The analysis and interpretation of water-oil-ratio performance in petroleum reservoirs

Abstract

Our goal in this work is to develop and validate a multivariate relation for the behavior of the water-oil-ratio (WOR) and/or water cut (f[]) functions, where this relation would incorporate the reservoir and fluid properties for both phases (oil and water). The only significant assumption that we make in this work is that pseudosteady-state flow conditions must exist in the entire reservoir system. Our proposed model is an extension of traditional (i.e., steady-state) methods for the case of pseudosteady-state flow - for both the oil and water phases. In this work, the pseudosteady-state model reproduces observed field performance substantially better than any of the steady-state models. We believe that this approach can be applied to any reservoir system undergoing waterflood. The specific tasks achieved in this work include: 1. Development of a rigorous model for the simultaneous flow of oil and water at pseudosteady-state flow conditions. This model has been validated against 28 different field cases (all cases are included in Appendices A and B), and in all cases, the new model gives an excellent representation of the data. 2. Development of a "reciprocal rate plot" for the estimation of both the original oil-in-place (N), as well as the "movable oil" (N[][]) at current producing conditions. This approach requires a plot of the reciprocal rate (1/q[]) versus the "oil material balance time," (N[]/q[]). 3. Development of a diagnostic technique for assessing (qualitatively) the efficiency/ effectiveness of a waterflood. This technique involves the use of the following log-log format plots: (the "associated functions" include the WOR-derivative, the WOR-integral, and the WOR-integral-derivative functions) -- WOR and WOR associated functions versus production time. WOR and WOR associated functions versus N[]/q[]. WOR and WOR associated functions versus (N[]+W[])/ (q[]+q[]). 4. Application/interpretation of the following extrapolation methods for the water-oil-ratio (WOR) and the water cut (f[]) functions: q[] versus N[]. log(f[]) versus N[]. 1/f[] versus N[]. f[] versus N[]. log(WOR) versus N[]. Unfortunately, the formulation of the two-phase (oil-water), pseudosteady-state flow relation does not provide for a simple extrapolation formula for the estimation of movable fluids. This is an area for further investigation.