Abstract

A three-dimensional, three-phase black oil simulator is developed which incorporates both static and dynamic patch-type local grid refinement procedures; and is capable of handling both horizontal and vertical wells. In static local grid refinement the refined grids are embedded within the coarse grids during the entire length of simulation. This refinement scheme has been used around the wellbores where large pressure and saturation changes are anticipated. The dynamic local grid refinement algorithms identify various sections of the reservoir undergoing large pressure and/or saturation changes at each timestep. A pre-determined uniform refinement is applied to these patches; and local grid simulation is performed. The local grids and the base (coarse) grid interact with each other through a specially developed data transfer method; in which the local gridblock pressures are arithmetically averaged to get updated coarse gridblock pressure, and capillary pressure is used to back calculate phase saturations. Once all the patches are solved then the corresponding coarse gridblock pressure, saturation and flowrate entries are updated from the entries of the local grids.

The performance of the developed model is examined through several different scenarios. These cases include sealed reservoir, bottom water drive, and edge water drive utilizing horizontal wells. The proposed refinement algorithms provide good estimates of bottom-hole flowing pressures, WOR and GOR values and flowrates for all the configurations. The run-time for the dynamic grid runs is about 100-200 folds less than that of the fine-grid model, and is comparable to the run-time of conventionally refined grid model. Local grid simulation in various patches of the reservoir do not share or transfer data among each other at a particular timestep. Hence, this technique can be easily implemented on machines having parallel processors. Such applications would drastically reduce run-time.

Introduction

Finite-difference technique has been the principal numerical tool employed in building reservoir simulators. Finite-difference equations replace the continuum problem described by differential equations, and approximate the solution at a finite set of discrete points within the domain of interest. These discrete points should be selected very carefully to match the reservoir geometry. Needless to say, the accuracy, time, and cost involved in a simulation study depend upon the number of these grid points and the spatial dimensions.

The finite-difference technique deals with averages. In reservoir studies the gridblocks are relatively large. Pressure and saturation values as calculated by the simulators lead to average gradients which mask local gradients. Hence larger number of gridblocks are required to capture the details of the local changes occurring. In general, reductions in grid and timestep sizes result in accurate solutions. However, increased number of gridblocks increases computational time, computer storage and cost of the study.

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