system Betha log dy inf dy a dy p dy_1ant 2 deltat Kc0 K z0 dy p dy int dy_ 1anity 2 7 4 tp Ko Betha T_osc K_z sqrt z z_star taul_z 3 T_osc z z_star disp FEED TO OLGA AND FIND THE MAXIMUM STABILITY SMODEL zt 0 2 0 001 1 n length z_t Pin zeros 1 n K_z t zeros 1 n for i lin fz z t 1i cd sgrt l1 z_t 1i 2 cd 2 Pin i a fz 2 p_fo 1000 Kz t 1 2 a z t 1 3 cd 2 1000 end figure 1 clf plot 2_t Pin banetiern 2 5 xlabel Z ylabel Inlet Pressure kPa hold on grid on 0o o0 666666O0penloop and Steady state load Openloop Z Olga Openloop 1 P_max Openloop
42. controller instead of control valve dynamics Figure 5 19 compares the closed loop response of IMC based 105 controller for the two valves With the slow valve the IMC based controller has been able to decrease set point in a wider range down to a lower level 7 5 Control simulations using OLGA The OLGA model was developed based on the first series of experiments with valve 1 and the implemented PID controller was fine tuned using the different tuning strategies Results of the experiments verified those of the simulations In open loop condition there was a good match between the OLGA model and the experimental model of valve 1 see figure 5 37 The same as the experimental results the simulated ones proved that simple PI tuning rules with gain scheduling for the whole operating range of the system Jahanshahi and Skogestad 2013 is the best tuning method providing the largest stability region for the slugging system The PI controller in the simulations tuned by this method could increase the stability limit up to the valve opening of Z 75 from the open loop stability of Z 26 see table 5 16 or figure 5 38 From the simulation results it can be said that the IMC based tuning method Jahanshahi and Skogestad 2013 is the second best systematic manner to tune the controllers for the slugging system The PID controller tuned by this method increased the stability limit from 26 to 50 of choke valve opening The Shams s se
43. ctive feedback control of the topside choke valve can make it possible to stabilize the flow at the conditions where normally severe slugging is predicted This reduces the need for additional topside equipment and allows a higher rate of oil recovery The control system is called anti slug control and its main objective is to keep the multiphase flow as stable as possible by manipulating the topside choke valve using the parameters such as pressure or density as the control variables In the way of developing new technologies for stabilizing control of severe slugging in riser systems many researches have been done at the Norwegian University of Science and Technology The work has been guided by Skogestad Skogestad 2003 Storkaas 2005 Shamsuzzoha and Skogestad 2010 Jahanshahi and Skogestad 2011 Skogestad and Grimholt 2011 Jahanshahi and Skogestad 2013 and performed at the department of Chemical Engineering Storkaas Storkaas 2005 Sivertsen Sivertsen 2008 Jahanshahi Jahanshahi and Skogestad 2011 and numerous master students have worked on modeling and controlling of riser systems Companies like ABB Havre Stornes et al 2000 Statoil and Total have all researched prevention of slugging and built installations at offshore locations Statoil completed in 2001 their first slug control installation at the Heidrun oil platform Siemens is also involved in slugging research and funds a PhD program which this thesis is connect to In the a
44. cture 14 2 9 Tuning of PID and PI controllers Many tuning methods for different systems have been introduced so far by researchers and engineers Depending on the characteristics of the system plant for instance nonlinearity and stability different levels of robustness is achieved by different tuning methods Three different tuning methods have been applied in this thesis Two of them are quite new and have been recently developed Jahanshahi and Skogestad 2013 They are specified for the slugging system In fact this thesis is a verification of these new methods 2 9 1 Method 1 Shams s set point overshoot method for closed loop systems Some systems like slugging system are originally unstable in open loop For these systems model from closed loop response with P controller can be used to find the appropriate tuning parameters A method called Shams s set point overshoot method was first constructed by Shamsuzzoha et al Shamsuzzoha and Skogestad 2010 Skogestad et al Skogestad and Grimholt 2011 developed this method further into a two step closed loop procedure A step by step description of the two step closed loop Shams s method is presented below The closed loop system with P controller should be at steady state initially that is before the set point change is applied Then a set point change Ay is applied The step change and the P controller gain K should be adjusted in a way that the overshoot
45. d was tried only by the second valve 5 1 1 4 2 Applying time delay in the controller One important issue regarding the slow valve tests that needs to be mentioned is about applying time delay It was aimed to check the robustness of control system by implementing delay on measurement In order to do this an algorithm was implemented in LabVIEW by one of the lab technicians It was a digital delay line which delayed the samples of the measured data by a desired given time The desired delay time could be set from the front panel Yet the delay setting couldn t work in a desired way Meaning that even for very small values of delay the system switched to severe slugging and the control was impossible It was clear that for such a long pipeline riser system small values of delay in the range of milliseconds couldn t crash the control and the reason of inconveniency may be from LabVIEW It might be because of mistakes in the algorithm or in the connections inside LabVIEW Since the system was in medium scale and no one else except for the lab technicians was able to do modifications in the system or LabVIEW and also due to time issues it was decided to ignore implementing time delay after counseling with my supervisor It was an extra work to be done in the thesis while the next required experiments were not started yet at that time 56 5 1 2 Series of experiments with valve 2 fast choke valve The next series of experimental work in this thesis
46. different sections This model needed to be modified for an S shaped riser to be used in the thesis A good assumption of valve equation is very important in using the simple model The reason is that the slugging gain of the system as a function of valve opening is derived based on this equation Jahanshahi assumes the valve equation as the following w K f CNPA Equation 2 33 Where w is the inlet mass flow rate to the riser K is the valve constant and f z is the characteristics of the valve which is defined as the following for the linear valve used in experiments Equation 2 34 Tyas and as follows for the OLGA valve model in simulations z cd fR dera Equation 2 35 Ap is the pressure drop over the valve and as it is clear in the valve equation it s a function of valve opening that can be written in the following form 2 Ap i as Equation 2 36 P K f 2 Then the simple model for the inlet pressure is P Ap P Equation 2 37 23 P is the inlet pressure at fully open position of the valve and has been calculated from the below equation P P Ap Equation 2 38 P isa large enough inlet pressure to overcome the riser slugging P z pre 5g P caer Equation 2 39 Here p is the density of liquid which is water in our system g is the gravity and L is the length of riser P is the separator pressure in downstream and P in is the minimum pressured drop over the valve and has been considered
47. e density signal does not show a clear response to the step change and is very noisy This signal couldn t be a suitable measurement for the control targets In order to have an efficient cascade control with density as the inner loop control variable more accurate signals of density are required Trying each loop separately to evaluate their response independently could be considered as an alternative work But this was not practical since the backup of the LabVIEW file was lost and the compiled file couldn t be manipulated or modified Making a new file was not possible due to time issues 69 5 2 Comparison of Slow valve and Fast valve In this section it has been tried to compare the dynamics of the applied control valves slow valve and fast valve by investigating their related results For this target the open loop and closed loop results of the two valves were compared Our criterion to evaluate control loop is the stability For a fast stability the dynamic response of the valve is important It means a small dead time for the valve The criterion for evaluating the stability of the slugging control loop has been usually the level of valve opening Z However this criterion couldn t be useful for comparing control valves with each other The reason gets back to the valve inherent characteristics that will be explained in the following The relation between the flow rate and the level of valve opening is an inherent characteristic of
48. e fast valve are as follows Manufacturer ASCO Diameter 2 inch Material Stainless Steel Operation NC Normally Closed Pilot Pressure 4 10 bar Maximum Working Pressure 6 bar Operator Diameter 90 mm Signal 4 20 mAmp Opening Time 2 sec Closing Time 2 5 sec Figure 3 13 Choke valves left Fast valve Right Slow valve and its positioner 37 3 2 11 Conductance probe C In the second series of experiments with the fast valve a cascade control structure was used with outflow density and the top pressure as the control variables Conductance probe was applied to measure the density of the outflow from the riser The probe has been calibrated by Kazemihatami Kazemihatami 2012 very recently The output of the probe was in the form of voltage The calibration curve presented by Kazemihatami was used to find the relation between voltage and holdup Equation 3 1 shows this relation H means holdup and V means voltage H 0 9857V Equation 3 1 The density of mixed flow is found from the equation 3 2 Pa Proar FP VHA Equation 3 2 After inserting the related values in the above equation the density of mixed flow is found as a function of voltage P 984 513V 1 204 Equation 3 3 Figure 3 14 The conductance probe 38 3 2 12 LabVIEW The Laboratory Virtual Instrumentation Engineering Workbench LabVIEW software developed by National Instruments was used for instrumentation control and data logging The user inter
49. e has been already fast enough for our control targets and there has been no need to valve 2 faster control valve In other words the stability of the slugging system is more affected by the tuning parameters for the controller instead of control valve dynamics 72 IMC based PI Controller 190 Setpoint from SLOW valve 180 j HN i Pa real Hf Measurement from SLOW valve F At AAA AA ANAN Setpoint from FAST valve o 170 ror WI Na AAAARNANAADAL Measurement from FAST valve AURA PAT 7 PaM WE Til AY be MoAL t i CR MAT AIRT D 1 I Way T TADS Mih M E 160 a TOV HA Mil HV a hi c 2 150 ii 140 0 200 400 600 800 1000 1200 1400 50 Valve opening from SLOW valve Valve opening from FAST valve i 40 r 30 J AL VARY E aa AN N 20 be Why y A 10 0 0 200 400 600 800 1000 1200 1400 time sec IMC based PID Controller 190 zes Setpoint from SLOW valve 180 AAAA N il Measurement from SLOW valve me Ws Ny i ji r Ni Setpoint from FAST valve Measurement from FAST valve 170 PHEW VON am i An n ma 2 160 mini CAM cit a z na HALAL ac niet Mt Lhe i E 150 140 0 500 1000 1500 50 Valve opening from SLOW valve 40 Valve opening from
50. e in KPa Stability after control Stability after control with IMC based PI with IMC based PID controller controller Simulations 0 26 153 0 46 139 5 0 50 138 5 Stability before control Although the simulated closed loop results show a higher level of valve openings still the amount of set point reduction is larger for the experiments Both models confirm that the IMC based tuning method is a fine approach for the slugging system Moreover they agree that the IMC based PID controller has a better performance compared to the PI 5 4 3 Comparison of control results from Simple online tuning method Simple online tuning method based on MATLAB model was not tried in the series of experiments with valve1 See section 5 1 1 4 for more explanations Instead it was tried with valve2 Therefore the results can t be numerically compared since the OLGA simulations are based on the experiments with valve1 However the experimental and simulated results do agree on confirmation of this method as the best method of tuning with the highest level of stability for the slugging system This will be seen more clearly in the next section 96 5 4 4 Comparison of tuning methods An overview of all experimental and simulated results from the applied tuning methods is presented in table 5 16 in numeric form The maximum valve opening achieved as well as the minimum obtained set point for each closed loop test or simulation is illustrated It ca
51. e initial position of 40 Figures 5 24 and 5 25 show the step test using initial choke valve opening of 30 as the basis inflow condition and the result of control by Shams s method respectively Figures 5 26 and 5 27 are presented for the initial choke valve opening of 40 Two initial points were used for tuning to improve the results However as it is clear from the figures no notable change is observed in the results of control Decreasing set point even for a very small value more than the final value shown in the figures caused system to become unstable Severe slugging occurred and the simulator could not converge As seen in the results the second controller tuned at the initial point of Z 40 hasn t been able to stabilize the system for any further valve openings It hasn t been able even to achieve the point that has been tuned for This may not be strange since the Shams s method has been designed for the stable systems while the slugging system is unstable 80 Inlet pressure controlled variable 151 A ne N 150 Setpoint Measurement 149 i i 100 200 300 400 500 600 Valve position manipulated variable 0 3 0 25 N 0 2 0 15 0 100 200 300 400 500 600 time sec Figure 5 24 Set point step change using initial choke valve opening of 30 and the initial gain of K 0 1 An overshoot of D 0 3 as the recommended val
52. ed in this thesis Air water Sever slugging control experiments in S shaped riser has been one of the main parts of this thesis in addition to modeling and simulations A series of tests have been conducted at a medium scale setup located in NTNU multiphase flow laboratory at department of Energy and Process Engineering See figure 3 1 It has been tried to evaluate the applicability of three tuning methods explained previously in different conditions Experiments in this issue and comparing them with simulated results are also valuable in the way of approving prediction of simulations The experimental work include trying two different choke valves with different dynamics as the actuator and running series of control experiments for each valve separately Series of control experiments have been in the following order First the open loop experiments have been run in order to make the open loop bifurcation diagram of the system Then a P only controller has been used to close the loop and the set point step change test has been run with the aim of finding appropriate tuning parameters Finally after calculating different tuning rules based on the data of step change test closed loop experiments were run and the closed loop responses of different controllers tuned with different methods were evaluated Buffer tank pressure riser inlet pressure in the real systems has been selected as the control variable CV in series of control experiments Moreov
53. ed to the separation process Avoiding variations in the flow entering the processing unit at the outlet of the multiphase pipelines is the issue of interest for control Bratland 2010 The ability of predicting the flow patterns and reserving a stable flow is of great importance which is the objective of the thesis Figures 2 1 and 2 2 adapted from Bratland Bratland 2010 describe possible flow patterns inside the horizontal and vertical pipelines ii Annular flow with iii Elongated bubble flow iv Slug flow v Stratified flow vi Stratified wavy flow Figure 2 1 Gas liquid flow regimes in horizontal pipes gt y C gt T Fs F x z gt 3 a gt t z ea lt rh Figure 2 2 Gas liquid flow regimes in vertical pipes Slug flow is the point of interest in the thesis Changing multiphase flow between different flow regimes can be described by a typical flow regime map shown in figure 2 3 adapted from Taitel Taitel 1986 The boundaries between stable and unstable regions are clearly shown in the flow regime map With applying feedback control these boundaries can be moved and thereby the stable region can be increased STEADY FLOW a BOE QUASI EQUILIBRIUM AA _ CRITERION SEVERE SLUGGING l STABLE l STABLITY CRIT UNSTABLE STEADY FLOW STEADY STATE STABILITY CRITERION UNSTABLE OSCILLATIONS Figure 2 3 Stability map for mu
54. eferente Sinmegimennin a a 107 LOW pass Miter in LabVIEW crnini a 109 Simulated results to get the best step tests for Shams s method 008 110 Some examples of MATLAB SCTiDts scssssssesssesesseesssessersserassessaearsesasssasessensaseeseseass 111 vi vil 1 Introduction Multiphase pipelines are a common feature of offshore production in the North Sea They connect subsea wells to the topside processing facilities or the platforms In many points of transportation these pipelines get the shape of L shaped or S shaped risers The stability of multiphase flow inside these pipeline riser systems is of great importance and many efforts have been spent on this issue so far In low reservoir pressures or low flow rate conditions the liquid phases tend to accumulate in low points and form liquid slugs This leads to the pipeline or riser blockage and can be more dangerous when the length of slugs is comparable to the length of the riser This phenomenon is called Severe slugging also Terrain slugging or Riser slugging and is characterized by large oscillatory variations in pressure and flow rates Storkaas 2005 These large variations lead to a poor separation unwanted flaring and even a plant shutdown in the worst case Reducing opening of the topside choke valve has been a traditional way to suppress severe slugging However this increases the valve back pressure and therefore decreases the production rate from the well A
55. emistry process design and development 25 1 252 265 Shamsuzzoha M and S Skogestad 2010 The setpoint overshoot method A simple and fast closed loop approach for PID tuning Journal of process control 20 10 1220 1234 Sivertsen H 2008 Stabilization of desired flow regimes Department of Chemical Engineering Norwegian University of Science and Technology Master Skogestad S 2003 Simple analytic rules for model reduction and PID controller tuning Journal of process control 13 4 291 309 Skogestad S and C Grimholt 2011 The SIMC method for smooth PID controller tuning PID Control in the Third Millennium Springer 147 175 Storkaas E 2005 Control solutions to avoid slug flow in pipeline riser systems Chemical Engineering Trondheim Norwegian University of Science and Technology PhD Storkaas E 2005 Stabilizing control and controllability Control solutions to avoid Slug flow in pipeline riser systems Norwegian University of Science and Technology Taitel Y 1986 Stability of severe slugging International journal of multiphase flow 12 2 203 217 Yan K and D Che 2011 Hydrodynamic and mass transfer characteristics of slug flow in a vertical pipe with and without dispersed small bubbles International journal of multiphase flow 37 4 299 325 108 A Low pass filter in LabVIEW In order to implement the low pass filter in the experiments the function PID Advanced VI
56. en carried out using a medium scale two phase flow S riser loop A single loop control scheme with riser base pressure as the measurement was used The robustness of different tuning methods was compared by slowly decreasing the set point of the closed loop system which was the inlet pressure until instability was reached The choke valve opening was increasing gradually by decreasing the set point A control with a robust tuning method can maintain system stability in a large range of conditions The choke valve was then replaced with a quicker valve after the first set of experiments The same experiments were repeated and the effect of control valve dynamics was investigated thereafter The experiments were simulated in OLGA and the same control tests were performed The OLGA case was constructed based on the first series of tests with valve 1 and the designed controllers with different tuning strategies were applied Results of the experiments verified those of the simulations The tuning method with the highest robustness was thus the one which could stabilize the system at the largest choke valve opening the lowest inlet pressure The best tuning method with respect to robustness is the simple PI tuning rules with gain scheduling for the whole operating range of the system With this method it was possible to stabilize the experimental riser system up to a choke valve opening of 37 from an open loop stability of 16 It was also able to stab
57. ep change was applied in set point Different values of step change were tried to get a step response close to the recommend 0 3 overshoot Then the system was set with the choke opening at Z 40 and the same tries were implemented Value of the resulting overshoot was highly depended on the initial gain and the amount of step change In some cases with the same initial gain several tests with different amounts of step change were run in order to get the desired 0 3 overshoot All simulations run to get the 79 desired overshoot at different basis conditions of the controller are presented in Appendix B When the desired overshoot was achieved the Shams s method for closed loop systems explained in section 2 9 1 was used to find the appropriate tuning parameters Table 5 10 shows the resulting tuning parameters by Shams s method at different initial positions of choke valve K is the initial gain used in the tuning simulation K is the calculated proportional gain and 7 is the integral tuning parameter Table 5 10 Tuning parameters from SIMC method for the slugging system position 0 3 u 0 3085 0 0787 0 0614 34 5702 0 4 0 0 3210 2 1132 0 0904 3 1150 Using PI controllers with the parameters found in table 5 10 the system became unstable at a choke valve opening of approximate Z 38 84 with the controller tuned at the initial position of 30 and at a choke valve opening of approximate Z 39 45 with the controller tuned at th
58. er cascade control experiment using topside pressure combined with outflow density as the control variables has been tried 26 a wes can e a N PA 7 o pem EE d kea i J X l s J Is x EA if Figure 3 1 Medium scale experimental setup of multiphase flow laboratory located at department of Energy and Process Engineering of NTNU 3 1 Setup Description The three dimensional overview of the multiphase flow rig used to perform the series of experiments in this thesis is shown in figure 3 2 The flow loop was consisting of water and compressed air supply 27 Figure 3 2 Multiphase Test Rig Layout NTNU Lilleby 2003 Figure 3 3 shows a schematic overview of the experimental setup with more details The whole system is placed at two levels Large storage water and pressurized air tanks T1 and T2 and water pump P1 were placed at basement Flow lines continued to lab level and all flow meters control valves horizontal test section and S riser were placed at this level The flow line of test with inner diameter of 50mm was connected to a mixer inlet section containing the air water supply and the multiphase flow was forced up the S riser The air buffer tank T3 was installed upstream the mixing point to increase the air volume and emulate a long pipeline The air volume should be large enough to force the liquid up the riser and cause slugging to occur As one of the most important equipment choke valve V
59. ergy and Process Engineering was used The reason to use such geometry is that the simulation results are to be compared with the experimental results in the thesis The exact geometry is presented in table 4 1 The X Y coordinates have been calculated with respect to table 4 land the resulting geometry has an overview of the figure 4 1 According to the experimental setup in multiphase flow laboratory the sources of air and water are placed in the beginning and the end of the buffer tank respectively Table 4 1 The geometry of the S riser experimental set up Pipe ul ale EE IEDC INE o aw os a s ewo oos 40 s w oos ae f sa oos me o ae ose w uw oos mao 11 1 150 0 05 90 N 2 S riser geometry 3 2 1 0 1 5 0 5 d 10 15 Figure 4 1 Geometry of S riser in OLGA 4 2 2 Fluid properties All fluid properties had been written in PVT file by Jahanshahi and Nilsen 2012 It is a table of phase compositions at different temperatures and pressures and is made by a program called PVT Sim By specifying temperature and pressure limits and the compositions of the fluids involved the program calculates the values for the phase compositions Heat transfer and temperature change were not important in simulations due to experimental condition Water was assumed as an incompressible flow Heat transfer and temperature related properties such as enth
60. es of gain parameter were tried to check which gain can create stability with the highest level of valve opening Z For each gain value it was tried to find the minimum amount of buffer inlet pressure as Set point or in other words the maximum level of valve opening as manipulated variable by stepwise reduction of the Set point Table 5 8 shows different values of gain that have been tried and the corresponding minimum value of Set point and maximum value of Z Table 5 8 different tried P only controllers initial valve K Minimum Maximum opening Set point value Manipulated variable P Z a 0 3686 0 4497 0 6454 0 6305 Pe ee _ o es o _ 0 3 The best controller that gives stability with the highest level of Z and the lowest level of achievable set point is the one withK 0 5 With this controller the bifurcation point was moved from Z 26 into Z 65 Figure 5 21 shows the result of control by P_Only controller for K 0 5 For the controller with K 0 01 specified by the star in the table the simulator could converge in some values of Set point However the result was not good and there were many oscillations in pressure and valve opening It was almost impossible to make a reduction in the Set point For the controller with K 1 control was difficult and the Set point reduction was challenging Figure 5 22 shows the result of control by for K 1 The steps of reduction had to be selected very small and the simulat
61. esistant to corrosion 3 2 1 Main water storage tank Water is filled in a separator T1 It is a 3m acid proof tank placed in the basement From the separator water is pumped through the infrastructure into the test section and returned to the separator again Figure 3 5 Main water storage tank located in basement 30 3 2 2 Air reservoir tank The air supply T2 is connected to the central high pressure supply This supply is a pressure vessel made by Nessco and gives a pressure of 6 7 bars which is then reduced through a pressure reduction valve to the operational pressure of usually approximately 3 bars Figure 3 6 Air reservoir tank located in basement 31 3 2 3 Air buffer tank The air buffer tank T3 with a volume of 200 liters and the type DN50 flange has been made by the company Laguna It is installed before the mixing point To make slugging possible a large pipe volume for pressure buildup is necessary The buffer tank is used to emulate this large pipe volume The maximum pressure the buffer tank can withstand is limited For safety the tank has been equipped with a safety valve to ensure that the pressure not will exceed 3 Bars Figure 3 7 Air buffer tank 32 3 2 4 Overflow tank An overflow system is made to achieve pressure dependent liquid flow It is a vented steel tank T4 filled with water Flexible pipes connect the tank to the separator A bypass flow will flow into the
62. essure in the simulations Therefor the initial value of the inlet pressure at each open loop simulation for a specified valve opening was used to be compared with those of obtained from the model Figure 5 34 compares simple static model to the OLGA case As clear in the figure there is quite a good match between the model and OLGA The MATLAB model is attached in Appendix C 7 90 220 Simple static MATLAB model OLGA case 200 pd lee 160 Inlet Pressure kPa 140 120 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 Figure 5 34 Simple static MATLAB model compared to the OLGA model The blue midline in the figure presents the steady state values of the inlet pressure from OLGA simulations and the red midline is the values of inlet pressure from the MATLAB model The top and bottom blue lines show the maximum and minimum values of pressure oscillations at each operating point in the open loop system 5 3 3 3 2 Calculating Tuning Parameters based on MATLAB model In order to find tuning parameters based on the identified MATLAB model a closed loop test with step change of set point was required The step test was done by a P only controller as it was proposed by Jahanshahi Jahanshahi and Skogestad 2013 The same step tests applied in section 5 3 3 2 were used here too Two different step tests one with the gain value of K 0 1 at the initial valve position o
63. f Z 0 3 and the other with the gain value of K 0 15 at the initial valve position of Z 0 4 were used to find two sets of tuning parameters The method of how to find the tuning parameters has been described in section 2 9 3 2 5 3 3 3 3 Results of tuning using initial valve position of Zo 0 3 With respect to the information extracted from the step test the parameter 7 has been found from the equation 2 41 as 8 0 2848 The period of slugging oscillations in open loop simulations have been T 140 Sec The model has been run for each OSC Operating point separately meaning that the parameter Z has been changed after each 91 running of the MATLAB model The parameters K z and 7 z have been found as functions of valve opening Z by the equations 2 42 and 2 43 and are presented in table 5 13 Table 5 13 PI tuning values in OLGA simulations with initial choke valve position of 30 Set point K T Inlet pressure Valve opening kpa 1 5465 1292 3 135 3 0 7562 Then gain scheduling with multiple controllers based on multiple identified models was used to stabilize the system To do this in the simulations 12 PI controllers were implemented in OLGA with the related found tuning parameters The controllers could stabilize the flow up to 75 5 of valve opening Changing bifurcation point from Z 26 into Z 75 5 could be a very good result Figure 5 35 illustrates the result of control using gain scheduling between
64. f their work which this thesis has been done based on that will be presented below 2 9 2 1 Model Identification To identify process model Jahanshahi and Skogestad use the step test information in a closed loop stable system to do online model identification The suggested model has two unstable poles and is in the form of bis b O E S Pasta Equation 2 16 Four parameters b b a and a need to be estimated by information extracted from closed loop step response Jahanshahi uses a systematic manner to find the related four parameters In his method the loop is closed by a proportional controller with gain K to get the closed loop stable system For closed loop transfer function from the set point to the output one similar to the model used by Yuwana et al Yuwana and Seborg 1982 is considered K 1 Ts 2 G s Ps 2 rs 1 Equation 2 17 19 The four parameters K 7 7 and are estimated by using six data Ay Ay Ay Ay t and At observed from the closed loop response see figure 2 10 Then they use a systematic procedure to back calculate the parameters of the open loop unstable model in equation 2 16 Jahanshahi and Skogestad 2013 2 9 2 2 IMC design for unstable systems To design the IMC controller C the identified model g is used as the plant model sya Astha s g s a ae Equation 2 18 1 k s U K s m1 s 2 Equation 2 19 g s o They al
65. face is illustrated in figure 3 15 The pressures flow rates and valve position could be monitored directly from the interface In addition it was possible to run the loop manually by manipulating choke valve opening or automatically by setting tuning parameters for PID PI P controllers Some modifications were applied in case of control Two modes of control were implemented in the program a single mode and a cascade mode The single mode used buffer pressure as control variable and the cascade mode was using top pressure and outflow density as control variables A schematic view of control modes are presented in figure 3 16 RRL RSEOEORERD 7 W iy Figure 3 15 LabVIEW user interface 39 CASCADE MODE Select manual or Select single PID or Final output to valve automatic PID control cascade PID control regardless of mode Set filter cut off frequency fem Example If time constant of 2 seconds i required Use 0 5 Hz Enable input filter on PV Output range for PID controller PID gains Create a new Stop logging Current file location logfile and start and close logging current logfile SINGLE MODE Figure 3 16 Implemented control modes in LabVIEW 40 4 Simulation of experimental cases 4 1 OLGA multiphase simulation tool OLGA OiL and GAs simulator is a commercial multiphase flow simulator widely used in the oil and gas industry It solves many numer
66. firiou 1989 The method supposes a model states desirable control objectives and from these proceeds in a direct manner to obtain both the appropriate controller structure and parameters For the objectives and simple models common to chemical process control the IMC design procedure leads naturally to PID type controllers occasionally augmented by a first order lag Rivera Morari et al 1986 Consider the block diagram for the IMC structure See figure 2 11 Here g is model of the plant that in general has some mismatch with the plant g is inverse of minimum phase part of and f s is a low pass filter for robustness of the closed loop system The goal of control system design is fast and accurate set point tracking y y vt Vd Equation 2 13 Efficient disturbance rejection y y d Vt Vd Equation 2 14 and insensitivity to modeling error Figure 2 11 The internal model control IMC structure 18 Jahanshahi and Skogestad do not use this configuration for the unstable system instead they use an equivalent as shown in figure 2 14 where C EJ o Equation 2 15 Figure 2 12 Closed loop system with IMC controller Jahanshahi and Skogestad 2013 They propose online identification of linear model by a closed loop step test They design an IMC Internal Model Control based on the identified model Then they use the resulting IMC controller to obtain tuning parameters for PID and PI controllers A summary o
67. for the active control of severe slugging Jahanshahi Skogestad et al 2012 Meland 2011 In the article by Jahanshahi Jahanshahi Skogestad et al 2012 one pressure measurement from the pipeline combined with choke flow rate has been suggested as the best measurements for a multivariable structure At the beginning of the thesis it was decided to try a similar structure with top pressure combined with riser outflow density as the measurements But this didn t become practical during the thesis due to the inconvenient density sensor See section 5 1 3 The new tuning methods applied in this thesis can be tried by other measurements and control structures in the future As the first step an accurate density sensor shall be used to give correct measurements of densities Then it can be used in the new control structures 101 6 3 Discussable issues related to experimental activities 6 3 1 Oscillations in flow rates In order to have a fixed U and U in each test it was important to have constant and consistent flow rates The air and water flow rates had many oscillations and it was very difficult to set the exact required flow rates Specially for the case of air this problem was more challenging The reason was that the control valve for the air was broken and the air flow rate had to be set with a manual valve far from the screen The manual valve made a big change in air flow rate even when it was tried to open or close it very lit
68. from LabVIEW was used The function implements a PID controller using a PID algorithm with advanced optional features Figure 5 6 adapted from the National Instruments website shows the block diagram of related the function gamma alpha manual contral autor iT output range setpoint process wariable setpoint range PID gains dt ts reinitialize F beta linearity Figure A 1 PID Advanced DBL In the presented figure alpha specifies the derivative filter time constant and can be a value between 0 and 1 The default is NaN which specifies that no derivative filter is applied The relation between 7 from the method and from LabVIEW is as follows u Equation A 1 109 B Simulated results to get the best step tests for Shams s method In this appendix all simulations run to get the desired overshoot at different basis conditions of the controller are presented The simulations are related to tuning of the controller by Shams s method See section 5 3 3 1 Table B 1 presents the initial and final values of buffer inlet pressure used as control variable in simulations before and after step change and the resulting overshoot The units are in kilo Pascal K is the initial gain used in the tuning simulations The values specified by the red color are the best results those were used to find tuning parameters Table B 1 Resulting overshoots to the different step tests at different initial positions of choke val
69. from valve1 is shown in figure 5 37 It can be seen in the figure that the bifurcation point is fairly the same for the both models It occurs at the same valve opening of Z 0 26 for both models but at a higher pressure for the experiments Models are slightly deviated from each other For the OLGA simulations the maximum of inlet pressure oscillations are located at higher values Open loop Bifurcation Diagrams 220 OLGA simulations Experiments 200 a 180 g i o NS B 2 160 ee S _ fom E 120 100 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 Valve opening Z Figure 5 37 simulated results from the OLGA case compared with the experimental results from valve1 The bifurcation point is fairly the same for both models 95 5 4 2 Comparison of control results from IMC based tuning method A comparison of simulated and experimental closed loop responses from controllers tuned with IMC based method is presented in table 5 15 Max Z shows the maximum valve opening achieved with that controller and Min P presents the minimum value of set point that is inlet pressure in kilo Pascal The numbers are the rounded values The controllers have been tuned at the initial valve position of Z 0 30 Table 5 15 Comparison of simulated and experimental results from controllers tuned with IMC based method Z is the level of valve opening and P is the inlet pressur
70. g methods Z Max is the maximum level of valve opening and P min is the minimum set point achieved that is the riser inlet pressure in Kilo Pascal Open Shams s IMC IMC simple PI loop set point based PI based PID tuning Stability overshoot tuning tuning with gain scheduling Set 1 of Experiments NOT with slow Performed valve Set 2 of Experiments valve en 153 135 5 See aoa a 0 26 0 38 0 46 0 50 0 75 Comparison of different tuning methods from simulations 220 200 a A 180 s pe Open loop 5 Shams P 160 IMC based D Trial and error 2 140 Simple online 120 100 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 Valve opening Z Figure 5 38 Comparison of stabilizing control results from different tuning methods applied in the simulations It can be said that simple online method with gain scheduling is the most stabilizing and the IMC based designed method is the second best as systematic manners to tune the controllers 98 Comparison of closed loop and open loop stability from experiments with valve 1 210 200 190 j lee bd N Open loop IMC based j Sg Inlet Pressure Kpa j O 130 120 110 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 Valve opening Z Figure 5 39 Comparison between the stabilizing control resu
71. gas flow rates The values of Z and the related flow regime types are presented by table 5 7 Table 5 7 Different values of valve opening Z used in open loop simulations Z Flow regime stability 0 20 Stable 0 25 Stable 0 26 Stable 0 27 Unstable 0 28 Unstable 0 30 Unstable 0 40 Unstable 0 50 Unstable 0 60 Unstable 0 70 Unstable 0 80 Unstable 0 90 Unstable 1 00 Unstable Figure 5 20 describes the open loop bifurcation diagram from simulations The diagram shows the maximum minimum average and steady state values of buffer pressure versus the valve openings The applied fixed flow rates have been w 0 3927 kg sec for water and w 0 0024 kg sec for air The same as experiments These flow rates correspond to U 0 2 m sec and Usg 1 m sec as the liquid and gas superficial velocities The critical stability point the bifurcation point is the maximum choke valve opening the system can have while being stable In a bifurcation diagram the critical stability point is where the maximum and minimum pressures approach a finite value In the presented bifurcation diagram the red line shows the steady state 74 values of the buffer pressure at different valve openings and the average values of the pressure are on the mid black line that is higher than the steady state line The coefficient of discharge was changed to Cqa 0 34 in order to manipulate the placement of the critical valve opening the bifurcation point based
72. gns of instability at Z 1 5 1 1 1 2 Bifurcation diagram The experiments were started with the valve opening of Z 0 2 Then the valve was open stepwise until it was fully open The results of buffer pressure were logged and the related bifurcation diagram was plotted presented in Figure 5 2 The critical stability point the bifurcation point is the maximum choke valve opening the system can have while being stable In the presented bifurcation diagram the top line tracks the maximum values of pressure at each operating point the bottom line presents the minimum values of pressure and the middle line shows the average values of the buffer pressure at different valve openings As clear in the figure the critical stability point was found to be at approximately 26 choke valve opening Z 0 26 48 Open loop Bifurcation Diagram Valve 1 210 N j ee O gt Q pd N J Inlet Pressure Kpa j O 120 110 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 Figure 5 2 Open loop bifurcation diagram from the slow choke valve experiments The bifurcation point occurs at valve opening of Z 0 26 The top and bottom line illustrate the maximum and minimum values of oscillations for inlet pressure respectively at each operating point The middle line shows the average values of pressure 5 1 1 2 Closed loop step test In order to apply each of tuning method
73. ical equations to simulate the flow by considering the system dynamics and offers heat and mass transfer models The experimental case was constructed in OLGA The designed controllers with different tuning strategies were used and the results were compared In order to fit the OLGA model with the MATLAB models and experiments some of the parameters were manipulated within limited ranges OLGA version 7 1 was used for the simulations In this chapter the case construction with implementing the S shaped riser geometry fluid properties numerical settings and boundary conditions is explained stepwise 4 2 Construction of the case Establishment of a good case with appropriate particular items such as fluid properties numerical settings initial and boundary conditions and flow path geometry was the initial step for simulation process The S riser simple case made by Jahanshahi Jahanshahi and Skogestad 2011 was basically used for the open loop simulations Some improvements and modifications were applied after the file was received For open loop simulations the modifications were in terms of numeric and for the closed loop simulations they were related to implementing the PID controller into the case In terms of numeric some Integration parameters were manipulated in Properties window of the program 41 4 2 1 Flow path geometry The S riser simple case with a geometry based on the experimental set up at the Department of En
74. id that applying gain scheduling between the IMC based controllers may also lead to a higher level of stability compared to applying a single IMC based PID PI controller This can be tried in the future Generally both IMC based method and simple online method are very useful systematic approaches to tune the controllers for the slugging system Previously trial and error was mostly used for tuning the controllers in the slugging system It can be said that the tuning rules used in this thesis are from the first systematic rules for anti slug control and give very clear fine results In future works time delay can be added to the measurements in the experiments in order to have a better investigation of the system robustness Actually this was tried in this thesis as an inconclusive effort See section 5 1 1 4 2 One important point needs to be mentioned in relation with tuning based on IMC design The IMC based PID tuning rules include a filter time constant that means an IMC filter must be implemented on the derivative action of the PID controller This was impossible in OLGA and therefore had to be neglected Although the simulation results do agree with the experimental results it can t be denied that neglecting filter action deviates the simulated results from the reality This may be possible in future versions of the simulator 100 About simple online method the MATLAB model is discussable From the results it can be observed that
75. ilize the simulated riser system until a choke valve opening of 75 from an open loop stability of 26 Top side measurements were in general difficult to use in anti slug control Measurement of the topside density using a conductance probe installation was not successful Therefore no cascade anti slug control schemes could be tested lii Contents ed AS 6s 6 caer ert meer cee are ere ee er eee ae cee eee eee eee ee i ADELA Seen ae eer tocar erm erste meena errr rece eee eee ee ee ee a ee ii L Mrodu cHolauenen a a ener eer ee 1 1 1 S Ope ofthe thesis ascenesteneii hee eee nee eee 2 2 TAC ONIN aane eiaa enc en a aAa ie A Ea a aSa 3 ZA Mu ul phase transpor Esasenae a aa aitlole ties nteeetetis 3 2a Ue NOW eraa AAA E errant et arr eee eee 5 Zo RISers CONntaming Multiphase NoWissciusessrsanenei a a 6 2H FRISCH SIIB COINS aeseutee went euetaoivah a ai elaee eerie 7 29 Ant ug OPC PallONS wevetveseveesveyivseurere sein we aaa O 11 as Ummm 6 5 greener nee enece erin enone eeae mE Pe ena E rere reer ee ee ren eer eer reer 11 Toa C Ue ee eae eee 11 29 3 Sp CIC NEES ae eee ere eere eer reTe eeere eerene t eee re nr ae en ee ee eer eee 12 LOA ACUVECONEO aggin a E A 12 07 Modelngofriser systeMS k snsienna 13 24 Bifurcation diag ta MSscisirin a A E E TN 13 Z 0 PID aid Prcontrollef Sasss ele aes een neces 14 29 Tuning of PID and Pl COMtrOUGIS seiseraseaevette aw ee aa 15 2 9 1 Method 1 Shams s set point overshoot method f
76. ler 220 A Setpoint a 200 Measurement 180 A A Weil RATANA col i Diiia A VW a 1404 V 120 0 200 400 600 800 1000 1200 1400 1600 1800 2000 100 50 N eV J X 1810 o Y 30 19 0 200 400 600 800 1000 1200 1400 1600 1800 2000 time sec Figure 5 11 Result of control using the IMC based PID controller The controller has been able to move the bifurcation point from Z 16 up to Z 30 19 about the double value IMC based PI Controller am 200 Setpoint A A Measurement S 180 5 A i x 160 it p T 140 0 200 400 600 800 1000 1200 1400 1600 1800 100 50 N AAAA X 1526 Y 29 35 0 200 400 600 800 1000 1200 1400 1600 1800 time sec Figure 5 12 Result of control using the IMC based PI controller The controller has been able to move the bifurcation point from Z 16 up to Z 29 35 62 5 1 2 3 3 Simple online PI tuning based on MATLAB model with gain scheduling Simple PI tuning rules described in section 2 9 3 was used as the last method of tuning the controller Since the method is based on the simple static MATLAB model of the system the MATLAB model needed to be identified and fit to the experimental steady state model For a reaso
77. ltiphase flow Taitel 1986 Stability boundaries are clearly shown in the map 2 2 Slug flow Among the flow assurance concerns management of slugging in system deliverability has received much interest in recent years Godhavn Fard et al 2005 Slug flow is one of the flow patterns characterized by alternating slugs of gas and liquid flowing in the pipes In this type of flow regime elongated bubbles of gas separated by slugs of liquid travel from one end of the pipe to the other end It can be either due to different velocities of gas and liquid phase which is referred as hydrodynamic slugging or pipeline geometry which is referred as terrain induced slugging The latter one is common in risers and its main reason is the gravity A schematic map of slug flow is shown in figure 2 4 adapted from Yan and Che 2011 The master unfavorable effect of slug flow is its instability that has a negative impact on the operation of offshore production facilities The periodic oscillations of liquid and gas phases due to their inhomogeneous distribution cause oscillatory pressures and decreases the level of production as large as 50 The average of these oscillations is lower than the equilibrium production and this gives the production losses More over these oscillations can damage the pipe and the separation process For these reasons 5 suppressing the slug flow is of dominant importance A homogeneous steady flow with very small bubbles of ga
78. lts from IMC based tuning method and the open loop system for the experiments with valve 1 Comparison of different tuning methods from experiments with valve 2 220 200 T Inlet Pressure Kpa Open loop 160 N MC based Simple online 140 120 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 Valve opening Z Figure 5 40 Comparison of stabilizing control results from different tuning methods applied in the experiments with valve 2 Simple online method with gain scheduling shows the best performance 99 6 Discussion and further works 6 1 Tuning methods The main objective in this thesis was to verify the very recently developed tuning methods Jahanshahi and Skogestad 2013 by medium scale experiments and OLGA simulations and identify the most robust tuning method for the slugging system From the results it can be seen that the highest level of stability is related to the controllers tuned by simple online method based on MATLAB model It should be noted that in this thesis wherever simple online method has been applied gain scheduling between multiple controllers has been also performed Since the slugging system is nonlinear and the gain of system changes drastically with changing level of valve opening tuning the controllers at each operating point and then connecting them via gain scheduling has a huge effect on the control performance It can be sa
79. lugging oscillations in sec in the open loop system Betha log dy_inf dy_u dy_p dy_inf 2 deltat KcO K_z0 dy_p dy_inf dy_inf 2 4 tp Kc Betha T_osc K_z sqrt z z_star baul z 3 T sc z2 z star disp FEED TO OLGA AND FIND THE MAXIMUM STABILITY SMODEL zt 0 2 0 001 1 n length z_t Pin zeros l1 n K_z_t zeros 1 7 for i Len fz s z 1 Cd sore l 2 t 1 2 cd 2 Pin i a fz 2 p_fo 1000 K z t i 2 a z_t i 3 cd 2 1000 end figure 1 clf plot z t Pin r a LinenNidth 243 xlabel zZ ylabel Inlet Pressure holda n kPa 118 6 6 666OLGA MODEL load Openloop Zz Olga Openloop 1 P_max Openloop 2 P_ min Openloop 3 3 P_ss Openloop 4 figure 1 plot z_oldga P_ss b LineWidth 2 5 hold on legend Simple static MATLAB model OLGA case 2 plot 2 olga P max b linen Lach 2 5 hold on Plot Zz olga FP min bp binewidch 2 5 grid on C 7 Simple static model fitted to the OLGA simulated model cle clear all 6 666666STEP TEST INFORMATIONS 333 o O load 230 1482 150 so 20 Deo 6Initial valve position in step test KcO 0 1 6gain used for the step test dy_s 2 6 t_init 200 dt 0 1 Es 230_145_150 2 1 e y 230 _ 140 150 2 7 es E Z230 1489 150 3 s U Z230 146 150 4 gt load z40_141_142 z0 0 4 S6Initial valve position in step test
80. lugs and are not the signs of instabilities 57 Open loop Bifurcation Diagram Valve 2 220 200 180 160 Inlet Pressure Kpa 140 120 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 Figure 5 8 Open loop bifurcation diagram from the fast choke valve experiments The bifurcation point occurs at valve opening of Z 0 16 The top and bottom line illustrate the maximum and minimum values of inlet pressure respectively at each operating point The middle line shows the average values of pressure 5 1 2 2 Closed loop step test Just like the experiment series with valve 1 the first step to tune the controller with any tuning method was a closed loop step test with a step change in set point the buffer pressure The loop was closed with a P only controller with a gain value of K 250 The step change was done in a region that is unstable in open loop position The average of valve opening was Z 0 18 The related plot is shown in figure 5 10 Since the response was noisy a low pass filter in MATLAB from the type of Simple infinite impulse response filter was used to reduce the noise effect A smoothing factor of 0 25 was used to smooth the signal as well as required 1 means no filtering 58 166 164 D j N _ j oy ON C _ G1 Oo Inlet Pressure Kpa p gi uN j Sg N
81. ments using the fast valve 7 3 Control using top pressure combined with density Measurement of the topside density using a conductance probe installation was not successful The open loop step test proved that the probe is not applicable as an appropriate sensor to measure the flow density The probe signal couldn t show a clear response to the step change and therefore was not a suitable measurement for the control targets See figure 5 16 In order to have an efficient cascade control with density as the inner loop control variable more accurate signals of density are required Therefore no cascade anti slug control schemes could be tested 7 4 Investigating effect of control valve dynamics The criterion to evaluate the slugging control loop is the stability and since the valves inherent characteristics are different the level of valve opening can t be used to compare the valves performance in the control loop Instead the minimum achievable set points in the closed loop responses and also the achieved range of set point reduction were used to compare the valve behaviors From the closed loop responses it was proved that the slow valve has a better performance compared to the fast valve This means that the slow valve has been already fast enough for our control targets and there has been no need to valve 2 faster control valve In other words the stability of the slugging system is more affected by the tuning parameters for the
82. minating severe slugging In this method the hydrostatic head of the riser is reduced with gas injection and thus the pipeline pressure will be reduced The injected gas lifts the liquid towards up the riser If sufficient gas is injected the liquid will be continuously lifted and a steady flow will occur The drawback of gas lift is the large gas volumes needed to obtain a satisfactory stability of the flow in the riser and this is too expensive Storkaas 2005 11 2 5 3 Slug catchers One other way to accommodate slugging is common to install a large separator as a Slug catcher at the exit of the pipeline The slug catcher is the first element in the processing facility and determining its proper size is vital to the optimal operation of the entire facility The fundamental purpose of slug catcher is to remove free gas from the liquid phase and to deliver a relatively even supply of liquid to the rest of the production facility An advantage of this set up is that inspection and maintenance on the slug catcher can be done without interrupting the normal operation There are mainly two types of slug catchers the vessel and the multiple pipe types and the use of each type depends on the type of flow stream Multiple pipe separators have been widely applied in gas condensate processing facilities Miyoshi Doty et al 1988 Installing slug catchers has several drawbacks it puts a lower bound on the operating pressure of the pipe which again limits
83. n be said that the best tuning method for the slugging system is the simple online PI tuning rules with gain scheduling for the whole operating range of the system based on MATLAB model Tuning based on IMC design also works very well for the slugging system These tuning methods are able to move the critical stability point significantly and considerably increase the production rate as a result It was also tried to make a clear comparison between the applied tuning methods by using figures To do this the open loop and the closed loop bifurcation diagrams were plotted for the simulations and each series of experiments Figure 5 38 compares the results of stabilizing control simulations by different tuning methods Figures 5 39 and 5 40 do the same for the results of control experiments The bifurcation point as a sign of stability level is shown before and after control with each tuning method The rightmost bifurcation point is related to the best tuning method that provided the most stability in each series It should be noted that Shams s method didn t work in the experiments This is not surprising since it has been developed for the systems that are stable in open loop while the slugging system is highly unstable Simple online tuning method based on MATLAB model was not tried in the series of experiments with valvel See section 5 1 1 4 for more explanations 97 Table 5 16 Comparison of simulated and experimental results from all tunin
84. nable result it was first required to have an accurate model of the experiments To find the model the loop was closed with a PI controller and was run in the region after stability point in open loop bifurcation diagram This was done such that set point was set to a value lower than the corresponding value of the bifurcation point then it was waited until steady state was reached and data were logged The average of valve opening was found from logged data and the obtained point was located on the steady state experimental model By repeating this for some other set point values the steady state line of experimental model was found It is shown in figure 5 13 with the black midline Next step was to modify the MATLAB static model and fit that with the experimental model As described in section 2 9 3 1 the MATLAB model is derived based on the valve equation and is a function of valve opening Therefore a good assumption of valve equation is very important in using the simple model The valve equation is as the form w K f Z V PAP Equation 5 7 The valve is linear and its characteristic is defined as f Z Equation 5 8 The simple model for the inlet pressure is as defined in section 2 9 3 1 and the Static gain of the system becomes in form of 2 Woss ae PRK Since the tuning parameters are found based on this MATLAB model a good match between this model and the experimental model is very important meaning that the values of inlet
85. nd delay margin was obtained for the controller _ 340 7491 S 0 005194 0 000356 Equation 5 6 SCS 0 0816 The IMC controller as a second order transfer function was then written in form of a PID controller with a low pass filter applied on its derivative action We may say a PIDF controller A PI controller was also obtained by reducing the order of IMC controller to 1 The related tuning rules are shown in table 5 5 Table 5 5 IMC based PID and PI tuning parameters PIDF 3 4736 2 3368 1189 9378 PI 340 7491 229 2276 The function PID Advanced VI from LabVIEW was used to implement the low pass filter in the experiments see appendix A The PID tuning parameters were implemented in LabVIEW First the system was run in open loop manner with a manual valve opening of Z 0 2 and data were logged Then the loop was closed with a set point P 170 kPa that results in an average valve opening of Z 0 16 After couple of minutes it was tried to decrease the set point value in a stepwise manner At each step it was waited until the steady state was reached and then a new step of reduction was applied The same was done with PI tuning parameters Figures 5 11 and 5 12 describe the results of control using the IMC based PID and PI controllers respectively The experimental slugging system could be stabilized up to Z 0 30 with IMC based PID controller and up to Z 0 29 with IMC based PI controller 61 IMC based PID Control
86. ng rules are K FE Equation 2 31 7 AP Equation 2 32 2 9 5 Method 3 Simple online PI tuning method with gain scheduling One main part of the thesis is tuning the controller by a new method called Simple online PI tuning rules proposed by Jahanshahi and Skogestad Jahanshahi and Skogestad 2013 One advantage of this method is that Nonlinearity of the slugging system has been considered when providing the tuning rules Gain of the slugging system changes drastically for different operating conditions and as the source of nonlinearity makes control of the system difficult The method consists two parts First a simple MATLAB static model for the static nonlinear gain is identified at each operating point valve opening Then the identified model at each operating point is used and simple PI tuning rules based on single step test but with gain correction to counteract nonlinearity of the system are proposed as functions of valve opening In this method of tuning Jahanshahi and Skogestad have used gain scheduling with multiple controllers based on multiple identified models The MATLAB model and the obtained PI tuning rules for each controller will be explained below 22 2 9 3 1 Simple MATLAB static model The simple model for an L shaped riser considering static nonlinearity was made by Jahanshahi Jahanshahi and Skogestad 2013 The model is based on the mass balances and it calculates the phase distributions over the
87. nlinearity as the important characteristic of slugging system provides some challenges for control However a good control system using a model that is most consistent with the plant could have good results in achieving desired stable flow regimes 12 2 6 Modeling of riser systems The main objectives of modeling of production flow in pipelines and risers are to predict the pressure drop the phase distributions the potential for unsteady phase delivery slugging and the thermal characteristics of the system Pickering Hewitt et al 2001 The reliability of these simplified models is however questionable The analysis and modeling of multiphase flows relies heavily on empirical correlations and the predictions for the models are only as reliable as the empirical data on which they are based Therefore it can be questioned whether the models would be valid if applied to real systems They are tested by the use of small diameters experimental risers and may be more than good enough for such systems but they still may be invalid for use in larger systems Pickering Hewitt et al 2001 The tuning methods used in this work are provided via linear and nonlinear multiphase flow models based on the mass balances over the different sections of the pipeline riser system The simplified four state mechanistic model made by Jahanshahi and skogestad Jahanshahi and Skogestad 2011 uses simple relationships to calculate the phase distributions over the
88. nrnesnnnonnensneonnensnennnnnnnnnnnnnnns 95 5 4 2 Comparison of control results from IMC based tuning method nsss 96 5 4 3 Comparison of control results from Simple online tuning method 96 5 4 4 Comparison of tuning methodsS ss ssssssssssssrssnsrrsnsnrsnsnrsnnnnsnnnnnnntennnnennnnennneennnnnnnnnnnnnen nnes 97 V 6 7 N w p Discussion and further works esssessuessunnuunnunnunnuunnnunnunnunnnnnnnunnunnunnnnnnnunnnnnnunnnnnnnnnnnnnnnnnn 100 OL Tunne methods ssni E E a aA 100 6 2 CONTOS UCUTOS masnrana nnan a 101 6 3 Discussable issues related to experimental activities s sssssssessrsesrsesreesressressrrsennes 102 GLL OScilatiOns IN TOW rates saote aa 102 6 3 2 Water flow back into the buffer tanK sssssssssssersenssrssnrnessrnsnsnnsnnnessnnennnnsnnnnnnnnnnnns 102 63 5 Leakage iN Stee connectoren aaa A 102 CONCUSSION an A E act ated 104 7 1 Stabilizing control experiments using bottom pressure sssssssesssssesreserressrrsesreserneses 104 7 2 Testing online tuning rules on S riser experiments ss sssssssessersessrssrsrrsernessrnsesrnsesneses 104 7 3 Control using top pressure combined with density s sssssssessrresrssrrsresnrerenessresennes 105 7 4 Investigating effect of control valve dynamics sss sssssssssesssrssnsresnrnessrnsnsnnsnnnnsnnnsnnnnsennenns 105 7 5 Control simulations using OLGA ssssssesssssssssrnssenssnnnesnnnsonnneonnnnnnneonnnnonnnnnnnnnnnnennnnnnnnnnnnnnnnnnnn 106 R
89. nti slug control system it is very important that the controllers are fine tuned Otherwise the control system is not robust in practice and the closed loop system becomes unstable after a plant change The slugging system is highly nonlinear since the gain changes at different operating points For such a system the controllers need to be retuned at each operating point 1 1 Scope of the thesis In this thesis three different tuning methods will be tested with experiments and simulations to find the most robust solution for anti slug control system High robustness will be obtained if the system can maintain stability at large deviations from open loop conditions This means large choke valve openings The tuning methods are systematic and have been developed very recently Shamsuzzoha and Skogestad 2010 Jahanshahi and Skogestad 2013 The experiments of this thesis will be carried out at the department of Energy and Process Engineering Two series of experiments will be run using a medium scale two phase flow S riser loop The difference between the two series is the type of choke valve The aim is to investigate the effect of control valve dynamics on performance of the control system in addition to robustness of the tuning methods Possibility of different control structures will be also investigated The experiments will be simulated in multiphase flow simulator OLGA and the same control tests will be performed Finally the simulated and e
90. ntroller Setpoint Measurement 200 400 600 800 1000 1200 1 a x 1266 Y 38 39 200 400 600 800 time sec 1000 1200 1400 Figure 5 7 Result of control using the IMC based PI controller The controller has been able to move the bifurcation point from Z 26 up to Z 38 39 55 5 1 1 4 Inconclusive efforts and the related practical issues When working with the first valve some efforts were inconclusive and no results were produced Below some explanations are given 5 1 1 4 1 Tuning the controller by Simple online method based on identified MATLAB model of the system As the last method of tuning it was tried to use simple PI tuning rules described in section 2 9 3 The method has been proposed by Jahanshahi Jahanshahi and Skogestad 2013 and is based on the identified MATLAB static model of the system To implement this method first the simple static MATLAB model of the system which tuning rules are based on needed to be modified and fit to the experimental steady state model For a reasonable result it was required to have an accurate model of the experiments Though right in that time the lab technician replaced the current valve with the fast valve since he was going to vacation and this couldn t be done for a long time Therefore this tuning metho
91. on is highly undesirable The large liquid production might cause overflow and shut down of the separator Fluctuations in gas production might cause operational problems during flaring and the high pressure fluctuations might reduce the production capacity of the field Jansen Shoham et al 1996 It can reduce operating capacity for separation and compression units The reduced capacity is caused by the need of larger operating margins to handle the larger disturbances Larger disturbances require a larger back off from the optimal operation point and thus reducing the throughput Storkaas 2005 Severe slugging can occur in two different modes of I and II In type I of severe slugging the liquid fully block the bend while in type II there is a partial blockage at bend and gas passes through The type I is characterized by large oscillations in pressure and accelerated blow out In fact the pressure oscillations reflect static head of the riser There are small pressure oscillations in the severe slugging of type II and the slug length is shorter than the height of the riser But flow oscillations can be large Type II slugging is not usually critical for a stable operation Figures 2 7 and 2 8 adapted from Malekzadeh Malekzadeh Henkes et al 2012 illustrate SS1 and SS2 respectively Figure 2 7 is based on a measured cycle of the riser APfor SS1 corresponding to U 0 20ms and U co 1 00ms Figure 2 8 is based on the experimental cycle for the
92. oned there Section 5 2 evaluates the effect of control valve dynamics through comparing results of slow valve with those of fast valve The simulated results will be explained in section 5 3 In section 5 4 the experimental results are compared with simulated results In section 5 5 the three different used tuning methods have been compared and the best tuning method has been investigated 5 1 Experimental results The operating procedures and the results from experimental activities done at NTNU multiphase flow laboratory are discussed in this section For each series of experiments with valve 1 slow valve or valve 2 fast valve the open loop system with basic conditions would be explained first Then the procedure of implementing closed loop step test and calculating the tuning parameters by using different tuning methods will be discussed The results of tuning in the form of tuning rules are explained thereafter Finally the closed loop responses using calculated tuning parameters will be presented as the main results of the experimental work 46 5 1 1 Series of experiments with valve1 slow choke valve The experimental work in this thesis started with using slow choke valve as the actuator The goal was to repeat the same series of tests with a slow and a fast choke valve and then evaluate the effect of control dynamics on the final results 5 1 1 1 Open loop experiments The starting point in the experiments was running the loo
93. op Automatic Control in O shore Oil and Gas Production Trondheim Norway Jansen F O Shoham et al 1996 The elimination of severe slugging experiments and modeling International journal of multiphase flow 22 6 1055 1072 Kazemihatami M 2012 Experiments on Liquid Flushing in Pipes Master Project Trondheim Norwegian University of Science and Technology Lilleby K 2003 User s Manual for Multiphase Flow Loop Trondheim Norwegian university of science and technology Malekzadeh R R Henkes et al 2012 Severe Slugging in a Long Pipeline Riser System Experiments and Predictions International journal of multiphase flow Meland K O 2011 Stabilization of two phase flow in risers from reservoirs Chemical Engineering Trondheim Norwegian University of Science and Technology Master Miyoshi M D Doty et al 1988 Slug catcher design for dynamic slugging in an offshore production facility SPE Production Engineering 3 4 563 573 Morari M and E Zafiriou 1989 Robust process control Morari Olsen H 2006 Anti slug control and topside measurements for pipeline riser system Master s thesis Norwegian University of Science and Technology Pickering P G Hewitt et al 2001 The prediction of flows in production risers truth amp myth IIR Conference 107 Rivera D E M Morari et al 1986 Internal model control PID controller design Industrial amp engineering ch
94. or closed loop systems 15 2 9 2 Method 2 Tuning based on IMC CeSiQN ce eeeeseeceeseeeeteeeeteseeteseeteteeteneaeeneeeneaeeee 18 2 9 3 Method 3 Simple online PI tuning method with gain scheduling 22 3 TEXDCRIMION Va WOM cacti a sclera ect ea lacl cabal cteca uated 26 Su Setup Des ChIDLION wicca ns ahw er ian nei 27 3 2 BOUIDMENC anses adnan annadtananamnennineas 30 3 2 1 Main water storage CAIN a Seesceces tees carers sepa cueascuereiett neice aeent vetneerteense ere maneeee 30 SA A RESET VOIl TAN E ia ined anneal O 31 3 2 3 WA UIP tank ansan a a a a ictal vel aaa a aaa N 32 SAF Overnlow tank ssas hi 33 329 Press retransMiie eno a E aie 33 32250 Small separa O nnna iR a daioi iiaea au EN EE te 34 3 2 7 Centrifugal Water puMp ss sussrssaranarasararonunoannsannnanaranasnnnnnnnnonnonnnnandnanasanannnnontannnnnndnnnananane 34 3 ANON METET asi E ice Oe aaa yen leet aco netat 35 S29 Waterflow Meter cin ciaet tee ce inlet ces irae ie ear aencaas 35 3 2 10 GOK Valves siciticesiaiesataniie in teteartepederastte leh oat ase hase ei verte te vawresd O 37 3 2 11 COMAGUCTAN CE ProDE C esisiini aats eSi ae aaa eA Eea EEA E ai 38 3 2 12 LADVIE Wisner 39 4 Simulation of experimental cases sn se snr snnonnornonunnronnronnnnnonronnnnnnnnnenennennrnnnnnnennrnnennee nnn 41 4 1 OLGA multiphase Simulation t0Ol sss sssessssssrrssrresrnesrnnssnessnensrensnnesnrennnennnnsnnnsnnnsnnesnnesrnnnns 41 A2 sCOMSITUCHON ONECA
95. or could not converge with a larger step than it is observed in the figure For the values filled with dash the simulator could not converge for any values of Set point meaning that it was impossible to control the system with the gain values higher than 1 A P only controller with 0 05 lt K lt 1can stabilize the system 76 Inlet Pressure Controlled variable 150 Set point Measurement O ne 140 130 500 1000 1500 2000 Valve position Manipulated variable 1 prune I N 0 5 X 2179 H Y 0 6436 0 0 500 1000 1500 2000 time sec Figure 5 21 Simulation result of control by P Only controller for K 0 5 with OLGA This has been the best result from trial and error due to the lowest achievable set point or in other words the highest level of valve opening Inlet Pressure Controlled variable 150 i Set point Measurement a 140 130 0 500 1000 1500 2000 2500 Valve position Manipulated variable 1 b s N 0 5 X 2370 F Y 0 6306 0 0 500 1000 1500 2000 2500 time sec Figure 5 22 Simulation result of control by P Only controller for K 1 5 3 2 2 PI controller PI controller was used to stabilize the system in the second series of simulations by trial and error The controller was designed by inserting 7 O
96. ow rate of water which was not high 0 39 kg sec the water control valve was open in small values instead 34 Figure 3 10 Centrifugal water pump 3 2 8 Air flow meter The vortex flow meter of type DN40 wafer manufactured by JF Industrisensorer was used to measure the air flow rate FIT1 01 The number that it gave was in the unit of Kg hour and needed to be converted into the desired unit kg sec It was located upstream the air buffer tank The working range of the air flow meter was 5 2180 kg h 3 2 9 Water flow meter The Electro magnetic water flow meter of type 1 2 union manufactured by JF Industrisensorer was located upstream of the mixing point FIT2 01 It has a working range of 0 19 6 4 m h 35 Figure 3 11 Air flow meter f I FIT 2 01 a Figure 3 12 Water flow meter 36 3 2 10 Choke valves Two different choke valves V have been used in this thesis and the series of experiments have been run with both First a slow valve was used as the actuator to run the control experiments and then it was replaced with a fast valve The effect of their dynamics was then investigated They are angle seat valves located on the top of the riser upstream of the separator The choke valve is operated by pressurized air 4 bars supplied from the pressurized air system in the laboratory through the valve positioner The specifications of the old slow valve were not available while the specifications of th
97. p in manual mode The tests were run in different valve openings with fixed liquid and gas flow rates while no controller was implemented in the system It was aimed to present the system behavior in natural conditions without control The inflow conditions and the related bifurcation diagram are presented below 5 1 1 1 1 Inflow conditions The applied fixed flow rates have been w 0 3927 kg sec for water and w 0 0024 kg sec for air See figure 5 1 These flow rates correspond to U 0 2 m sec and Usg 1 m sec as the liquid and gas superficial velocities The water flow rate could be set in lab view by adjusting the pump frequency and the control valve while the air flow rate needed to be set with a manual valve in the path of the flow The reason was that the control valve for the air was broken The manual valve was far from the screen and this made it difficult to obtain the exact flow rate The water flow rate was not also easy to set Large variations in the flow rate were eliminated by running the pump with a high frequency and opening the control valve in a small value The more opening the choke valve the more slugging the flow regime and the more unstable the flow rates were resulted In the following series of experiments a constant flow rate of air and water was used As a result the water and air flow rates needed to be readjusted when the valve opening in open loop was changed However when using a controller in clo
98. pening of Z 0 35 Changing bifurcation point from Z 16 into Z 35 could be a very good result 66 Table 5 6 PI tuning values and the corresponding operating points from simple online tuning method based on MATLAB model These five controllers were connected and performed gain scheduling with multiple controllers for the nonlinear slugging system 2000 8383 aie er 0 31 4080 2676 641 25 0 38 Multiple controllers with gain scheduling 5 200 Setpoint ry Measurement 180 N A LEY a eA j ha af 160 E NAAN i D E 140 0 200 400 600 800 1000 1200 1400 1600 1800 100 50 N 0 0 200 400 600 800 1000 1200 1400 1600 1800 time sec Figure 5 14 Results of gain scheduling using four PI controllers When the system was switched into the fifth controller the instability was appeared meaning that the maximum level of stability was reached with four controllers tuned by simple online tuning rules The controllers have been able to move the bifurcation point from Z 16 up to Z 35 67 5 1 3 Cascade Control using top pressure combined with density One of the tasks in the thesis has been running the closed loop using a cascade control structure with selecting top pressure and density of outflow as the control variables The intentions were tuning this control structure by trial and error and then analyze the cont
99. pressure and the static gain obtained by the model needed to be true Equation 5 9 values The parameters L length of riser P_V_ minimum Pressure drop over the min valve and K the valve constant were manipulated many times until the desired match with the experimental model was reached Below is a discussion of these parameters 63 Length of riser In MATLAB model length of riser is directly used to calculate the static pressure of the riser when it is filled with liquid and thereafter this static pressure is used to find the inlet pressure at any level of valve opening Therefore manipulating of that could be very helpful in producing desired results The exact length of riser in the experimental setup has been 6 433 m Though it was changed to 6 7 m in model to provide the best results Minimum pressure drop over the valve This parameter is used in several calculations in the model The most important one is the value of inlet pressure in the fully open position of the valve that uses P _V in directly See section 2 9 3 1 Level of the curve in the inlet pressure plot of the model was quite affected by inlet pressure at fully open position of the valve A value of P_V 3kPa was used to get the best fitness of the models Valve constant The valve constant K has a major effect on the slope of the curve in the inlet pressure plot of the model A value of K 1 6x 10 was used in the MATLAB model Figure
100. r and the discharge coefficient of the valve were quite effective A description regarding this issue will be presented below Length of riser as the first manipulated parameter In MATLAB model length of riser is directly used to calculate the static pressure of the riser when it is filled with liquid and thereafter the static pressure of the riser is used to find the inlet pressure at any level of valve opening Therefore manipulating that could be very helpful in producing desired results The exact length of riser that was used in simulations is 7 7054 m Though it was changed to 5 15 m in model to provide the best results Discharge coefficient of choke valve cd as the second manipulated parameter The coefficient of discharge in the valve equation is a constant which depends on the pressure drop over the valve In order to fit the simple static MATLAB model to the OLGA case this parameter was manipulated Decreasing the value of cd caused the model to have a better match with the simulations The parameter cd used in OLGA case was 0 34 while a value of 0 31 was implemented in MATLAB mode The simplest way to check if the model is correct is comparing the values of inlet pressure and static gain from the MATLAB model by the same values from OLGA simulations To do this the steady state values of inlet pressure from OLGA simulations were used The simulator gives the steady state values as the initial value of any variable including inlet pr
101. re Measfrement S Pi 4 Fal Air Wa s ab t CHEQk 4 Figure 4 2 OLGA case with PID controller The controller receives the measurement S RISER signal from the pressure transmitter and sends the output signal into the choke valve located at top of the riser When applying a PID controller in OLGA several specifications need to be established by user depending on the desired conditions and results The more important specifications that have been manipulated many times during simulations are the PID parameters and the time varying specifications When it comes to PID 44 parameters in property window of the simulator AMPLIFICATION refers to the gain of the controller BIAS is the desired initial output value it was used as the desired valve Opening in our simulations DERIVATIVECONST is the time constant for the derivative action and INTEGRALCONST is the time constant for the integral action As the time varying specifications the MODE was set to AUTOMATIC and the SET POINT values were changed from one simulation to another 45 5 Results and discussion The purpose of this chapter is to present the results from experiments and simulations and a clear comparison of them The experimental results from two series of experiments using a slow and a fast choke valve will be presented in section 5 1 The effort of cascade control experiment using top pressure combined with density as measurements and the faced issues has been also menti
102. riable 150 Setpoint Measurement a 145 aah A 140 0 500 1000 1500 2000 2500 Valve position manipulated variable 0 6 N AARARADANAANSLE NA 0 4 X 2417 Y 0 4707 0 2 0 500 1000 1500 2000 2500 time sec Figure 5 30 Simulation result of control using the IMC based PI controller tuned at the initial choke valve position of 30 85 5 3 3 2 2 IMC based tuning at Z 40 as the initial valve position The same simulation as the one explained in previous section was run at Z 40 The loop has been closed by a P only controller with an initial gain K 0 15 and set point has been changed by 1 kPa at Z 40 The same procedure and calculations as described in previous section was used to find IMC based PID and PI tuning parameters The closed loop stable system was identified as the following 7 011 S 0 805 Equation 5 14 23 648 2 278 1 G 5 The implemented step change and the identified closed loop transfer function are illustrated in figure 5 31 Closed loop step response 143 hi li 142 5 i rm i ai I cj i w i a 142 PE OE ia al aB I Fa Au 141 5 pian Setpoint OLGA Measurement a Identified model 250 300 350 400 450 500 550 600 650 700 time sec Figure 5 31 Closed loop respon
103. robe installed in the outlet of the riser 68 However it seemed that the conductance probe is not a good measuring device for the density After some unsuccessful tries to control the system by tuning the loops with trial and error it was decided to perform a step test in open loop situation of the system and evaluate the open loop step response of the conductance probe It was aimed to check the applicability of probe as an appropriate sensor to measure the density To do this the loop was run in manual mode at the stable region with a valve opening of Z 7 Data from density meter Conductance probe and top pressure sensor was logged After some minutes the valve was changed to Z 12 while it was tried to keep the system in the stable region Figure 5 16 presents the open loop step response of the probe as the density meter Open loop response 0 1 N 0 08 0 06 0 100 200 300 400 500 600 V x vi D fem Ax 0 100 200 300 400 500 600 lt 2 A 15 0 100 200 300 400 500 600 time sec Figure 5 16 Open loop step response of conductance probe density meter in the stable region The first plot Z shows the step change in valve opening the second plot presents the step response of top pressure in Kilo Pascal and the third plot illustrates the step response of the outflow density in kg sec As seen in the figure th
104. rollability characteristics in comparison with the single loop structure 5 1 3 1 The test practical issue test incomplete The outflow density was used as the control variable of inner loop and the top pressure was Selected as the control variable for the outer loop Having a right measure of density could be very important in controlling slugging system with the cascade structure Figure 5 15 illustrates a schematic overview of cascade structure in LabVIEW The device used for measuring the outflow density was the conductance probe explained in section 3 2 11 CASCADE MODE Select manual or Select single PID or Final output to valve automatic PID control cascade PID control regardless of mode Set filter cut off frequency f ift Example If time constant of 2 seconds i required __ Use 0 5 Hz Osr E cmo 0 Enable input filter _ on PV Output range for PID _ controller PID gains proportional gein Ke 11 000 integral time Ti min 0 010 integral time Ti min 90 010 ime Td min J000 derivative time Td min fo 00 Create a new Stop logging Current file location logfile and start and close logging current logfile Figure 5 15 A schematic view of cascade control structure in LabVIEW The outer loop receives signal from top pressure sensor as the measurement and produces the set point signal for the inner loop The inner loop uses the density signal from the conductance p
105. s to get an appropriate controller for the slugging system a closed loop step test is required with a step change in set point the buffer pressure To do this it was tried to control the system by trial and error A P only controller was selected and as the initial guess for the gain a big value of 100 was tried The reason was that the set point value was a small number pressure in bars and the gain had to be selected in a way that it could change the output Z in a large range after a small change in set point Increasing the gain resulted in a more stable flow with smaller pressure variations or smaller amplitude of slugs Finally a high value of K 220 was selected to perform the step test Set point was manipulated to get the average valve opening higher than 0 26 and the obtained value of 0 29 was satisfying It was aimed to do the test in a region that is unstable in open loop position After the system was stabilized four step tests were implemented and data were logged The related specifications are presented in table 5 1 and the related diagrams are shown in figure 5 3 49 Table 5 1 Closed loop step test specifications run with slow choke valve Ko Initial set point Final set point CO Test_4 1 49 1 70 Test 1 Test 2 1
106. s well distributed in the continuous liquid phase is most desired In such desired situation the pressure remains constant over time Pipe wall Taylor bubble Liquid film Liquid slug Figure 2 4 Schematic map of slug flow in a vertical pipe in a slug unit Yan and Che 2011 2 3 Risers containing multiphase flow Risers are a special type of pipeline developed for vertical transportation of materials from seafloor to production and drilling facilities on the water s surface They can be in types of rigid risers flexible risers and hybrid risers that is a combination of the rigid and flexible Risers can have many different configurations However in this thesis all the S shaped types are the point of interest regardless of their differences The functional suitability and long term integrity of the riser system affects the selection of riser configuration Bai 2001 Figure 2 5 shows prevalent riser configurations J Lazy S Lazy wave Catenary Figure 2 5 Common riser configurations applied in the oil and gas industry Bai 2001 2 4 Riser slugging Riser slugging also called severe slugging terrain induced slugging is the toughest type of slugging happening in a pipeline riser system where a downward inclined pipeline is connecting into an upward riser Storkaas Storkaas 2005 explains the cyclic behavior of riser slugging illustrated schematically in figure 2 6 It can be broken down into four steps Step 1 Slug formation gra
107. se of step change at initial valve opening Z 0 4 The dashed black line shows the transfer function of the IMC based identified model The open loop unstable system has the form of 2 966 S 0 3405 a Equation 5 15 S 0 2006S 0 00825 P s 86 The designed IMC controller is 0 16877 S 0 043458 0 001998 Coja e eee Equation 5 16 S S 0 1148 And finally the related PID and PI tuning parameters have been calculated as shown in table 5 12 Table 5 12 IMC based PID and PI tuning parameters tuned at the initial choke valve position of 40 PIDF 0 038293 13 0406 29 6774 PI 0 16877 57 4753 Just like the previous part the filter time constant was neglected due to impossibility of applying low pass filter in OLGA and a PID controller was used instead Figures 5 32 and 5 33 describe the results of control using the IMC based PID and PI controllers respectively tuned for Z 40 The controllers were tuned for valve opening of Z 40 The PID controller could stabilize the system up to Z 54 61 In fact with this controller the bifurcation point has been moved from Z 26 into Z 54 61 The PI controller could stabilize the system up to Z 51 As well as the result for the initial point of Z 30 the PID controller shows a better performance with less oscillations in output and a higher level of valve opening has been achieved 87 Inlet pressure controlled variable Setpoint
108. sed loop mode it was considered not to be reasonable to readjust the inflow conditions Figure 5 1 compares variations of flow rates and pressure in two different valve openings 47 Basis condition with 20 valve opening x 10 Basis condition with 100 valve opening 1 gt lt 9 oO 5 D D 9 D N Air Flowrate kg sec N N Air Flowrate kg sec l 50 100 150 200 250 300 350 N N ey N Ww A gt un ee w eo gt w gt D ul gt D gt Ww N w ua Water Flowrate kg sec Water Flowrate kg sec a w N 0 100 200 300 400 0 50 100 150 200 250 300 350 200 3 l ry 200 A A 1989 7 180 o o hm hm 2 196 Mat N ii n i 1 a 160 N N F 194 i UTE a F 140 Qu Qu o o 192 120 lae ie 190 100 100 200 300 400 0 50 100 150 200 250 300 350 time sec time sec Figure 5 1 Illustration of basis open loop conditions in case of flow rates and pressure The left series of plots are illustrating the system with valve opening Z 0 2 that is related to the stable region while the right side plots present the system with valve opening Z 1 that is related to the unstable region Large oscillations are clear si
109. so design the filter f s for robustness of the system as explained by Morari et al Morari and Zafiriou 1989 The filter is in the following form 2 as astl Equation 2 20 As 1 i is an adjustable filter time constant The coefficients and a are calculated f s by solving the following system of linear equations 2 3 T T a An 1 1 l Equation 2 21 M T Qy Ax 1 1 Filter only acts to the derivative action Finally the resulting IMC controller is found as the following l 2 MFE a s OS 1 C s Equation 2 22 s st 20 2 9 2 3 PID and PI tuning based on IMC controller Jahanshahi writes the IMC controller of equation 2 22 in form of a PIDF controller and propose the tuning parameters based on that PIDF is a PID controller which a low pass filter has been applied on its derivative action K Ks Kop K Equation 2 23 S t st Where the tuning parameters are tT 1 9 Equation 2 24 Tp l a Equation 2 25 k K K a a KT Equation 2 26 K K a K t Equation 2 27 An important point to be considered in tuning of PI PID controllers based on IMC design is choosing an appropriate A It must be chosen in a way that the required following conditions are satisfied K lt 0 Equation 2 28 Equation 2 29 kK lt 0 21 A PI controller has been also obtained by reducing the order of IMC controller to 1 1 Kp s TF Equation 2 30 Ti And the suggested tuni
110. t point overshoot method Shamsuzzoha and Skogestad 2010 was used to tune the PI controller in two initial points of Z 30 and Z 40 in the simulations The one tuned at the initial point of Z 30 could surprisingly stabilize the system up to the valve opening of Z 38 However the other one tuned at the initial point of Z 40 wasn t able even to achieve the stability for the point that has been tuned for 106 8 References Bai Y 2001 Pipelines and risers Elsevier Science Bratland D O 2010 The Flow Assurance Site from http www drbratland com PipeFlow2 chapter1 html Fabre J L Peresson et al 1990 Severe slugging in pipeline riser systems SPE Production Engineering 5 3 299 305 o Godhavn J M M P Fard et al 2005 New slug control strategies tuning rules and experimental results Journal of process control 15 5 547 557 Havre K K O Stornes et al 2000 Taming slug flow in pipelines ABB review 4 55 63 Jahanshahi E and S Skogestad 2011 Simplified dynamical models for control of severe slugging in multiphase risers World Congress Jahanshahi E and S Skogestad 2013 Closed loop model identification and PID PI tuning for robust anti slug control Mumbai India 10th IFAC International Symposium on Dynamics and Control of Process Systems Jahanshahi E S Skogestad et al 2012 Controllability analysis of severe slugging in well pipeline riser systems IFAC Worksh
111. t to the stability limits they provided See table 5 16 and also figures 5 39 and 5 40 The Shams s set point overshoot method Shamsuzzoha and Skogestad 2010 failed to stabilize the system in both sets of experiments This was not far from the expectation since Shams s method has been developed for the stable systems while the slugging system is highly unstable For implementing the IMC Internal Model Control based tuning method Jahanshahi and Skogestad 2013 the model of the system was identified from a closed 104 loop step test The identified model was used for an IMC design and then PID and PI tunings were obtained from the resulted IMC controller The IMC based PID tuning rules could increase the stability limit from 26 to 40 of choke valve opening in the first set of experiments using the slow valve and from 16 to 30 of choke valve Opening in the second set of experiments using the fast valve The simple PI tuning rules with gain scheduling for the whole operating range of the system was used as the last tuning method and proved to be the best tuning approach for the slugging system To implement this method a MATLAB model was modified and fitted to the steady state model of experiments Then based on this MATLAB model and also a single closed loop step test the simple PI tuning rules were found This tuning method could increase the stability limit from 16 to 35 of choke valve opening in the second set of experi
112. the MATLAB model did fit to the simulated results from OLGA and also the experimental results However the manipulations done to fit the model to the simulations and experiments may lead to the inaccuracy of the results Also in the MATLAB model the valve is assumed to have a linear characteristic however this may not be the case for the valve in the experiment See section 5 2 Shams s tuning method has been designed for the stable systems while the slugging system is unstable Therefore it may not be far from the expectation that it couldn t work for the slugging system This method didn t work in any of the experimental series Though it worked in simulations but didn t give very good results This even small stability found with this method in OLGA simulations may deviate from the reality This deviation may be due to inappropriate assumptions or inaccurate initial and boundary conditions in OLGA model The overall result can be that this method can t be a Suitable one to tune the controllers in the slugging system Instead the recently developed IMC based and simple online methods perform much better 6 2 Control structures The control structure used in the series of experiments and simulations was a SISO control with buffer pressure as the control variable This measurement is the riser inlet pressure in real subsea systems and may not be very easy to measure However it has been proved previously that it s the best control variable
113. the valve that has been defined as the valve equation AP Imis K yf Z Equation 5 10 Here q is the volumetric flow rate K is the valve constant AP is the pressure drop over the valve and p mix is the mixed density of outflow Both valves have been considered linear with f z z Butin reality valve 2 fast valve could be nonlinear to some extent meaning that it produces the same flow rate as the slow valve even with lower levels of valve openings Figure 5 17 describes this concept more clearly by illustrating the characteristic curves for the two valves If we specify a level of flow rate and try to find the corresponding levels of valve opening for each of the valves it will be seen that the slow valve may give higher level of valve opening for the same flow rate The main desired result that can be affected by the valve dynamics is the minimum inlet pressure the system could obtain For the open loop system this is defined as the minimum inlet pressure at fully open position of the valve and for the closed loop system it will be defined as the minimum set point the controller can stabilize the system Figure 5 18 compares the open loop behavior of the system for the slow valve with that of fast valve As clear in the figure the slow valve gives lower inlet pressures at most operating points of valve opening including the fully open position of the valve Z 1 70 QUICK OPENING a XI N ab Wi ay
114. tions in open loop experiments has been 7 90 Sec When running the model at a special operating point the parameters K z and 7 z were found for the specified Operating point as functions of valve opening Z by the equations 2 42 and 2 43 By running the model with a loop for a wide range of Z values it was possible to find multiple tuning parameters each for a controller at a specified operating point Then gain scheduling with multiple controllers was used to stabilize the system To do this in the experiments five PI controllers were used with the related found tuning parameters Table 5 6 shows the resulted controller for each operating point of valve opening 65 In order to perform the gain scheduling between the controllers the corresponding value of inlet pressure to that specific operating point of valve opening was determined from the model and then this pressure value as the set point together with the related tuning values were entered in LabVIEW The closed loop was run and it was waited until the system was in steady state Then the next pressure value set point corresponding to the next valve opening was tried and the new tuning values were entered in LabVIEW very fast I was working as the control woman This action was repeated until the instability was appeared Figure 5 14 shows the results of control with gain scheduling tuned by simple online tuning method The controllers could stabilize the flow up to a valve o
115. tle It was necessary to go and come many times to make a flow rate close to the desired value For water flow rate the centrifugal water pump was the reason of oscillations However it was tried to deal with this issue through running the pump in a very high level of power 80 of the maximum and opening the water control valve in small values instead 6 3 2 Water flow back into the buffer tank When the buffer pressure became lower than the pressure inside pipeline water did flow back into the buffer tank This reduced the volume of buffer tank and caused the buffer pressure deviates from the real values This discrepancy could distract the controller performance and therefore it was very important to remember to drain the buffer tank between the experiments Installing an automatic sensor to quickly sense the water in the buffer tank could be very helpful to overcome this issue 6 3 3 Leakage in steel connection The laboratory facility was in a way that a single pipeline needed to be connected to any of the risers Steel S riser Hose L riser or Horizontal pipeline On the other hand several people were working in the lab and on the different setups during the semester This caused the pipeline risers connections needed to be changed several times a week This was not a very easy job and sometimes the connection couldn t be fitted quite well even with trying many different sealing rubber O rings screws and nuts Therefore there was some flow
116. tuning parameters tuned at the initial choke valve position of 30 PIDF 0 03204 16 6113 23 9802 PI 0 11916 61 7797 E Implementing low pass filter was not possible in OLGA Therefore despite the fact that the filter time constant was an important part of tuning parameters it was neglected in simulations and a PID controller was using instead Figures 5 29 and 5 30 describe the results of control using the IMC based PID and PI controllers respectively The controllers were tuned for valve opening of Z 30 But they can stabilize the system up to very larger valve openings The PID controller could stabilize the flow with a maximum of 50 27 valve opening and the PI controller could stabilize the system up to valve opening of Z 47 The PID controller has shown a better performance compared to the PI A lower set point as well as a higher level of valve opening has been achieved with PID controller In addition the output from the PID controller is less oscillatory 84 Inlet pressure controlled variable 150 Setpoint Measurement 145 3 A 140 0 500 1000 1500 2000 2500 Valve position manipulated variable 1 N 0 5 X 2440 Y 0 5027 0 500 1000 1500 2000 2500 time sec Figure 5 29 Simulation result of control using the IMC based PID controller tuned at the initial choke valve position of 30 Inlet pressure controlled va
117. ue by Shams has been achieved Inlet pressure controlled variable 150 Setpoint Measurement A 145 A 140 0 500 1000 1500 2000 2500 3000 3500 Valve position manipulated variable 0 5 0 4 Hs N X 3452 0 3 Y 0 3884 0 2 0 500 1000 1500 2000 2500 3000 3500 time sec Figure 5 25 Simulation result of control by Shams s closed loop method for the initial choke valve position of 30 The values of Z 0 389 and P 142 kpa have been the maximum achieved valve opening and the minimum achieved set point respectively 81 Inlet pressure controlled variable 146 Setpoint Measurement 3 144 A 142 0 100 200 300 400 500 600 Valve position manipulated variable 0 6 N 0 4 0 2 0 0 100 200 300 400 500 600 time sec Figure 5 26 Set point change using initial choke valve opening of 40 and the initial gain of K 0 15 An overshoot of D 0 32 near to the recommended value by Shams has been achieved Inlet pressure controlled variable Setpoint 146 Measuremet 0 500 1000 1500 2000 Valve position manipulated variable 9 0 4 t AAnnnAA TTT AMUUUUUUUUUUVUVUVVVVVVVVVVVVV N Ev X 1952 0 2 Y 0 39
118. ve Initial set Final set point Bias P Overshoot a oa vane a 3 4058 0 5 R 1 7426 2 1049 0 5741 0 6318 naa 1 2219 0 5402 0 1 0 5609 0 4894 0 3108 0 3308 0 3085 Oo 14 142 08839 oa LS o 142 04471 0 40 0 5028 w _ 0 3535 0 15 145 0 3210 110 C Some examples of MATLAB scripts C 1 Tuning by Shams s method cle clear all load Data subplot Zz 1 1 Plot tyr TE tyr k binewiccn 1 5 xlim 0 1000 title Inlet pressure controlled variable ylabel P Kpa legend Setpoint Data 2 Grid on hold on subplot 2 152 plot t u k Linewidth 1 5 xlim 0 1000 xlabel time sec ylabel Z title Valve position manipulated variable grid on o o 1 init find t t_init y_plant y i_init end t_plant t i_init end u_plant u i_init end y init y 1 1nit 200 u_init u i_init 200 yp max y_plant dy p abs yp y_init i_yp find y_plant yp t_pl mean t_plant i_yp yu min y plant i yp 10 i_yp dy u abs yu y init i_yu find y_plant yu t_u mean t_plant i_yu yini y plant end dy inr abs y int y Init tpar pLa Con 111 Overshoot abs dy_p dy_inf dy_inf D Overshoot Offset abs dy_s dy_inf dy_inf B Offset A 1 152 D 2 1 607 D 1 r 2 A B K 1 KCo0 BJ Tetha tp 0 309 O 209 ex0 0 6125 taul r Tetha
119. ves one for steady state conditions and the two others showing the maximum and minimum of oscillations at each value of valve opening over the work range of choke valve 13 2 8 PID and PI controllers PI proportional integral and PID Proportional integral derivative control are of the earlier control strategies The PID controller includes the proportional action P integral action I and derivative action D The controller uses the error signal e t to generate the proportional integral and derivative actions A mathematical description of the PID controller is de t u t K le t e r d r 7 E equation 2 4 Where u t is the input signal to the plant model The error signal e t is defined as e t r t y t and r t is the reference input signal Fabre Peresson et al 1990 After a Laplace Transform the controller can be shown as l c K LFF Equation 2 2 g Where K z and 7 are the respective tuning parameters for the P I and D actions PI and PID controllers are the most widely used controllers in the industry However they need to be tuned appropriately for robustness against plant changes and large inflow disturbances Jahanshahi and Skogestad 2013 Thus finding the most appropriate amounts of K 7 and T could be extremely required A typical structure of a PID control system is shown in Figure 2 9 Desied 5 tate Feedback Signal Measwed 5 tate Figure 2 9 A typical PID control stru
120. vity causes the liquid to accumulate in the low point and a prerequisite for severe slugging to occur is that the gas and liquid velocity is low enough to allow for this accumulation Step 2 Slug production The liquid blocks the gas flow and a continuous liquid slug is formed in the riser As long as the hydrostatic head of the liquid in the riser increases faster than the pressure drop over the riser the slug will continue to grow Step 3 Blowout When the pressure drop over the riser overcomes the hydrostatic head of the liquid in the slug the slug will be pushed out of the system and the gas will start penetrating the liquid in the riser Since this is accompanied with a pressure drop the gas will expand and further increase the velocities in the riser Step 4 Liquid fall back After the majority of the liquid and the gas has left the riser the velocity of the gas is no longer high enough to pull the liquid upwards The liquid will start flowing back down the riser and the accumulation of liquid starts again Figure 2 6 Graphical illustration of a slug cycle Yan and Che 2011 Slug formation is shown in part 1 Slug production is shown in part 2 Blowout in part 3 and liquid fall back in part 4 Severe slugging causes periods of no liquid or gas production into the separator followed by very high liquid and gas rates when the liquid slug is being produced Length of liquid slugs can be several times the length of the riser This phenomen
121. xperimental results will be compared 2 Background 2 1 Multiphase transport When it comes to offshore production of oil and gas long transport of multiphase flow has recently become of great attention Many pipelines and risers are carrying the combination of natural gas condensate oil and water from the North Sea to shore Previously large production platforms equipped with process facilities were built on the sea floor with the aim of separating gas oil and water Today this can be too expensive and multiphase transportation can save billions of dollars for the oil companies instead Design and operation of multiphase transportation systems raise many new challenges These challenges could be either related to the flow fluid or the pipe integrity Pressure drop boosting Slugging liquid emulsion temperature change scaling hydrate and wax formation can be examples of them Overcoming these challenges and having a safe and uninterrupted multiphase flow refers to the term flow assurance This term was first used by Petrobras in the early 1990s and it originally referred to only thermal hydraulics and production chemistry issues encountered during oil and gas production Fabre Peresson et al 1990 One important issue in flow assurance is stabilizing the multiphase flow inside the pipeline riser systems From a control engineering point of view this can be referred as control of the disturbances in the multiphase flow as the fe
122. zero in the simulations Ap is the pressure drop over the valve at the critical valve opening of the system bifurcation point Then based on the above equations the static gain of the slugging system is derived as a function of valve opening by differentiating P with respect to Z Finally the simple model for the static gain of the system is OP k z a Equation 2 40 Z 2 9 3 2 Simple PI tuning rules based on identified MATLAB model Jahanshahi and Skogestad Jahanshahi and Skogestad 2013 then perform a closed loop step test with a P only controller at the initial valve position of Z The parameter 2 is then calculated by using data Ay Ay Ay t and At observed from the closed loop response see figure 2 10 and the static model given in equation 2 40 Ay A Ay A In Vo Yu K ok zo Yz Yo Ay AY Ay B ot a _ 7 Equation 2 41 2At 4t P 24 Where K is the proportional gain used for the step test The suggested PI tuning parameters as functions of valve opening are given as the following K z PT c mea e ee Equation 2 42 i KZN Zyl Z d A A A RE Equation 2 43 T is the period of slugging oscillations when the system is in open loop position OSC and zis the critical valve opening of the open loop system where slugging starts 25 3 Experimental work Control of Severe Slugging and creating a stable flow regime by applying control using new online tuning methods has been verifi

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