This report deals with a variety of topics all centered around the main goal of making numerical reservoir simulation results conform more closely with geologic descriptions. The first part of the report discusses results on conditional simulations of miscible displacements in randomly heterogeneous permeable media. The focus here is on local or macroscopic dispersion, the dispersion experienced at a fixed point in the medium. Macroscopic dispersivity has many of the same dependencies on reservoir properties as does megascopic dispersivity, but it seems to be less time dependent and is always smaller. We have not discovered a mathematical model to describe its behavior. A major portion of the report deals with statistical descriptions. We investigate the bias and precision of standard measures of heterogeneity, the Lorenz and Dykstra-Parsons coefficient. After this, the work explores the benefits of using a distribution type characterization parameter in exploring heterogeneity. The final major protion of the report describes our mapping efforts on the Page sandstone outcrop in northern Arizona. The mapping is to be used in generating both deterministic descriptions and in calibrating the stochastic descriptions discussed above. 128 refs., 95 figs., 10 tabs.