B-GROWTH Gas bubble growth in decompressing
Contents
1. and Oy The default option Best selects the most time efficient scheme based on the values of p and y shown in Fig 2 Options 1 to 8 force the software to use the corresponding limit cases shown in Fig 2 which are described in Forestier Coste et al 2012 The option Simplified flux uses B Growth User Manual Page 4 the approximation of the advection diffusion equation described in Mancini et al 2015 Finally the option Full uses the generic resolution from Forestier Coste et al 2012 These last two options accept negative decompression rates so as to simulate a compression of the magma 10 10 10 10 107 10 10 107 10 10 v Figure 2 Numerical schemes available in B Growth as a function of the two dimensionless parameters p and Oy See Mancini et al 2015 for the implementation of the Simplified flux scheme and Forestier Coste et al 2012 for the other schemes The third panel Run Parameters allows the user to calculate important additional parameters of the run The Calculate button updates the two dimensionless numbers p ThetaD and ThetaV which characterize the dynamical regime of the run the bubble number density with respect to the total volume BNDtot and the bubble number density with respect to the melt BNDmelt These four quantities are displayed with the numerical scheme in the text box on the left of the Calculat2. in magmas Bulletin of Volcanology Ni H and Zhang Y 2008 H20 diffusion models in rhyolitic melt with new high pressure data Chemical Geology v 250 p 68 78 Whittington A G Hellwig B M Behrens H Joachim B Stechern A and Vetere F 2009 The viscosity of hydrous dacitic liquids implications for the rheology of evolving silicic magmas Bulletin of Volcanology v 71 p 185 199 Zhang Y and Ni H 2010 Diffusion of H C and O components in silicate melts Reviews in Mineralogy amp Geochemistry v 72 p 171 225 B Growth User Manual Page 6 Table 1 Meaning of variable names of the main window and the input output files Symbols in parenthesis are initial values Symbol Main window Input file Output file Variable AnS3 Crpm 3 WaterMass kg Total water mass kg C Cy Melt water conc Co ConcValue MeltWaterContent Meltwaterconcentration EquConc wt Cr Total water concentration D Do way a Diffusivity m s Water diffusivity in melt m s H20 molar mass 2 1 8x103 kg mol Universal gas constant z 8 3144 J mol K Ky Henry constant KHenry Solubility constant Pa Pa Scaled single bubble mass kg M Mo single bubble mass is 4nM 3 N Mesh points for N MeshPointsNb Number of mesh points for melt C r water concentration P BubblePressure MPa Bubble pressure Pa P Po Pressure Po Pi f f Pa Po Final pressure pf AmbientPressure MPa Ambient pressure Pa Decompr rate D
3. 0_out txt and Rhyolite950_out txt files Since the input file Rhyolite850 txt has the Write concentration files option checked running it also produces the output files Rhyolite850_out_c txt and Rhyolite850_out_r txt The batch mode can be tested by clicking on Batch and selecting the BatchRhyolite txt file which will have for effect to generate automatically the 5 output files listed above Be sure to first edit the BatchRhyolite txt file and make sure that the 3 files listed there have the correct absolute path e g C Users My Name B Growth Rhyolite750 txt 4 References Forestier Coste L Mancini S Burgisser A and James F 2012 Numerical resolution of a mono disperse model of bubble growth in magmas Applied Mathematical Modelling v 36 p 5936 5951 Giordano D Romano C Papale P and Dingwell D B 2004 The viscosity of trachytes and comparison with basalts phonolites and rhyolites Chemical Geology v 213 p 49 61 Hess K U and Dingwell D B 1996 Viscosities of hydrous leucogranitic melts A non Arrhenian model American Mineralogist v 81 p 1297 1300 Lensky N G Navon O and Lyakhovsky V 2004 Bubble growth during decompression of magma experimental and theoretical investigation Journal of Volcanology and Geothermal Research v 129 p 7 22 Mancini S Forestier Coste L Burgisser A James F Castro F 2015 An expansion coalescence model to track gas bubble populations
4. B GROWTH Gas bubble growth in decompressing magmas USER MANUAL Alain Burgisser CNRS ISTerre F 73376 Le Bourget du Lac France http isterre fr annuaire pages web du personnel alain burgisser article softwares Version 2015 B Growth User Manual Page 1 1 Introduction This user manual describes the software B Growth which enables the user to calculate the evolution in time of a monodisperse population of gas bubbles in a magma undergoing a constant decompression Among the assumptions made two are particularly important First bubbles have all the same size and are assumed to be growing in place without relative motion due to buoyancy Rigorously this means that the characteristic rise time bubble diameter divided by the Stokes terminal velocity should be much smaller than the decompression time scale For most volcanological purposes this translates into the fact that melt viscosity should not be too low typically gt 102 Pa s The second assumption is that the only volatile considered is water the gaseous form of which is assumed to obey ideal gas law This means that pressure should be kept between atmospheric to 200 MPa The theory and further limitations of B Growth are described in Forestier Coste L Mancini S Burgisser A and James F 2012 Numerical resolution of a monodisperse model of bubble growth in magmas Applied Mathematical Modelling 36 5936 5951 and Mancini S Forestier Coste L Burgisser A
5. James F Castro F 2015 An expansion coalescence model to track gas bubble populations in magmas Bulletin of Volcanology The physical basis of the bubble growth model is explained in the work of Lensky et al 2004 Table 1 at the end of this user manual summarizes the variable symbols following the convention used in Mancini et al 2015 and how they are referred to in the software and in the input output files The source code is implemented in C using CodeLite 7 0 and wxWidgets through the wxCrafter interface embedded in CodeLite A version compiled for Windows 7 and compatible with Windows 8 is available at isterrefr annuaire pages web du personnel alain burgisser article softwares Compilation for other systems Linux Mac can be done by installing CodeLite on the desired system loading the B Growth workspace file and selecting Build Run from the main menu This creates an executable file in the B GrowthWS Release directory 2 User interface description We use here the nomenclature of Mancini et al 2015 whereby a model run tracks the evolution in time f of the bubble radius as a function of the ambient pressure P tilde indicate dimensional variables Variables and their representation in the software are listed in Table 1 n n u The main window Fig 1 is separated into four horizontal panels Initial Values Control Run Parameters and Output Control Run The first panel Initia
6. P PStep DecompressionRate AP Time between PStepValue MPa s Decompression rate Pa s jumps F Distance from bubble center m R Ro Bubble radius RO Radius um Single bubble radius m So Influence zone radius m t Time s Time s ot Max time step DtMin DtMax Dt Time step dimensionless Min time step T Temperature a Porosity a a Max porosity Min porosity x Surface tension Effective viscosity fm fmo Op ThetaD Oy ThetaV Bs Pm Melt density BNDtot BNDmelt Number of records Numerical scheme T ao Alpha AlphaMax AlphaMin Sigma Visc fimo ViscValue Rhom NbRecords ForceRecords Scheme WriteConc Temperature C Porosity vol SurfaceTension N m Viscosity Pas ThetaD ThetaV MeltDensity kg m Temperature K Porosity Surface tension N m Effective magma viscosity Pas Melt viscosity Pas Diffusion parameter Viscous parameter Gas density kg m Melt density kg m Bubble number densities m Number of time steps in output file Numerical resolution method Flag indicating whether the concentration files are recorded B Growth User Manual Page 7
7. anually option Constant value 2 vary as a function of ambient pressure options f P which means that water content is constant from bubble edge to melt shell edge or 3 vary as a function of ambient pressure and distance from bubble edge options f P r In option 2 if the Full numerical scheme is selected the water content for melt viscosity is calculated using the total water content Melt viscosity can be either of rhyolitic Hess and Dingwell 1996 dacitic Whittington et al 2009 or phonolitic Giordano et al 2004 No consistency check is done between the run temperature Initial Values panel and the temperature range over which these relationships are valid The second panel Run Control of the main window regroups variables affecting how a run is executed The simulation stops when either the Final pressure value or the Max porosity value is reached whichever occurs first The run also stops when the Min porosity value is reached which may for instance occur if the melt water concentration is manually set to a value far from equilibrium at the initial ambient pressure see the discussion on initial values in Forestier Coste et al 2012 section 2 2 The number of points for the discretization of the distribution of the melt water concentration Mesh points of C r is set to 50 by default as it ensures relative errors lt 10 3 on R P and a Forestier Coste et a
8. e button Initial values that the user has opted to calculate automatically melt water concentration water diffusivity and effective viscosity are also updated The Calculate button tries to maintain some coherence among the various initial conditions selected such as forcing the numerical scheme on Full or Simplified flux if a negative decompression rate is specified but these cross checks are kept to a minimum e g a run with a negative decompression rate but a final pressure lower than the initial pressure will be executed and presumably stop when the minimum porosity is reached hence leaving the value of the final pressure unused The user is thus the ultimate judge of the physical consistency of the run Note that hitting the Enter key while editing any of the fields of the Initial Values and Run Control panels has the same effect as pressing the Calculate button The Load Input File and Save Input File buttons can be used to respectively read and write a text file that lists all the input and control parameters currently on display The symbols used in the input file are listed in Table 1 see the test file for syntax and the file can be modified using a standard text editor to create series of input files for batch runs see Output Control panel The fourth panel Output Control allows the user to either run a single simulation or a series of simulation in batch mode A sing
9. every step of the ambient pressure C f P which is abbreviated as f P in the software Note that some B Growth User Manual Page 3 numerical schemes see Run Control panel are assuming constant water content throughout the run and will ignore the setting f P r Water diffusivity can be set to 1 a constant value manually option Constant value 2 vary as a function of ambient pressure option f P which means that water content is constant from bubble edge to melt shell edge or 3 vary as a function of ambient pressure and distance from bubble edge option f P r In options 2 and 3 water diffusivity is calculated according to the melt type chosen under Effective viscosity In option 2 if the Full numerical scheme is selected the water content for the diffusivity is calculated using the total water content The relationships by Ni and Zhang 2008 Eq 13 and Zhang and Ni 2010 Eq 19 are used for rhyolite and phonolite respectively In the absence of current data on water diffusion in phonolitic melts but using the observation that melt SiO2 content exerts stronger control on diffusion than alkali content Zhang and Ni 2010 phonolite diffusivity is assumed to be the same as that of a rhyolite If no melt type has been chosen Constant value under Effective viscosity the relationship for rhyolite is assumed The effective viscosity can be set to 1 a constant value m
10. l 2012 The number of time steps recorded in the output file is set under Number of records Time steps vary according to the convergence criteria developed in Forestier Coste et al 2012 except for the Simplified flux numerical scheme which uses the smallest value between Eq 32 and 33 of Forestier Coste et al 2012 but also forces the change in time step from one iteration to the next to vary by a factor lt 2 The user can control this automatic adjustment by specifying minimum and maximum values Min time step and Max time step respectively Note that these values are dimensionless which means that they are bounded between C standard precision 10 15 and 1 They can be converted to dimensional times by multiplying them by P AP This convention was chosen because it allows the user to estimate instantly how many time steps are needed to complete a run e g dt 10 8 means that 108 iterations are needed to reach the final pressure The option Adapt time step to records ensures that the run processes at least the number of time steps under Number of records so as to obtain a complete output file The Numerical scheme option allows the user to select how the system of equations is solved The two dimensionless parameters p and first proposed by Lensky et al 2004 are used to characterize the different dynamical regimes of the equations system _ REAP __ 4 imoAP a DoPo E p2 Po
11. l Values regroups the main physical variables and their initial values The first series of variables are either set to their initial values bubble radius ambient pressure and porosity or are kept constant during the run temperature Henry s constant melt density surface tension and decompression rate The decompression rate can be negative in which case pressure increases until either of the minimum porosity or the final pressure has been reached see Run Control panel Such compression runs are possible only with the Simplified flux and Full numerical schemes The initial melt water concentration can be either set to a constant value manually or set to the equilibrium value at the initial pressure using the solubility law by checking the Equilibrium value option B Growth User Manual Page 2 i5 x INITIAL VALUES Bubble radius um 10 Porosity vol 10 Pressure MPa 100 Melt density kg m3 2400 Temperature C aso Surface tension Nm for Henry constant Pa 1 2 3 44e 6 Decompr rate MPa s ai Melt water conc wt E _ FF Equilibrium value Water diffusivity m2 s Constant value x le 12 F Instant decompression Effective viscosity Pa s constant value le5 FRUN CONTROL Final pressure MPa 0 1 Number of records 1000 Min porosity vol le 5 Min time step 1e 15 1 le 12 Max porosity vol 75 Max time step 1e 15 1 le 2 Mesh points for C
12. le simulation is run by first indicating the name of the output file using the Browse button The symbols used in the tab delimited output file are listed in Table 1 Checking the Write concentration files option will record two additional tab B Growth User Manual Page 5 delimited concentration files with the suffixes _c and _r added to the output file name Each line of these two concentration files correspond to one time step of the output file Each line of the _c file lists N values of melt water concentration C F Each line of the _r file lists N values of distance from the bubble edge f Note that for schemes 1 2 6 and Simplified flux N 1 in these files as Cis constant across the melt shell The Run Simulation button launches the single run and the current iteration number is updated at the bottom of the panel A batch simulation is run by pressing the Batch button and selecting a text file that lists the full path and name of a series of input files that will be read and run sequentially see the test file for syntax Finally the Quit button closes B Growth 3 Test files Three input test files are provided Rhyolite750 txt Rhyolite850 txt and Rhyolite950 txt They can be loaded by using the Load Input File button Fig 1 Clicking successively on Browse to define an output file name and on Run Simulation should give outputs identical to those in the Rhyolite750_out txt Rhyolite85
13. r 50 IV Adapt time step to records Numerical scheme Best x RUN PARAMETERS Pere Calculate Load Input File Save Input File M OUTPUT CONTROL Browse Output Fie F Write concentration file Run Simulation Batch Quit Iterations 0 0 Figure 1 Main window of B Growth The ambient pressure either changes linearly Instant decompression unchecked or instantly changes every time intervals set under Time between jumps Instant decompression checked so that the resulting series on pressure jumps approximates the linear decompression rate set under Decompr rate The pressure jumps option cannot be set for compression runs i e negative decompression rates Melt water content C can be calculated in two ways during a run If the least number of assumptions is made it varies as a function of the distance from the bubble edge 7 R to the edge of the melt shell Thanks to the solubility law it is a function of ambient pressure at the bubble edge and its distribution within the melt shell is controlled by the advection diffusion equation on C f Hence this first case implies that C f f P f which is abbreviated as f P r in the software In the second case water content is assumed constant from bubble edge to melt shell edge which can be calculated using the total water content Mancini et al 2015 Since is this case water concentration is updated at
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