Summary
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.
Introduction
The equation defining the coefficient of isothermal compressibility at
pressures above the bubblepoint pressure is rather simple:
(Equation 1)
However, in application the situation becomes somewhat complex. Usually the
equation is integrated by separating variables:
(Equation 2)
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%.
© 2007. Society of Petroleum Engineers
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History
- Original manuscript received:
1 July 2005
- Meeting paper published:
9 October 2005
- Revised manuscript received:
5 September 2006
- Manuscript approved:
10 October 2006
- Version of record:
20 February 2007
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