Abstract
Full-field EOR performance predictions are generally obtained from scale-up tools, since three-dimensional finite-difference simulations would be too CPU intensive. Existing scale-up techniques require the user to define pattern elements and then to derive performance curves to apply to each injector-producer pair in the elements. Accurate assignment of these elements is difficult because the actual shape and size of the swept volumes are sensitive to reservoir faulting, well rate changes, and regional flux. In reality, the actual sweep region is not an input parameter, but should be determined by the regional pressure field which changes as well rates vary and new wells are drilled. Thus, a major source of error in using existing scale-up tools is trying to define representative pattern elements. In the current paper, we describe a scale-up technique in which the user does not have to define pattern elements or injector-producer pairs. In the new technique, the pressure field is computed at each time step and then a front-tracking algorithm propagates water and miscible injectant throughout the reservoir. By using an analogy between oil mobilization and adsorption/desorption of tracers, the miscible-gas process is modeled. The parameters for the model are obtained by fine-scale, two-dimensional, compositional, finite-difference simulations in a vertical cross-section. In the new approach, the injected solvent is divided into an effective and an ineffective portion. This approach reduces a three-dimensional problem to a two-dimensional, areal one in which the declining displacement efficiency of the solvent, which is caused by vertical effects, is captured by decreasing the injected concentration of effective solvent with time. In this paper, we show how the new scale-up tool has been used to model the miscible WAG process in the Eastern Peripheral Wedge Zone of the Prudhoe Bay field. We show a comparison between field response and model predictions.
Introduction
Good reservoir management requires the prediction of reliable oil and gas rates. In general, the degree of difficulty in making these predictions depends on the displacement process. For example, good predictions of primary depletion or gravity drainage by gas-cap expansion can usually be obtained by coarsely gridded finite-difference simulations. However, processes where injected water or gas must be tracked from injector to producer typically require finely-gridded simulations. Accurate prediction of oil and gas rates frequently require finely gridded simulations which contain (1) rock-measured relative permeabilities and (2) a reservoir description that accurately predicts high-permeability zones (thieves) and low-permeability barriers (e.g., shale location, size, and continuity). At Prudhoe Bay, modeling of miscible gas processes generally requires vertical grid blocks of the order of one foot to match field-measured saturation profiles. At the present time, three-dimensional, compositional modeling of gas displacement processes that satisfy these two requirements require at least a week of CPU time on IBM-590 workstation for a single pattern. Thus, it is not currently practical to use finely gridded finite-difference simulators to model large sections of a field.
Traditionally, three approaches have been used to address this problem -- pseudo relative permeabilities, tank models, and streamtubes. Pseudo relative permeabilities are generally successful only when the saturation history experienced in the coarse-grid simulation will always be similar to the fine-grid simulation. Tank models can be difficult to apply when the original pattern changes by infill drilling or well conversions, and streamtube models have had difficulty when the initial conditions are not homogeneous along each streamline.
To address the above problems, a new approach was created that can reproduce the response and timing characteristics of the produced components, but also has the ability to propagate and track injected fronts. In addition, the model does not require user-supplied injector-producer allocation factors. We explain, below, our new front-tracking technique and how this new scale-up tool has been used to model the miscible WAG process in the Eastern Peripheral Wedge Zone of Prudhoe Bay. P. 329
Quasi-two-dimensional approximation for numerical simulation of flows in engine ducts