Many coalbed methane reservoirs and Devonian shale reservoirs are naturally fractured with part of the gas adsorbed in the low permeability matrix. The adsorption mechanism is controlled by reservoir pressure; during the depletion of the reservoirs, the adsorbed gas in the matrix is released as free gas flowing from the matrix to the fractures and then to the w'ellbore. In addition, these reservoirs are frequent layered. This paper presents an approximate analytical model for modeling commingled (multilayer) gas reservoir with sorption effects. Our work shows that this model can be developed based on an analytical model developed for slightly compressible liquid commingled systems. To take into account the nonlinearity of the total gas reservoir system, each layer has to be treated as a nonlinear system individually and combine all the individual single-layer solutions with the boundary condition at the wellbore. For this reason, we applied pseudopressure and pseudotime concepts in each layer. The pseudotime definitions take into account the nonlinearity coursed by both the pressure-dependent gas properties and the sorption effects in each layer, both of which we assume to be controlled by average pressure within the layer. We used a numerical simulator to verify our model. The results show that our model agrees well with the numerical simulator.

You can access this article if you purchase or spend a download.