A general method for the scale up of highly detailed, heterogeneous reservoir cross sections is presented and applied to the simulation of several recovery processes in a variety of geologic settings. The scale up technique proceeds by first identifying portions of the fine scale reservoir description which could potentially lead to high fluid velocities, typically regions of connected, high permeability. These regions are then modeled in detail while the remainder of the domain is coarsened using a general numerical technique for the calculation of effective permeability. The overall scale up method is applied to the cross sectional simulation of three actual fields. Waterflood, steamflood and miscible flood recovery processes are considered. In all these cases, the scale up technique is shown to give coarsened reservoir descriptions which provide simulation results in very good agreement with those of the detailed reservoir descriptions. For these simulations, speedups in computation times, for the coarsened models relative to their fine grid counterparts, range from a factor of 10 to a factor of 200.