The equations describing the flow of gas through porous media are non-linear due to the dependence of coefficients on pressure. Several techniques have been applied in the past to deal with the non-linearity. The topic continues to generate research activity, and points to the need for developing more efficient and accurate techniques of handling the non-linearity in the gas equations. Drawing upon the ideas and approaches from the previous studies, a new solution methodology to the non-linear equations governing gas flow is presented in this paper. Whereas the previous studies had access to the non-linear gas solutions (numerical solutions), and could correlate back to the liquid-mode (linear) solutions, we approached the problem differently: to transform the liquid-mode solutions to the unknown and correct solutions of the non-linear equations. The time transformation was completely redefined. New equations were derived to relate the liquid time to the gas time scale. Low-pressure reservoirs were found to require special analytical formulas. The new solution methodology was validated using numerical simulator results.

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