During history matching of observed production data of brown fields, one of the key matching parameters is the water break-through time. Water break-through time is the time at which significant water production begins at a producing well. During the simulation of an immiscible displacement process, numerical dipersion is a well known undesirable simulation artifact which makes water flood-front to move faster when the simulation grid-blocks are coarser. In this paper, we present an approach to reduce numerical dispersion and ensure that the simulated flood-front movement is similar, whether we use coarse grid-blocks or fine grid-blocks in simulation. The approach is based on the correction of laboratory relative permeability data, using the shock front water saturation (Swbt) obtained from fractional flow curve. Swbt is the water saturation at the contact point between a tangent drawn from the connate water saturation (Swi) to the fractional flow curve. Once we obtain Swbt, we then set the critical water saturation of the water relative permeability curve to Swbt. We created different scenarios of grid block sizes and simulated a steady state water injection process using the corrected water relative permeability curve. We based our study conclusions on results from both line drive and 5-spot water injection patterns. The result showed six (6) months difference in predicted water break-through dates when we used the laboratory relative permeability data as is, but with this new approach, the various scenarios of grid block sizes showed similar water break-through dates. This new methodology effectively eliminates the impact of simulation grid size on water break-through prediction results. During geo-model construction, we do not know in advance what impact our chosen grid size would have on flow dynamics, and once the geo-modeling is finalized it could be time consuming to re-do the gridding and layering of the geo-model. We also take note that many times we are constrained to build simulation models with large grid-sizes because of computational limitations, especially in large reservoirs. The new approach presented in this paper would ensure that any size of grid-block used in simulation, would predict similar flood-front movement and hence similar water break-through time as fine grid simulation. Our approach helps to ensure better reliability of simulation results in cases where computational limitations or large size of reservoir makes it necessary to build coarse grid simulation models.
In this paper, we investigate the cause of the time-shift that occurs between the derivatives of the observed and simulated pressure transient data and present a methodology to perform full-field transient modeling without the need for single well fine grid sector models. Pressure transient modeling is the process of simulating an observed well test sequence with the goal of comparing the derivative of field measured pressure transient to the derivative of numerically simulated pressure transient. Beginning from first principles, we investigated and showed in the current paper that simulation grid-block size introduces an undesireable shift in the derivative of simulated data which disappears as we approach fine grid simulation. We have termed this shift as grid-block storage phenomenon. As a result of this undesireable shift that occurs when coarse gid blocks are used, transient modeling is currently done using local grid refinement on sector models. The limitations of the current practice include; (i) large simulation run times due to use of fine grid simulation (ii) error related to boundary conditions when using sector models. In this paper, we develop the equations governing pressure buildup behavior during grid-block storage dominated period as a function of simulation grid-size and simulation grid permeability. The insight from the derived equations reveals that the infinite acting radial flow stabilization (IARF) of the derivative of simulated pressure transient is always the same regardless of simulation grid-size. However, the onset of this stabilization is delayed as simulation grid-size increases and as simulation grid permeability decreases. Based on this insight, we then present the basis for an approach to history match the derivative of observed pressure transient without using local grid refinement on sector models. This approach is based on the use of derivative time-shift. Instead of using a fine grid sector model, we simply use the coarse full-field model to simulate pressure transient until the onset of IARF stabilization. We then shift the derivative of observed pressure transient right-wards to overlay corresponding features of the derivative of simulated data in a manner similar to type-curve matching. This new approach called Time-Shift Methodology (TSM), presents a practical and efficient way of performing transient modeling on a full-field multi-well model without resorting to the time consuming conventional approach of using several single-well fine grid sector models.
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