Sensitivity of Steamflood Model Results to Grid and Timestep Sizes

Abstract

Abstract Numerical simulation of complex processes in oil reservoirs has become a standard tool. The grid size and timestep sensitivity of a simulator are of prime concern in reaching the correct conclusions in any study. This paper presents an analysis of the sensitivity to timestep and grid size of a one-dimensional (1D) and two-dimensional (2D) compositional multiphase steamflood model used to simulate a heavy-oil reservoir. The behavior of primary variables before breakthrough in the 1D and 2D cases is presented for clearer understanding of steamflooding heavy-oil reservoirs. The peculiar features exhibited by primary variables of the production and injection blocks for the 1D reservoir plus timestep and grid-size effects on primary variables for 2D cases studied are discussed. Sensitivity studies of grid and timestep size are meaningful only if each is carried out while the other variable has minimum truncation error. The recovery performance parameters are less sensitive to timestep size than to grid size. They are also less sensitive in the 2D runs than in the 1D runs. The time/pore-volume-injected (PVI) relationship is very sensitive to grid size, and to a lesser extent, to timestep size. Introduction Numerical dispersion is particularly important in simulating multiphase flow, miscible displacement, and compositional phenomena. Settari recommends that detailed study be carried out on grid- and timestep-size effects. A grid-size sensitivity study is recommended when a reservoir is simulated to define the necessary grid size used. Such a study requires a series of simulation runs with increasing or decreasing grid definition. When simulators with fully implicit formulation are used, where large time steps are possible, the time truncation error also can become important. Therefore, a timestep sensitivity study for these simulators is also necessary."Sensitivity analysis" refers to the sensitivity of the primary variables and recovery performances to grid and timestep size. A review of recent literature reveals that grid and timestep effects have not been studied on all primary variables for 1D simulations and are lacking for 2- or 3D simulations. Sensitivity analyses for both 1- and 2D simulation of a heavy-oil reservoir along with a study of the behavior of primary variables in steamflooding are presented. Simulator and Data Used The simulator used in this study was developed by Abou-Kassem. A brief description of the simulator is given in Ref. 9. It is a fully implicit, compositional, three-phase steamflood model. The model employs a sophisticated well model and a nine-point finite-difference scheme in two dimensions only. It can be operated in 1- and 2D modes with the choice of block-centered or point-distributed grid. In this paper only results of a block-centered grid with gas hysteresis and with no heat loss to surrounding formations are presented. The reservoir is represented by a one-fourth five-spot flood pattern with dimensions of 137 × 137 × 63 ft [41.76 × 41.76 × 19.2 m]. The permeability and porosity are 4 darcies and 0.38, respectively. The reservoir is initially saturated with 18 % water and 82 % heavy oil composed of 70 % nonvolatile oil component and 30 % methane. The nominal mobility ratio is 285,000, which corresponds to an effective mobility ratio of about 10,000. The Appendix provides more detailed data. Steam of 0.70 quality at an injection pressure of 1,000 psia [6.9 MPa] was injected into the reservoir having an initial pressure and temperature of 554 psia [3.9 MPa] and 60F [288.7K], respectively. The maximum steam injection rate was 883 cu ft/D [25 m3/d] cold water equivalent (CWE). The production well was put on "deliverability" control with a bottomhole pressure (BHP) of 400 psk [2.8 MPa]. The reservoir is simulated with a uniform grid (with square block for 2D). Results and Discussion Results of the simulator used in this study were compared with results obtained from a commercial steam model in 1D and 2D modes. Excellent agreement was obtained when the simulator was run with the five-point finite-difference formulation. The 2D results presented next are for a diagonal grid with the nine-point difference scheme. Behavior of Primary Variables in Steamflood Simulation. Primary Variables of Injection Well Block (1-D Simulation). The behavior of the primary variables associated with the injection block as a function of PVI is shown in Fig. 1. As steam injection begins, the pressure increases first moderately then very rapidly because the system has been compressed and all fluids are almost immobile. The pressure of the injection block is slightly less than the maximum injection pressure. SPEJ P. 65^