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DoubletCalc v143 manual english

1. 5 14E 04 6 07E 04 5 89E 04 5 32 14 3 85E 04 5 8E 04 5 71E 04 5 64E 04 3 28E 04 5 52E 04 5 45E 04 5 39E 04 3 33E 04 5 2 E 04 5 22E 04 5 16E 04 3 10E 04 5 05E 04 5 00E 04 46 45 Part 2 initial hydrostatic aquifer properties injector TNO report TNO 2014 R11396 HYDROSTATIC AQUIFER PROPERTIES INJECTOR Z m 0 49 905 7 99 8113 149 717 199 623 249 528 299 434 349 34 399 245 449 151 499 057 548 962 598 808 648 774 6098 079 748 585 798 491 845 396 898 302 945 208 998 113 1048 02 1093 63 1138 1182 38 1226 76 1271 14 1315 52 1359 9 1404 28 1448 06 1493 04 1537 42 1581 8 1626 18 1670 56 1714 94 1759 32 1803 7 1848 06 1892 38 1936 7 1981 02 2025 35 2069 67 2113 99 2158 31 2202 03 2246 96 2291 28 2335 60 2379 92 2424 24 2408 50 P bar 1 5 892693 10 79318 15 7014 20 6173 25 54082 30 47189 35 41045 40 35646 45 30983 50 27052 55 23846 60 21358 65 19584 70 18515 75 18146 80 18471 85 19483 90 21176 95 23543 100 7658 105 3028 109 9115 114 4016 118 8966 123 3968 127 9019 132 412 136 927 141 4468 145 9715 150 501 155 0351 159 574 164 1174 168 6655 173 2181 177 7752 182 3368 186 9008 191 4652 196 0339 200 6069 205 1841 209 7654 214 3509 218 9405 223 5341 228 1318 232 7334 237 3389 241 9484 246 5616 251 1787 T degC S ppm 10 11 54708 13 09415 14 64123 16 1883 17
2. Figure 17 shows the deviation against the productivity index ratio which is the ratio between the productivity index for a deviated well and that for a vertical well It is clear that for deviation angles less than about 40 the effect on the productivity index is negligible about 1096 for lani 1 and ha 1000 0 0 1 0 2 0 4 30 E 3 g 40 gt 0 3 5 0 4 lani 1 hd 200 6 0 ani 1 hd 1000 lani 2 hd 200 7 0 lani 2 hd 1000 8 0 4 0 10 20 30 40 50 60 70 80 deviation angle Figure 16 Skin due to penetration angle as a function of angle TNO report TNO 2014 R11396 22 45 4 0 lani 1 hd 200 lani 1 hd 1000 lani 2 hd 1000 lani 2 hd 200 35 3 0 2 9 2 0 productivity index ratio Jdev Jvert 1 5 1 0 T 20 30 40 50 in i deviation angle Figure 17 Ratio of the productivity indices for a deviated and a vertical well as a function of devi ation angle TNO report TNO 2014 R11396 23 45 4 Theoretical background of the DoubletCalc model The premises for the calculation of the geothermal energy given the aquifer wells and heat exchanger characteristics are Mass balance the mass flow kg s is constant in the doublet system from the intake in the production well until the injection in the aquifer Impulse balance pressure balance this is valid for the entire doublet syste
3. probabilistic plots generates a new window graphically showing the probability distribution of the pump volume flow In the upper left corner of the window there is an option to show similar graphs for the geothermal power and the coefficient of performance COP Figure 7 Choosing the button Export CSV file will export the graphs numerical data to a text file Figure 8 TNO report TNO 2014 R11396 12 45 Doublet Calculator 1 4 3 Probabilistic Pk Beri probability probability v 900 1100 1300 1500 1700 1900 2100 pump volume flow m h geothermal power MW COP KWAN export CSV file probability 5 v 260 270 280 29 0 300 310 320 n0 340 350 COP kW kW Figure 7 Probabilistic plots for pump volume geothermal power and COP Save in Ui doubletcalc143 F 5 k runtime Recent Items Flename meeentomacd o o s Fiesoftype oy Yael Figure 8 DoubletCalc 1 4 3 Export Fingerprint to file screen 2 3 2 Fingerprinting graph Figure 9 shows the graph that is generated using the Fingerprinting button DoubletCalc will calculate the geothermal power green curve COP purple flow rate red and the required pump energy blue for varying pump pressure differences that are around the specified pump pressure difference The calculation of these graphs uses the median values from the input screen TNO report TNO 2014 R11396 13 45 2 3 3 Doublet Calculator 1 4 3 F
4. 04 142 3268 4 732362 0 08127 2495 283 2335 6 27 36306 6 625 1 2 263 0292 35 79986 1089 016 9 62E 04 142 3062 4 733048 0 08125 2545 189 2379 92 27 36306 6 625 1 2 267 6817 35 86169 1089 172 9 61E 04 142 2858 4 73373 0 08123 2595 094 2424 24 27 36306 6 625 1 2 272 3349 35 92525 1089 328 9 60E 04 142 2654 4 734408 0 08121 2645 2468 56 27 36306 6 625 1 2 276 9888 35 99051 1089 482 9 59E 04 142 2452 4 735082 0 08119 2645 2468 56 16 41131 9 439272 1 2 260 6382 0 990511 1084 85 9 73E 04 142 8537 262 5908 1 95255 co oU PF NF 5 55 ee gt S o000000000o0o0o0o0o0o0o0o0oc 27 8 9 91 5 5 e IIS S S ID J nn Q MN HB O gt O O O O O O O O O T C CO OYL L O O OOO O 5 OO RD 5 OO O O OOO TA OO O OO 5 O 5 O O 5 O O O O P SO O O Ol O 5 co ss 5 95 38 95 5p P p 5 p P PB op B oU C QU 9 QQ QJ QQ CO QQ QQ N N N N N N N N N N N N N N N N N N N N F TNO report TNO 2014 R11396 50 45 Part 5 pressures and temperatures at specified doublet nodes DOUBLET NODES Node P bar T degc 1 Aquifer Prod 255 0826 89 2825 2 Aquifer Prod Bottom 241 303 89 2825 Prod Top Entry HE 16 35055 86 50769 Exit HE Inj Top 16 35055 35 Inj Bottom Aquifer 270 9888 35 99051 Aquifer Inj 251 1787 89 2825 Part 6 base case results calculated for the specified median values BASE CASE RESULTS aquifer kH
5. 23345 65 60059 56 956891 69 73124 71 11241 72 49358 73 87474 75 25591 70 03708 78 01824 79 39941 80 78058 82 16174 83 54231 84 92408 86 30525 87 68641 S ppm 0 2375 4751 7127 3502 11878 14254 16629 19005 21381 23756 26132 28508 33259 35635 38011 40386 42762 45138 47513 49889 52117 54229 36342 58455 60567 62680 64793 66905 69018 71130 73243 75356 77468 79581 61694 83806 85919 88033 90168 92302 94436 96571 98705 100839 102974 105108 107242 109376 111511 113645 115779 117914 120048 Density k Viscosity Pa s 398 3188 1000 507 1002 084 1003 649 1005 202 1006 742 1008 271 1009 787 1011 291 1012 783 1014 262 1015 729 1017 183 1015 624 1020 053 1021 469 1022 872 1024 262 1025 64 1027 004 1028 355 1029 694 1030 937 1032 105 1033 263 1034 411 1035 543 1036 676 1037 733 1038 899 1039 995 1041 081 1042 157 1043 222 1044 277 1045 322 1046 357 1047 381 1048 395 1049 4 1050 404 1051 398 1052 382 1053 356 1054 319 1055 273 1056 216 1057 15 1058 073 1058 987 1059 891 1060 785 1061 67 1062 545 1063 411 0 001251 0 001211 0 001173 0 001138 0 001105 0 001074 0 001045 0 001018 9 93E 04 9 69E 04 9 46E 04 9 25E 04 3 04E 04 8 85E 04 8 66E 04 8 49E 04 8 32E 04 8 16E 04 8 00E 04 7 85E 04 7 1E 04 7 58E 04 7 A5E 04 7 34E 04 7 23E 04 7 12E 04 7 02E 04 6 92E 04 5 83E 04 b 3E 04 6 64E 04 6 55E 04 6 47E 04 6 38E 04 6 30E 04 6 22E 04
6. 4 the top and base of the casing liner section measured in meters vertically true vertical depth or TVD 5 the inner diameter of the casing liner per section inch through which the water is produced 6 the roughness of the casing milli inch The roughness and inner diameter de termine the resistance the water encounters when flowing Figure 5 which is the graphical representation of the well design in Figure 2 shows which parameters should be entered The part of the well inside the reservoir solid blue in the figure should not be specified under C Well Properties if the well is completed using a slotted screen and or gravel pack in an open hole In all cases the drill bit size should be entered as outer diameter producer injector If the top part of the casing is unperforated this will result in extra resistance This part of the casing must be entered in the scheme The detail in the upper right of Figure 5 shows how water will flow towards the perforated section in an inclined well The area though which water can enter the well is increased by the inclined path of the well through the aquifer More information can be found in paragraph 3 2 Penetrating the aquifer and chapter 8 The effect of penetrating the reservoir obliquely The depth of the top of the aquifer is varied stochastically during calculation of the geothermal power Therefore the specified architecture of the casing with a fixed end dept
7. 73538 19 28245 20 82953 22 3766 23 923068 25 47075 27 01783 28 56491 30 11198 31 65906 33 20613 34 75321 36 30028 37 84730 39 39443 40 94151 42 48858 43 90239 45 27815 46 65392 48 02969 49 40545 50 78122 52 15699 53 53276 54 90852 27 00006 59 03582 60 41159 61 78736 63 16312 64 53889 65 31466 67 28984 68 66382 70 03779 71 41177 72 78574 74 15972 75 5337 76 90767 78 28165 79 65562 61 0296 82 40358 83 77755 85 15153 86 5255 0 2390 4781 7172 9562 11953 14344 16734 19125 21516 23906 26297 28688 31078 33469 35860 38251 40541 43032 45423 47813 30204 52389 24515 26641 58767 60893 63013 65145 67271 69396 71522 73648 75774 77900 80026 82152 84278 86404 885298 30652 92776 94899 97022 99145 101268 103392 105515 107638 1095761 111884 114008 116131 115254 Density k Viscasity Pa s 998 9168 1000 517 1002 104 1003 678 1005 241 1006 791 1008 329 1009 654 1011 367 1012 867 1014 355 1015 83 1017 293 1015 742 1020 179 1021 602 1023 013 1024 411 1025 795 1027 167 1028 525 1029 87 1031 1032 262 1033 426 1034 58 1035 723 1026 856 1037 978 1039 089 1040 191 1041 282 1042 362 1043 432 1044 492 1045 541 1046 58 1047 608 1045 627 1049 635 1050 631 1051 618 1052 594 1053 56 1054 517 1055 463 1056 4 1037 326 1058 243 1059 151 1060 048 1060 936 1061 815 1062 684 0 001251 0 001211 0 001172 0 001137 0 001104 0 001073 0 001044 0 00
8. The doublet system is a closed system as was already remarked in chapter 3 The DoubletCalc model Consequently following the mass balance the mass flow Qm kg s is equal in all elements of the doublet system S SECON SION eq 1 Volume flow The volume flow Q m3 s is required for the calculation of the pressure loss caused by viscous forces This follows from The water density p kg m is a function of pressure temperature and salinity Pressure and temperature are difference at each location in the doublet system Impulse balance The impulse balance pressure balance is given by N 1 gt Ap y 0 k 1 in which N is the number of nodes in the doublet system Figure 18 Table 10 and AP ik Prai T Pr eq 4 and specifically Api N Pstat p i i eq 5 Pstatp and Psa are the initial hydrostatic pressures at the production and injection wells respectively see paragraph 5 7 Initial hydrostatic aquifer pressure near the production and injection well oubstitution of 5 in 3 gives N 1 P stat p T S A P stati 0 k Each of the elements of the above listed equations is described in the following paragraphs Pressure losses in the surface pipes and the heat exchanger are ignored like mentioned in Table 10 TNO report TNO 2014 R11396 27 45 5 4 Pressure development in the aquifer from or towards a well The pressure development in the produ
9. around the well Using empirically derived data k g 3 W m K and a4 1 2x10 m s for the calculation The calculation of heat loss is executed for time t 1 year since the start of the production Following the energy balance the heat loss to the environment is equal to the heat release of the formation water dlg Dw put eq 19 with Twe temperature of the water in the well I length distance along the well Co water heat capacity paragraph 5 3 Rewriting equation 17 yields als Q well dl Won The temperature decrease in the production well is 1 3 C for a typical doublet Given a temperature difference in the heat exchanger of about 25 40 C the loss of geothermal power is about 3 10 In the injection well during injection the water will first cool until the temperature of the cooled production water is equal to the ambient temperature and then as the ambient temperature keeps on rising reheat again The total temperature effect is less than 1 C The only effect is on the viscosity of the injected water Temperature decrease in the heat exchanger The temperature decrease in the heat exchanger is AT he he in eon TNO report TNO 2014 R11396 33 45 Thein lS the temperature at the inlet of the heat exchanger It is equal to the temperature at the well head of which the calculation is described in paragraph6 2 Theout 18 the temperature at the outlet
10. for the flow direction in the reservoir As a result of the inclined perforation the length of the intersection of wellbore and reservoir generally exceeds the thickness of the aquifer Consequently the flow will be larger for an inclined than for a perpendicular well This effect can be accounted for by introduction of an extra skin For an inclined well the sign of the skin is negative Choi et al 2008 and Rogers amp Economides 1996 present an overview of the TNO report TNO 2014 R11396 21 45 relation between skin and deviation angle anisotropy thickness of the aquifer and well diameter DoubletCalc accounts for the positive effect on the influx of water by using the skin The software calculates the skin using the equations presented in chapter 8 Figure 16 shows the skin as a function of the deviation angle for varying values of the aquifer thickness H or hg and anisotropy lani The negative skin as a result of the inclined well increases with increasing deviation angle and decreasing aquifer thickness see paragraph 0 As an example the skin due to the penetration angle will be calculated for two combinations of the aquifer thickness and anisotropy and a common well diameter H 20 or 100 meter lani 1or2 0 10 meter corresponding to a well diameter of 8 200 or 1000 H ry Figure 16 shows the skin as a function of the deviation angle for a well distance of 1600 meter and a 0 10 m well diameter Similarly
11. hydrostatic aquifer properties at producer and injector calculated per section calculation length subdivision TNO report TNO 2014 R11396 14 45 OoOo o o dPGrav pressure difference as a result of gravity operating on the density of the water pressure difference as a result of varying viscosity dPpump pressure difference as a result of pump input screen Table 2 Base case details file parts 3 and 4 parameters calculated per section calculation length subdivision for the production and injection well DOUBLET NODES res To Aquifer Prod 255 08 89 28 static aquifer pressure and tem perature near the producer Aquifer Prod Bottom 241 30 89 28 bottomhole flowing pressure and temperature at the producer Prod Top Entry HE 16 35 86 51 wellhead pressure and tempera ture at the producer iN L Z S Inj Bottom Aquifer 2 6 99 35 99 bottomhole flowing pressure and temperature at the injector Aquifer Inj 251 18 89 28 static aquifer pressure and tem perature near the injector Table 3 Base case details file part 5 pressure and temperature at specific locations in the doublet schedule The numbers refer to the doublet nodes shown in Figure 18 Node 8 is only relevant if a separate injector pump is installed The pressure and temperature values in this table result from the example scenario 7 amp 9 Exit HE Inj Top 16 35 35 00 wellhead pressure and tempera ture at the injec
12. large number of simulation runs in which per run parameter values are drawn from a triangular distribution defined by the user specified min median max values The values in this table result from the example scenario aquifer pressure at producer bar aquifer pressure at injector bar pressure difference at producer bar pressure difference at injector bar 2 4 Error messages DoubletCalc can generate the following error messages Erratic input erratic input was specified in the input This can for example be TNO report TNO 2014 R11396 16 45 amedian value smaller than the min value a depth value that is not corresponding to other depth values like a pump depth deeper than the total depth of the well anon numerical value where a numerical value is expected for some fields a value of zero is not allowed like for instance anisotropy geo thermal gradient pump pressure and tubing inner diameter afield that was left empty Erratic input Please check i Erratic input Please check Max lt Median A Segment length TVD gt segment length AH C Figure 10 DoubletCalc error message input parameters Data is not converging this error message originates from proper input values that in combination with other input resulting from stochastically obtained values of for instance depth and thickness results in an impossible configuration between well and aquifer Examples are extreme values for
13. net Dm mass flow kg s pump volume flow m h required pump power kW geothermal power MW COP kW kW aquifer pressure at producer bar aquifer pressure at injector bar pressure difference at producer bar pressure difference at injector bar aquifer temperature at producer temperature at heat exchanger C pressure at heat exchanger bar Part 7 stochastic results calculated for the specified median values aquifer kH net Dm 21 26 mass flow kg s 43 51 pump volume flow m h 148 5 required pump power kW 21 270 4 geothermal power MW 8 33 COP kW kW 28 30 5 aquifer pressure at producer bar 255 12 aquifer pressure at injector bar 251 24 pressure difference at producer bar 13 68 pressure difference at injector bar 25 7 aquifer temperature at producer 5 89 28 temperature at heat exchanger C 86 58 end of file TNO report TNO 2014 R11396 51 45 B Sub layers in an aquifer DoubletCalc assumes that the aquifer consists of a single continuous layer The input data for DoubletCalc can be calculated using the approximation specified below in case the aquifer consists of various sub layers Figure 21 shows an example of a complex reservoir aquifer Figure 21 Example of an aquifer consisting of various sub layers with different characteristics The stratification of the aquifer influences the effective average permeability net height and net to gross ratio T
14. process and or special treatment of the well This effect is called skin Skin reflects the difference in pressure drop from the aquifer to the well for the original homogeneous aquifer and current situation after drilling completion etc Skin is usually caused by wellbore damage like drilling mud that hasn t been flushed Figure 19 Constipation of pores by fines very fine grained components of the aquifer rock like clay can also contribute progressively to the skin in the course of water production and injection Treatment of the well stimulation has as objective to decrease the pressure drop around the well TNO report TNO 2014 R11396 28 45 5 5 p zone infiltrated by drillmg mud gt X Ber are aa enar eir E er a a Figure 19 Horizontal sketch of the wellbore showing casing annulus and reservoir A and drill ing mud infiltration into the aquifer B The difference in pressure drop is represented by the second term of equation 8 u O 5 pP skin Q 2 i H leg 8 Skin is a dimensionless figure A positive skin value indicates wellbore damage and extra pressure loss A negative skin value is representative for a well that has been stimulated cleaned acidized fractured and a reduced pressure drop Pressure development in a casing Casings and other pipes are present at numerous locations in the doublet system Because the pipes belonging
15. pumped from producer to injector In order to prevent negative pressures in the well it is advised to increase the pump pressure iteratively until the DoubletCalc output shows a well head pressure of at least 1 bar TNO report TNO 2014 R11396 43 45 For a depleted reservoir in practice the pump pressure will have to be increased considerably to prevent negative pressures and to enable the extraction of water from the reservoir Similarly the injection pressures can be very low for a depleted reservoir The flow rates will be high Another possibility to prevent negative pressures is to increase the friction in the injector by reducing the casing diameter pinching TNO report TNO 2014 R11396 44 45 13 References Batzle M amp Wang Z 1992 Seismic properties of pore fluids Geophysics Vol 57 1396 1408 Beggs H amp Brill J 1973 A study of two phase flow in inclined pipes Journal of Petroleum Technology May 1973 607 617 Bonte D Van Wees J D and Verweij J M 2012 Subsurface temperature of the onshore Netherlands new temperature dataset and modelling Netherlands Journal of Geosciences v91 4 p491 515 Choi S K Ouyang L B and Huang W S 2008 A comprehensive comparative study on analytical PI IPR correlations SPE 116580 Dake L P 1978 Fundamentals of reservoir engineering Elsevier Develooments in Petroleum Science 8 Farshad F amp Rieke H 2006 Surface roughness
16. ro gt D 3 e N lt Go DDR G D D x thermal diffusivity m s difference tubing casing roughness m geothermal gradient K m water viscosity Pa s 1cP 0 001 Pa s pump efficiency density kg m densify fresh water kg m 1 781072 with Euler s constant y 0 577216 well deviation with respect to vertical lt Goo o sS gt s p o Subscripts ani anisotropy aq aquifer C casing db pressure balance TNO report TNO 2014 R11396 gt he in out sur siat top rock geothermal hydrostatic heat exchanger injection well inner diameter or radius node number outer diameter or radius production well surface static pressure temperature top aquifer well 54 45
17. the Input Screen and consequently used during the calculation The column Geotechnics Output on the right hand side shows the results of the calculation The first block Monte Carlo cases shows the results of the stochastic simulation The second block Base case shows the results of a calculation in which only the median values were used in case a range was specified TNO report TNO 2014 R11396 2 3 1 Doublet Calculator 1 4 3 Result Table 11 45 igixi probabilistic plots fingerprinting file d doubletcalc143 example xml Geotechnics Input export base case details Property min median max aquifer permeability mD 1500 2500 5000 aquifer net to gross 075 os 085 aquifer gross thickness m 95 0 1050 150 aquifer top at producer m TVD 22550 25050 27560 aquifer top at injector m TVD 22210 24680 27150 aquifer water salinity ppm 100000 0 120000 0 140000 0 Property wie number of simulation runs 4000 aquifer kh kv ratio surface temperature C 10 0 geothermal gradient C m 0031 midaquifertemperatueproducertC 00 inital aquifer pressure at producer bar initial aquifer pressure at injector bar o exttemperatueheatexchanger C 350 distance wells at aquifer level m 44600 pump system efficiency 0 61 production pump depth m 00 pump pressure difference bar w outer diam
18. the next page Look in Ui doubletcalc 143 fe Figure 3 DoubletCalc Open Scenario screen Recent Items z Desktop Figure 4 DoubletCalc Save Scenario screen TNO report TNO 2014 R11396 9 45 Casing schedule In DoubletCalc 1 4 3 the casing scheme has to be specified including the relevant characteristics of the pipes inner diameter and roughness to the top of the aquifer The Along Hole AH and True Vertical Depth TVD depth must be specified according to the same surface reference level as the aquifer depth values in the Netherlands NAP or Amsterdam Ordnance Level Using these parameters the resistance encountered by the water while flowing through the casing can be calculated Figure 2 under C Well Properties shows the essential well input parameters for DoubletCalc 1 4 3 1 the outer diameter of the producer and injector in the reservoir section This diameter specified as inches determines the areal extent of the surface through which water can enter the wellbore This is the open hole diameter 2 the inclination of the well trajectory in the aquifer in degrees relative to the verti cal In combination with the reservoir gross thickness and net to gross ratio this determines the length of the production interval DoubletCalc assumes that the entire reservoir section is connected to the well 3 the top and base of the casing liner section measured in meters along hole mAH
19. values the productivity improvement is about 10 per unit skin Jvenical Jhorizontal 1 1 for a skin of 1 also see Figure 16 and Figure 17 TNO report TNO 2014 R11396 38 45 9 Solution method The pressure balance fs equation 31 given geological and installation parameters is a function of pump pressure Appump and mass flow Qm Nl Jo Sud AB aeui foU cas eq 32 k l At a given pump pressure Q is solved from the pressure balance using the commonly employed secant numerical method The pressure balance is build segment after segment starting at Pstatp the static aquifer pressure at the production well Figure 18 shows the order of segments and nodes Pressure and temperature are known in the aquifer at the production well node 1 From here pressure and temperature difference are calculated for each subsequent doublet element Figure 18 Table 10 and Table 11 at given pump pressure APpump and mass flow Qm The pressure and temperature differences over a doublet element can be calculated explicitly for each element with the exception of the wells calculation user specified section length provided the pressure and temperature at the inlet point of the doublet element are known The wells are split into a number of segments to increase the accuracy of the calculation of pressure and temperature difference over the well this is the segment length under C Well properties in Figure 2 It is advisable
20. 1 Introduction DoubletCalc v1 4 3 is a software tool that was developed by TNO It enables to calculate a pre drill indicative geothermal power of a future geothermal doublet by specifying the key reservoir parameters the casing scheme and the pump details DoubletCalc v1 4 is the successor to DoubletCalc v1 3 The major difference with respect to v1 3 is the possibility to specify the casing scheme of the production and injection wells and a minimum median maximum range for the expected salinity DoubletCalc v1 4 3 has largely the same functionality as DoubletCalc v1 4 Both the output to screen and to file has been extended This document first explains how the software is used Next it describes the way in which a doublet is modelled Finally the software implementation is substantiated including a description of all equations The software can be downloaded from http www nlog nl nl geothermalEnergy DoubletCalc html TNO report TNO 2014 R11396 6 45 2 2 1 2 1 1 User manual DoubletCalc v1 4 Installation of the software The software can be found on the website www nlog nl http www nlog nl nl geothermalEnergy DoubletCalc html It is distributed as a compressed ZIP file In order to use the program the ZIP file needs to be downloaded and saved on the computer Next the compressed files need to be unpacked The user can choose in which folder the files will be stored In principle a folder named DoubletCalc14 wi
21. 1017 9 91E 04 9 6 7E 04 3 45E 04 9 23E 04 9 03E 04 8 83E 04 8 65E 04 8 A47E 04 8 30E 04 8 14E 04 7 99E 04 7 64E 04 7 69E 04 7 56E 04 7 A4E 04 7 32E 04 7 22E 04 7 11E 04 7 01E 04 6 91E 04 6 61E 04 b 72E 04 6 62E 04 6 54E 04 6 45E 04 6 3 7E 04 6 28E 04 6 20E 04 6 13E 04 6 05E 04 3 98E 04 5 80E 04 5 83E 04 5 bE 04 5 0E 04 5 63E 04 5 57E 04 5 50E 04 3 44E 04 23 38E 04 23 32E 04 2 26E 04 2 21E 04 2 15E 04 3 10E 04 3 04E 04 47 45 TNO report TNO 2014 R11396 48 45 Part 3 parameters calculated per calculation length section in producer E o O 5 m L m Z m Angle de Inner diat Roughne P bar T degC S ppm Density k Viscosity Qvol m3 dPGrav b dPVisc be dPpump bar 0 0 16 35055 86 50769 119999 1056 001 5 06E 04 146 755 49 59259 49 5926 1 2 21 81337 86 60029 119999 1056 138 5 05E 04 146 736 5 136058 0 326759 99 18519 99 1852 1 2 27 27679 86 69111 119999 1056 276 5 05E 04 146 717 5 136726 0 326699 148 7778 148 778 1 2 32 74083 86 78016 119999 1056 414 5 04E 04 146 698 5 137397 0 326639 198 3704 198 37 1 2 38 20548 86 86744 119999 1056 553 5 04E 04 146 679 5 138071 0 326579 247 963 247 963 1 2 43 67075 86 95294 119999 1056 692 5 03E 04 146 659 5 138749 0 326519 297 5556 297 556 1 2 49 13664 87 03667 119999 1056 833 5 03E 04 146 64 5 13943 0 326459 347 1481 347 148 1 2 54 60315 87 11861 119999 1056 974 5 03E 04 146 62 5 140114 0 3264 396 7407 396 741 1 2 60 07029 87 19877 11
22. 146 036 4 636321 0 077847 2479 63 2327 8 26 05201 6 625 1 2 222 4373 89 26015 119999 1061 352 4 91E 04 146 015 4 63697 0 077835 2529 222 2372 35 26 05201 6 625 1 2 227 1528 89 26839 119999 1061 502 4 91E 04 145 995 4 637623 0 077824 2578 815 2416 91 26 05201 6 625 1 2 231 8689 89 27486 119999 1061 653 4 91E 04 145 974 4 638279 0 077812 2628 407 2461 46 26 05201 6 625 1 2 236 5856 89 27956 119999 1061 804 4 91E 04 145 953 4 638939 0 077801 2678 2506 01 26 05201 6 625 1 2 241 303 89 2825 119999 1061 957 4 91E 04 145 932 4 639603 0 077789 2678 2506 01 16 18007 8 165329 1 2 224 9524 2 774806 119999 1058 505 4 96E 04 146 408 260 1134 4 839067 TNO report TNO 2014 R11396 49 45 Part 4 parameters calculated per calculation length section in injector L m Z m Angle de Inner diat Roughne P bar T degC S ppm Density k Viscosity Qvol m3 dPGrav b dPVisc be dPpump bar 0 0 16 35055 35 119999 1079 509 9 73E 04 143 5594 49 90566 49 9057 5 1 2 21 29768 34 9699 119999 1079 72 9 74E 04 143 5313 5 283714 0 33659 99 81132 99 8113 12 36106 1 2 26 57867 34 93612 119999 1079 946 39 74E 04 143 5013 5 284783 0 00379 149 717 149 717 12 375 1 2 31 86079 34 90469 119999 1080 171 9 75E 04 143 4715 5 285885 0 00377 199 6226 199 623 12 375 1 2 37 14401 34 87562 119999 1080 395 9 75E 04 143 4417 5 286983 0 00377 249 5283 249 528 12 375 1 2 42 42832 34 84889 119999 1080 618 9 76E 04 143 4121 5 288076 0 00376 299 434 299 434 12 375 1 2 47 7137
23. 2 34 82452 119999 1080 84 9 76E 04 143 3827 5 289165 0 00376 349 3396 349 34 12 375 1 2 53 00021 34 80248 119999 1081 061 9 76E 04 143 3533 5 29025 0 00376 399 2453 399 245 12 375 1 2 58 28778 34 78279 119999 1081 281 9 77E 04 143 3241 5 291331 0 00376 449 1509 449 151 12 375 1 2 63 57642 34 76544 119999 1081 501 9 77E 04 143 295 5 292406 0 00376 499 0566 499 057 12 375 1 2 68 86614 34 75042 119999 1081 719 9 77E 04 143 2661 5 293478 0 00376 548 9623 548 962 12 375 1 2 74 15692 34 73773 119999 1081 937 9 77E 04 143 2373 5 294545 0 00376 598 8679 598 868 12 375 1 2 79 44877 34 72737 119999 1082 153 9 77E 04 143 2086 5 295607 0 00376 648 7736 648 774 12 375 1 2 84 74168 34 71933 119999 1082 369 9 78E 04 143 1801 5 296665 0 00376 698 6792 698 679 12 375 1 2 90 03563 34 71361 119999 1082 584 9 78E 04 143 1517 5 297718 0 00376 748 5849 748 585 12 375 1 2 95 33064 34 7102 119999 1082 797 9 78E 04 143 1234 5 298767 0 00376 798 4906 798 491 12 375 1 2 100 6267 34 70912 119999 1083 01 9 78E 04 143 0953 5 299811 0 00376 848 3962 848 396 12 375 1 2 105 9238 34 71033 119999 1083 222 9 78E 04 143 0673 5 30085 0 00376 898 3019 898 302 12 375 1 2 111 2219 34 71386 119999 1083 433 9 78E 04 143 0394 5 301885 0 00376 948 2075 948 208 12 375 1 2 116 5211 34 71969 119999 1083 643 9 78E 04 143 0117 5 302915 0 00376 998 1132 998 113 12 375 1 2 121 8213 34 72782 119999 1083 852 9 77E 04 142 9842 5 30394 0 00375 1048 019 1048 02 12 375 1 2 127 1225 34 738
24. 205 119999 1086 555 9 72E 04 142 6284 4 728476 0 02202 1796 604 1714 94 27 21842 8 625 1 2 197 7852 35 10982 119999 1086 727 9 72E 04 142 6059 4 729224 0 02201 1846 509 1759 32 27 21842 8 625 1 2 202 4932 35 14943 119999 1086 897 9 71E 04 142 5835 4 729969 0 02201 1896 415 1803 7 27 21842 8 625 1 2 207 2019 35 19089 119999 1087 067 9 71E 04 142 5613 4 730709 0 022 1946 321 1848 06 27 26572 7 970936 1 2 211 8989 35 23348 119999 1087 236 9 70E 04 142 5392 4 729434 0 03249 1996 226 1892 38 27 36306 6 625 1 2 216 5434 35 27631 119999 1087 402 9 69E 04 142 5174 4 726014 0 08144 2046 132 1936 7 27 36306 6 625 1 2 221 1887 35 32087 119999 1087 567 9 69E 04 142 4957 4 726734 0 08142 2096 038 1981 02 27 36306 6 625 1 2 225 8348 35 36717 119999 1087 732 9 68E 04 142 4742 4 727451 0 0814 2145 943 2025 35 27 36306 6 625 1 2 230 4816 35 4152 119999 1087 895 9 67E 04 142 4528 4 728164 0 08139 2195 849 2069 67 27 36306 6 625 1 2 235 1291 35 46497 119999 1088 058 9 67E 04 142 4315 4 728873 0 08137 2245 755 2113 99 27 36306 6 625 1 2 239 7773 35 51647 119999 1088 22 9 66E 04 142 4103 4 729579 0 08135 2295 66 2158 31 27 36306 6 625 1 2 244 4263 35 5697 1088 381 9 65E 04 142 3892 4 73028 0 08133 2345 566 2202 63 27 36306 6 625 1 2 249 0759 35 62465 1088 541 9 64E 04 142 3683 4 730978 0 08131 2395 472 2246 96 27 36306 6 625 1 2 253 7263 35 68133 1088 7 9 63E 04 142 3475 4 731672 0 08129 2445 377 2291 28 27 36306 6 625 1 2 258 3774 35 73973 1088 858 9 63E
25. 24 119999 1084 06 9 77E 04 142 9567 5 30496 0 00375 1097 925 1093 63 23 95632 9 074433 1 2 131 9541 34 75002 119999 1084 249 9 77E 04 142 9319 4 848853 0 01718 1147 83 1138 27 21842 8 625 1 2 136 6513 34 76359 119999 1084 431 9 77E 04 142 9078 4 719209 0 02207 1197 736 1182 38 27 21842 8 625 1 2 141 3492 34 77903 119999 1084 613 9 77E 04 142 8839 4 720002 0 02207 1247 642 1226 76 27 21842 8 625 1 2 146 0479 34 79634 119999 1084 793 9 76E 04 142 8601 4 72079 0 02206 1297 547 1271 14 27 21842 8 625 1 2 150 7475 34 81553 119999 1084 973 9 76E 04 142 8364 4 721575 0 02206 1347 453 1315 52 27 21842 8 625 1 2 155 4478 34 83659 119999 1085 153 9 76E 04 142 8128 4 722357 0 02206 1397 358 1359 9 27 21842 8 625 1 2 160 1488 34 85951 119999 1085 331 9 76E 04 142 7893 4 723134 0 02205 1447 264 1404 28 27 21842 8 625 1 2 164 8507 34 8843 119999 1085 508 9 75E 04 142 766 4 723909 0 02205 1497 17 1448 66 27 21842 8 625 1 2 169 5533 34 91096 119999 1085 685 9 75E 04 142 7428 4 724679 0 02204 1547 075 1493 04 27 21842 8 625 1 2 174 2567 34 93947 119999 1085 861 9 74E 04 142 7197 4 725446 0 02204 1596 981 1537 42 27 21842 8 625 1 2 178 9609 34 96983 119999 1086 036 9 74E 04 142 6967 4 726209 0 02203 1646 887 1581 8 27 21842 8 625 1 2 183 6659 35 00206 119999 1086 21 9 73E 04 142 6738 4 726969 0 02203 1696 792 1626 18 27 21842 8 625 1 2 188 3716 35 03613 119999 1086 383 9 73E 04 142 6511 4 727724 0 02202 1746 698 1670 56 27 21842 8 625 1 2 193 078 35 07
26. 4 0 00346 1091 037 1087 95 20 32742 9 574402 1 2 92 41572 88 28591 119999 1057 58 4 96E 04 146 536 4 822798 0 012338 1140 63 1132 05 27 21842 8 625 1 2 97 01063 88 34536 119999 1057 702 4 96E 04 146 519 4 574137 0 020769 1190 222 1176 15 27 21842 8 625 1 2 101 6061 88 40305 119999 1057 824 4 96E 04 146 502 4 574664 0 020765 1239 815 1220 25 27 21842 8 625 1 2 106 202 88 45895 119999 1057 947 4 95E 04 146 485 4 575195 0 020761 1289 407 1264 35 27 21842 8 625 1 2 110 7985 88 51308 119999 1058 071 4 95E 04 146 468 4 575729 0 020758 1339 1308 45 27 21842 8 625 1 2 115 3955 88 56543 119999 1058 196 4 95E 04 146 451 4 576267 0 020754 1388 593 1352 56 27 21842 8 625 1 2 119 9931 88 61599 119999 1058 322 4 95E 04 146 433 4 576809 0 02075 1438 185 1396 66 27 21842 8 625 1 2 124 5912 88 66477 119999 1058 448 4 94E 04 146 416 4 577354 0 020747 1487 778 1440 76 27 21842 8 625 1 2 129 1898 88 71176 119999 1058 576 4 94E 04 146 398 4 577903 0 020743 1537 37 1484 86 27 21842 8 625 1 2 133 789 88 75697 119999 1058 704 4 94E 04 146 381 4 578456 0 02074 1586 963 1528 96 27 21842 8 625 1 2 138 3888 88 80038 119999 1058 833 4 94E 04 146 363 4 579012 0 020736 1636 556 1573 06 27 21842 8 625 1 2 142 9891 88 84199 119999 1058 963 4 94E 04 146 345 4 579572 0 020733 1686 148 1617 16 27 21842 8 625 1 2 147 5899 88 88181 119999 1059 094 4 93E 04 146 327 4 580136 0 020729 1735 741 1661 26 27 21842 8 625 1 2 152 1914 88 91983 119999 1059 225 4 93E 04 146 309 4
27. 580704 0 020726 1785 333 1705 37 27 21842 8 625 1 2 156 7934 88 95605 119999 1059 358 4 93E 04 146 29 4 581275 0 020722 1834 926 1749 47 27 21842 8 625 1 2 161 3959 88 99047 119999 1059 491 4 93E 04 146 272 4 58185 0 020719 1884 519 1793 57 27 21842 8 625 1 2 165 9991 89 02308 119999 1059 626 4 93E 04 146 253 4 582429 0 020716 1934 111 1837 71 27 12172 8 459204 1 2 170 6089 89 05376 119999 1059 761 4 92E 04 146 235 4 586984 0 022824 1983 704 1882 26 26 05201 6 625 1 2 175 3175 89 08125 119999 1059 902 4 92E 04 146 215 4 630649 0 077953 2033 296 1926 81 26 05201 6 625 1 2 180 0267 89 10701 119999 1060 043 4 92E 04 146 196 4 631265 0 077941 2082 889 1971 37 26 05201 6 625 1 2 184 7365 89 13102 119999 1060 185 4 92E 04 146 176 4 631884 0 077929 2132 481 2015 92 26 05201 6 625 1 2 189 4469 89 15329 119999 1060 328 4 92E 04 146 156 4 632507 0 077917 2182 074 2060 48 26 05201 6 625 1 2 194 158 89 17382 119999 1060 472 4 92E 04 146 137 4 633133 0 077905 2231 667 2105 03 26 05201 6 625 1 2 198 8696 89 19259 119999 1060 616 4 92E 04 146 117 4 633763 0 077894 2281 259 2149 58 26 05201 6 625 1 2 203 5819 89 20962 119999 1060 762 4 92E 04 146 097 4 634397 0 077882 2330 852 2194 14 26 05201 6 625 1 2 208 2948 89 22489 119999 1060 908 4 92E 04 146 076 4 635035 0 07787 2380 444 2238 69 26 05201 6 625 1 2 213 0084 89 2384 119999 1061 055 4 91E 04 146 056 4 635676 0 077858 2430 037 2283 24 26 05201 6 625 1 2 217 7225 89 25016 119999 1061 203 4 91E 04
28. 9999 1057 116 5 02E 04 146 6 5 140802 0 326341 446 3333 446 333 1 2 65 53807 87 27715 119999 1057 258 5 02E 04 146 581 5 141494 0 326281 495 9259 495 926 1 2 71 00648 87 35374 119999 1057 401 5 01E 04 146 561 5 142188 0 326222 545 5185 545 519 11 76914 1 2 36 15039 87 44253 119999 1056 141 5 01E 04 146 736 5 139471 0 004441 595 1111 595 111 12 375 1 2 41 29057 87 53023 119999 1056 268 5 00E 04 146 718 5 136714 0 003468 644 7037 644 704 12 375 1 2 46 43137 87 6158 119999 1056 395 5 00E 04 146 7 5 137333 0 003467 694 2963 694 296 12 375 1 2 51 5728 87 69923 119999 1056 524 4 99E 04 146 683 5 137957 0 003466 743 8889 743 889 12 375 1 2 56 71485 87 78053 119999 1056 654 4 99E 04 146 665 5 138585 0 003465 793 4815 793 481 12 375 1 2 61 85753 87 85968 119999 1056 784 4 99E 04 146 646 5 139218 0 003464 843 0741 843 074 12 375 1 2 67 00085 87 9367 119999 1056 916 4 98E 04 146 628 5 139856 0 003463 892 6667 892 667 12 375 1 2 72 14481 88 01157 119999 1057 049 4 98E 04 146 61 5 140498 0 003463 942 2593 942 259 12 375 1 2 77 28942 88 08429 119999 1057 182 4 97E 04 146 591 5 141146 0 003462 991 8519 991 852 12 375 1 2 82 43467 88 15485 119999 1057 317 4 97E 04 146 573 5 141798 0 003461 nu N F O Un n n n n n n n n Cn O O O O Scoooooo0o0o0o00000000000000000000000000000000000 80000000000 1041 444 1041 44 0 12 375 1 2 87 58059 88 22327 119999 1057 452 4 97E 04 146 554 5 14245
29. ATIC AQUIFER PROPERTIES PRODUCER Z m 0 49 5926 99 1852 148 778 198 37 247 963 297 330 347 148 396 741 446 333 495 926 545 519 395 111 b44 704 094 296 743 589 793 481 843 074 892 007 942 259 991 852 1041 44 1087 95 1132 05 1176 15 1220 25 1264 35 1308 45 1352 56 1396 66 1440 76 1484 80 1528 96 1573 06 1617 16 1661 26 1705 37 1749 47 1793 57 1837 71 1862 20 1926 81 1971 37 2015 92 2060 48 2105 03 2149 58 2194 14 2238 09 2263 24 2327 8 2372 35 2416 91 2461 46 2506 01 P bar 1 5 861976 10 73165 15 60836 20 49385 25 38627 30 28615 35 19343 40 10806 45 02998 49 95911 54 89541 59 83882 64 78926 69 746608 74 71102 79 68222 84 66021 89 641492 94 63631 99 6343 104 6388 109 3376 113 7987 118 2649 122 7361 127 2123 131 6933 136 1792 140 6699 145 1653 149 6655 154 1703 158 6798 163 1939 167 7125 172 2356 176 7631 181 7951 185 8353 190 4226 195 0142 199 6102 204 2104 208 8149 213 4235 218 0363 222 6532 227 2741 231 8991 236 528 241 1609 245 7977 250 4383 255 0826 T degc 10 11 53737 13 07474 14 61211 16 14948 17 68685 19 22422 20 761593 23 83633 25 3737 20 91107 28 44844 29 98581 31 52318 33 06056 34 59793 36 1353 37 67267 39 21004 40 74741 42 28478 43 7264 45 09354 46 46068 47 82781 49 194935 51 92922 53 29636 54 6635 56 03063 57 39777 58 76491 60 13204 61 49918 62 86631 64
30. DoubletCalc is to be able to calculate the indicative geothermal power on the basis of a model of a geothermal doublet taking into account the geological aquifer uncertainties Aquifer and installation parameters are required in order to calculate the geothermal power The modelling assumes that the installation parameters are known and that the uncertainties of the system are a consequence of uncertainties in the estimation of the aquifer characteristics The following tables list the parameters that are required for the operation of DoubletCalc min mean max dimension pemeiy Tf TT CNN net gross fraction brine salinity Total Dissolved Solids NaCl equivalent Table 6 DoubletCalc input geological parameters with uncertainty range The uncertainty imposed on the depth is 1096 see paragraph 2 2 parameter value geothermal gradient lt Im average surface temperature _ e kn kv ratio of the aquifer anisotropy a ae Table 7 DoubletCalc input geological parameters without uncertainty range parameter ae dimension casing scheme productonwel easing scheme injectonwe m inner diameter production mA absolute roughness production casing mirer Borehole diameter production welat aquifer lve reh borehole diameter injection well at aquifer level inch skin resistance around well in reservoir section production well fixed value skin resistan
31. TNO report TNO 2014 R11396 DoubletCalc 1 4 manual English version for DoubletCalc 1 4 3 Date Author s Copy no No of copies Number of pages Number of appendices Sponsor Project name Project number All rights reserved 1 October 2014 H F Mijnlieff A N M Obdam J D A M van Wees M P D Pluymaekers and J G Veldkamp 54 incl appendices No part of this publication may be reproduced and or published by print photoprint microfilm or any other means without the previous written consent of TNO In case this report was drafted on instructions the rights and obligations of contracting parties are subject to either the General Terms and Conditions for commissions to TNO or the relevant agreement concluded between the contracting parties Submitting the report for inspection to parties who have a direct interest is permitted 2014 TNO innovation for life m EEE Oil and Gas Princetonlaan 6 3584 CB Utrecht P O Box 80015 3508 TA Utrecht The Netherlands www tno nl T 31 88 866 42 56 F 31 88 866 44 75 TNO report TNO 2014 R11396 2 45 2 1 2 2 2 3 2 4 3 1 3 2 5 1 5 2 5 3 5 4 9 5 5 6 5 7 6 1 6 2 6 3 7 1 7 2 7 3 7 4 10 11 11 1 11 2 11 3 12 12 1 12 2 12 3 Contents PINTROGUCU ON e M 5 User manual DoubletCalc v1 4 oiii J J J Q J J 6 InStallatlon OF ite SOTWETO cn uequ
32. ayers or in other words increasing anisotropy decreases the positive effect of the inclined well Appendix 2 goes into the details of dealing with sub layers The ratio between the productivity index with and without skin due to penetration angle provides a better understanding in the effect of having an oblique penetration angle than the skin Productivity is calculated as equation 6 5 from Verruijt 1970 and Dake 1978 oPw Paq 1 5 with J well productivity m s Pa Pw pressure in the well near the aquifer bottom hole pressure Pa Pag initial hydrostatic pressure in the aquifer near the well Pa Q Qm p flow taken positive for flow from the well towards the aquifer m3 s TNO report TNO 2014 R11396 37 45 water viscosity see paragraph 7 2 Pa s aquifer permeability m aquifer height m ng Net to gross ratio distance between the production and injection wells m outer diameter of the well filter m skin The productivity index ratio for a well with and without skin due to penetration angle after some rewriting is gt T lt Ns L beatae lIn Jinclined well ll eq 31 Jvertical well in so with L distance between the production and injection wells m So skin due to penetration angle lw outer diameter of the well filter m L is typically between 1500 and 2000 m and ry about 0 1 m For these
33. capacity are a function of temperature and salinity A detailed theoretical description of the calculation is presented in chapter 4 Remarks regarding the model Figure 5 shows that the well is split into a number of sections with varying properties A new segment should be specified in the DoubletCalc input where a change in well diameter is foreseen The inclination of the section is calculated from the along hole and true vertical depths This results in a stepwise deviation trajectory which closely approaches the true deviation and therefore is fit for purpose The flow resistance and the heat loss on the way up producer or heat gain on the way down injector can be calculated from the deviation and the specified casing diameter and roughness This is described in detail in chapter 4 The aquifer is modelled as homogeneous with a uniform thickness net to gross ratio permeability anisotropy and salinity An inclined aquifer can be modelled by entering different TVD values for the top aquifer at producer and injector There is no direct relation between aquifer and well in the model It is implicitly assumed that the entire aquifer or aquifer interval has been drilled and completed The model also assumes in principle that the aquifer is drilled vertically The improved flow towards the well as a result of drilling an inclined well like the example shown in Figure 5 is accounted for by entering a penetration angle for produ
34. ce around well in reservoir section injection well fixed value inclination between production well trajectory and reservoir inclination between injection well trajectory and reservoir Oo degrees Table 8 DoubletCalc well specification input degrees TNO report TNO 2014 R11396 19 45 3 1 parameter value injection temperature distance between production and injection well at aquifer EE level pump efficiency Eug m pump depth in production well pump pressure difference Table 9 DoubletCalc input for pump and doublet Flow The theoretical flow rate is calculated from the variables in Table 6 to Table 9 and an imposed pressure drop at the boundary between aquifer and well The calculation of the geothermal power takes the following into account pressure loss caused by flow in the aquifer to the production well and from the injection well pressure loss around production and or injection well caused by skin pressure loss in the production and injection wells as a result of friction by flow pressure difference caused by gravity pressure difference caused by the pump in the production well heat loss in the production and injection wells as a result of the release of heat to the environment Correlations have been used to determine the relevant water properties density viscosity and heat capacity Density is a function of pressure temperature and salinity Viscosity and heat
35. cer and or injector a in Figure 5 The skin due to penetration angle shown in the input screen is calculated automatically see paragraph 3 2 Penetrating the aquifer TNO report TNO 2014 R11396 20 45 3 2 The reservoir temperature that is used in the model is calculated by multiplying the depth of the middle of the aquifer by the geothermal gradient increased by the average surface temperature The middle of the aquifer is calculated for each simulation by adding the stochastically drawn value of the top of the aquifer and the drawn half aquifer thickness Penetrating the aquifer obliquely The intersection of well and aquifer is modelled as a vertical transect In reality the production and or injection wells are rarely perpendicular to the aquifer Inclined wells have an effect on the distance between the wells in the aquifer flow to and from the well These effects are discussed below Figure 15 Inclined penetration of the aquifer Distance between production and injection well The result of having an inclined well is that the distance between the production and injection wells depends on the well trajectory The distance between the wells is used for the calculation of the well productivity chapter 8 When calculating the distance between the wells the inclination is accounted for by using the distance between the wells at the centre of the aquifer Effect on flow The inclination has consequences
36. ction well and the pressure increase in the injection well for a doublet is Verruijt 1970 equation 6 5 and Dake 1978 Ji L A In S Pwag Pw Pag Q 2akHR r uoc MEME eq 7 with Pw pressure in well at aquifer bottom hole pressure Pag initial hydrostatic pressure in the aquifer at well Q Q p flow positive for flow from well to aquifer u water viscosity function of temperature and salinity k permeability of the aquifer H thickness of the aquifer Hag net to gross ratio distance between production and injection well at aquifer level Outer diameter of the well filter diameter S skin factor This equation is valid for stationary flow to vertical wells and a homogeneous aquifer The initial pressure and temperature in the aquifer at the production well are used for the calculation of p and u The pressure in the bottom of the well and the outlet temperature of the heat exchanger are used for the injection well The salinity is considered to remain constant as described in paragraph 7 4 The right hand side of equation 7 depends on pressure and temperature because p depends on temperature and pressure and u on temperature The first term of equation 7 gives the pressure loss caused by flow in a homogeneous aquifer However the aquifer characteristics in the direct surroundings of the well usually differ from those in the rest of the aquifer as a results of the drilling
37. design values for modern pipes SPE Drilling amp Completion Vol 21 212 215 Feistel R amp Marion G 2007 A Gibbs Pitzer function for high salinity seawater thermodynamics Progress in Oceanography 515 539 Garcia Gutierrez A Espinosa Paredes G amp Hernandez Ramirez 2001 Study on the flow production characteristics of deep geothermal wells Geothermics Vol 31 141 167 Grunberg L 1970 Properties of sea water concentrations Third International Symposium on Fresh Water from the Sea Vol 1 pp 31 39 Odeh A S 1980 An Equation for Calculating Skin Factor Due to Restricted Flow Entry JPT Rogers E J Economides M J 1996 The skin due to slant of deviated wells in permeability anisotropic reservoirs SPE 37068 Saidikowski R M 1979 Numerical Simulations of the Combined Effects of Wellbore Damage and Partial Penetration Paper SPE 8204 presented at 1979 AFTCE Las Vegas NV September 23 26 Verruijt A 1970 Theory of Groundwater Flow Macmillan 1970 TNO report TNO 2014 R11396 14 Signature Utrecht lt datum gt lt naam afdelingshoofd gt Head of department 45 45 TNO H F Mijnlieff A N M Obdam J D A M van Wees M P D Pluymaekers and J G Veldkamp Authors TNO report TNO 2014 R11396 A Doublet Calculator 1 4 Base Case Details Example of the base case details file Part 1 initial hydrostatic aquifer properties producer HYDROST
38. e Pee ua uie v e e Gees 6 INPUT a aa Tasa 7 ease eaten TU 10 Emor IMGSS8066 uuu haqa yaasta 19 The DoubletCalc miodel 18 Remarks regarding the model 19 Penetrating the aquifer obliquely 20 Theoretical background of the DoubletCalc model 23 M ss Dall ANC E ERTEILEN 26 WAS ERE 26 VOIUME deans 26 Impulse balance a a nnn nnns nnns sina n nennen 26 Pressure development in the aquifer from or towards a well 27 Pressure development in a casing r 28 Pressure development in the pump 29 Initial hydrostatic aquifer pressure near the production and injection wells 30 Energy DalanGe e 31 dradieril aseo edes reus kaka uapa saka akaun skaSaqi 31 Heat loss in the production well 31 Temperature decrease in the heat exchange
39. eat ZL J QQ W 4 The gross thickness H the net to gross ratio Rng equation 3 and the permeability k equation 4 are entered into the DoubletCalc input screen TNO report TNO 2014 R11396 53 45 C Explanation of characters and symbols The units given below are in Sl The parameters in the DoubletCalc input and output screens are entered reported in practical units for example milli Darcy for permeability ppm for salinity and C for temperature Internally DoubletCalc uses SI units except for emperical functions which as used as published in literature English Cp heat capacity J kg K CoP Coefficient of Performance d depth positive downward from surface level m dip depth to top aquifer m tubing casing diameter m friction number gravitational acceleration 9 80665 m s aquifer thickness measured perpendicular to the strata m permeability m thermal conductivity W m K length along tubing casing m distance production injection well at aquifer level m pressure Pa power W heat exchange well surroundings W m volume flow m s mass flow kg s radius of tubing casing m Reynolds number net to gross ratio salinity salt content of aquifer brine weight fraction ppm skin time s temperature K average water velocity in the tubing m s height measured negative downward from surface level m lt S OS VOR gt x x
40. eat capacity calculation 5 328 9 760 107 s 4 040 10 s 6 913 105 7 351 10 s 3 150 10 s Jr 9 600 10 1 927 10 s 8 230 10 6 ir 2 500 10 1 666 10 s 7 125 10 s Jr TNO report TNO 2014 R11396 35 45 7 4 with Cp water heat capacity KJ kg K S salt content salinity of the water g kg ih temperature K Keep in mind that in in Grunberg the sixth coefficient contains an error 3 15 10 instead of 3 15 10 Salt content Two regimes apply for the salt content salinity of the water Static the initial equilibrium in the subsurface dynamic during the production in the doublet system The salt content s of the water in its initial equilibrium as a function of depth d follows from d dy D muu Tum mn yn eq 27 s d s salinity of the aquifer brine kg kg or ppm depth of the top of the aquifer at the production well m TVD aquifer thickness at the production well m From the formula follows that at surface level the salinity is 0 The salinity increases linearly with depth to the user specified value at reservoir depth The production water is circulated during production The salinity of the production water is assumed to be equal to that of the reservoir brine everywhere in the doublet system top p a eq 28 TNO report TNO 2014 R11396 36 45 8 The effect of penetrating the reservoir
41. eat exchanger In most cases this is caused by the difference between the reservoir pressure HP es and the static pressure of the water column in the production well at reservoir level bottom hole pressure BHP If negative pressures result from a scenario a popup will be shown Figure 14 but the calculation will be finished normally The density and hence the static pressure of the water column in the well is determined by the salinity of the reservoir brine which is constant over the entire well trajectory In the subsurface it is assumed that the salinity increases linearly with depth from 0 ppm at surface level to the specified salinity at reservoir level see equation on page 35 Therefore the reservoir pressure is lower than the static pressure in the water column In reality at atmospheric well head pressure the water will flow back from the producer into the reservoir and the water level in the producer will drop below surface if the pump is switched off and the producer is not connected to the injector DoubletCalc assumes a closed doublet system with balanced pressures The software will return negative pressures in case the pump pressure is specified too low to overcome the difference in reservoir pressure and the static pressure in the water column This may also be the case if the pump depth is set too shallow in the production well Because a negative pressure is physically impossible this means that the water cannot be
42. ed 26 09 2014 14 26 Windows Batch File Size 207 bytes Figure 1 Location of the DoubletCalc files as visible in the Windows default file manager The file to be executed is named DoubletCalc v1 4 3 exe If DoubletCalc does not start the following check can be performed Was the correct version of Java installed version 6 or newer This information can be verified on the website http www java com en download installed jsp Java can be downloaded from hitp www java com en download manual jsp Alternatively execute the batch file start doubletcalc bat in a command window run cmd exe Installation on Apple computers Follow the same instructions as for Windows computers and execute the shell script start doubletcalc osx sh from the terminal TNO report TNO 2014 R11396 7 45 2 2 If DoubletCalc does not start the following check can be performed Assign execute permission to the start script This can be done in a terminal window by entering chmod u x start_doubletcalc_osx sh Input screen After the Java installation the DoubletCalc 1 4 3 input screen appears Figure 2 The input screen enables the user to specify the essential parameters that are required to calculate the geothermal power estimate Only the white fields are obligatory The values in the grey fields are calculated by the software The min and max values of the aquifer tops are calculated as 10 of the median value Excessive as this
43. er The net power Poump net the pump should supply is ES LS QAP pump p pen Cen ed 34 The gross power is pump gross P pump net 7 with 7 being the user specified pump efficiency Coefficient of performance COP De Coefficient of Performance COP is defined as the geothermal power extracted by the heat exchanger from the produced water divided by the power needed for producing and injecting the water COPS He eq 36 pump gross TNO report TNO 2014 R11396 41 45 12 12 1 12 2 Considerations Power gain by density difference between production and injection well The temperature of the water is several tens of degrees Celsius lower in the injection well than in the production well After all the hot production water has been cooled in the heat exchanger Therefore the density of the water is higher in the injection well than in the production well The resulting difference in hydrostatic pressure Ap between the two wells is Ap Pu p s n eq 37 With Dn Php hydrostatic pressure in the injection and production wells respectively p p average density in the injection and production wells respectively Ah average depth from top to bottom of injection and production wells The increased power P is For a typical doublet the pressure difference is approximately 1 2 bar At a typical flow rate Q of 150 m h the extra power is 4 8 kW In practice
44. er _ gravity ignored 7 outlet heat inlet injection casing viscous forces and exchanger pump gravity ignored inlet injection outlet injection pump not modelled separate pump pump ly see 5 6 outlet injection 10 top injection casing viscous forces and pump well gravity ignored 10 top injection 11 ottom injection tubing viscous forces and well well casing gravity bottom injection 12 static aquifer aquifer viscous forces well pressure at injection well Table 10 Pressure balance TNO report TNO 2014 R11396 25 45 from node middle aquifer at production well bottom produc aquifer none tion well inlet production tubing pipe with surroundings pump outlet produc tion pump 2 bottom produc 3 tion well 3 inlet production 4 pump pomp with surroundings ignored tubing pipe with surroundings ae with surroundings ignored 7 outlet heat heat ex heat loss to heat ex exchanger changer changer outlet produc 5 tion pump top production well O1 inlet heat ex changer top production well inlet heat ex changer 7 outlet heat inlet injection with surroundings exchanger ignored pump Outlet injection pump not modelled separate ly 5 6 with surroundings ignored middle aquifer aquifer water warmed by heat at injection well inlet injection pump pump outlet injection 10 pump top injection well nature heat excha
45. ermal gradient The initial temperature profile is required for the calculation of the initial aquifer temperature and the heat loss in the production well l T d UR O TEE eq 15 With a depth positive downward Ts Tg d 0 yearly average temperature at surface level For the Netherlands this is10 5 C Bont et al 2012 A geothermal gradient For the Netherlands this is 0 031 C m on average Bont et al 2012 The initial aquifer temperature at the injection well is T stet A du eq 16 with Atop depth top aquifer at production well H aquifer thickness Heat loss in the production well The hot formation water loses heat to the relatively cold environment on its way up to the surface The heat loss per unit length follows from Garcia Gutierrez et al 2001 Ank T T Qu EC M 55 eq 17 In 2 Or with Qw wer heat loss per unit length W m TNO report TNO 2014 R11396 32 45 6 3 Te casing temperature considered to be equal to the temperature of the wa ter in the well time since start of heat flow Kj thermal conductivity of the rocks surrounding the well inner radius of the casing e 1 781072 with Euler s constant y 0 577216 g thermal diffusion coefficient of the aquifer rock k p 8 a i Xr Mm eq 18 with Cog heat capacity of the aquifer rocks around the well Po density of the aquifer rocks
46. eter producer inch BAB skin producer 00 skin due to penetration angle p EE pipe segment sections p m AH 5000 10540 1930 0 2678 0 pipe segment depth p m TVD 5000 10540 18330 2505 0 pipe inner diameter p inch 504238852662 pipe roughness p milli inch 3221232 outer diameter injector inch 6 13 skin injector o0 skin due to penetration angle i 0 97 pipe segment sections i m AH 500 10540 1930 026450 pipe segment depth i m TVD 500 10540 18330 2468 0 pipe inner diameter i inch 6012389 62662 pipe roughness i milli inch JEZZZX I I II II IIJILIIM I IYZO E Figure 6 DoubletCalc 1 4 3 output screen Geotechnics Output Monte Carlo cases stochastic inputs Pao P50 P10 geothermal power ea ea nz asa cave median vano Inputs vae Baauer amp imeom ao ao pump volume now mmy 1465 required pump powere 2677 geoterma power mwy 812 owm oa aquifer pressure atinjedor war 25148 A A lemperature atheat exchanger 8651 pressure at heat exchanger oa 1635 mid aquifer depth The output screen has three options for presenting the results in different ways probabilistic plots fingerprinting export of the base case details The detailed output is described in the following paragraphs Probabilistic plots The button
47. h does not fit the top of the aquifer anymore To deal with this problem DoubletCalc will extend or shorten the tubing segment with the largest diameter accordingly For reasons of calculation accuracy DoubletCalc will split the well into segments of equal length during the simulation the calculation length subdivision under section C Well Properties in the input screen of Figure 2 A weighted average of the properties is assigned to segments crossing a tubing section boundary see the pase case details file in paragraph 2 3 3 It is advisable to choose the segment length in accordance with the well design A very small segment length increases the calculation time whereas a very large length decreases the calculation accuracy TNO report TNO 2014 R11396 10 45 2 3 depth depth m TVD m AH 1054 Flow towards perforation filter 1833 SD Penetration angle b Aquifer degrees Figure5 Schematic casing design The part of the casing located in the reservoir solid blue should only be specified under specific circumstances 2505 2712 The calculation of the geothermal power can be started when all parameters have been entered button Calculate When finished the Doublet Calculator 1 4 3 Result Table Figure 6 will appear Output screen The output screen shows on the left hand side in the column Geotechnics Input the input parameters that were entered in
48. he geothermal gradient The above mentioned parameters are considered to be independent of each other Therefore it is possible to calculate a probability distribution of the geothermal power from the parameter range using stochastic simulation Monte Carlo The probability distribution of the parameters is modelled as a double triangle Figure 20 o e EY probability A 40 50 60 70 80 90 100 reservoir thickness m Figure 20 Example of a double triangle probability distribution The user specified minimum median and maximum values in this example are 50 65 and 90 The resulting average is 66 7 dashed line The surface under both triangles is equal TNO report TNO 2014 R11396 40 45 11 Calculated characteristics of the geothermal doublet system After running the Monte Carlo simulation three characteristics of the doublet system are presented in a probabilistic plot chapter 10 Parameter range Flow at the inlet of the heat exchanger Geothermal power Coefficient Of Performance COP The following paragraphs explain how these characteristics are calculated Geothermal power Once the mass flow at given pump pressure is calculated the power issued to the heat exchanger is given by E Sun M eq 33 The heat capacity of water c can be calculated because pressure temperature and salt content at the inlet of the heat exchanger are known Required pump pow
49. hese parameters are used for calculating the productivity index J see Verruijt 1970 equation 6 5 and Dake 1978 PPP 1 with Pw bottom hole pressure Dag initial hydrostatic pressure in the aquifer near the well Q 0 flow positive from well to aquifer M water viscosity function of temperature and salinity ke aquifer effective permeability H aquifer gross thickness Hag aquifer net to gross ratio L distance between production and injection well at aquifer level bw outer diameter of the well in the aquifer filter S skin For a stratified aquifer the factor KHRnig in equation 1 should be interpreted as Rag 25d k AiRntgi Teeter enn 2 with Hi and Rag being the permeability gross thickness and net to gross ratio of the individual layers The assumption is the flow is parallel to the stratification in the TNO report TNO 2014 R11396 52 45 aquifer The DoubletCalc input parameters k H and Ra should be chosen in such a way that the product kHR i4 meet the result of equation 2 The gross aquifer thickness H is also used for more calculations within the software than just the product of k H and R Therefore the value of H cannot be changed at will The parameters net to gross and permeability can be changed as long as the product KHR remains correct The net to gross ratio follows from n H R ee eee ee 3 The permeability follows from t
50. ingerprint Plot median values i cf x export CSV file 600 0 12 0 90 0 70 0 400 0 60 0 300 0 50 0 200 0 40 0 30 0 0 0 3 0 20 0 5 I 2 11 0 7 800 5000 lU 2 10 0 4 P ad v 90 2 P d g a L 80 S E E o S 9 w E o 5 0 E 100 0 3 o ae gt E 3 a i 5 pump pressure difference bar intake discharge Figure9 DoubletCalc Fingerprint graph Base case details The button export base case details in the output screen writes the following information to a CSV file hydrostatic aquifer properties at the producer and injector calculated along the well path per section as specified in the calculation length subdivision pres sure temperature salinity density and viscosity Table 1 base case details at the producer and injector calculated along the well path per section as specified in the calculation length subdivision Table 2 base case pressure and temperature at a number of key doublet nodes Table 3 base case results calculated for the doublet as a whole Table 4 Stochastic results P90 P50 and P10 for a number of parameters calculated for the doublet as a whole Table 5 Appendix 1 shows an example of the base case details file junit 4 top depth of calculation segment Table 1 Base case details file parts 1 and 2 initial
51. ll be created for example in which the following files are stored the release notes DoubletCalc143 release notes txt the program files named DoubletCalc 143 26092014 jar the JavaFX runtime folder example file of a DoubletCalc scenario example xml the windows executable DoubletCalc v1 4 3 exe the batch file start doubletcalc bat as an alternative executable the shell script start doubletcalc osx sh for executing on OS X Linux Installation on a Windows computer Java version 6 or newer should be installed In order to execute DoubletCalc double click DoubletCalc v1 4 3 exe in your favourite file manager PR doubletcalci43 i D x Ge Js m Computer PC 20376 Data D doubletcalc143 Search d Organize Open Print New folder gt fl A x E Favorites Name Date modified Type Size Data tsn tno nl runtime 07 10 2014 12 00 File folder BE Desktop wo DoubletCalc vi 4 3 exe 07 10 2014 12 00 Application 936 KB DoubletCalc143 release notes txt 07 10 2014 12 00 TXT File 2KB KG Data tsn tno nl U k ten tno nl i DoubletCalc 143 260920 14 jar 07 10 2014 12 00 Executable Jar 578 KB Outlook Files 55 example xml 07 10 2014 12 00 XML Document 2KB 33 Recent Places G start doubletcalc bat RA Data tsn tno nl __Jstart_doubletcalc_osx sh 07 10 2014 12 00 SH File 1KB start_doubletcalc bat Date modified 07 10 2014 12 00 Date creat
52. ls The initial static pressure follows from equation 9 where v 0 and dz dl 1 d P gp eq 14 with the precondition D Patmospheric 1 bar at the surface g is the gravitational acceleration The water density o is a function of pressure temperature and salinity The temperature at any location in the well is determined by the geothermal gradient which is described in paragraph 6 1 The salinity at any location in the well is determined by the static salinity profile described in paragraph 7 4 Equation 9 becomes implicit in pressure once temperature and salinity are given This equation is solved numerically for the hydrostatic pressures Pstatp and Pstar at the production and injection wells respectively The initial hydrostatic pressures are reported in the base case details file see Table 1 TNO report TNO 2014 R11396 31 45 6 6 1 6 2 Energy balance The energy balance is solved for each system element individually using the pressure and temperature at the inlet of each system element This yields the temperature at the outlet of the system element Heat is exchanged at only two locations in the system production well heat exchanger Starting point for the calculation is the temperature at the production well which is calculated from the geothermal gradient paragraph 6 1 The temperature loss in the production well and the heat exchanger is covered the paragraphs 6 2 and 6 3 Geoth
53. m and for all of the elements within the system The sum of the pressure differ ences over all element in the system is zero The pressure balance determines the mass flow at a given pump pressure Energy balance this is valid for all elements within the system Release of heat to the immediate surroundings of the well and temperature drop in the heat ex changer are taken into account Figure 18 is a schematic representation of the doublet system The numbered nodes listed in Table 10 and Table 11 are used to describe the components of the pressure and energy balances QN injection pump K J depth top depth production top aquifer injection aquifer well distance L Figure 18 Schematic overview of a geothermal doublet with reference to the nodes used in Table 10 and Table 11 TNO report TNO 2014 R11396 24 45 from node to node cause of pressure equation difference static aquifer 2 bottom produc aquifer viscous forces 7 pressure at tion well production well 2 bottom produc 3 inlet production tubing viscous forces and tion well pump casing gravity 3 inlet production 4 outlet produc pump pressure increase by 13 pump tion pump pump outlet produc 5 top production tubing viscous forces and 4 tion pump well casing gravity top production inlet heat ex casing viscous forces and changer gravity ignored well inlet heat ex 7 outlet heat heat ex viscous forces and changer exchanger chang
54. may seem it also accounts for the uncertainty in the geothermal gradient which is not user specified The number of simulation runs and the calculation length subdivision both in blue can be entered if desired It was deliberately decided to leave as many fields as possible empty after start up with the exception of those values that in the Netherlands vary the least like the geothermal gradient and the surface temperature This was done to prevent that proposed default values that are unrepresentative for a scenario are used in that scenario erroneously the user is now forced to select representative values Zero values of the optional parameters between square brackets are ignored The input screen enables to open an existing scenario Open scenario In the Open scenario screen the XML file containing the required scenario can be selected Figure 3 After opening the parameters of this scenario are shown On the other hand the user can also start by entering scenario parameters Once the parameters have been entered the new scenario can be saved Save scenario Figure 4 TNO report TNO 2014 R11396 Figure 2 Doublet Calculator 1 4 3 umber of simulation runs 11000 Calculate file d doubletcalc143 example xml Geotechnical input A Aquifer properties Property min median max Property vawe aquifer permeability mD 160 250 500 awWerkwwrio 1 aquifer ne
55. ness R Reynolds number for flow in pipes D R pv in Pai eq 12 Farshad and Rieke 2006 among many others have published reference values for common pipe wall surface roughness Pressure development in the pump The pressure development in the pump is a constant that is specified by the DoubletCalc user AD unc COBSIGRU eee eee ee t DUE eer cee ee cere eq 13 Currently the software ignores a possible relationship between Appump and Q On account of the pressure development in the production well the presence and location of a pump in the production well is essential Otherwise at any location starting from the aquifer underpressure will result The use of an injection pump is not strictly necessary However for technical reasons it may be more efficient to do so rather than having only a pump in the production well The model does not model a potential injection pump separately This results in a negligible difference in the density of the water in the trajectory from the outlet of the production pump to the inlet of the injection pump The production pump pressure difference that is specified by the user in the DoubletCalc input screen is in case an injection pump is used the sum of the pressures of the production and injection pumps The pump efficiency is the effective efficiency of both pumps TNO report TNO 2014 R11396 30 45 5 7 Initial hydrostatic aquifer pressure near the production and injection wel
56. nge 20 20 21 20 0 top injection 11 well bottom injec tion well N N bottom injec tion well exchange with reser voir rock ignored paragraph 11 2 Table 11 Energy balance The equations listed in Table 10 and Table 11 are described in chapter 5 The letters and symbols used in the equations is given at the end of this chapter Because the doublet is a closed system the mass balance dictates that the mass flow Qm kg s is equal in all elements of the system In the dynamic system the salinity is constant and equal to the salinity of the aquifer water For the calculation of the hydrostatic pressure it is assumed that the salinity increases linearly with depth from zero at surface level to the specified median value at target reservoir level see paragraph 7 4 The pressure and energy balances are solved simultaneously for a given pump pressure or mass flow This results in a value of pressure and temperature at each node in the doublet system The resulting geothermal power and the electrical power required to operate the pump are easily calculated The calculation of pressure and temperature starts in the aquifer at the production well node 1 From this node onward the pressure and temperature at each node are calculated on the basis of the calculated pressure and temperature differences over each element TNO report TNO 2014 R11396 26 45 5 1 5 2 5 3 Mass balance Mass flow
57. obliquely The effect of penetrating the reservoir obliquely i e the angle between the reservoir and the wellbore is not 90 is that the wellbore reservoir interface can be longer than the reservoir thickness This has a positive effect on the flow rate The extra skin as a result of obliquely drilling the reservoir is calculated as Rogers and Economides 1996 g sin yeu Sg 2 4 L 03964 for lani ND EE AEE E E A ANNET eq 29 with So skin as 8 result of obliquely drilling the reservoir dimensionless 0 well deviation from the vertical h aquifer sub layer thickness m w wellbore outer diameter m hg dimensionless aquifer sub layer thickness L k horizontal permeability m ky vertical permeability m lani anisotropy index le The layer thickness is measured perpendicularly to the aquifer strata Figure 15 This is also valid for the deviation angle The equation is valid for deviation angles up to 85 This skin is calculated automatically from the penetration angle of the producer and injector that are specified by the user in the DoubletCalc input screen It has a negative sign During the simulation it is added to potential skins resulting from other factors like well damage or stimulation which can be entered by the user directly If impermeable layers occur within the aquifer the layer thickness is the thickness of the permeable sub layer The presence of impermeable l
58. of the heat exchanger This is an external variable specified by the user in the DoubletCalc input screen T he out Z 01002177 mcm eq 22 TNO report TNO 2014 R11396 34 45 7 1 7 2 7 3 Water properties Density The density of water as a function of pressure p salinity s and temperature T is calculated using the equations of Batzle and Wang 1992 Pa 1 10 80T 3 3T 0 00175T 489p 2Tp 0 016T p 1 3 10 T p 0 333p 0 002Tp eq 23 p D s 0 668 0 44s 10 300 p 2400 ps T 80 5T 3300s I3p 47ps eq 24 with pw fresh water density kg m p salt water density kg m p pressure MPa S salt content salinity ppm 1 000 000 or kg kg T temperature C Viscosity The water viscosity is calculated using the correlation given by Batzle and Wang 1992 u 0 1 0 3335 TEUER eq 25 t 1 65 4 91 95 exp 0 42 s 0 17 0 045 T ones with u water viscosity cP S salt content salinity ppm 1 000 000 or kg kg T temperature C Heat capacity The heat capacity c of water depends on temperature salinity and pressure The heat capacity of salt formation water can be approximated using the polynomials used by Grunberg 1970 Despite the fact that this is a relatively old publication it is considered to be reliable because recent publications like Feistel and Marion 2008 refer to Grunberg as a reliable source for h
59. r 32 Water a 34 Bai e T T NE 34 VISCOSILY E 34 pisiigelerie PvE 34 AL COWS du es TTE 35 The effect of penetrating the reservoir obliquely 36 Solution method iiio Eu Er is IE 38 Parameter trange ai 39 Calculated characteristics of the geothermal doublet system 40 Geothermal power sss eene nennen nnns nhan nnns naar nnns nena sare sese nans 40 Required HUMO DOW CN R V P 40 Coefficient of performance COP k uuu ul uum S iu umau aswaa 40 Considerations iin Deco a usuchun u Asus 41 Power gain by density difference between production and injection well 41 Difference between produced and injected flow 41 Viscosity of the injected water r 42 TNO report TNO 2014 R11396 3 45 12 4 Depleted reservoir and negative pressures 42 13 Re IereniereSu MN 44 14 eiii rH 45 Appendices A Example of the base case details file B Sub layers in an aquifer C Explanation of characters and symbols TNO report TNO 2014 R11396 4 45 TNO report TNO 2014 R11396 5 45
60. rt TNO 2014 R11396 42 45 12 3 12 4 Viscosity of the injected water The temperature of the injected water is approximately equal to the temperature of the water at the outlet of the heat exchanger This low temperature has a considerable effect on the viscosity of the injected water For example at a production water temperature of 60 C the viscosity is about 0 63 cP whereas the viscosity of the injected water at 30 C is about 0 94 cP The 50 increase in viscosity results in a pressure drop from injection well to aquifer of that is 50 higher than at the production well The choice of the right temperature for the injected water for calculation of the viscosity is therefore important There are two opposing effects The injection water reheats quickly like described in paragraph 12 2 This reduc es the pressure drop from injection well to aquifer Over time the aquifer rocks surrounding the well will cool down to the tempera ture of the injected water The largest pressure drop will take place around the well Ap In r with r begin the distance to the well This justifies the chosen approximation to use the temperature of the injected water near the bottom of the well for calculating the viscosity Depleted reservoir and negative pressures Negative pressures in the upper part of the production well may be observed in the base case details file and possibly in the result table lower right hand side pressure at h
61. the skin or negative permeabilities and depth values ih Iteration is not converging Please choose other input values Figure11 DoubletCalc error message for an incorrect combination of stochastically drawn parameter values Well segments must reach top aquifer the TVD depth of the last segment specified under Well properties must be at least equal to the value specified as aquifer top under the Aquifer properties Erratic input Please check Well segments must reach top aquifer Figure 12 DoubletCalc error message for an incorrect specification of the well segments Segment length TVD segment length AH the true vertical depth must always be smaller than or equal to the along hole depth TNO report TNO 2014 R11396 17 45 Figure 13 DoubletCalc error message for an incorrect combination of AH and TVD depths Negative pressures if the pump pressure is set too low or if the depth of the pump is chosen very shallow negative pressures may result see paragraph 12 4 A Negative pressure at producer Please change pump pressure pump depth or well configuration ex A Negative pressure at heat exchanger producer injector Please change pump pressure pump depth or well configuration Figure 14 DoubletCalc error messages resulting from negative pressures TNO report TNO 2014 R11396 18 45 3 The DoubletCalc model The objective in the design of
62. this means that at a given pump pressure the flow rate will be higher if the density difference is taken into account The increased power is calculated by the software Difference between produced and injected flow One of the starting points of the calculation is that the average pressure in the aquifer remains constant during production This is the case if the volume of the produced water equals the volume of the injected water However this is not the case The temperature of the water that is being injected into the reservoir is approximately equal to the temperature of the water at the outlet of the heat exchanger The temperature of the produced water is approximately equal to the initial reservoir temperature Therefore the density of the injected water is higher than that of the produced water Because the mass flow is similar in the entire system paragraph 5 2 the volume of the produced water exceeds the volume of the injected water This will result in a decrease of the average reservoir pressure The total effect is negligible because The density difference caused by the temperature difference is only about 196 The injected water is being reheated by the reservoir rock which initially has the temperature defined by the geothermal gradient and the average surface tem perature Only about 20 40 of the volume of the injected water remains at the lower injection temperature Therefore this effect is ignored TNO repo
63. to choose the segment length neither smaller than the length of the shortest tubing segment for this will cause uncertainty nor very small for this will increase the calculation time Equations 9 and 19 are solved simultaneously for each segment using the secant method at given pressure and temperature at the inlet of the well segment This yields pressure and temperature at the outlet of the well segment In this way all segments are calculated subsequently The result of the calculation is an estimate of pressure temperature mass flow and volume flow at each node TNO report TNO 2014 R11396 39 45 10 Parameter range A number of parameters in the DoubletCalc input screen must be specified in terms of 8 minimum median and maximum value chapter 5 Gross thickness and net to gross ratio of the aquifer The range of these parameters can be estimated from the corresponding values in the available wells or maps Aquifer permeability the range the permeability can be estimated from the reservoir average permea bilities of relevant well tests and or petrophysical analyses Depth to top aquifer Only a median value must be specified for the depth DoubletCalc automatically calculates the min and max values by subtracting resp adding 1096 This may seem a large uncertainty for a depth map The reason for having 10 is that the uncertainty in depth is used to take account for the fact that no uncertainty is al lowed for t
64. to the surface system are relatively short in comparison with the underground casing and have a relatively large diameter their resistance is ignored Table 10 The pressure differences in the casing of the production and injection wells are important for the pressure balance Three factors contribute to pressure difference during flow in a tubing gravity friction viscous forces jnertion acceleration forces The latter two result from flow However the inertial forces can be ignored because water is hardly compressible Consequently the pressure development in a pipe is given by the Darcy Weissbach or Fanning equation Beggs and Brill 1985 dp fev _ de gp dl 2D in d eq 9 The first term results from viscous forces the second from gravity with length distance along pipe height of pipe inner diameter of pipe gravitational acceleration 9 80665 m s Q ON lt TNO report TNO 2014 R11396 29 45 5 6 fluid density friction number the section average velocity 40 2 c eq 10 Given common flow rates and inner tubing diameters of doublet systems the flow is probably non laminar flow R gt 5000 see below for the definition of Therefore an adequate approximation of fis Beggs and Brill 1985 p99 lt gt d I H I lt II 2 21 25 f 14 210 a 09 NEC NUT eq 11 with inner tubing roughness amp D inner tubing relative rough
65. tor TNO report TNO 2014 R11396 15 45 BASE CASE RESULTS 4 amome esuiea pumppowerw 202 SSS aquifer pressure at producer bar 255 08 JM aquifer pressure at injector bar OO pressure difference at producer bar 13 78 pressure difference between well face and aquifer in the production well pressure difference at injector bar 25 81 pressure difference between well face and aquifer in the production well aquifer temperature at producer C 89 28 temperature at heat exchanger C 86 51 MERERI pressure at heat exchanger bar 16 35 j w 7 Table 4 Base case details file part 6 base case calculation results as observed in the output screen right hand side column third and fourth blocks from above The values result from a single calculation in which only the median parameter values are used The values in this table result from the example scenario STOCHASTIC RESULTS PO P50 P10 aquifer kH net Dm 32 72 mass flow kg s 57 93 pump volume flow m h 197 00 required pump power kW 358 80 geothermal power MW 11 12 COP kW kW 32 80 4 68 2723 aquifer temperature at producer C 93 64 temperature at heat exchanger C 90 75 Table 5 Base case details file part 7 stochastic results for the doublet calculation as observed in the output screen right hand side column first and second blocks from above The values result from a
66. tto gross C ozs oso oss ufactempeaueCc 70 quifer gross thickness m ses n5 geemalgadenCcm o0 aquifer top at producer m TVD 2559 2505 27560 midaqufertemperstureproducerCO o aquifer top at injector m TVD 22210 2468 27150 initalaquifer pressure at producer bar 00 aquifer water salinity ppm 100000 120000 140000 finial aquifer pressurelatinjector oan 0 0 B Doublet and pump properties value exittemperature heat exchanger C 35 distance wells at aquifer level m 1460 pump system efficiency 0 61 ion pump depth m 500 C Well properties alculation length subdivision m so outer diameter producer inch 6125 outer diameter injector nen 6425 skin producer o niedon LLL 5 a skin due to penetration angle p 0 97 sim duetopenetrationanglei 997 Segment pipe pipe pipe inner pipe Segment pipe pipe pipe inner pipe segment segment diameter p roughness segment segment diameter i roughness i sr 4 I vb p m Basa ub Lu i m oe sof s 12 mul oof of s 12 mua 2678 2505 e005 12 uuua 2005 4 sess 12 EE ee ee ee Br EmI r NEN 1 m 3 EE JC optional 8 45 DoubletCalc 1 4 3 input screen the boxed numbers refer to the text under the casing scheme on

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