Ability of Geostatistical Simulations To Reproduce Geology: A Critical Evaluation

Abstract Geostatistical techniques are being used increasingly to model reservoir heterogeneity on multiple scales. Several techniques are now available which differ in their underlying assumptions, complexity and applications. This paper compares the geostatistical sequential gaussian, sequential indicator, and truncated gaussian simulation techniques with the more traditional geological hand mapping description technique and compares their influence on flow simulation performance. The base geological description was generated using a hand drawn map of the geological facies associations within a 3-D model area in a fluvio-deltaic environment. The average values of porosity and permeability were assigned to the respective facies associations. A second description was generated using sequential gaussian simulation by honoring the porosity and permeability well data, the corresponding vertical variograms, and the inferred lateral variograms. A third description was generated using sequential indicator simulation to distribute porosity and permeability instead of sequential gaussian simulation. Both of these simple geostatistical descriptions were not constrained by explicit geological facies association information. A final more complex geostatistical description was generated in which the underlying geological framework of facies association was first simulated using truncated gaussian simulation and then the porosity and permeability were distributed within each facies association using sequential gaussian simulation. All of the fine scale descriptions were compared in detail and scaled up to large grid blocks appropriate for flow simulation using a pressure solver. A comparison of the 3-D hand drawn facies association map with the one computed using truncated gaussian simulation showed that the hand drawn map contained less variations than the geostatistical facies association map when conditioned to the same well data. Comparison of the fine scale porosity and permeability maps showed that the distribution of the average values of porosity and permeability in the 3-D hand drawn facies association map failed to reproduce the complex texture of the rocks giving a considerably more uniform distribution of these attributes. It was found that distributing porosity and permeability geostatistically without the influence of explicit facies association information significantly reduced the effective control on the distribution of these attributes, resulting in a more continuous distribution of porosity and permeability than that obtained when facies association information was used. Comparison of the fine scale permeability distributions to those obtained after scaleup showed that the pressure solver maintained the major permeability features apparent in the fine scale distribution which were important to reservoir performance. The influence of these description techniques on reservoir performance was compared using a fluid flow simulator.