We describe the construction of a general unstructured grid, parallel, fully-implicit simulator for complex physics associated with heavy oil thermal recovery. The primary focus of the simulator is on the physics associated with steam injection and Steam Assisted Gravity Drainage (SAGD) and to simulate such models efficiently using parallel processing. The simulator solves component material balance, energy balance and mass equilibrium equations for component mole fractions, saturation, temperature and pressure using the Newton-Raphson method. External heat sources and sinks are included in source terms to model the energy interaction with over-burden and under-burden rocks. The solution procedure and the treatment of phase transition to achieve stable non-linear iterations are discussed. The simulator is verified by comparing results from problem No. 3 of the Fourth SPE Comparative Solution Projects and a cyclic steam injection case with other commercial simulators. We also demonstrate the performance and parallel scalability of the simulator via testing a large scale SAGD model with 9 horizontal well-pairs. Introduction Numerical simulation of thermal processes, such as steam flooding, steam assisted gravity drainage (SAGD), and cyclic steam stimulation, plays an important role in design of a thermal project. The frequent use of simulation results in the reservoir engineering decision-making process indicates confidence in reservoir simulation techniques. Since thermal simulation started in the early 1970's, many papers have been published for models with structured grids (Coats 1980; Chien 1989; Mifflin 1991; Watts 1996). In recent years, several papers describe general simulators using unstructured grids (Beckner 2001; Debaun 2005; Beckner 2006; Liu 2007). These papers noted that unstructured grids reduced simulation cycle-time significantly via integration with geologic models. On the other hand, unstructured grids can achieve accurate geologic features by using fewer grid blocks and save simulation time dramatically. Liu, et al. (2007) described a general unstructured grid thermal simulator based on mass variable formulation with the selection of pressure, energy and component moles as primary variables. This paper describes a general unstructured grid, fully-implicit thermal simulator based on a nature variable formulation. The first section describes the mathematical formulation used in simulator, solution procedure, primary variable selection, fluid property calculation, and heat loss model. The second section presents comparison of simulation results against other simulators to verify the physical results. Mathematical Formulation The thermal model described here is based on the assumption that Darcy's law and instantaneous phase equilibrium are valid. It is also assumed that the aqueous phase contains no components that partition into either of the hydrocarbon phases, and that the water component could not reside in the hydrocarbon liquid phase. Balance Equations The governing equations include component material balance equations, an energy balance equation, mass equilibrium equations, and saturation, and composition constraint equations. For thermal models where water component could reside in the gas phase, the total number of variables for grid cells containing three phases is 2Nc+6, where Nc is the total number of components in the fluid models, excluding water component using natural variable formulation.

Simulation models are often compromised (coarse cells, property up-scaling, incomplete physics), due to limitations in simulator technology and access to high computing power. Both computing power and technology have vastly evolved over the past 30 years. Unfortunately, previous choices made in the legacy reservoir simulators have limited their ability to adopt, and hence prevented them from harnessing these advances in an optimal fashion resulting in inefficiencies in parallel runs. We present the results of a next generation highly scalable commercial simulator on a Giga cell multi-component, compositional model of a gigantic field with several hundred wells and several years of production. The previous model was a 5.7 million active cell, multi-component compositional model that did not properly capture the main lateral and vertical heterogeneities. These heterogeneities consist of very thin high permeability streaks that play a major role in the pressure depletion. With the acquisition of a next generation simulator technology, a higher resolution model, with 47 million active cells was built. The performance of our next generation simulator, complemented with in-house developments, was a substantial 4-fold faster in CPU time than the same case using a legacy commercial simulator. However, the average cell size was still in the order of hundreds of meters laterally for this new model. A refinement of the cell size resulted in a billion cell (Giga) model. This model was simulated using our high-performance cluster computer. We also discuss the challenges of the simulation workflow in terms of pre-post Processing and IT environment. Introduction Reservoir rocks have a highly complex disorderly structure over a wide range of length scales. The heterogeneities in these rocks play a very dominant role in the transport of fluid within them. Therefore, better understanding of the processes that determine the amount of hydrocarbon that can be recovered is an important objective for the oil industry. To understand and better predict how fluids will flow in the reservoir, it is necessary to determine the nature, extent and distribution of non-reservoir intervals. The latter highlights the importance of understanding the nature of reservoir heterogeneity, which occurs at various scales from large-scale faults, external and internal sand body characteristics, to microscopic features such as porosity and permeability. To deal with these uncertainties, the conventional approach is to build a detailed geological model, which is then upscaled and entered into a legacy reservoir simulator. Important geological features are most times lost during this upscaling process. Legacy reservoir simulators were developed at a time when high performance computing technology was still at its infancy. Unfortunately, choices made in the development of these simulators limited their ability to adopt, and hence prevented them from harnessing the advancement in computing power and technology in an optimal fashion. This led to some compromises in the building of reservoir simulator models. However, with the advancement of computer technology especially in the domain of parallel and high performance computing, modifying the legacy simulators to take full advantage of these technologies was not only cumbersome but compromises had to be made.

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In reservoir simulation, the nonlinear solver is used to solve the nonlinear system of conservation and phase-equilibrium equations at each time step. The convergence behavior of this solver is vital for the robustness and performance of any reservoir simulator. Based on the basic solution variables used in a reservoir simulator, we have natural variable based simulators with phase-dependent solution variables (e.g. phase saturations), and mass/overall variable based simulators without phase-dependent solution variables. The nonlinear convergence behavior between these two types of simulators has been compared previously. It has been found that natural variable based simulator works well for immiscible and miscible flow, while sometimes it has apparent convergence issues for near-miscible flow. In this paper, we analyze the fundamental physical and numerical causes for the nonlinear convergence difficulty encountered for near-miscible flow for a natural variable based simulator and study why the same issues do not appear in both immiscible and miscible flow. Based on our analysis, some carefully designed user tuning parameters can be applied to partially alleviate the convergence issue for near-miscible flow. Unfortunately this is neither general nor good enough. To fundamentally solve this issue, we propose a straightforward nonlinear solver modification which is applicable for all types of displacements (immiscible/miscible/near-miscible/mixed). We demonstrate improvements on the real field cases with different types of flow. For near-miscible and mixed type of displacements, the improvements in Newton iterations can be significant, while for the other types, our nonlinear solver modification does not show the adverse effect. For reference, we also compared the convergence behavior of the proposed solver with that from a standard mass variable based commercial simulator.