Thermodynamic Equilibrium Computation of Systems with an Arbitrary Number of Phases Flow Modeling with Lattice Boltzmann Methods: Application for Reservoir Simulation


Cédric Fracès Gasmi







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Reservoir recovery processes involve complex mass and heat transfer between the injected uid and the resident rock-fluid system. Thermal-compositional reservoir simulators can be used to plan such displacement processes, in which the phase behavior is computed with an Equation of State (EoS). These thermodynamic-equilibrium computations include phase-stability tests and ash calculations, and can consume a significant fraction of the total simulation time, especially for highly detailed reservoir models and a large number of components. Here, we propose a general Compositional Space Parameterization (CSP) method for complex mixtures, especially those where more than two uid phases can coexist in parts of the parameter space. For a given pressure (P), temperature (T) and overall composition, a unique tie-simplex (tie-line for two phases, tie-triangle for three phases, etc.) can be defined. For a particular composition at P and T, the tie-simplex provides the necessary phase equilibrium information (i.e., phase state and phase compositions). For compositional ow simu- lation, a set of tie-simplexes can be calculated in a preprocessing step, or adaptively constructed during the simulation. The tie-simplex representation can be used to replace standard phase-equilibrium calculations completely, or it can be used as an initial guess for standard EoS calculations. Challenging examples with two and three phases are presented to validate this tie-simplex CSP approach. Standard EoS meth- ods, which are widely used in industrial compositional simulators, are compared with CSP-based simulations for problems with large numbers of components and complex two- and three-phase behaviors spanning wide ranges of pressure and temperature. The numerical experiments indicate that our multi-dimensional tie-simplex represen- tation combined with linear pressure and temperature interpolation in tie-simplex space, which is implemented as an adaptive tabulation strategy, leads to highly ro- bust and ecient computations of the phase behavior associated with compositional ow simulation.

The characterization of reservoir models requires information such as porosity, permeability, relative permeability, and capillary pressure. Various techniques are used to describe the pore-scale details and model the ow dynamics. This knowledge is then used to estimate the macroscopic (Darcy-scale) properties and solve the macroscopic equations governing ow and transport in very large domains. We survey different pore-scale simulators based on Lattice Boltzman methods. We present qualitative and quantitative results obtained from available simulators, as well as, our own implementation of existing algorithms. We document and test different approaches and give an overview of the advantages and the challenges that remain to be resolved.

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