Automatic Differentiation Framework for Compositional Simulation on Unstructured Grids with Multi-Point Discretization Schemes

Zhou, Yifan; Tchelepi, Hamdi A.; Mallison, Bradley T.

doi:10.2118/141592-ms

Cited by 65 publications

(32 citation statements)

References 24 publications

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“…The first expression-template-based AD dates back to 2001 when Aubert et al [2] applied it in a flow control problem. In recent years, expression-templatebased AD has been introduced to reservoir simulators [12,[33][34][35]. However, these AD implementations all make use of the forward mode which is convenient for application but computationally inefficient for sophisticated expressions.…”

Section: Backward Mode By Expression Templatesmentioning

confidence: 99%

A backward automatic differentiation framework for reservoir simulation

Zhang

2014

Comput Geosci

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In numerical reservoir simulations, Newton's method is a concise, robust and, perhaps the most commonly used method to solve nonlinear partial differential equations (PDEs). However, as reservoir simulators incorporate more and more physical and chemical phenomena, writing codes that compute gradients for reservoir simulation equations can become quite complicated. This paper presents an automatic differentiation (AD) framework that is specially designed for simplifying coding and simultaneously maintaining computational efficiency. First a parse tree for a mathematical expression is built and evaluated with the backward mode AD, and then the derivatives with respect to the expression's arguments are transformed to derivatives with respect to the PDE's independent variables. The first stage can be realized either by runtime polymorphism to gain higher flexibility or by compile-time polymorphism to gain faster execution speed; the second stage is realized by linear combinations of sparse vectors, which can be accelerated by recording the target column indices. The AD framework has been implemented in an in-house reservoir simulator. Individual tests on some complex mathematical expressions were carried out to compare the speed of the manual implementation, the runtime polymorphic implementation and the compile-time polymorphic implementation of the differentiation. Then the performance of the three was analyzed in complete simulations. These cases

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Section: Backward Mode By Expression Templatesmentioning

confidence: 99%

A backward automatic differentiation framework for reservoir simulation

Zhang

2014

Comput Geosci

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“…Using the capabilities of ADETL, an Automatic Differentiation General Purpose Research Simulator (ADGPRS) was developed (Voskov and Tchelepi, 2012). ADGPRS is a unified reservoir simulation framework providing an extensive set of nonlinear formulations (Voskov, 2012;Zaydullin et al, 2013); flexible spatial discretization (Zhou et al, 2011); extended physics models (Iranshahr et al, 2013;Zaydullin et al, 2014a;Garipov et al, 2016); inverse capabilities (Kourounis et al, 2010;Volkov and Voskov, 2016); geothermal formulation (Wong et al, 2015). We use ADGPRS for the implementation and performance comparisons in this study.…”

Section: Introductionmentioning

confidence: 99%

Operator-based Linearization for Non-isothermal Multiphase Compositional Flow in Porous Media

Khait¹,

Voskov²

2016

Proceedings

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SUMMARYNon-isothermal multiphase compositional simulation is based on the solution of governing equations describing mass and energy transfer in the subsurface. The solution strategy requires a linearization of strongly nonlinear governing equations describing the process. Usually, a Newton-based method is used for the linearization that demands an assembly of a Jacobian matrix and residuals for a fully coupled system of equations. Recently, a new linearization approach was proposed for compositional problems and tested for simulation of binary compositional and low-enthalpy geothermal flow. The key idea of the approach is the transformation of discretised mass conservation equations to an operator form with separate space-dependent and state-dependent components. This transformation provides an opportunity for an approximate representation of exact physics (physical properties) of the problem. Specifically, each term of conservation equations is represented as a product of two different operators. The first operator depends on a current physical state of a system and contains different properties such as density, viscosity, relative permeability, etc. The second operator captures both spatially altered properties such as permeability and the rest of state variables such as pressure in the discrete approximation of the gradient. At the pre-processing stage, all state-dependent operators are uniformly parametrized within the physical space of the problem (pressure-composition intervals). During the simulation process, a multi-linear interpolation is applied to approximate the first type of operators, while the second type of operators is processed based on the conventional approach. In this work, we have extended this approach to general purpose simulation. We introduced the operator-based parametrization of mass and energy conservations equation based on the pressure, composition, temperature, and porosity. In addition, the approach has been extended and tested on truly multi-component systems of practical interest. The accuracy and robustness of the new method have been tested against the results of simulations based on the conventional approach.

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“…This framework is designed to simulate thermal multiphase multi-component flow in porous media [11,33]. AD-GPRS has several nonlinear formulations [28,34], generic multi-point flux approximation for space discretization, flexible adaptive implicit method for time discretization [36], and shared-memory parallel realization [22]. An important part of the AD-GPRS framework is the optimization module [24].…”

Section: Introductionmentioning

confidence: 99%

“…The reservoir model equations are discretized using a flexible discretization framework [36]. The fully implicit method and two-point flux approximation are applied for the time and space discretizations, respectively.…”

Section: Introductionmentioning

confidence: 99%

Effect of Time Stepping Strategy on Adjoint-based Production Optimization

Volkov

Voskov

2014

Proceedings

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The adjoint gradient method is well recognized for its efficiency in large-scale production optimization. When implemented in a sequential quadratic programming (SQP) algorithm, adjoint gradients enable the construction of a quadratic approximation of the objective function and linear approximation of the nonlinear constraints using just one forward and one backward simulation (with multiple right-hand sides). In this work, the focus is on the performance of the adjoint gradient method with respect to the adaptive time step refinement generated in the underlying forward simulations. First, we demonstrate that the mass transfer in reservoir simulation and, as a consequence, the net-present value (NPV) function are more sensitive to the degree of the time step refinement when using production bottom-hole pressure (BHP) controls than when using production rate controls. Effects of this sensitivity on optimization process are studied using six examples of uniform time stepping with different degrees of refinements. By comparing those examples, we show that corresponding optimal solutions for target production BHPs deviate at early stages of the optimization process. It indicates an inconsistency in the evaluation of the adjoint gradients and NPV function for different time step refinements. effects of this inconsistency on the results of a constrained production optimization. Two strategies of nonlinear constraints are considered: (i) nonlinear constraints handled in the optimization process and (ii) constraints applied directly in forward simulations with a common control switch procedure. In both strategies, we observe that the progress of the optimization process is greatly influenced by the degree of the time step refinement after control update. In the case of constrained simulations, the presence of control switches combined with large time steps after control update forces adaptive refinement to vary the time step size significantly. As a result, the inconsistency of the adjoint gradients and NPV values provoke an early termination of the SQP algorithm. In the case of constrained optimization, the inconsistencies in gradient evaluations are less significant, and the performance of the optimization process is governed by a satisfaction of nonlinear constraints in SQP algorithm.

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Automatic Differentiation Framework for Compositional Simulation on Unstructured Grids with Multi-Point Discretization Schemes

Cited by 65 publications

References 24 publications

A backward automatic differentiation framework for reservoir simulation

A backward automatic differentiation framework for reservoir simulation

Operator-based Linearization for Non-isothermal Multiphase Compositional Flow in Porous Media

Effect of Time Stepping Strategy on Adjoint-based Production Optimization

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