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 wellbore. 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.
Coal bed methane reservoirs and Devonian shale reservoirs arc considered important unconventional sources of gas. These reservoirs differ from conventional gas reservoirs in that a large part of gas is adsorbed in the low permeability matrix with the sorption mechanism controlled by pressure. As the reservoirs are depleted, the gas adsorbed in the matrix is gradually released as free gas flowing from matrix to fractures and then to the well bore. Fig. 1 is a plot of adsorbed methane content versus pressure for two isotherms. These isotherms are considered typical or average isotherms for a black shale and a gray shale, respectively, in the area of Pike County, Kentucky. When pressure is below a certain value, the adsorbed gas may account for as high as 50 to 60% of the total gas stored. Therefore, the adsorbed gas will play an important role in long term production. Production forecasts without desorption effects could be for too pessimistic.
Some coalbed methane reservoirs and most Devonian shale reservoirs have low mobil water content. Some of them are properly considered as multilayer, naturally fractured reservoirs. The objective of this paper is to develop an approximate analytical model for modeling multilayer, naturally fractured reservoirs with single-phase gas flow, taking account of sorption effects.