Summary Analytic solutions to reservoir flow equations are difficult to obtain in all but the simplest of problems. Under the assumption of steady-state conditions, incompressible flow, and a translationally invariant permeability tensor, the Darcy equation leads to Laplace's equation for the hydrostatic potential. Methods of potential theory in both two and three dimensions may then be brought to bear on the problem, which is usually classified by the type of boundary condition. Dirichlet and Neumann-type boundary conditions, where the value of the potential and the flow respectively are specified on the boundary, are elegantly solved by simple superposition of sources in the case where the boundary is at infinity, or by Green's function techniques in cases with finite boundaries. Reservoir simulators, limited by the finite extent of their models, impose conditions on the flow at the boundary, which through Darcy's equation is proportional to the gradient of the potential. Analytic solutions to these Neumann boundary conditions are in general approached using the method of images to explicitly construct the Green's function for a point source. However, as can be easily shown, problems with no-flow boundary conditions lead to an infinite array of images. The sum of the potentials of the infinite lattice results in the solution in the simulation box. In this paper, we make use of the direct analogy between the reservoir flow equations and electrostatics to illustrate a method commonly used in the field of solid-state physics to sum the potentials of crystal structures. The advantage of this method is that it is fast, easily implemented, and may be used for an arbitrary configuration of injecting and producing wells, as long as net flow is zero. In addition, it is useful for a very general class of simulation boxes, not limited to orthogonal axes.