Reduced-Dimension Profile Inversion for Material Balance Analysis of Water-Drive Gas Reservoirs

Trade-offs between gas expansion and delayed aquifer support complicate the joint estimation of original gas in place (OGIP) and aquifer response parameters in water-drive gas reservoirs. Here, we combine response time parameterization and analytical aquifer-state propagation under piecewise linear pressure histories with the established variable-projection principle. The OGIP and aquifer capacitance are estimated using bounded conditional linear least squares, leaving a one-dimensional nonlinear search over the response time. Synthetic tests are used to recover prescribed parameters and characterize sensitivity to pressure errors and sampling density, while approximate 95% profile likelihood confidence intervals quantify parameter uncertainty under a specified withdrawal error model. In the synthetic pressure-thinning test, retaining 60% of the noninitial pressure observations gives a response time error of −2.06% when the OGIP and aquifer capacitance are fixed. Applied to approximately 20 years of field history, the method yields an OGIP estimate 0.67% above the operator-provided reference value and a normalized root mean square error of 0.009375. The field profiles reveal compensating parameter adjustments and branches governed by active bounds. The formulation supports joint evaluation of gas volume and aquifer dynamics while making parameter compensation and the role of physical constraints explicit.