Comparison of Black Oil Tables and EOS Fluid Characterization in Reservoir Simulation

Transcription

1 Comparison of Black Oil Tables and EOS Fluid Characterization in Reservoir Simulation An MSc Thesis by Mihály Gajda Submitted to the Petroleum and Natural Gas Institute of University of Miskolc in partial fulfilment of the requirements for the degree of MASTER OF SCIENCE in Petroleum Engineering Miskolc, 07/05/2014

2 Table of Contents List of Figures Nomenclature iv vi 1. Introduction 1 2. Basic Description of PVT Calculation Models Equation of State Black-Oil Formulation Traditional Black-Oil Formulation Modified Black-Oil Formulation Comparison 5 3. Fluid Samples Used for Comparison Highly Volatile Under Saturated Oil Rich Gas Condensate Near Critical Gas Condensate Saturated Oil 6 4. Development of PVT models EOS Fluid Characterization Check of Sampling Check of Measurements C7+ Characterization EOS Tuning Check of the Results Grouping Modified Black-Oil Tables Methods for Black-Oil Table Creation Whitson-Torp Method Recommendation for Different Fluid Types 23 i

3 Check of Tables Summary for PVT Model Development Description of the Numerical Reservoir Model Grid and Rock Properties Relative Permeability Curves Wells Development Strategy Volatile Oil Fluid Models Development Strategies Results Case 1 (Depletion) Case 2 (Aquifer) Discussion and Conclusion Gas Condensate Fluid Models Development Strategies Results Case 1 (Depletion) Case 2 (Aquifer) Discussion and Conclusion Near Critical Gas Condensate Fluid Models Development Strategies Results Case 1 (Depletion) Case 2 (Aquifer) 40 ii

4 8.4. Discussion and Conclusion Saturated Oil Reservoir Fluid Models Development Strategies Results Case 1 (Depletion) Case 2 (Aquifer) Discussion and Conclusion Summary and Conclusion 46 References 47 Acknowledgement 51 Appendix A 52 Appendix B 53 Appendix C 58 Appendix D 59 Appendix E 60 iii

5 List of Figures Figure 2.1-Schematic of Traditional Black-Oil Formulation... 4 Figure 2.2-Schematic of Modified Black-Oil Formulation... 5 Figure 4.1-Hoffmann Plot for Sample NC... 8 Figure 4.2-Hoffmann plot for the CVD measurement of Sample NC Figure 4.3-Gamma Distribution Fitted on the C7+ fraction of Sample NC Figure 4.4-Relationship Between Molar Mass and Density Figure 4.5-Simulation of CCE without Tuning (Sample NC) Figure 4.6-CCE Liquid Dropout After Matching for Sample NC Figure 4.7-Simulated CCE - Equilibrium Ratios for Sample NC Figure 4.8-CCE - Liquid Dropout - Comparison of the Original and Pseudoized Fluid Characterization for Sample NC Figure 4.9-Schematic of Whitson-Torp Method Figure 4.10-Oil FVF vs Pressure Figure 4.11-Oil Properties vs Pressure Figure 4.12-Gas Properties vs vaporized oil-gas ratio Figure 4.13-Schematic of Black-Oil Table creation for Saturated Oil Reservoirs Figure 4.14-Density of Reservoir Oil and Gas Calculated with EOS and BO Table Figure 4.15-Compressibility of Reservoir Gas and Oil Calculated with BO Tables Figure 5.1-Grid Constructed for the Problem Figure 5.2-Location of Well and Faults Figure 5.3-Oil-Water Relative Permeability Curves Figure 6.1-Simulation Results of Sample VO - Case Figure 6.2- Oil and Gas in Place During Depletion (Sample VO - Case 1) Figure 6.3-Simulation Results of Sample VO - Case Figure 7.1-Simulation Results of Sample GC - Case Figure 7.2-Simulation Results for Sample GC - Case 1 (Zoomed) Figure 7.3-Gas and Oil in Place During the Depletion Figure 7.4-Simulation Results of Sample GC - Case Figure 8.1-Simulation Results for Sample NC - Case Figure 8.2-Free Gas and Liquid Oil in Place (Sample NC - Case 1) Figure 8.3-Simulation results of Sample NC - case 2 (MBO-CVD vs. EOS15) Figure 8.4-Simulation Results of Sample NC - Case 2 (EOS15 vs EOS7) iv

6 Figure 9.1-Simulation Results for Sample VO - Case Figure 9.2-Simulation Results for Sample SO - Case v

7 Nomenclature B g - Gas formation volume factor [m 3 /sm 3 ] B gd - Dry gas formation volume factor [m 3 /sm 3 ] B o - Oil formation volume factor [m 3 /sm 3 ] c g - Gas compressibility (apparent) [1/bar] c o - Oil compressibility (apparent) [1/bar] F gsp - Mol fraction of separator gas [-] K i - Equilibrium ratio [-] k ij - Binary-Interaction-Parameter [-] M - Molar mass [g/mol] p - Pressure [bar] p c - Critical pressure [bar] Q - Gas rate [sm 3 /day] R s - Solution gas-oil ratio [sm 3 /sm 3 ] R sp - Separator gas-oil ratio [sm 3 /sep.m 3 ] r s - vaporised oil-gas ratio [sm 3 /sm 3 ] T - Temperature [ C, F, K, R] T b - Boilingpoint temperature [ C, F, K, R] T c - Critical Temperature [ C, F, K, R] x i - Liquid mole fraction [-] y i - Gas mole fraction [-] Z - Deviation factor [-] γ g - Specific gravity of gas [-] γ STO - Specific gravity of oil [-] ρ g - Gas density [kg/m 3 ] ρ o - Oil density [kg/m 3 ] Ω a - EOS numerical constant [-] Ω b - EOSnumerical constant [-] vi

8 1. Introduction PVT calculations are used to describe the phase behaviour and to determine the thermodynamic properties of hydrocarbon systems at the given pressure and temperature. PVT properties of reservoir fluids are required by the most of petroleum engineering calculations including : reservoir simulation, well testing, pipeline flow calculations and separator design and the accurate prediction of phase behaviour is essential in case of planning some tertiary recovery methods like gas injection or in situ combustion. As this is an input data for the mentioned calculations its accuracy is crucial, wrong PVT properties lead to erroneous calculation results, so the applied calculation method must be chosen carefully. Beside accuracy, simplicity and calculation speed are also important aspects in the selection. Due to technological improvements in the latest decades the calculation speed is not as important as it was, except reservoir simulation where it is still an issue. In the solution of a problem, it is a common practice to select the simplest method that provides the desired accuracy [1], so simplicity can also be a favourable property of a calculation method. The first objective of this thesis is to briefly describe the creation of PVT calculation models, equation of state and black-oil tables used in reservoir simulation. The two calculation models will be compared in respect of accuracy and calculation speed. The main objective of this thesis is to give some advice about which PVT model should be used in case of different fluid types or recovery methods. The EOS fluid characterizations are developed with PETEX PVTp, but black-oil tables are created by hand based on simulation of PVT experiment with PVTp. Eclipse100 and were used for the simulations. All of the figures are created by me with MS Visio, Excell or Eclipse. 1

9 2. Basic Description of PVT Calculation Models In the petroleum industry two approaches are used to calculate the PVT properties of reservoir fluids. The first and the simplest is the black-oil formulation that determines the necessary properties of the fluid based on separation data. The second is equation of state (EOS) which provides both the compositional and the volumetric properties of the reservoir fluid at given conditions based on its overall composition. Both methods have their advantages and disadvantages that have to be taken into consideration in the selection. The methods will be detailed in the next subchapters Equation of State Cubic equation of states provide relationship between pressure, volume and temperature. They accurately describe the volumetric and phase behaviour of pure compounds and mixtures. In addition, EOS gives information about the composition of equilibrium gas and oil which is crucial in the planning of some recovery methods which aim the increase of recovery of more valuable compounds. van der Waals proposed the first cubic equation of state in 1873 [2]. Many EOS's have been created with the modification of this equation since then. Nowadays Peng-Robinson (PR) [3] and Soave-Redlich-Kwong (SRK) [4] are the two most commonly applied EOS's in the petroleum engineering calculations. All of them use an attraction and a repulsion parameter to account the non-ideal behaviour of the fluid. Their common weakness is the poor liquid density prediction, which was eliminated by the introduction of the volume translation parameter [5]. With this modification the PR and SRK EOS's provide satisfactory vapour-liquid equilibrium and liquid density predictions. The EOS's require the critical properties and the acentric factor of the components of reservoir fluid and its overall composition. Two-phase flash calculation with EOS is an iterative process, the calculation time increases as the number of components increases and conditions approach the critical point of the fluid. The main advantages of EOS are: This is the most accurate method that is commonly used to calculate the PVT properties of reservoir fluids. Wide range of phase behaviour problems can be treated with EOS even the most difficult ones like gas injection or multi-phase flash calculation. 2

10 The main disadvantages of the application of EOS are: Significantly increased calculation time compared to other methods. Development of an EOS fluid characterization requires detailed PVT reports that seldom available in case of old fields. Creation and application of EOS fluid characterization need more experience Black-Oil Formulation Black-oil formulation is used to make relationship between surface and reservoir volumes. In traditional black-oil formulation three engineering quantities are introduced for this purpose : solution gas-oil ratio (R S ), oil formation volume factor (B o ) and gas formation volume factor (B g ). In modified black-oil formulation solution oil-gas ratio (R v ) is introduced as the forth property to take vaporized oil into consideration, and gas FVF is defined differently. The basic differences between the two formulations will be discussed in the following subchapters Traditional Black-Oil Formulation The definition of the three basic black-oil properties are: (2.1) (2.2) (2.2) Traditional black-oil formulation has the following assumptions [6]: Reservoir oil consists of two surface "components", stock-tank oil and surface (total separator) gas. Reservoir gas does not yield liquids when brought to the surface. Surface gas released from the reservoir oil has the same properties as the reservoir gas has. Properties of stock-tank oil and surface gas do no change during the depletion of a reservoir. Figure 2.1 depicts the schematic of a traditional black oil formulation. Black-oil properties can be calculated with correlations or tables. Black-oil tables contain the properties of the reservoir fluid in tabular form. Black-oil correlations are simple empirical equations, their predictive capability is often really poor, they have no advantage over a 3

11 well designed black-oil table, therefore they will not be discussed in the following chapters. The proper creation of these tables is the topic of chapter 4. The main advantages of using traditional black oil formulation: Low calculation time and memory requirement. Simple to use and create. The main disadvantages of the method: It cannot describe fluids with complex phase behaviour like gas condensates. It cannot treat recovery methods where vapour-liquid equilibrium is crucial like in gas injection. Reservoir Gas From Reservoir Gas: Surface Gas Equilibrium From Reservoir Oil: Surface Gas Reservoir Oil Surface Oil Figure 2.1-Schematic of Traditional Black-Oil Formulation Despite its drawbacks traditional black-oil formulation can be efficiently applied for less volatile oil, dry gas and any oil reservoirs depleted above its bubble point Modified Black-Oil Formulation Modified black-oil formulation introduces a new forth property, vaporised oil-gas ratio that is defined as [7]: (2.4) The schematic of modified black oil formulation can be seen in Figure 2.2. The modified gas FVF, called as "dry-gas" FVF is defined differently taking liquid dropout into consideration [7]. These modifications greatly improve the accuracy of the method and make it capable to treat volatile oil and gas condensate reservoirs. Several efforts were taken to take the density change of surface gas and oil into consideration [8], but they are rarely available in commercial software's, so they will not be detailed here. Therefore the surface oil and gas 4

12 densities are assumed to be constant during the depletion of the reservoir. In addition, the density of the surface oil is the same whatever it originates from: reservoir gas or reservoir oil and it is also true for the surface gas. Other modifications were also proposed to make this method capable to treat gas injection [9, 10], but it is out of the coverage of this thesis. From Reservoir gas: Surface Gas Reservoir Gas Equilibrium Surface Oil From Reservoir Oil: Surface Gas Reservoir Oil Surface Oil Figure 2.2-Schematic of Modified Black-Oil Formulation 2.3. Comparison EOS is more sophisticated calculation model than black oil formulation. Although the EOS requires more calculation time and memory, it can provide the necessary accuracy in a wide range of circumstances. Black oil tables can be generated from simple separation data, but the best way is that if it is generated with a well tuned EOS characterization. Therefore the creation of an adequate black oil table also requires detailed PVT report, so this does not make difference between them. The most crucial factors are the calculation time and accuracy in the decision. To save computation time, the simpler model - black-oil table - should be chosen if it can provide the desired accuracy. Otherwise EOS must be used regardless of the increased calculation time and memory requirement. 5

13 3. Fluid Samples Used for Comparison Four fluid samples were chosen for the comparison: highly volatile under saturated oil, rich gas condensate, near critical gas condensate and saturated oil. These four samples represent the four most commonly occurring type of fluid systems whose phase transition is significant. This chapter will briefly introduce these samples. The first three samples are real, but the saturated oil sample is synthetically made from the volatile oil sample Highly Volatile Under Saturated Oil The C1 content of this oil sample is %, while its C7+ content is 18.44%, its intermittent content is not significant. The reservoir temperature is 118 C and the reservoir pressure is 610 bars. The bubble point pressure is 379 bars at reservoir temperature. The zero flash GOR of the oil is 416 sm 3 /m 3 and its API gravity is More detailed information can be found in Appendix A (short name of the sample in the followings : Sample VO) Rich Gas Condensate The C1 content of this gas condensate sample is 66.9 %, it has a significant intermittent content, 9.7 % CO 2, and its C7+ content is 9.6%. The reservoir temperature is 191 C and the reservoir pressure is 505 bars. The dewpoint pressure is bars at reservoir temperature. The zero flash GOR of the sample is 1218sm3/m3 and the API gravity of the stock-tank oil is More information can be found in Appendix A (Sample GC) Near Critical Gas Condensate The C1 content of the sample is %, its C7+ content is % and its intermittent content is not significant. The reservoir temperature is 91 C and the reservoir pressure is 534 bars. The Dewpoint pressure of the sample is 467 bars at reservoir temperature. The zero flash GOR of the sample is 776 sm3/m3 and the API gravity of the stock tank oil is More detailed information can be found in Appendix A (Sample NC) Saturated Oil There was not available sample from a saturated oil reservoir, so it is made synthetically by flashing of the volatile oil sample at 300 bars. Therefore the saturation pressure of the oil and gas phase is 300 bars. The received gas phase represents the gas cap and the oil phase represents the oil body. The composition of the phases can be found in Appendix A (Sample SO). 6

14 4. Development of PVT models Both PVT models can provide the necessary accuracy, but only then if they are sufficiently developed. The creation of an accurate PVT table needs a well tuned EOS characterization thus it is better to start with its description. The development of an EOS characterization requires more experience and time. Presently lots of guidelines and case studies are available in the literatures that make our work easier EOS Fluid Characterization Peng-Robinson EOS is chosen for the calculations, because this is the most widely used EOS in the petroleum industry. The main steps of the development of an EOS characterization are the following: 1. Checking the PVT measurement and sampling 2. Characterizing C7+ fraction 3. Tuning of EOS to measurements 4. Checking the result 5. Reducing components These steps are essential to gain reliable EOS characterization. However many practicing engineers omit some of them, but this can lead to inaccurate or inconsistent model Check of Sampling Sampling can be performed in two ways: bottomhole sampling and separator sampling. All the samples were taken from the separator during the well test. Separator sampling means two different samples from the produced liquid and gas, which are recombined later to gain the wellstream fluid. It is highly recommended to check the consistency of the sample and the quality of recombination. The compositions of the samples taken from the separator are always measured. Problems in sampling may occur, therefore it has to be checked to ensure the quality of the samples (it should be done by the laboratory before recombination, although it is not done many times). Thereafter the two samples get recombined based on production data. Sometimes the composition of the wellstream determined only by mathematical recombination of the compositions of the samples. In other cases after the physical recombination the compositions of the received wellstream get measured and it should be checked. 7

15 Log(K p) Hoffmann-Crump-Hocott proposed a method for checking the consistency of the samples [11]. Equation 4.1 is the basic equation of the method, it says that if log(ki*p) values are plotted vs. F i characterization factor (defined by eq. 4.2), the points have to be on a straight line in the case of light components. Ki p A0 A1 Fi log (4.1) 1 T Fi 1 T bi bi 1 T 1 T ci p log p ci sc (4.2) where: A 0, A 1 - parameters of the line Temperature is in K or R. Figure 4.1 depicts the Hoffmann plot for Sample NC, it can be seen that the light components are on the line except C6. This is an anomalous behaviour, but the adequacy of the sampling is still acceptable regardless of this anomaly. In case of the other samples the accuracy is within the error range at all components N2 C1 CO2 C2 C3 C4 C5 C6 C7 C8 C F Characterization Factor Figure 4.1-Hoffmann Plot for Sample NC 8

16 The mathematical recombination of the sample pairs requires their mole fraction that can be determined from the production data. First the measured gas rate must be corrected with the measured gas properties, because assumed properties were used in the measurement of the gas rate. The appropriate formula for this purpose is: Q gc Q g field lab Z Z field lab (4.3) Thereafter the next step is the determination of gas-oil rate related to separator conditions. It can be done in the following way from the production gas-oil ratio: R R Q s cg sp (4.4) Bo Qo Bo The mol fraction of separator gas can be calculated in the knowledge of the separator gas-oil ratio, the density and the average molar mass of separator liquid: F gsp M o Rsp osp 1 (4.5) where units are ρ osp in lbm/ft 3, M osp in g/mol and R sp in scf/bbl. Then everything is given for the mathematical calculation of the overall composition of wellstream by the following equation: z i gsp i Fgsp xi F y 1 (4.6) There is a decent match between the measured and mathematically recombined composition for all samples Check of Measurements The most commonly performed PVT measurements are: separator test, constant composition expansion (CCE), constant volume depletion (CVD) and differential liberation experiment (DLE). With CCE experiment the saturation pressure and the under saturated density of the fluid are measured. The multistage separator test is conducted on an oil sample primarily to provide basis for converting differential-liberation data from a residual-oil basis to a stock-tank oil basis. CVD is intended to simulate the depletion of gas/gas condensate reservoir and provide the desired volumetric and compositional information that can be used to tune the EOS fluid characterization. As the quality of the EOS characterization strongly depends on this sample, therefore it is recommended to check it. The DLE has a similar purpose, but for oil reservoirs. Its adequacy should also be checked, but the PVT reports seldom publish the data which would be necessary for the 9

17 log(k p) check. The short summary of the most important measurements can be found in Appendix B. Whitson and Torp published an appropriate method for the check of CVD measurements [12]. It is basically a material balance written up for every component. During the CVD experiment the composition of the removed gas is measured. With the help of this method the composition of the liquid, which is dropped out in the PVT cell, can be calculated and in the knowledge of that it is easy to determine the equilibrium ratios. Thereafter the Hoffmann plot [11] can be used to check the received results. Figure 4.2 depicts the results for Sample NC C6+ C5 C4 C3 N 2 CO C2 2 C F Characterization Factor 425 bar 375 bar 325 bar 275 bar 225 bar 175 bar 125 bar 75 bar Figure 4.2-Hoffmann plot for the CVD measurement of Sample NC The equilibrium ratios must decrease as the F characterization factor decreases and values of a pressure step must be on a straight line. In this case these criterions are not satisfied at the four highest pressure steps and the C6 differs from normal behaviour at every pressure step. It seems in Figure 4.2, that C6+ components have higher equilibrium ratio than C5's and C4's, and they seem to be on a different straight line than lighter components. This is physically unrealistic behaviour resulting from measurements error. The removed gas is separated into "produced" gas and liquid, their composition is measured and recombined mathematically to gain the composition of the removed gas. The fact is that C6+ components are on a different straight line indicating that perhaps the 10

18 mathematical recombination was wrong, which may comes from the incorrect measurement of liquid properties. Therefore these properties should not be used for the tuning of the EOS fluid characterization of Sample NC, except liquid dropout and the liquid density, because these are not affected by this error. Other measurements have found to be correct C7+ Characterization EOS calculation needs the critical properties, acentric factor and binary-interaction parameters (BIP) of the components, therefore they must be determined in case of component of the reservoir fluid. The light components and their properties are well known, the C7+ components deviate from them in many aspect that is why they treated differently. However the mole fraction of the C7+ fraction is low, it still has a great impact on phase behaviour [13]. Accordingly, the proper description of this fraction is crucial. After C6, the number of isomers starts to increase rapidly; these isomers can be paraffinic, naphthenic or aromatic with completely different properties. The whole C7+ fraction contains thousands of different compounds, the identification of all of these compounds is impossible, for this reason the measured composition is just an assumption. The other problem is that the critical properties of the compounds heavier than C20 are not known. Therefore this fraction must be approximated somehow; this procedure is the C7+ characterization. Both mathematical and empirical methods are used for this purpose. The characterization can be grouped into three main tasks [14]: Dividing the C7+ fraction into a number of fractions with known molar compositions. Defining the molecular weight, specific gravity, and boiling point of each fraction. Estimating the critical properties, the acentric factor of each fraction and the key BIP's for the specific EOS being used. The composition of a reservoir fluid can be determined with true boiling point distillation (TBP) or gas chromatography (GC). GC can determine the composition up to C35-C40, meanwhile the limit is only C15-C20 for TBP distillation, but it determines also the molar mass, density and boiling points of fractions. The other significant difference between them, that the TBP distillation is more expensive and takes more time than GC. In case of Sample VO both measurements were performed, the composition of Sample GC was measured with GC, while the composition of Sample NC was determined with TBP distillation. 11

19 Before the creation of C7+ sample, something must be cleared up. All of the compounds with similar boiling points are grouped into single carbon number fractions (SCN), therefore C8 means not only n-c8, but the mixture of compounds with boiling point similar to n-c8 [15]. Grouping based on molar mass leads to inadequate characterization. The molar mass of SCN fractions cannot be measured by GC, but Katz and Firoozobadi published a table [16], which contains the average properties of the SCN fractions and can be used for estimation. When the composition is only determined up to C15 or so, it has to be extrapolated to ~C35. The best solution for the problem is to fit a distribution function on the C7+ fraction, and then with the help of this function the molar mass and molar fraction of the heavier components can be determined. The most recommended is the gamma distribution because of its flexibility [17]. Three parameters of the distribution function used for the fitting are: the smallest molar mass (η), the average molar mass of the C7+ fraction (M C7+ ) and α, shape factor. Figure 4.3 depicts the measured and the extrapolated composition of the C7+ fraction of Sample NC. Measured composition is represented by red squares, blue squares represent the values calculated by gamma distribution, and green triangles represent the composition measured on another sample from the same reservoir. The values calculated by gamma distribution show a decent match with the composition measured on another sample, which proves the potency of gamma distribution. Figure 4.3-Gamma Distribution Fitted on the C7+ fraction of Sample NC 12

20 After the composition is determined up to C35+, the SCN fractions have to be grouped into pseudo components. Usually from two to seven pseudo components are required to describe appropriately the phase behaviour of the fluid. Whitson published an empirical rule that can be used to determine the number of required components and the molar mass boundaries used to organise pseudo components [17]. Six pseudo components were formed for all the three samples, because more complex phase behaviour requires more pseudo components to describe. Thereafter the densities of fractions have to be determined; hence a function is needed to relate density to molar mass. Equation 4.7 is a flexible formula published by Søreide that can be fitted to distillation densities [18]. i f i c a C M b (4.7) where a, b, c and C f are the parameters of the function. (standard values: a=0.2855, b=66, C=0.13 and C f is between 0.27 and 0.31) Figure 4.4-Relationship Between Molar Mass and Density For Sample NC the measured densities, the fitted correlation and its parameters can be seen in Figure 4.4. The fitted function accurately approximates the measured values, therefore it is sufficient to determine the densities of the pseudo components. For Sample GC, there was no distillation data, so standard values are used, and stock-tank density is matched by adjusting C f parameter. 13

21 Liquid Dropout [%] There are many correlations in the literature that can be used to determine the boiling point temperature from density and molar mass. Søreides correlation [18] is the most recommended [19, 20] therefore it was used for all the three samples. The formula is the following: T bi exp M i i M i i M i i (4.8) where T bi is in R. The other required properties can easily be calculated in the knowledge of molar mass, density and boiling point temperature. Twu's correlation was used for critical properties [21], Edmister's correlation for acentric factor [22], and Chue-Prausnitz's formula for BIP's [23]. The pseudo-component properties of Sample NC (for example) can be found in Appendix C. Now the EOS fluid characterization is ready for the calculations EOS Tuning Mostly even if the C7+ fraction is characterized appropriately, the predictions of the EOS are inaccurate. The 10 % error in saturation pressure is usual, as well as 5% error in density and several percent in mole fraction of key components. It can also happen, that the EOS predicts bubblepoint as saturation condition instead of dewpoint or vice versa, this problem can be seen in Figure 4.5 at Sample NC. This problem often occurs in case of near critical fluid Measured Calculated Pressure [bar] Figure 4.5-Simulation of CCE without Tuning (Sample NC) 14

22 The two main sources of prediction error are: assumptions of EOS and the uncertainty in C7+ properties. Therefore, to receive accurate and reliable predictions the EOS fluid characterization has to be matched to the measured data. The three main phase of the tuning process: Comparison of calculated and measured data Matching measured data in several ways Evaluation and choosing the best resulting model Someone may think that it is meaningless to put so much energy into C7+ characterization, because the C7+ properties will be adjusted. It can be stated after many attempts to match EOS to measurements, that if the C7+ characterization is inadequate, the desired accuracy cannot be reached or only with a thermodynamically inconsistent model. The matching is done by adjusting different properties of the fluid components. It can be done with "trial and error" or regression. Trial and error is time consuming and tiring [14], therefore it is seldom used nowadays. The tuning methods that use non-linear regression are fast and automatic, but the result can be unrealistic, so they have to be used carefully [24]. The regression based methods can be categorized into three groups [25]: 1. Modification of Ω a, Ω b numerical constants and BIP's. 2. Modification of critical properties and BIP's. 3. Modification of the inspection properties of C7+ fraction(molar mass, density, boiling point or even molar distribution) and BIP's. The method published by Coats and Smart can be classified into the first group [26]. It changes the Ω a and Ω b numerical constant of methane and the heaviest fraction and BIP between them. The method is really simple and efficient, it is recommended to choose if someone does not have too much experience in fluid characterization. The phase behaviour of a system is really sensitive for these parameters, so the search for optimal values is an easier mathematical problem than in the other two cases. There are lots of publications dealing with the second part including guidelines and case studies [14, 27]. Therefore it is well documented and with a little bit more experience it yields more accurate models than group one. These methods basically assume that the basic properties of the C7+(molar mass, density and boiling point) are accurate, and the error comes from the uncertainty of the critical property correlations. The method may yields unrealistic results, so the checking after regression is crucial for this method. The third group is the most novel, only some recently proposed method can be classified into this one [19,20]. It can be interpreted as the method suppose that the 15

23 Liquid Dropout [%] correlations calculating critical properties are accurate and the error comes from the erroneous inspection properties of the C7+ fraction. It means that the regression recharacterize the whole C7+ fraction in every iteration step. Although these methods require the most experience, there is much lower chance for receiving unrealistic results. In spite of these, methods are "superior" compared to the other two groups; they are still not available in commercial software's. The measurements were matched by adjusting critical pressure and temperature of C7+ components and BIP's between them and the methane. The results are evaluated in the next subchapter. The modified critical properties of Sample NC can be found in Appendix C Check of the Results After the EOS fluid characterization is matched to the measured data, its predictions are greatly improved compared to its original accuracy. Figure 4.6 shows the liquid dropout of the CCE experiment for Sample NC, as it can be seen that EOS predictions are almost perfect after matching. After the matching the other parameters were also predicted with the same accuracy for all samples Measured Original After Matching Pressure [bar] Figure 4.6-CCE Liquid Dropout After Matching for Sample NC To accept a fluid model, that is not enough to inspect only its accuracy, but also its thermodynamic consistency should be checked. As a result of regression, the model is physically unrealistic many times, even though it satisfies the problem mathematically. Therefore the check of thermodynamic consistency is necessary. 16

24 Thermodynamic consistency desires the increase of critical temperature and the decrease of critical pressure as the molar mass increases. When other parameters are also changed like BIP's and numerical constants, the check is not so simple. Whitson published a method, which is sufficient for this purpose[19]. A CCE experiment has to be simulated with the matched EOS fluid characterization and the equilibrium ratios have to be plotted in the function of pressure. The plot has to fulfil two criterions: The equilibrium ratios have to monotonically decrease as the molar mass increases The equilibrium ratio line must not cross each other (mostly caused by alternating BIP's) Figure 4.7-Simulated CCE - Equilibrium Ratios for Sample NC Figure 2.1 shows the mentioned plot for Sample NC, the fluid characterization satisfy every expectation, therefore it is thermodynamically consistent. The other two tuned EOS fluid characterization also fulfil these criterions Grouping However, the technology has improved a lot in the previous decades, the computation time and memory are still crucial issues in case of reservoir simulation. Flash calculations have to be performed in every block during every time step, this means many million times. The number of components is the main factor that affects the calculation time (and can be changed). On the other hand, the number of components also has a significant effect on accuracy; therefore the reduction of components has to be done carefully. 17

25 The accurate simulation of some recovery methods requires more components, while others require less; there is no general rule for it. To reduce the number of components, two or more of them are grouped into pseudo components. The grouping has to be based on volatility [15]. Generally the N 2 can be lumped with C1, and CO 2 with C2, if the intermittent content is not too high. The n-c4 can always be grouped with i-c4 and also n- C5 with i-c5. Thereafter the grouping should be made by "trial and error" and step by step followed by regression. That means one component grouped with another component or group, and if the accuracy is deteriorated considerably, the component should be grouped with other component or should not be grouped at all. After every step of grouping matching with regression is suggested [14, 27]. The second task is to determine the properties of newly grouped pseudo components. Mixing rules are used for this purpose. The most simple is Kay's mixing rule [28], which is given by equation 4.9, it is basically a mole-fraction average. The molar mass of the components should always be calculated by this rule. z i i ii I (4.9) zi ii where θ=any property and I is the index for pseudo components. The specific gravity of the pseudo components should always be determined with equation 4.10 that assumes ideal solution mixing. The generalized mixing rule for BIP's is given by equation i i ii I (4.10) zi M i i ii ii jj z M k z z k (4.11) IJ i j ij The critical properties can also be calculated with Kay's mixing rule. Some authors suggest weight-fraction average [29], whereas others suggest the mix of weight- and molar-fraction average [30]. Lee-Kesler proposed different mixing rules for every property, that needed by EOS or viscosity calculation [31] and it has many advantages over the simple mixing rules. Based on personal experience[25] and the recommendations of some authors[14] the method published Coats [32] gives the best solution for the problem. The approach is simple and accurate; it tries to eliminate the error caused by pseudoization. The method forces the pseudoized fluid characterization to reproduce the volumetric 18

26 behaviour of the original fluid characterization in undersaturated condition, this is succeeded by the determination of Ω ai and Ω bi with equation 4.12 and For the calculation of other critical properties and accentric factor any method can be used. ai ii ji z z a a i j i j 1 k ij 2 2 R TcI pci I ii z i 2 (4.12) bi ii zibi ii z R TcI pci I i (4.13) Coats' method and Kay's mixing rule were used to determine the properties of the pseudo component. The number of components was reduced from to 7 at each samples, the further decrease of components seriously deteriorated the accuracy. The accuracy of the pseudoized fluid characterization of Sample NC can be seen in Figure 4.8. The properties of the pseudo-components can be found in Appendix D (for Sample NC). Figure 4.8-CCE - Liquid Dropout - Comparison of the Original and Pseudoized Fluid Characterization for Sample NC 4.2. Modified Black-Oil Tables The creation of a modified black-oil table requires a matched EOS fluid characterization. Thereafter the table is made by the simulation of a depletion experiment. The kind of depletion experiment depends on the type of the fluid and depletion process desired to simulate. Firstly, the general process of creation and then the differences for 19

27 each reservoir fluid type will be detailed. The check of tables are also recommended [33], because a black-oil table may contain inconsistencies that cause non-physical behaviour in reservoir simulation Methods for Black-Oil Table Creation The biggest advantage of black-oil tables is the low calculation time, whereas their accuracy is satisfying. Since that they are still the topic of research nowadays. The earliest methods used for creating black-oil tables did not take vaporized oil-gas ratio into consideration. Therefore their predictions were erroneous for volatile oils and gas condensates. They are not recommended for this reason. The first breakthrough was the method published by Whitson and Torp [11]. They suggest the simulation of a depletion type experiment with EOS fluid characterization. At every depletion stage, the equilibrium gas and oil are passed through a separator train to determine the black-oil properties. Constant stock-tank gravities are considered during the whole depletion, the reservoir densities can be calculated with equation 4.14 and As consequence the reservoir densities are wrong and don't satisfy the mass balance, which is the biggest drawback of their method [32] o STO R B g 350 g B o gd STO g r S S (4.14) (4.15) Coats claims that the R s and B o calculated by the Whitson-Torp method lack the physical meaning [32]. He proposed a method similar to Whitson-Torp method, but R s, B o and B gd are rather determined by mass balance than flashing. The method provide correct reservoir oil and gas density. Goldthorpe and Drohm suggest the correction of MBO properties with surface densities[34]. As a result of this, it also yields correct reservoir densities and satisfies the mass balance. Recently Whitson et all published a new approach for the problem [33]. The saturated fluid is passed through a separator train to get surface gravities, then the R s and r s are determined with the desired simulation experiment. Thereafter an EOS fluid characterization is developed with two components: surface oil and gas. It is used to calculate reservoir fluid densities. Finally equation 4.14 and 4.15 are rearranged to provide B o and B gd. 20

28 Most of the mentioned methods are not implemented in commercial PVT software's, for this reason the method published by Whitson and Torp will be detailed and applied to create the black-oil tables Whitson-Torp Method The method was already introduced briefly. The schematic of the method can be seen in Figure 4.9. The applied separator train must be identical with the one used at the field. The saturated R s, r s, B o, B g, η o and η g are determined by this approach. Saturation Pressure Stage 1 Stage 2 Stage 3 Figure 4.9-Schematic of Whitson-Torp Method It can happen that the pressure increases in the reservoir because of water injection for example. In this case the saturated fluid becomes undersaturated due to pressure increase, so variable saturation pressure model is needed. Therefore R s becomes the primary independent variable. For oils R s vs pressure relationship determines that fluid is saturated or not at specified R s and pressure. Figure 4.10 depicts schematically the B o vs pressure relationship calculated for oil phase. At point A the oil is saturated, as the pressure decreases to point B the oil remains saturated and its R s will decrease. As the pressure starts to increase due to water injection, the oil becomes undersaturated and its FVF will decrease on B-C path to point B and while its R s stays unchanged. If the pressure decreases again, first the oil FVF will increase to Point B, the oil will be saturated again and while its R s remains unchanged. If the pressure decreases further, the oil FVF will decrease to point D and its R s will also decrease. 21

29 R s1 A Bo D B C R s2 R s3 Pressure P b3 P b2 P b1 =original Figure 4.10-Oil FVF vs Pressure Figure 4.11 plots schematically the other two oil properties in the function of pressure. RS Viscosity R s3 R s2 R s1 Pressure Pressure Figure 4.11-Oil Properties vs Pressure The gas properties depicted in Figure The problem for gas phase is similar, but the function is not single-valued between dewpoint pressure and vaporised oil-gas ratio. This means that vaporised-gas oil ratio does not identify the condition of the gas phase certainly. Therefore pressure is the primary independent variable and the properties plotted in the function of vaporised gas oil ratio. 22

30 PDEW Bgd p 4 p 3 p 2 p 1 r s Viscosity p 3 p 2 p 1 r s r s Figure 4.12-Gas Properties vs vaporized oil-gas ratio Different depletion experiment(s) is/are required for every fluid type to create accurate an black-oil table, therefore in the following subchapter every fluid type will be detailed with respect to the suggested depletion experiment. The black-oil table created for Sample GC (CVD) can be found in Appendix E Recommendation for Different Fluid Types Undersaturated Oil Reservoirs Usually two depletion-type experiments are performed on oil samples: constant composition expansion (CCE) and differential liberation expansion (DLE). CCE is a flash experiment, meanwhile DLE is a differential one, which mean the overall composition in the PVT cell is changing during the experiment. Both methods can be used to create PVT tables for undersaturated oil reservoirs. Whitson et al. suggest the CCE experiment for this purpose [35]. In this thesis the tables were created by simulating a CCE experiment. Gas Condensates Also two depletion-type experiments can be performed on gas condensate samples: CCE and constant volume depletion (CVD). CVD is a differential experiment, performed 23

31 on gas samples. Whitson et al. recommend the use of CCE for gas condensates [35], in this thesis the two possible way of creation of black-oil tables will be compared. Saturated Oil Reservoir In Saturated oil reservoirs there are two phases initially at reservoir: gas cap and oil body. The general recovery strategy for these reservoirs that first the oil body is depleted with or without pressure maintenance, then the gas cap is depleted. Whitson et al. suggest two different experiments for the two phases as it can be seen in Figure 4.13 [35]. The properties of reservoir gas are determined with CVD experiment, while the properties of the reservoir oil are determined with DLE. This recommended method was used to create black-oil tables for Sample SO (Saturated Oil Reservoir Sample). Reservoir Gas Gas Oil Water Dewpoint Reservoir Oil Bubblepoint P 1 =Saturation Pressure P 2 P 3 Figure 4.13-Schematic of Black-Oil Table creation for Saturated Oil Reservoirs Check of Tables Erroneous PVT tables can even be created with consistent EOS fluid characterization or measurements. The two most significant properties that can be wrong are fluid densities and compressibility's. Both calculated from other properties and even if those properties 24

32 are adequate, the calculated properties can be inaccurate. The source of the error can be different and sometimes cannot be perfectly eliminated. The error in density originates from the assumption that the specific gravity of stocktank oil and gas are constant during the depletion. Figure 4.14 illustrates the problem in case of Sample VO. The error varies with the pressure, for reservoir gas the maximum error is 4.5% at bubblepoint, for reservoir oil the maximum error is 2% at low pressure. Whitson suggests the adjustment of surface densities to gain accurate reservoir densities[35]. With the application of this method the maximum error in reservoir densities is reduced below 1%. If the error is still unacceptable in a particular case, then other PVT method should be chosen. Figure 4.14-Density of Reservoir Oil and Gas Calculated with EOS and BO Table The compressibility's (apparent) can be determined with the following formulas [33]: c c o g 1 B o 1 B gd dbo dp db dp gd Bgd rs Bo dr s 1 r R dp s s (4.16) Bo Rs Bgd dr s 1 rs Rs dp (4.17) Figure 4.15 depicts the calculated compressibility values for Sample VO. The basic blackoil properties were calculated at every 25 bar from 450 to 50 bars, plus at bubblepoint. Negative oil compressibility can occur near the bubblepoint, this can be avoided by including additional data close to saturation pressure. In this case the saturation pressure is 379 bars and the closest point at 375 bars, which is quite close; therefore there was no need for additional pressure point. The discontinuities are caused by the change in derivates at 25

33 pressure nodes. As the difference between derivates increases the magnitude of discontinuity also increases. The discontinuity influences the performance and stability of simulation. The discontinuity can be reduced by including more pressure nodes in the saturated region. Figure 4.15-Compressibility of Reservoir Gas and Oil Calculated with BO Tables After the check is performed on the created black-oil tables they are ready to be used in simulation. Some other consistency checks are also recommended, but those are trivial or important only for tables generated to simulate gas injection [33] Summary for PVT Model Development The two most important PVT calculation models were reviewed in this chapter. Both models rely on PVT measurements preformed on reservoir fluid samples, this implies the importance of the quality check of sampling and measurements. The methods used for the creation of PVT models have to be chosen carefully in order to receive accurate and consistent model. The consistency of each PVT model has to be checked as well, otherwise it can lead to unexpected errors in simulation, material balance or pipe flow calculations. Different tasks in reservoir engineering desire different PVT calculation methods. Simulation of gas injection requires sophisticated and accurate PVT model. History matching can be tiring and time consuming, where fast calculation models are favourable. Memory requirements can also be a limiting factor in the simulation of huge fields. Therefore there is no superior calculation method. For every particular case the appropriate PVT model has to be chosen based on comparison. 26

34 5. Description of the Numerical Reservoir Model A static reservoir model is artificially created for the comparison. The reservoir can be found in an anticline structure, the grid generated for the reservoir can be seen in Figure 5.1. The reservoir rock is siliciclastic with single porosity and permeability. The top of the reservoir is at -2800m, while the water-oil/gas contact is at -2900m. The reservoir is 2000 m long and 1500 m wide. Five wells were created for the depletion of the reservoir. Further details will be described in the following subchapters. Figure 5.1-Grid Constructed for the Problem 5.1. Grid and Rock Properties Block centred grid is used for the problem; it consists of cells with 50*50*5 dimension (the height of the cells is slightly varying). Grid refinement was applied around the wells. The reservoir model consists of two different layers. Two sealing faults are also defined in the model; their position can be seen in Figure 5.2. The reservoir rock is consolidated sandstone, rock properties defined as the most common values specific for this rock type (at the boundary of medium and good reservoir rock.). The porosity is 21% in the top layer and 19% in the bottom layer. The net-gross ratio varies from 0.75 to Horizontal permeability changes between 120 and 80 md, while vertical permeability changes between 50 and 30 md. Hall correlation was used to 27

35 take compaction into consideration [36]. The permeability curve will be described in the next subchapter. The capillary pressure was neglected in the absence of measurements. The cells found under -2900m are saturated with water. In some cases, a Carter-Tracy aquifer model [37] is assigned to the reservoir with the following parameters : 3000 external radius, 40 md permeability, 0.2 porosity and 50 m thickness. Figure 5.2-Location of Well and Faults 5.2. Relative Permeability Curves The Corey formula was used to describe the permeability curves [38]. The characteristic points of the curves were taken from the literature [39]. The connate water saturation is 30%, the residual gas saturation is 20% and the residual oil saturation is 25%, critical gas saturation is 5%. The end-point of oil and gas is 0.7, while the end-point of water is