A simple model for the displacement of a viscous fluid by a nonviscous fluid in a porous medium has been developed. This model is based on the Witten-Sander model for diffusion-limited aggregation and employs a multifractal lattice to represent both short- and long-range heterogeneities in the porous medium. It is shown that such heterogeneities can have important effects on both the local and global structure of the displacement pattern. Long-range heterogeneities enhance the effects of the outer boundary on the overall shape of the cluster and shorter-range heterogeneities reduce the thickness of the ``viscous finger'' generated by the displacement process. Our results indicate that the effective fractal dimensionality of the displacement patterns is decreased as the magnitude of the heterogeneity is increased.