An Explicit Method for Estimating the Average Reservoir Pressure and Gas in Place Based on the Gas Property Polynomial Function

Abstract

The fast and accurate determination of average reservoir pressure (ARP) and gas reserves is vital for the analysis and forecasting of gas well performance. An explicit and relatively rigorous method for estimating the ARP and gas in place, based on the dynamic material balance equation and the gas property polynomial function (GPPF), is presented to circumvent such drawbacks as high cost, empiricism, poor adaptability to variable production schedules, and the necessity for iteration processes, by which current approaches usually have been limited. The gas flow model is solved by introducing pseudofunctions and considering the compressibility effects of rock and irreducible water, and the pressure-rate correlations during boundary-dominated flow (BDF) which constitute the theoretical proofs of this method are derived from the superposition principle coupled with the constant rate solution. Production data under different production scenarios prove it effective. The error of estimation for formation pressure and gas reserves hardly ever goes beyond 4% given that the BDF condition is generally satisfied by the rate and bottom hole flowing pressure (BHP) data. We employ the GPPF to capture the nonlinear variations of gas viscosity and$Z$-factor, helpful to implement a quick conversion between pressure and pseudopressure and to solve the integral equation concerning pseudopressure and thus valid in overcoming the limitations of previous methods concerning pressure or pressure squared. The proposed methodology boasts its simpleness and practicability, which not only dispenses with iterations on pseudotime but also applies to various production systems of gas wells under constant BHP, constant rate, or variable BHP/variable rate conditions.