Nonlinear Convergence for Near-Miscible Problem: A Mystery Unveiled for Natural Variable Simulator

Cao, Hui; Zaydullin, Rustem; Obi, Eguono

doi:10.2118/182633-ms

Cited by 7 publications

(1 citation statement)

References 12 publications

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“…That can be avoided if a standalone simulator is implemented entirely from the OBL perspective, as shown by Khait et al (2017) For all simulations, we used the same discretization operators (Eqs. 6 and 8) derived from the seventh layer of the SPE10 model (Christie and Blunt 2001) shown in Fig. 3.…”

Section: The Performance Of the Obl Approachmentioning

confidence: 99%

Adaptive Parameterization for Solving of Thermal/Compositional Nonlinear Flow and Transport With Buoyancy

Khait

Voskov

2018

SPE Journal

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Summary The nonlinear nature of flow and transport in porous media requires a linearization of the governing numerical-model equations. We propose a new linearization approach and apply it to complex thermal/compositional problems. The key idea of the approach is the transformation of discretized mass- and energy-conservation equations to an operator form with separate space-dependent and state-dependent components. The state-dependent operators are parameterized using a uniformly distributed mesh in parameter space. Multilinear interpolation is used during simulation for a continuous reconstruction of state-dependent operators that are used in the assembly of the Jacobian and residual of the nonlinear problem. This approach approximates exact physics of a simulation problem, which is similar to an approximate representation of space and time discretization performed in conventional simulation. Maintaining control of the error in approximate physics, we perform an adaptive parameterization to improve the performance and flexibility of the method. In addition, we extend the method to compositional problems with buoyancy. We demonstrate the robustness and convergence of the approach using problems of practical interest.

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Section: The Performance Of the Obl Approachmentioning

confidence: 99%

Adaptive Parameterization for Solving of Thermal/Compositional Nonlinear Flow and Transport With Buoyancy

Khait

Voskov

2018

SPE Journal

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Relative Permeability of Near-Miscible Fluids in Compositional Simulators

Alzayer

Voskov

2017

Transp Porous Med

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A Variable-Switching Method for Mass-Variable-Based Reservoir Simulators

Alpak

Vink

2018

SPE Journal

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Summary Field-scale simulations of complex processes often suffer from long simulation times. One of the main reasons is that the Newton-Raphson (NR) process used to solve each simulation timestep requires many iterations and small timestep sizes to converge. Because the selection of solution variables affects the nonlinearity of the equations, it is attractive to have a practical method to rapidly explore the use of alternative primary variables in general-purpose reservoir simulators. Many reservoir simulators use pressure, saturations, and temperature in each gridblock as the primary solution variables, which are referred to as natural variables. There is also a class of reservoir simulators that uses pressure, total component masses (or moles), and internal energy in each gridblock as primary variables. These simulators are referred to as mass-variable-based reservoir simulators. For a given choice of primary variables, most simulators have dedicated, highly optimized procedures to compute the required derivatives and chain rules required to build the Jacobian matrix. Hence, it is usually not possible to switch between mass and natural variables. In this work, however, we establish a link at the numerical-solution level between natural- and mass-variable formulations and design a novel (nonlinear) block-local method that transforms mass-variable shifts (computed at each NR iteration) into equivalent natural-variable shifts. We demonstrate on a number of simulation models of varying complexity that by use of the proposed approach, a mass-variable-based flow simulator can still effectively use natural variables, where the change of variables can be made locally per gridblock. Results indicate that in some models the total number of NR iterations, linear-solver (LS) iterations, and timestep-size cuts (caused by the nonconvergence of the NR procedure, also known as backups) are reduced when using natural variables instead of mass variables. However, the improvement is relatively modest and not generally observed. Our findings also signify that depending on the specific characteristics of the simulation problem at hand, mass-variable-based simulators may perform comparably or outperform natural-variable-based simulators. The proposed variable-switching method can be used effectively to evaluate the effect of using different primary solution variables on problem nonlinearity and solver efficiency. With this method, the effect of interchanging primary solution variables on problem nonlinearity can be rapidly evaluated.

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Nonlinear Convergence for Near-Miscible Problem: A Mystery Unveiled for Natural Variable Simulator

Cited by 7 publications

References 12 publications

Adaptive Parameterization for Solving of Thermal/Compositional Nonlinear Flow and Transport With Buoyancy

Adaptive Parameterization for Solving of Thermal/Compositional Nonlinear Flow and Transport With Buoyancy

Relative Permeability of Near-Miscible Fluids in Compositional Simulators

A Variable-Switching Method for Mass-Variable-Based Reservoir Simulators

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