The Proper Interpretation of Field-Determined Buildup Pressure and Skin Values for Simulator Use

Scaling factors for the proper application and interpretation of field-determined skin effect and pressure buildup values for use in simulators are derived. Reservoir engineering calculations for the actual well are based on a continuous physical system and the total effective formation thickness. For use with a simulator, the system is discretized, and the cell thickness replaces the total thickness. The scaling factors are to correct for the differences between the two systems. Without the scaling factors, the well inflow equations used in the simulators would calculate an erroneous pressure drop component as a result of the physical skin and the nondarcy flow effect. In the case of pressure values, an equation is derived that gives the buildup time, At, when the field-measured wellbore pressure becomes equal to the wellblock pressure in a three-dimensional simulator. This is important for history matching. This paper shows that the pressure-At relation is strongly coupled to the skin scaling factor. Introduction Reservoir simulation calculations consist mainly, of two parts:(1) the fluid saturation and pressure distribution and parts:the fluid saturation and pressure distribution andthe well inflow. The fluid saturation and pressure distribution result from the solution of the nonlinear partial differential equations that express the mass balance partial differential equations that express the mass balance for oil, water, and gas. Most of the research on reservoir modeling has been concerned with the solution of these equations, and significant progress has been achieved. Compared with this, the treatment of the well is still in its infancy. This is disconcerting since the well calculations are critical to the matching and prediction phases of simulation. In reservoir engineering, the well inflow calculations have reached a high degree of sophistication. The effects of the well completion, restricted entry to flow, noncircular drainage area, and nondarcy flow can be accounted for. The treatment of these factors relies on three basic assumptions:the physical model is continuous-i.e., no discretization is involved as it is in the numerical model,the thickness used in the calculations is the total effective thickness of the formation, andthe permeability is the integrated average of the permeability is the integrated average of the permeability values in the drainage area of the well. This is permeability values in the drainage area of the well. This is normally obtained from flow test analyses. In reservoir simulators, all three basic assumptions are violated. The reservoir is discretized; the thickness used in the inflow equation is the thickness of the cell, which is usually much less than the formation thickness; and the permeability of the cell with a well is different from the average permeability in the majority of cases. This introduces a permeability in the majority of cases. This introduces a scaling problem. If the field-determined well inflow parameters are not scaled properly for use in the parameters are not scaled properly for use in the simulators, the simulation results may not reflect the true well behavior. Furthermore, the pressure values used for matching purposes may be the wrong values. In this paper, the scaling of the skin factor and the problems associated with it are considered. A scaling factor problems associated with it are considered. A scaling factor that gives an acceptable match between the field pressure drop caused by skin and the model-calculated value is determined. Also, an equation that gives the buildup time, At, when the well pressure becomes equal to the cell pressure is derived. The equation accounts for pressure is derived. The equation accounts for three-dimensional (3D) flow and the completion of the well. The implication of using the incorrect At during the history matching phase of a simulation study is analyzed. Skin Effect Consideration The difference between the discretized mathematical model and the continuous physical system is most apparent in the treatment of the skin factor in the inflow equations. The skin factor is an indication of the efficiency of the well completion. The skin concept was introduced to the petroleum industry by Hurst and van Everdingen. petroleum industry by Hurst and van Everdingen. They considered the skin to result from a permeability change in the vicinity of the wellbore. The skin concept was extended by Brons and Marting and by Odeh to account for restricted entry and by Ramey to account for nondarcy flow. The normal procedure for calculating the skin effect is based on the net effective thickness of the formation. In the classical skin determination from buildup data, it is calculated by .....................................(1) where S T == SA + S R, and k is obtained from the flow test analysis. The pressure drop caused by skin, is .....................................(2) SPEJ