Our work uses fractals to characterize the spatial correlation structures of porosity and permeability of vertical and horizontal logs in a braided-fluvial sandstone reservoir. The data comprise cores and logs of adjacent vertical wells and logs of horizontal wells. Small-scale realizations of interwell heterogeneity were generated with successive random additions (SRA) technique for new observed fractal models, A deterministic description is also developed. Effects of fractal and deterministic reservoir heterogeneity on reservoir performance were studied for waterflood and water-alternating-gas (WAG) injection processes. The effects of scale up on spatial correlation of porosity was investigated. The fractal model of fractional Brownian motion (FBM) in the horizontal direction, having same intermittency exponent as for fractional Gaussian noise (FGN) in the vertical direction, is not supported by log observations in horizontal wells. Fractal character of core and log data of vertical wells is similar. The incremental WAG recovery response compared to waterflooding response is more sensitive to reservoir heterogeneity. Scale-up experiments indicate that spatial correlation structure of reservoir properties may be different at different scales. Results of this paper will be useful for evaluation of infill drilling, and design, selection, and optimization of an EOR process. The proposed techniques also provide a framework to quantify uncertainty in reservoir performance.