Transient Behavior of Multilateral Wells in Numerical Models: A Hybrid Analytical-Numerical Approach

Abstract

Abstract This paper presents an extension of transient well index approach to simulate pressure transient behavior of multilateral wells. This approach uses an analytical solution for the well index at early times and switches to the numerical well index at late times. The use of the transient well index eliminates the need for excessive grid refinement around the well. In this paper, we have improved the accuracy of the transient well index approach and have provided for a flexible and easily implementable approach to place multilaterals in conventional, Cartesian-grid reservoir models. Introduction Pressure-transient responses of wells are conventionally analyzed and interpreted by using analytical solutions of diffusion equation for relatively simpler reservoir architectures. For more complex reservoir situations, involving multi-phase flow and reservoir heterogeneity, numerical simulation is usually the only resort. Numerical simulators generally focus on the long-term performance of reservoirs. These simulators are not very sensitive to the short-term characteristics of flow in the near-wellbore region, which is the focus of the short-term, pressure-transient tests. For example, the conventional transmissibility and well indices used in numerical simulation may adequately represent fluid movement between relatively large grid blocks as well as the fluid withdrawal or injection at well blocks over relatively large time steps when the transient radius of investigation of the well is sufficiently large. Furthermore, these simulators fail to account for the flow convergence near the well accurately at shorter times unless very small grid and time steps are used. Grid refinement around well has been used both to improve numerical calculation of bottom-hole pressure during transient period and flow convergence. However, a cursory grid refinement may not produce the desired accuracy; thus, increasing the need for very fine grid that requires more computational power and time. In addition, special grid structures are often required to capture the details of flow convergence around complex wellbores and to simulate the associated transient flow regimes, add to the overall complexity of the numerical computation. Objective The objective of this paper is to improve the representation of single- and dual-lateral wells in numerical models for more accurate and computationally efficient simulation of pressure-transient responses. Also, a practical approach will be presented to model the dual-lateral wells in uniformly distributed, Cartesian grid. This approach involves proper accounting for the orientation, length, and friction-head loss of the multi-lateral segment crossing a grid block. The proposed approach can be easily implemented in the conventional reservoir simulators without compromising the computation time. Outline After a summary of the pertinent literature and background, we first present the improvement of well transmissibility for a single lateral. Then, we discuss the addition of a second lateral to the model. We, finally, compare the accuracy of the numerical model against analytical solutions under various conditions of heterogeneity and skin effect. Literature Review Blanc et al. (1999) applied an unsteady-state, radial flow equation for vertical wells, known as transient well index, to simulate pressure transients more accurately. They defined a well-block radius that varied with time and was different from the steady- and unsteady-state definitions of the well-block radius proposed in the earlier studies by Peaceman (1977, 1983) and Babu et al. (1991). This approach eliminated the need for excessive grid refinement around the well.