A rigorous semi-analytical model is developed to study the production rate behavior of wells in gas reservoirs with Forchheimer's non-Darcy flow under constant or varying bottomhole pressure conditions. Rigorous modeling of gas property variation in reservoirs is integrated in this model.
Three dimensionless parameters, normalized gas viscosity and compressibility product, Forchheimer number, and normalized viscosity, are introduced to quantify their effects on non-Darcy flow in the reservoir. The variation of viscosity and compressibility product in the gas reservoir depletion process leads to a smaller production decline rate than that of exponential decline. The parameter b in Arps' decline equation under Darcy flow is defined as the base value, b*, that helps identify the production decline caused by reservoir non-Darcy flow. Under the condition of constant pressure drop the more severe the non-Darcy flow, the larger the Forchheimer number. Generally, non-Darcy results in a smaller production rate, a larger decline rate in the boundary-dominated period, and a longer transition period between these two periods. The viscosity variation enhances non-Darcy flow, which lowers the initial production rate but has very little effect on the production decline rate. A larger production decline rate during the boundary-dominated period may help petroleum engineers identify the non-Darcy flow effect from the production data.
Analyses show that the traditional quadratic equation is a good approximation only if non-Darcy flow is not severe and that for non-Darcy flow in the reservoir, the traditional Fetkovich's type curves may underestimate reservoir permeability, overestimate well skin factor, and misinterpret reservoir drainage area. A method of using the proposed model to identify the non-Darcy flow from production data is presented. Two examples from the literature are analyzed, and good type curve matches and more reliable results are obtained.
Production analysis has been widely used by petroleum engineers to investigate reservoir performance and estimate reservoir parameters. Unlike general production analysis methods for slightly compressible fluids, the production analysis for gas wells has to take into consideration the following two particulars:
Forchheimier's equation, rather than Darcy's law, has been widely accepted to describe the high-velocity flow of gases through porous media;
gas properties are highly pressure-dependent.
These particulars result in a highly non-linear gas flow equation that is difficult to solve analytically. Obtained by modifying the solution to the linear flow equation for slightly compressible fluids, traditional methods used for gas well production analysis may cause relatively large error; some production data cannot even be interpreted. Rigorously accounting for the non-Darcy flow and real-gas PVT behavior, this study provides an accurate semianalytical model for gas well production analysis. Not only can it be used to analyze production data under a constant bottomhole pressure, but it can also be employed to match the whole production history under different wellbore conditions, such as varying bottomhole pressure and skin factor change after well stimulation.
In 1901, Forchheimer (1) found Darcy's law is inadequate to describe high-velocity gas flow in porous media and added an additional pressure drop, which is proportional to the square of the flow velocity, to the pressure drop predicted by Darcy's law in order to account for the discrepancy.
