Reservoir Fluids Model for a Middle Eastern Sandstone Reservoir

Knowledge of the properties of reservoir fluids are very important in petroleum reservoir engineering (e.g. estimation of reserves in an oil reservoir, well test inflow performance calculations, and numerical reservoir simulation). The process of obtaining accurate values for these physical properties for hydrocarbon is most important in different oil industries. The main resource to get these properties is laboratory measurements but in many cases these measurements not available, thus other methods can be used to estimate these properties. This paper concerns with the prediction of the phase behavior and physical properties for a Middle Eastern sandstone reservoir by using multiphase equilibrium and properties determination program. Soave-Redlich-Kwong Equation of State & Peng-Robinson’s Equation of State and its modifications have been used to calculate the physical properties of reservoir fluid. To do so, each laboratory experiment was first simulated with the cubic Peng Robinson EOS without performing any regression and compared to the laboratory observations (PVT) as primarily results. Then splitting and lumping processes were used to tune or characterize the EOS so that it can reproduce the PVT experiments. The calculated PVT properties from these two steps are compared with the measured PVT data and the results show that the splitting and lumping processes given a good accuracy in predicting the PVT properties of the sandstone reservoir.

the behavior of these fluids is a laboratory PVT analysis; however, the evaluation of exploratory wells and the advanced design of equipment often require an estimate of the fluid behavior prior to obtaining a representative reservoir sample. Also, experimental data is often unavailable in reservoirs which do not warrant the cost of an in-depth fluid study.
Reservoir engineering techniques are applied to improve the understanding of the reservoir performance and fluid properties. The process includes the calibration of an EOS to describe the phase behavior of the reservoir fluid; input data tables for PVT fluid properties and rock-saturation dependent properties such as relative permeability; the initialization of the simulation model to assess the volume of the original hydrocarbon in place; and the history match to test the validity of the simulation model and prepare the model to predict future reservoir performance. The above equation depends on two major assumptions: • The volume of the gas molecules is insignificant compared to both the volume of the container and distance between the molecules.
• There are no attractive or repulsive forces between the molecules or the walls of the container.
Van der Waals (1873) (2) attempted to eliminate these two assumptions in developing an empirical equation of state for real gases. The attempt to eliminate the first assumption, van der Waals pointed out that the gas molecules occupy a significant fraction of the volume at higher pressures and proposed that the volume of the molecules, denoted by the parameter b, be subtracted from the actual molar volume, V, in above equation, which will be giving: Where the parameter (b) is known as the co-volume and considered to reflect the volume of molecules. The variable (V) represents the actual volume in (ft 3 per1mole) of gas. To eliminate the second assumption, van der Waals subtracted a corrective term, denoted by (a/V 2 ) from this equation to account for the attractive forces between molecules. In a mathematical form, van der Waals proposed the following expression: Many attempts have been made to develop an equation of state for the real fluids.
Where (A0, B0, a, b and c) are empirical constants defined for each pure gas.

PVT model
In this paper, WinProp simulator, the multiphase equilibrium and properties determination program (7) , has been WinProp include recombination of separator oil and gas, compressibility measurements, constant composition expansion, differential liberation, separator test and constant volume depletion.
WinProp can be used to analyze the phase behavior of reservoir gas and oil systems, and to generate component properties for CMG's compositional simulator GEM. WinProp contains a graphical interface which allow to prepare data, run the phase property calculation engine, view the output with an editor, and create plots with Excel.

Fluid Properties and Equation-of-State Characterization
The crude of the selected sandstone reservoir is a light oil with a stock tank gravity of 30.5°API and an initial An essential part of a compositional reservoir simulation of a miscible EOR method is the prediction of the complex phase equilibria during EOR processes. The objective of the fluid study was to tune an EOS that would reproduce the observed fluid behavior and production characteristics seen in field operations and to predict the CO2, natural gas/oil phase behavior in the compositional simulation. Cubic EOS have found widespread acceptance as tools that permit the convenient and flexible calculation of the phase behavior of reservoir fluids. They facilitate calculations of the complex behavior associated with rich condensates, volatile oils and gas injection processes (8) .
In this paper many equations of state have been tested such as Peng Robinson, Soave-redlich-kwong and its modification to obtain the best match for PVT properties. However, the Peng Robinson EOS was chosen to generate the EOS model because it gives the best agreement for measurement data and bubble point pressure for the selected reservoir. The viscosity model considered to match the oil viscosity of the reservoir fluid was the Pedersen Corresponding States model, which is a predictive model for gas or liquid viscosity.
In this paper, PVT laboratory sample data of the sandstone formation has been used in the tuning of the EOS.
These data includes differential liberation (DL) experiments and constant composition-expansion (CCE). Table   (2 ) lists the experiments and the measured parameters imported to the developed PVT model.

Constant Composition Expansion
Relative volumes, saturation pressure, oil Density, oil compressibility and oil viscosity Differential Liberation GOR, relative oil volume, gas Z factor, oil SG, gas SG, gas FVF

Preliminary Results by the Basic EOS.
Each laboratory experiment was first simulated with the cubic Peng Robinson EOS without performing any regression and compared to the laboratory observations (PVT). The preliminary results after the simulation were good, demonstrating that the behavior of the fluid was being reproduced with a basic (not yet tuned) EOS; however, some experiments were not fully matched. This was a clear indication that the parameters of the EOS should be adjusted in order to reproduce the behavior of the reservoir fluid. The statistical accuracy between measured and preliminary results of Constant composition Expansion and Differential Liberation data are shown in Tables (3) and (4) respectively. Figures (1) and (2) show the preliminary match of the experiments by the basic EOS.

Final PVT model with Splitting and Lumping Processes
Splitting and lumping processes were used to tune or characterize the EOS so that it is able to reproduce the PVT experiments. This was a multistep process that started by the splitting the heavy component as proposed by Whitson (10) . Whitson's method uses a six-parameter (2 stage-exponential) to characterize the molar distribution (mole fraction/molecular weight relation) and physical properties of petroleum fractions such as hexanes-plus (C6+). This method is used to enhance the EOS predictions. In this study several methods to splitting of C6+ have been tried such as seven, nine and ten pseudo component to achieve good match between measured and calculated data, but it has been found splitting of C6+ into the six pseudo components gave accurate match  between the data. The heavy component (C6+) was split into six pseudo components based on its relative mole fraction. The pseudo components were identified as (C6-C9), (C10-C12), (C13-C16), (C17-C20), (C21-C24) and C25+. Table (5) shows the new components after splitting. By splitting the heavy component (C6+), the total number of components of the reservoir fluid had increased from 10 to 15 components. This 15-component mixture was used to tune the EOS by regressions to match the observations. Several regressions were carried out during the process of tuning the EOS. The first regression was performed on all the experiments against the critical pressure of the pseudo components, C6+(C6 to C25). The results provided very good predictions with little error when compared against PVT data.
In general, the regression parameters were basically the C6+ (C6 to C25+) pseudo components critical pressure (Pc), critical temperature (Tc), a centric factor (ω) and binary interaction coefficients (δ). The shift parameters of the C6+(C6 to C25+) pseudo components were also regressed together, so that changes within the C6+ fraction were consistent.
After a satisfactory match of all the experimental data, the next step was to group the 15-component EOS into a reduced pseudo component EOS acceptable for a compositional simulation. Doing this reduction minimized the computational time constraint and the numerical complexity of the reserviorcomositional simulation.
The lumping process consisted of forming new pseudo components from existing components. Then regressions were performed to fine-tune the newly formed pseudo component EOS properties. This process was repeated a number of times to select the best grouping at each stage in the pseudoization process.
Since various combinations of grouped components are possible, the criteria for grouping were selecting components with similar properties and molecular weight and having as few components as necessary to match the PVT experiments.
The regression parameters to tune the EOS were the critical properties of the newly formed pseudocomponents. After performing these regressions, the PVT properties of the 6-component EOS model matched the 15-component EOS model almost exactly. From the 11-component EOS model, another grouping was conducted. The C6+ pseudo components, C6+ (C6 to C25+), were grouped into a single fraction (C6+). With this grouping a 6-component EOS model was obtained. The 6 component EOS model contained the following components: (CO2); (N2, C1); (C2, C3); (i-C4,n-C4); (C5-C6), and (C6+). Table (6) shows the new components and their mole fractions after lumping process. Regression was performed again, and the 6-component EOS model predicted PVT properties very similar to the 11-component EOS model. This EOS was accepted for use in reservoir compositional simulation. Table (7) summarizes the best regression parameters of EOS for the sandstone reservoir fluid after splitting and lamping processes. The statistical accuracy between measured and final results of Constant Composition Expansion and Differential Liberation data are shown in Tables (8) and (9)     In addition, the developed model shows a great accuracy for estimation bubble point pressure for the tested sandstone reservoir. The predicted bubble point pressure by the simulator after regression analysis is also compared with the measured one. Table (10) shows acceptable agreement between the estimated and measured bubble point pressure with absolute relative error (0.03%) compared with absolute relative error of 7.46% for the before regression estimation.

Phase Behavior Diagram
The other main purpose of this work is to predict the behavior of the reservoir fluid at different conditions of pressure and temperature. The effect of the two reservoir parameters (pressure and temperature) with the behavior reservoir fluid is performed using phase behavior diagram interpretations. This behavior is represented by developing the (P-T) diagram for reservoir fluid that provides the state of the reservoir fluid at any pressure and temperature which is of great importance for the analysis of many future reservoir processes.
For X-Y phase envelopes, the variable to be used on the X-axis (independent variable) and the Y-axis (dependent variable) must be selected. The choices are temperature and composition for the X-axis and Pressure or temperature for the Y-axis. For a Pressure-Temperature (P-T) diagram one should select temperature as the independent variable and pressure as the dependent variable. Figure (3) shows the P-T diagram for sandstone reservoir fluid predicted by the developed PVT model.