Permeability anisotropy, via full permeability tensor, has not been accurately accounted for in reservoir models because of the implementation complexity. Specifically, numerical implementation of the off-diagonal components of the permeability tensor is inconvenient and cumbersome. This paper shows how directional permeability, calculated from a full permeability tensor, can be used as a simple replacement both in coding numerical models and in day-to-day engineering analysis. For the former, we have implemented the directional permeability for single-phase flow in a 9-point finite-difference formulation, which is easy to code. This formulation, however, is easily applicable to any control-volume formulation including the perpendicular bisector (PEBI) grid. The implementation of this technique has produced excellent numerical results in numerical simulation of multi-phase flow displacement. For routine engineering applications, we have also applied this technique to generate pressure responses for a four-well interference test in a highly anisotropic system. The analysis of the test results by conventional type-curve matching produced the correct reservoir geometric-average permeability and a very good approximation for the direction of the maximum permeability, which is a testimony to the credibility of the formulation. The use of this formulation should be very useful in determining major natural fracture trends in reservoirs undergoing water or gas injection, and in modeling fracture trends in other fractured reservoir situations, such as tight sands.

This study develops a process that determines the critical hydraulic fracture parameters and quantifies their impact on the EUR by combining reservoir simulation with probabilistic analysis methods. The process is verified by a real field case example in a tight gas reservoir. The final product can be applied to other unconventional reservoirs to ultimately maximize revenues by planning superior fracturing operations and optimizing well spacing. A detailed dual porosity, 1 section reservoir model was created and history matched to model the flow mechanism. A fine layered (2-3ft) geostatistical model was utilized in simulation without upscaling. The dual porosity formulation enabled the simulation model to represent the hydraulic fracture - matrix interaction properly so that the flowback and formation water production could be matched also. During the history matching phase, the parameters that control the impact of hydraulic fractures on the recovery were identified as follows:Matrix-fracture exchange: this parameter represents the complexity of the fractures and is controlled by the surface area created during hydraulic fracturing.Fracture conductivity: this is effectively the permeability of the hydraulic fractureHalf length: this parameter impacts the extent of the hydraulic fracture, therefore the amount of matrix that has been accessed.Job size: The size of the frac fluid volume injected during the hydraulic fracturing process In this work, an internal proprietary technology that creates a response surface for the combination of the parameters defined above was utilized. This technology utilizes Experimental Design, Response Surfaces and Constrained Monte Carlo. The history matched simulation model was automatically modified to create the necessary cases to calculate a multi-dimensional response surface. The created response surface was then used to do Monte Carlo simulations to create P10 to P90 probabilities of the total gas production (EUR). The results of the study allowed us to understand not only the mechanisms operating in the reservoir being studied, but also the required hydraulic fracture parameters (ranges) to achieve a given EUR of a specific probability. The same algorithms were then be used to predict the future performance of other well spacing patterns and hydraulic fracture job sizes.