311UDC 622.276 A NEW APPROACH CALCULATE OIL-GAS RATIO FOR GAS CONDENSATE AND VOLATILE OIL RESERVOIRS USING GENETIC PROGRAMMING K.A. Fattah Petroleum and Natural Gas Engineering Department, College of Engineering, King Saud university, P.O. 800, Riyadh 11421, Saudi Arabia e-mail:
[email protected] Abstract. In this work, we develop a new approach to calculate oil-gas ratio (Rv) by matching PVT experimental data with an equation of state (EoS) model in a commercial simu lator (Eclipse simulator) using genetic programming algorithm of commercial software (Discipulus). More than 3000 data values of Rv obtained from PVT laboratory analysis of eight gas condensate and five volatile oil fluid samples; selected under a wide range of composition, condensate yield, reservoir temperature and pressure, were used in this study. The hit-rate (R2) of the new approach was 0.9646 and the fitness variance for it was 0.00025 and the maximum absolute error was 7.73 %. This new approach was validated using the generalized material balance equation calculated with data generated from a compositional reservoir simulator (Eclipse simulator). The new approach depends only on readily available parameters in the field and can have wide applications when representative lab reports are not available. Keywords: oil-gas ratio, PVT lab report, gas condensate, volatile oil, modified black oil simulation, genetic program Introduction The Modified Black Oil (MBO) simulation approach (also called Extended Black-Oil) was introduced by Spivak and Dixon (1973). These MBO simulations approach consider three components (dry gas, oil, and water). The main difference between the conventional black-oil simulation and the MBO simulation lies in the treatment of the liquid in the gas phase. The PVT functions for modified black oil (MBO) simulation and material balance calculations of gas condensate and volatile oil are: oilgas ratio, Rv; solution gas-oil ratio, Rs; oil formation volume factor, Bo; and gas formation volume factor, Bg. The MBO approach assumes that stock-tank liquid component can exist in both liquid and gas phases under reservoir conditions. It also assumes that the liquid content of the gas phase can be defined as a sole function of pressure called vaporized oil-gas ratio, Rv. This function is similar to the solution gas-oil ratio, Rs, normally used to describe the amount of gas-in-solution in the liquid phase. Whitson and Torp (1983) developed a procedure to calculate MBO properties from laboratory constant volume depletion (CVD) data of gas condensate. Coats (1985) developed a different procedure for gas condensate fluids by using EOS PVT program and a regression package to match laboratory PVT data. McVay (1994) _____________________________________________________________________________ © Electronic scientific journal “Oil and Gas Business”, 2012, № 1 http://www.ogbus.ru/eng/ Genetic programming Genetic algorithms.ru/eng/ . Genetic programming creates computer programs as solution whereas genetic algorithm creates a string of numbers to represent the solution. These given data that provided to Discipulus program were classified into three data types: "training data. 1998). is a computer program. № 1 http://www. Discipulus created mo- _____________________________________________________________________________ © Electronic scientific journal “Oil and Gas Business”. Genetic programming is based on the Darwinian principle of reproduction and survival of the fittest and analogs of naturally occurring genetic operations such as crossover and mutation (Koza.312 extended Coats procedure for volatile oil fluids. Due to their reported robustness in practical applications. (2006) showed that both Whitson and Torp. Rv approach using genetic program The Discipulus software. a commercial Genetic Programming system. Walsh and Towler (1995) also presented a simple method to calculate MBO PVT properties from the CVD experiment data of Gas Condensate reservoir fluids. Fattah et al. Discipulus output. Fevang et al. Create a new offspring population of computer programs by copying the best programs and creating new ones by mutation and crossover. The main difference between genetic programming and genetic algorithm is the representation of the solution. these techniques are gaining popularity and have been used in a wide range of problem domain. Designation of the best computer program in the generation." "validation data" and "testing data". Generate an initial population of random compositions of the functions and terminals (input) of the problem 2. Execute each program in the population and assign a fitness value. 4. From them. evolution strategies and genetic programming belong to the class of probabilistic search procedures known as Evolutionary Algorithms that use computational models of natural evolutionary processes to develop computer-based problem solving systems. 2012. Fattah et al. and Coats procedures provide excellent match with compositional simulation results when PVT experimental data are matched with an EoS model and then used to output the MBO PVT properties. Genetic programming uses four steps to solve a problem (Koza. was used to generate the new Rv approach. 1992): 1. (2009) also presented new correlations to develop MBO PVT properties of gas condensate and volatile oil when fluid samples are not available. Solutions are obtained using operations that simulate the evolution of individual structures through mechanism of reproductive variation and fitness based selection.ogbus. from data given to it. These data files contained matched inputs and outputs data for Rv. 3. (2000) presented guidelines to help engineers choose between MBO and compositional approaches. The samples were obtained from reservoirs representing different locations and depth. Fluid Samples Fattah (2005) presented PVT experiments for thirteen reservoir fluid samples [eight gas condensates. – Condensate Yield. № 1 http://www. The procedure suggested by Coats and Smart (1986) to match the laboratory results was followed.313 dels that allow us to predict outputs from similar inputs. lb/cu ft. psi. PVTi module of Eclipse was used to generate our database of Rv data. bbl/mm scf . and were selected to cover a wide range of oil and gas fluid characteristics. VO 5. lb/cu ft. (VO)]. psi. – Gas density at standard conditions. and Bg). CVD. C. The MBO PVT properties include the four functions required for MBO simulation are (Rv.ru/eng/ . The C code of the genetic program to calculate the new oil-gas-ratio Rv is given in the appendix. For consistency. Then the developed EoS model for each sample was used to output MBO PVT properties at different separator conditions using Whitson and Torp (1983) procedure. Our database of Rv data consists of 1850 points from 8 different gas condensate samples and 1180 points from 5 volatile oil samples. – Saturation reservoir pressure. Table 1 presents a description of the major properties of these thirteen fluid samples. After uploading the data files into the Discipulus and start the run.ogbus. DL. _____________________________________________________________________________ © Electronic scientific journal “Oil and Gas Business”. GC 1. Rs. Some samples represent near critical fluids (VO 2. 2012. (GC). and five volatile oils. an EoS model that matches the experimental results of all available PVT laboratory experiments (CCE. – Reservoir temperature. The input data for our new approach are: – Reservoir pressure. These PVT data were used in this study. – Oil density at standard conditions. and GC 2) as explained by McCain and Bridges (1994). the program give different types of results that show how the run in progress improved its fitness and performance. R. and separator tests) was derived. The models were created as computer programs in Java. The output data form it is oil-gas-ratio Rv. all EoS models were developed using Peng and Robinson (1976) EoS with volume shift correction (3-parameter EoS) (Fattah (2005)). Bo. Approach For every sample in Table 1. or assembler program. 14 66.75 0.59 8.6 5210 GC 2 286 NA 4278 NA 5410 GC 3 238 6000 NA NA 4815 GC 4 256 7000 4697 46.74 0.37 0.47 4.73 10.06 0.36 0.33 0.83 1. Characteristics of fluid samples Property Reservoir Temperature ( F) Initial Reservoir Pressure (psig) Initial Producing Gas-Oil ratio (SCF/STB) Stock Oil gravity (o API) Saturation Pressure (psig) Components CO2 N2 C1 C2 C3 iC4 nC4 iC5 nC5 C6 C7+ 2.10 1.34 0 72.93 8.07 65.97 0 1.22 5.85 1.4 0.14 1.37 0.52 1.ru/eng/ .72 6.16 69.83 8.50 1.69 1.79 0.48 6.1 9074 GC 1 312 14216 3413 45.94 0.62 63.57 2.314 Table 1.47 0.25 8.38 14.93 0.1 0.35 6.96 16.92 0.11 55.7 5.84 5.69 0.5 4527 VO 2 246 5055 2000 51.01 1.22 1.45 0.97 1.99 0.52 0.41 15.44 2.52 4.54 2.84 1.87 1.52 14.02 2.79 0.91 1.70 66.96 7.88 1.7 0.01 0.36 2.87 0.11 68.18 0.85 1.2 0.73 1.79 0.31 56.38 12.68 0.88 2.22 0.00 1.31 81.69 0.84 6.82 1.39 ____________________________________________________________________________________________________________________________________ © Electronic scientific journal “Oil and Gas Business”.96 12.79 6.91 2.36 1.81 0.37 3.56 6.03 1.35 2.62 1.94 9.23 5.00 0.12 0 2.72 14.21 4.ogbus.18 1.92 4.7 5465 GC 7 300 5985 6500 45.66 0.64 1.33 0.15 2.67 1.14 0. № 1 http://www.63 5.5 4000 GC 6 312 14216 8280 50.65 0.76 0.69 4.24 7.17 1.48 0.97 19.67 60.98 3.2 4821 VO 3 260 5270 2032 NA 4987 VO 4 190 NA 2424 36.66 0.89 1.85 2.73 9.74 4.02 11.93 3.13 61.5 6010 GC 5 186 5728 5987 58.37 1.98 1.8 7437 VO 5 197 13668 2416 34.2 0.06 11.17 59.1 8.84 0.8 o VO 1 249 NA 1991 45.6 5800 GC 8 233 17335 6665 43 11475 Composition (Mole %) 2.84 1.51 7. 2012.66 0.34 1.21 5.90 1. 9646 and the fitness variance for the new approach was 0. Eo. The reported error values prove the validity of the new approach. for a gas condensate sample (GC 1). 8 shows a plot of F versus the expansion term. (2009) correlation and the new approach. For simplicity. 9 is a similar plot F versus the expansion term. Eg. From this validation. 5 . i.1%. both reservoir simulation and material balance calculations were used to validate the new approach.ru/eng/ . The slope of the line passing through the calculated points gives the original fluid in place volume.0208. The plot shows that the slope of the line is 1. extracted Rv data from lab reports were statistically compared in this study with results predicted using Fattah et al.08%.4 show the match between the extracted Rv data and the predicted Rv data from the new genetic program.00025.999 which is equivalent to error in the oil in place calculation of approximately 0. The generalized material balance equation as an equation of a straight-line suggested by Walsh (1995) and Walsh et al. Fig. Fig. (1994) was used to validate the new Rv approach (for both gas condensate and volatile oil samples). Also. In addition to cross-plots to see how the new approach values compared to the values obtained from the PVT lab reports. _____________________________________________________________________________ © Electronic scientific journal “Oil and Gas Business”. The error percent in fluid in place calculations were calculated for most of the fluid samples in our database. the maximum absolute error was 7.1%. These values were compared to original hydrocarbon in place values obtained from compositional reservoir simulation for a tank model Fattah (2005). The general material balance calculations using the PVT properties (Rs. 2012. № 1 http://www. Figs.e. Figs.7 present cross-plots to see how the Fattah et al (2009) correlation and the new Rv approach values compared to the Rv values obtained from lab reports. 2 . the original fluid in place was normalized to 1. as suggested by Walsh procedure. Bo. The hit-rate (R2) of the new approach was 0. The results indicate that the new approach almost completely matches the extracted Rv data. The plot shows a line slope of 0. and reported the error percentages in Table 2. six case study (two volatile oil and four gas condensate). 1 shows the fitness of the genetic program with time.ogbus. The application of these correlations is of particular importance especially when representative fluid samples are not available. The new approach presented in this work can be used with other set of correlations to generate MBO PVT properties without the need for fluid samples or elaborate procedure for EoS calculations.0 BSTB for oil cases and 1 Bscf for gas cases. and Bg extracted from lab reports and Rv from the new approach) were used to calculate original hydrocarbon in place.73 % and the minimum absolute error was 0. the error in gas in place calculation is approximately 2. for a volatile oil sample (VO 1).315 Results and Discussion Fig. ru/eng/ . 1.ogbus. The best program fitness improvement with time Fig. 2. № 1 http://www. 2012. The extracted VS calculated Rv data for training data from genetic program _____________________________________________________________________________ © Electronic scientific journal “Oil and Gas Business”.316 Fig. The extracted VS calculated Rv data for applied data from genetic program _____________________________________________________________________________ © Electronic scientific journal “Oil and Gas Business”. 4. 2012.317 Fig.ru/eng/ . The extracted VS calculated Rv data for validation data from genetic program Fig. № 1 http://www. 3.ogbus. ru/eng/ . correlation) vs. 2012. № 1 http://www. correlation) vs.ogbus. 6. RV (driven from the EOS model) for volatile oil samples _____________________________________________________________________________ © Electronic scientific journal “Oil and Gas Business”. Cross-plot for RV (Fattah et al. 5. Cross-plot for RV (Fattah et al. RV (driven from the EOS model) for gas condensate samples Fig.318 Fig. 7.319 Fig. Cross-plot for RV (new approach) vs. 8. RV (driven from the EOS Model) for gas condensate and volatile oil samples Fig. № 1 http://www. Material balance as straight line calculations for a gas condensate sample (GC 1) _____________________________________________________________________________ © Electronic scientific journal “Oil and Gas Business”.ru/eng/ .ogbus. 2012. 0445 1.08 7.11 _____________________________________________________________________________ © Electronic scientific journal “Oil and Gas Business”.9689 Error (%) 0.1 4. Material balance as straight line calculations for a volatile oil sample (VO 1).45 2. Error in fluid in place calculation from generalized material balance calculations using the new Rv Approach Fluid Sample VO 1 VO 2 GC 1 GC 2 GC 3 GC 4 Original Fluid In Place 0.0563 0.320 Fig.ogbus. Table 2. 9.9227 1.73 5. 2012.0208 0.999 1. № 1 http://www.ru/eng/ .63 3. № 1 http://www.H. Coats K. 5.321 Conclusions 1. 6.D. 1870 .A. 7.H. a commercial Genetic Programming system. pp. Jr.299. Fattah K. 277 .ogbus. _____________________________________________________________________________ © Electronic scientific journal “Oil and Gas Business”. Simulation of Gas Condensate Reservoir Performance. Guidelines for Choosing Compositional and Black-Oil Models for Volatile Oil and Gas-Condensate Reservoirs // SPE Paper 63087 presented at the 2000 SPE Annual Technical Conference and Exhibition.2118/11197-PA 2. Volatile Oils and Retrograde Gases-What’s the Difference? Petroleum Engineer International. Oct. 2000. 2005). gas condensate PVT properties. Application of a Regression-Based EOS PVT Program to Laboratory Data. 2006. pp. El-Banbi A. Sayyouh M. From this validation. Coats K. and Bridges B. Fevang O. 35 .00025. and Whitson C..H.73 % and the minimum absolute error was 0. Acknowledgement The author expresses his thanks and appreciation to the Research Center at King Saud University..H. ECLIPSE suite of programs (Schlumberger. 2. 35 . Smart G. Fattah K. Jan 1994. pp. Sayyouh M.H.T.. 3. Thesis. 2009. Cairo University. was used to develop the new approach based on the concept of genetic algorithm. DOI 10.A. 4. Egypt 2005.2118/10512-PA 3. Ph. TX. Volume 37. Study Compares PVT Calculation Methods for Non Black Oil Fluids. the maximum absolute error was 7. Volume 107.9646 and the fitness variance for the new approach was 0. Issue 12. 1986. Dallas. Volume 104. pp. Number 3. References 1. New Rv approach was presented for oil-gas ratio of gas condensates and volatile oils. The new approach was validated using the generalized material balance equation calculations with data generated from a compositional reservoir simulator (Eclipse simulator) using six case study (two volatile oil and four gas condensate).1886. Singh K.. McCain W. 2012. 1985...39. Oil & Gas Journal.. College of Engineering for supporting this research.ru/eng/ . Volatile Oil and Gas Condensate Fluid Behavior for Material Balance Calculations and Reservoir Simulation. Journal of Petroleum Technology. Issue 20. Volume 1. El-Banbi A. DOI 10. DOI 10.1 %. Number 10.H. SPE Reservoir Engineering.. The hit-rate (R2) of the new approach was 0. 1-4.2118/63087-MS 8. Fattah K. The Discipulus software.D.36. Oil & Gas Journal.H. New correlations calculate volatile oil.A. 1992. Encyclopedia of Computer Science and Technology. 1976. #define TRUNC(x)(((x)>=0) ? floor(x) : ceil(x)) #define C_FPREM (_finite(f[0]/f[1]) ? f[0]-(TRUNC(f[0]/f[1])*f[1]) : f[0]/f[1]) #define C_F2XM1 (((fabs(f[0])<=1) && (!_isnan(f[0]))) ? (pow(2.Y. Number 3.64.322 9.B. Journal of Canadian Petroleum Technology. Robinson D. 29 . March 16-18. long double tmp = 0. A.63. DOI 10. Industrial and Engineering Chemistry: Fundamentals. Midland TX. 610 . TX 1994. pp.P. DOI: 10.43. Genetic Programming.. DOI 10. SPE Paper 27684 presented at the 1994 SPE Permian Basin Oil and Gas recovery Conference. 2012..F. Generation of PVT Properties For Modified Black-Oil Simulation of Volatile Oil and Gas Condensate Reservoirs. Thesis. Ph. 83 .ogbus. pp. DOI 10. Volume 39. Cambridge. Towler B. 819 p. Peng D.. Evaluating Constant-Volume Depletion Data. DOI 10. 1995. 59 .P. July 31. Whitson C. Appendix This appendix gives the c code of the genetic program to calculate the new oil-gas ratio. 17. Journal of Petroleum Technology. 14. _____________________________________________________________________________ © Electronic scientific journal “Oil and Gas Business”. pp. 1973. Method Computes PVT Properties for Gas Condensate. Texas A&M University. Raghavan R.2118/95-01-07 15. 10. Torp S. A Generalized Approach to Reservoir Material Balance calculations. Koza John R.ru/eng/ ..2118/10067-PA 16. Number 1. The MIT Press. pp. Jan.H. The New Generalized Material Balance As an equation of a Straight-Line: Part 1 . № 1 http://www. Koza John R..1021/i160057a011 11.P. 1994. McVay.f[0])-1) : ((! _finite(f[0]) && !_isnan(f[0]) && (f[0]<0)) ? -1 : f[0])) float DiscipulusCFunction(float v[]) { long double f[8]. Volume 35. D. 10-12. MA.620. 55 .86.. 1983. Spivak A. 1998. Volume 15.2118/27684-MS 13. OGJ.B. A New Two-Constant Equation of State. Walsh M. Volume 34. Genetic Programming: On the Programming of Computers by Means of Natural Selection.N. Dixon. T.2118/4271-MS 12. Walsh M. Houston.Application to undersaturated and Volumetric Reservoirs. Ansah J. pp. 1995.D. Simulation of Gas Condensate Reservoirs // SPE Paper 4271 presented at the 3rd Numerical Simulation of Reservoir Performance Symposium. int cflag = 0. Walsh M. 987620830535889f. 2012. f[0]*=pow(2. f[0]/=-0.09100413322448731f. f[0]+=f[2]. f[0]-=v[0]. L0: L1: L2: L3: L4: L5: L6: L7: L8: L9: L10: L11: L12: L13: L14: L15: L16: L17: L18: L19: L20: L21: L22: L23: L24: L25: f[0]-=v[4].TRUNC(f[1])). f[0]+=v[5]. f[0]*=1. f[0]*=0. f[0]*=f[0]. f[0]*=f[2]. f[0]*=1. f[0]*=-0. f[0]/=v[2]. f[2]-=f[0]. f[2]-=f[0]. № 1 http://www. } // This program was evolved with Discipulus(tm).ru/eng/ . f[0]-=f[2]. f[0]/=0.002621650695800781f.987620830535889f.ogbus. f[0]*=f[1]. f[0]*=f[1].03275442123413086f. if (!_finite(f[0])) f[0]=0.7790718078613281f. return f[0]. f[0]/=0. f[0]+=f[0]. f[0]-=f[1]. f[0]+=v[5]. f[0]+=v[5]. _____________________________________________________________________________ © Electronic scientific journal “Oil and Gas Business”.323 f[0]=f[1]=f[2]=f[3]=f[4]=f[5]=f[6]=f[7]=0.9486191272735596f. f[1]+=f[0].