Development and application of a transient well index

Abstract

In integrated reservoir studies flow simulation models are created with the goal of honoring diverse static and dynamic data types. If well test data are available, an integrated model should aim to honor these data. However, finite difference simulators using traditional well index formulations cannot always simulate well tests accurately, especially without using significant local grid refinement. This research presents a new well index, which is more suitable than the traditional Peaceman approach for modeling well tests in finite difference simulators. It allows well tests to be simulated accurately using relatively coarse gridding. Reservoir simulators require a well index to relate the pressures in the well block and the wellbore. The well index is needed to calculate the wellbore pressure when the flow rate is assigned, or the flow rate when the wellbore pressure is given. The Peaceman well index is the most commonly used well index. Its derivation is based on the analytical solution to radial incompressible steady-state flow. It includes a calculation of a radius r₀ at which the block pressure matches the pressure predicted by the analytical solution. Since p[wf] is a function of r₀, an error in r₀ translates to an error in p[wf] . As the Peaceman well index assumes steady-state flow, it is not necessarily appropriate for modeling or interpreting pressure transients. In this research, a transient well index proposed by Archer (Model 1) was implemented and tested. The well index was then extended to include non-square grid block geometry and anisotropic reservoir permeability. Archer's initial model was shown to have some problems matching very early time data so a second well index model (Model 2) was proposed and tested. Model 1 was evaluated using a Visual Basic program. Model 2 was evaluated using Mathematica. The well index results were then used as an input for reservoir simulation. Finally, the results of finite difference simulations using the proposed transient well index and the Peaceman well index were compared to analytical solutions. A good match was observed between simulated well tests using the proposed transient well index and the corresponding analytical solutions, even on coarse grids (e.g. 15 by 15 cells = 167 feet by 167 feet). However, when the same simulations were performed using the Peaceman well index the simulated pressure transients showed significant artifact wellbore storage, especially in low permeability reservoirs, and in coarsely gridded models.