Grid-System Requirements in Numerical Modeling of Pressure-Transient Tests in Horizontal Wells
- Nasser Saqer Al-Mohannadi (Colorado School of Mines) | Erdal Ozkan (Colorado School of Mines) | Hossein Kazemi (Colorado School of Mines)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- April 2007
- Document Type
- Journal Paper
- 122 - 131
- 2007. Society of Petroleum Engineers
- 5.6.3 Pressure Transient Testing, 4.1.2 Separation and Treating, 5.5 Reservoir Simulation, 5.1.5 Geologic Modeling, 5.3.1 Flow in Porous Media, 5.1 Reservoir Characterisation, 5.6.4 Drillstem/Well Testing
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The common approach of using refined grids and small timesteps 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. This paper presents an investigation of the grid and timestep requirements for the conventional well index (WI) to provide accurate simulations of horizontal-well pressure-transient responses. The results of this study indicate that the conventional WI should be used with log-distributed grid and timesteps to obtain a closer match to the analytical solution at early times. There is a limit to grid refinement beyond which the results do not improve. For these cases, the transient well index (TWI) introduced in this paper allows larger grids while improving the accuracy of simulations, especially at early times.
The need for numerical simulation of the pressure-transient behavior of horizontal wells often arises in the interpretation of complex structures and the calibration of static data used in reservoir models. To compute the bottomhole pressures, reservoir simulators require a relationship between the wellblock and wellbore pressures. This relationship is obtained by considering an appropriate well-deliverability equation, which expresses the flow rate as a function of the difference between the wellblock and wellbore pressures. The pressure calculated in numerical simulation is uniform within the wellblock, whereas deliverability equations consider the change of pressure as a function of distance from the wellbore. However, it is possible to find an equivalent distance in the wellblock at which the pressure corresponds to the simulated wellblock pressure. Therefore, the choice of the appropriate deliverability relationship and equivalent wellblock radius is essential for accurate numerical calculation of wellbore pressures. The selected deliverability relationship is invoked into the numerical algorithm in the form of WI.
Van Poollen et al. (1968) and Peaceman (1978, 1983) presented the first comprehensive discussions of the WI to simulate wellbore pressures. Peaceman (1978, 1983) introduced the probe radius formula to represent the equivalent wellblock radius in the WI. Peaceman's approach has been commonly accepted and widely used in most numerical simulators.
Steady-state and radial-flow assumptions are inherent in Peaceman's numerical WI. When this conventional WI concept is applied to wells with nonradial-flow regimes (e.g., wells off-centered in the grid and inclined or horizontal wells at late times) and used to calculate pressure-transient responses, the accuracy of wellbore pressures may not be satisfactory. The common approach for the solution of this problem is to reduce the grid size (and the timesteps) so that the flow convergence within smaller wellblocks becomes closer to the radial and steady-state assumption is more reasonable because of the smaller storativity of the wellblocks.
Peaceman's probe radius formula (Peaceman 1978, 1983) has been commonly used for horizontal wells without much critical assessment of success for early times. As an alternative, Babu et al. (1991a, 1991b) presented another WI and equivalent wellblock radius formula for horizontal wells. Their formula extended Peaceman's conventional WI to wellblocks with high aspect ratio and high anisotropy.
Blanc et al. (1999) proposed techniques including the use of a TWI to improve the grid-system requirements in modeling pressure responses of vertical wells, especially at early times. They implied the extension of their technique to horizontal wells but did not provide conclusive information.
In this paper, our objective is to provide a means of improving pressure-transient modeling in standard simulators. We intend to respond to two different categories of the modeler's needs. If the modeler has the option of modifying WI in the simulator, then we recommend the use of the TWI as introduced for horizontal wells in this paper. If an existing (commercial) simulator is to be used without revising WI, then we provide recommendations for the selection of the grid system and timesteps.
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