Accurate numerical solution of well-rest problems requires boundary-fitted orthogonal curvilinear grids that have high degree of refinement and are consistent with the flow geometry near the well. This paper presents an algorithm for automatic orthogonal 2-D grid generation tailored for well-test problems. The accuracy of numerical solutions based on these grids is demonstrated for a number of pressure-transient problems that have exact analytical solutions. The gridding algorithm has been implemented in an interactive grid-generation program that is closely integrated with a reservoir simulator.