Grid System Requirements in Numerical Modeling of Pressure-Transient Tests in Horizontal Wells

Abstract

The common approach of using refined grids and small time steps usually does not provide accurate and efficient numerical models to simulate horizontal-well pressure-transient tests. In most cases, this approach requires impracticably long computational times or creates artifacts on pressure and derivative responses that may be confused with the characteristics of certain flow regimes. The results of this study indicate that the conventional well index should be used with log-distributed grid and time steps to obtain closer match to the analytical solution at early times. There is, however, a limit to grid refinement beyond which the results do not improve. This paper introduces the transient well index that allows the use of larger grids while improving the accuracy of simulations especially at early times. Introduction The need for numerical simulation of transient pressure behavior of horizontal wells often arises in the interpretation of complex structures and calibrating the static data used in reservoir models. Several techniques1,2 have been proposed in the literature to improve the grid system requirements in modeling pressure-transient responses of vertical wells. These references have implied the extension of the same techniques to horizontal wells but no conclusive information has been presented. We first document the effect of grid size selection and the representation of horizontal wellbore within the grid blocks. Next, we present guidelines to determine the grid size and discuss modifications of the Peaceman's probe radius formula1 to improve the simulation of horizontal well pressure-transient responses. These techniques include the use of the appropriate well indices and transmissibility modifiers for transient flow in horizontal wells. The transient numerical well index (TNWI) presented in this paper is shown to be essential to reproduce the characteristics of the early-time pressure-transient characteristics of horizontal wells. We demonstrate that with the correct choice of the equivalent well grid radius, the proposed techniques considerably improve the simulation of the early time responses without requiring significant grid refinement. The techniques proposed can be easily implemented in the conventional simulation codes to simulate both short-term and long-term performances of horizontal wells. Background Several studies have searched for techniques to improve the numerical simulation of well tests. These studies included comparison of bottom-hole flowing pressure calculation methods using well-known steady-state productivity index versus the less common transient productivity index equations. In a related subject, the reservoir simulation literature focuses on the implementation of local grid refinement near the wellbore as the main method to improve the accuracy of the bottomhole pressure calculations. While the use of transient well index for numerical well test analysis has been discussed in the literature, these studies, in general, were for vertical wells. In this paper, however, we are specifically interested in transient well index for horizontal well applications. Below is an account of the relevant literature.

Well-Reservoir Coupling on the Numerical Simulation of Horizontal Wells in Gas Reservoirs

“…Horizontal wells in reservoir simulation have been modeled using local grid refinement (Zhao 1994, Al-Mohannadi et al 2007, hybrid grid (Pedrosa Jr. and Aziz 1986, Vicente et al 2000, Vicente et al 2001 2007) and including hydraulics wellbore effects , Ouyang et al 1998, Pourafshary et al 2009). …”

“…Mascarenhas and Durlofsky (1999) used numerical simulation to evaluate the performance of horizontal wells in heterogeneous reservoirs. The use of refined grids and small time steps may not lead to accurate results when simulating horizontal wells tests in cartesian coordinates (Al-Mohannadi et al 2007). For horizontal wells modeling, gridding plays an important role in the final results, and nonstructured grids have been suggested for field studies (Vestergaard et al 2008).…”

Semianalytical Representation of Wells and Near-Well Flow Convergence in Numerical Reservoir Simulation

“…To improve the representation of wells in nonuniform grid systems, Ding and Renard (1994) and Ding et al (1998) proposed the use of transmissibility modifiers. On another attempt, to improve the computation of transient wellbore pressures, Blanc et al (1999), Archer and Yildiz (2001), Al-Mohannadi et al (2004), and Aguilar et al (2007) proposed the use of transient well indices. There has been also interest in improving simulation by using local grid refinement and adaptive grids (Heinemann, et al 1983, Quandalle and Besset, 1985, Forsyth and Sammon, 1986, and Pedrosa and Aziz, 1986.…”