Applications of the Coefficient of Isothermal Compressibility to Various Reservoir Situations With New Correlations for Each Situation
- John Paul Spivey (Phoenix Reservoir Software) | Peter P. Valko (Texas A&M University) | William D. McCain (Texas A&M University)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- February 2007
- Document Type
- Journal Paper
- 43 - 49
- 2007. Society of Petroleum Engineers
- 5.6.4 Drillstem/Well Testing, 4.1.2 Separation and Treating, 5.3.1 Flow in Porous Media, 4.1.5 Processing Equipment, 4.6 Natural Gas, 5.5 Reservoir Simulation, 5.2.1 Phase Behavior and PVT Measurements, 5.6.3 Pressure Transient Testing, 5.3.2 Multiphase Flow, 5.2 Reservoir Fluid Dynamics
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The coefficient of isothermal compressibility (oil compressibility) is defined as the fractional change of oil volume per unit change in pressure. Though the oil compressibility so defined frequently appears in the partial-differential equations describing fluid flow in porous media, it is rarely used in this form in practical engineering calculations. Instead, oil compressibility is usually assumed to be constant, allowing the defining equation to be integrated over some pressure range of interest. Thus, the oil compressibility in the resulting equations should be regarded as a weighted average value over the pressure range of integration.
The three distinct applications for oil compressibility in reservoir engineering are (1) instantaneous or tangent values from the defining equation, (2) extension of fluid properties from values at the bubblepoint pressure to higher pressures of interest, and (3) material-balance calculations that require values starting at initial reservoir pressure. Each of these three applications requires a different approach to calculating oil compressibility from laboratory data and in developing correlations.
The differences among the values required in these three applications can be as great as 25%. Most published correlations do not indicate the particular application to which the proposed correlation applies.
A correlation equation for oil compressibility has been developed using more than 3,500 lines of data from 369 laboratory studies. This correlation equation gives the average compressibility between the bubblepoint pressure and some higher pressure of interest. Equations to calculate appropriate values of compressibility for the other two applications are presented.
The equation defining the coefficient of isothermal compressibility at pressures above the bubblepoint pressure is rather simple:
However, in application the situation becomes somewhat complex. Usually the equation is integrated by separating variables:
Moving oil compressibility outside the integral sign requires the assumption that it is constant. Because it is not constant, the use of this equation requires a value of oil compressibility that is a pressure-weighted average across the pressure range used in the calculations.
There are three applications for oil compressibility in reservoir engineering:
- The defining equation, for which the oil compressibility should be calculated as a single value at the pressure of interest, often used in pressure-transient analysis.
- The extension of fluid properties from correlations starting at the bubblepoint pressure to pressures above the bubblepoint pressure. This application is also used in black-oil reservoir simulation.
- The use of oil compressibility in black-oil material-balance equations in which the starting point is the initial reservoir pressure.
Values of oil compressibility should be calculated from laboratory data with these applications in mind. Most published correlations for oil compressibility do not indicate the particular situation to which the correlation applies, although values calculated for these three applications can differ significantly. For example, Fig. 1 gives values of oil compressibility calculated with the constant-composition-expansion data from a widely available black-oil laboratory report (Reservoir Fluid Study 1988). Two things are readily apparent. First, coefficients of isothermal compressibility are not constant as pressure changes. Second, the three applications require values that differ by up to 25%.
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