Pore sizes are typically on the order of nanometers for many shale and tight rock oil reservoirs. Such small pores can affect the phase behavior of in situ oil and gas owing to large capillary pressure. Current simulation practice is to alter the unconfined black-oil data for a fixed mean pore size to generate confined black-oil data with a depressed bubble-point pressure. This approach ignores compositional effects on interfacial tension and the impact of pore-size distribution (PSD) with variable phase saturations on capillary pressure and phase behavior.
In this paper, we develop a compositionally-extended black-oil model where we solve the compositional equations (gas, oil, and water components) directly so that black-oil data are a function of gas content in the oleic phase and gas-oil capillary pressure. The principle unknowns in the variable bubble-point fully-implicit formulation are oil pressure, overall gas composition, and water saturation. Flash calculations in the model are noniterative and are based on K-values calculated explicitly from the black-oil data. The advantage of solving the black-oil model using the compositional equations is to increase robustness of the simulations owing to a variable bubble-point pressure that is a function of two parameters; gas content and capillary pressure. Leverett J-functions measured for the Bakken reservoir are used to establish the effective pore size-Pc-saturation relationship, where the effective pore size depends on gas saturation. The input fluid data to the simulator, e.g. interfacial tension (IFT), phase densities and viscosities, are pre-calculated as functions of pressure from the Peng-Robinson equation of state (PREOS) for three fixed pore sizes. During the simulation, at any pressure and saturation, fluid properties are calculated at the effective pore radius by using linear interpolation between these three data sets. In the current simulator, the reservoir permeability is enhanced to allow for opening of the fracture network by hydraulic fractures. We compare the results of the compositionally-extended black oil model with those of a fully-implicit eight-component compositional model that we have also developed. The results for the Bakken reservoir show that including PSD in the model can increase estimated recoveries by nearly 10%. We also examine the sensitivities of production to various parameters, such as wettability and critical gas saturation.