Production rate and cumulative production models for advanced decline curve analysis of gas reservoirs

Production rate and cumulative production data from gas reservoirs are routinely analyzed using dimensionless "type curves", which are plots of numerical, analytical, or sometimes empirical solutions to the gas diffusivity equation. These solutions are theoretically developed by coupling the boundary-dominated flow equation with the gas material balance equation. Due to the mathematical difficulty of this process, past efforts have focused on approximate models based on simplifying assumptions. Two basic limitations of these models are: (1) The use of approximate linearization schemes (i.e., the zero-order and first-order polynomial models) for correlating the non-linear viscosity-compressibility term, and (2) Assumption of zero or constant bottomhole pressure production.;This work aims to eliminate these restrictive assumptions by proposing semi-analytical solutions developed from the rigorous equations underlying production rate-time analysis models. Pseudopressure and pseudotime functions are also avoided in this work because knowledge of average reservoir pressure is required for computing pseudotime which makes the procedure iterative.;We examine several linearization schemes (zero-order, first-order and general polynomial functions, as well as exponential function) for modeling the non-linear terms. Simulation studies conducted using different gas systems show that the general polynomial function is applicable to all gas reservoirs.;More importantly, this work demonstrates that a third-order polynomial function is adequate for linearizing the gas flow equation during reservoir depletion. Simultaneous solution of the linearized flow and gas material balance equations yields a first-order ordinary differential equation in terms of cumulative production and time. This formulation can be used for variable bottomhole pressure data analysis since bottomhole pressure is isolated explicitly.;The rate and cumulative production models are derived in terms of dimensionless variables to facilitate development of both analytical and graphical solutions (type curves). Closed form predictive equations for cases of constant bottomhole pressure production using the approximate exponential function are presented--these expressions are accurate only for high pressure gas reservoirs. Numerical solutions are also presented for the general polynomial model.;Comparison of the new solutions with Carter type curves shows excellent agreement between the rate responses. Finally, we can estimate reservoir parameters (original-gas-in-place and permeability) by applying these new solutions to field data.