Conventional rate transient analysis (RTA) is based on the solution of single-phase diffusivity equation, derived from mass balance with an assumption that fluid and rock compressibility are small and constant. The conventional technique also provides accurate practical results for gas and black oil reservoirs in engineering applications because (1) the mass balance is conducted at standard conditions of pressure and temperature, and (2) it is assumed that the gas and oil composition remains the same at standard conditions—thus, the viability of volume balance technique. On the other hand, for reservoirs with highly composition-dependent fluids, the invariance of composition at standard conditions is not accurate. For example, oils produced from liquid-rich shale reservoirs exhibit large variation in produced oil and associated gas composition with production time. In this paper we address these issues and present a compositional model for liquid-rich unconventional reservoirs using an improved compositional volume balance technique. Specifically, we reduce the component flow equations to a single pressure equation using partial molar volumes as weighting factors. This pressure equation is the unique feature of this paper and is used to analyze pressure and rate transient tests (RTA) to determine various flow regimes and reservoir properties in liquid-rich shale reservoirs.
In addition, the model is an excellent tool to forecast long-term production. The diagnostic models we have generated include: (1) a numerical model of flow for a well that has been stimulated by multi-stage hydraulic factures, and (2) an analytical composition-dependent model for the rate transient analysis (RTA) of light oils. The numerical model is a 2-D, three-phase, dual-porosity simulator, which uses compositional volume balance method. The algorithm decouples the hydrocarbon and aqueous phases in the matrix and fracture which reveals the clarity of underlying mass transport concepts and ease of coding.
Because of the explicit nature of the phase saturation calculations, we introduce a molar mass balance correction term to minimize the material balance errors of the computation. Furthermore, we validated our partial molar volume algorithm against published experimental data of Wu and Ehrlich (1973) and with the CMG GEM compositional simulator. Finally, unsteady state permeability measurements of several unconventional shale reservoirs were performed. These measurements show that tighter core with abundant micro and nano fractures exhibit a more stress dependent matrix permeability characteristics.