Mathematical Modeling of Transitional Fluid Phase Flows in Coal Bed Methane Reservoir

The chapter covers flow mathematics applicable to coal reservoirs. It provides equations and expressions of coefficients. The focus is on the cleat properties and the fluids present in it at each time step. Dewatering of the coal reservoir, followed by the combined flow of gas and water, is mathematically modeled. Gas flow is modeled as a single-phase. The chapter includes all the stages of flow phases, separated by a time interval, and the transitions between them under different reservoir conditions. Both the rock and fluid properties of the cleat, functions of dependent variables, vary at every time step. The cleat permeability and porosity are stress-dependent, indirectly a function of average reservoir pressure. The weakly non-linear, single-phase equation is transformed into the highly non-linear, multiphase equation. Gas compressibility plays an essential role in determining the hyperbolic and parabolic dominance of the equation. The chapter focuses on how linear/non-linear equations are solved. Implicit pressure explicit saturation is a commonly used decoupling method. The explanations are accompanied by plots showing the impact of one-dimensional cleat flow on average reservoir pressure, cleat properties, and fluid saturation.