Influence of cell boundary flux distribution on well pressure

Semi-analytic solutions to Poisson's Equation on two and three-dimensional rectilmear domains with Dirichlet and Neumann boundary conditions, and those extended to open systems using Green's Theorem, allow the role of boundary flux distribution to be exammed and its influence on well pressure quantified for a series of well trajectories. The pseudo- steady state flux distribution between interacting homogeneous domains is shown to be a function of distance from the well to the boundary. The character of the bjoundary flux transitions from nearly uniform to bell-shaped to cusped-shaped as a function of distance, strongly influencmg the mode of boundary integral assessment. Permeability contrast is shown to either sharpen or blunt the transition, dependmg upon the well cell permeability. In 2D and 3D case studies, the nature of the boundary flux distribution is demonstrated to be of considerable significance in accurate forecasting of reservoir observables. Computed boundary flux profiles on discretized mterfaces in multi-region problems, enforcmg continuity in flux and pressure, are shown to correspond to neither uniform flux nor uniform pressure. Leveraging analytic representation of pressure and flux, parametric representation of boundary normal flux as a linear combmation of uniform flux and that required for uniform pressure is suggested to accurately capture the influence of wells on boundary flux with significantly reduced bandwidth in solving heterogeneous problems using boundary integral methods. The methodology allows accurate forecastmg of well productivity without the need for local grid refinement within numerical reservoir simulation and is particularly pertinent when well pressure limits reservoir deliverability.