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In this work, we incorporated the effects of slippage and adsorption into the transient productivity index to determine the pressure in horizontal wells in the simulation of natural gas reservoirs. We modeled the gas slippage by introducing an apparent permeability, a function of the Knudsen number, while the adsorption is incorporated using the Langmuir isotherm. As for the productivity index, we included the transient effects using one of the classic Peaceman reservoir-coupling models, in which we determine the integral exponential function using a polynomial approximation with a wide range of applications. We studied different production scenarios, and the transient productivity index leads to a mitigation of numerical storage. Besides, we showed that the adsorption, slippage, and the horizontal well influence the natural gas production in reservoirs with low permeability.

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