SPE Journal
Volume 18,
Number 1,
February 2013,
pp. 57-68
Summary
The hydraulic diffusivity equation that governs the flow of compressible
fluids in porous media is nonlinear. Although the gas-well test analysis by
means of the pseudopressure function has become a standard field practice, the
effect of viscosity and gas-compressibility variation with pressure is often
neglected. Moreover, in field operations, the gas well is submitted to a
variable rate production to determine well/reservoir properties and an
estimation of the absolute open flow (AOF). For slightly compressible fluids,
variable rate can be properly handled by superposition in time. Unfortunately,
superposition cannot be casually justified for gas reservoirs because of its
nonlinear behavior. In this paper, a general solution that properly accounts
for both fluid property behavior and variable rate is presented. The proposed
solution, which is derived from the Green's-function method by recasting the
effect of the viscosity-compressibility product variation as a nonlinear source
term, can handle variable gas rate for several well/reservoir geometries of
practical interest. From the general solution, an analytical expression for
variable-rate tests of a fully penetrating vertical well in an infinite gas
reservoir is derived. This expression is applied to a synthetic data set to
calculate the pressure response for a buildup test in an infinite homogeneous
reservoir. The results compared with a commercial finite-difference numerical
simulator show close agreement for both drawdown and buildup periods. It is
also shown that the dimensionless pseudopressure converges to the slightly
compressible fluid solution for long shut-in times. Thus, during those long
times, Horner analysis and log-log derivative plot can be applied to obtain
good estimation of reservoir parameters, as discussed previously in
literature.
© 2012. Society of Petroleum Engineers
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History
- Original manuscript received:
22 December 2011
- Meeting paper published:
30 October 2011
- Revised manuscript received:
27 August 2012
- Manuscript approved:
31 August 2012
- Published online:
28 December 2012
- Version of record:
27 February 2013
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