Carbonate reservoirs are of great importance, due to their large hydrocarbon reserves. However, their complex structure makes them challenging targets to develop. In order to predict reservoir performance, we need to be able to model the effects of heterogeneity at a variety of scales. In this study, we have constructed a detailed geological model using published data for an outcrop of the San Andres Formation. The resolution of the model is 1.2 m x 0.6 m, much finer than a conventional reservoir simulation model. The aim of this work was to determine if we could develop a feasible approach to upscale the model. A number of single-phase upscaling methods were tested, including averaging (arithmetic/harmonic), and flow-based upscaling with local and extended boundary conditions. In addition the Well Drive Upscaling (WDU) method, a relatively new method, was applied. In this method a single-phase global simulation is performed with appropriate boundary conditions: high pressure at injection wells, low pressure at producers. The flows are then summed and the pressures averaged in order to calculate the effective transmissibilities between the coarse cells. The upscaling methods were tested by simulating a waterflood. Cases with single and multiple relative permeabilities were examined. The upscaling factor in each case was 65 by 5. In general, the coarse-scale models gave late breakthrough, and overestimated the recovery. The WDU method was consistently better than the other methods, because it was able to preserve the correct flow between coarse cells. On the contrary, the conventional flow-based methods with local boundary conditions gave poor results, sometimes worse than averaging. These results show that upscaling in a complex carbonate reservoir is feasible, providing a suitable method, such as the WDU method, is applied.