An Adaptive-Implicit Switching Criterion Based on Numerical Stability Analysis

This paper describes an Adaptive Implicit Method (AIM) for reservoir simulation. The method is based on an extension of the generalized compositional solution procedure. In addition to the creation of a robust method, we have tried to minimize the overhead associated with the method, so that our implementation is almost as fast as an IMPES (implicit-pressure-explicit-saturation) method when few implicit blocks are needed. Several test problems demonstrate important aspects of the switching logic and the tradeoffs between large highly implicit time steps and smaller time steps with less implicitness. We find that in most cases the greatest efficiency occurs when only a small number of blocks (less than 5 percent) are treated implicitly. In many cases the most efficient method is IMPES with time steps selected using the numerical stability calculations of AIM, Smaller time steps lead not only to higher efficiency, but also to solutions with less numerical dispersion. In general. AIM appears to benefit compositional problems more frequently than black oil problems.

SummaryRecently, graphics processing units (GPUs) have been demonstrated to provide a significant performance benefit for black-oil reservoir simulation, as well as flash calculations that serve an important role in compositional simulation. A comprehensive approach to compositional simulation based on GPUs has yet to emerge, and the question remains as to whether the benefits observed in black-oil simulation persist with a more complex fluid description. We present a positive answer to this question through the extension of a commercial GPU-based black-oil simulator to include a compositional description based on standard cubic equations of state (EOSs). We describe the motivations for the selected nonlinear formulation, including the choice of primary variables and iteration scheme, and support for both fully implicit methods (FIMs) and adaptive implicit methods (AIMs). We then present performance results on an example sector model and simplified synthetic case designed to allow a detailed examination of runtime and memory scaling with respect to the number of hydrocarbon components and model size, as well as the number of processors. We finally show results from two complex asset models (synthetic and real) and examine performance scaling with respect to GPU generation, demonstrating that performance correlates strongly with GPU memory bandwidth.NOTE: This paper is also published as part of the 2021 SPE Reservoir Simulation Conference Special Issue.

We propose a new, efficient, adaptive algebraic multigrid (AMG) solver strategy for the discrete systems of partial differential equations arising from structured or unstructured grid models in reservoir simulation. The proposed strategy has been particularly tailored to linear systems of equations arising in adaptive implicit methods. The coarsening process of the AMG method designed automatically employs information on the physical structure of the models; as a smoother, an adaptive ILUT method is employed, taking care of an efficient solution of the hyperbolic parts whilst providing adequately smooth errors for the elliptic parts. To achieve a good compromise of high efficiency and robustness for a variety of problem classes – ranging from simple, small black-oil to challenging, large compositional models – an automatic, adaptive ILUT parameter and AMG solver switching strategy, α-SAMG, has been developed. Its efficiency is demonstrated for eight industrial benchmark cases by comparison against standard one-level and AMG solvers as well as the pure one- level variant of the proposed new strategy. In addition, very promising results of first parallel runs are shown.

Practical considerations for adaptive implicit methods in reservoir simulation

Distinguished Author Series articles are general, descriptive representations that summarize the state of the art in an area of technology by describing recent developments for readers who are not specialists in thetopics discussed. Written by individuals recognized as experts in the area, these articles provide key references to more definitive work and presentspecific details only to illustrate the technology. Purpose: to informthe general readership of recent advances in various areas of petroleumengineering. "Today, desktop computers and a wide range of reservoir. simulation systemsprovide the engineer with an economic means to solve complex reservoir.engineering problems with efficiency." Introduction This paper describes the state of the art in reservoir simulation for thenonexpert, focusing primarily on advances that have occurred since a similarpaper was published by Coats1 in 1982. For completeness, a historyof simulation is given first, followed by a brief and simple review of thesimulation process. Advances in simulation technology are then described, highlighting those in reservoir description and simulation of naturallyfractured reservoirs, hydraulic fracturing, and horizontal wells. The future ofreservoir simulation is discussed last. Many papers have been presented since Coats' review in 1982. Rather thanrepeat the exhaustive list provided in the SPE indices, a reduced set ofpertinent references is given. I offer my apologies in advance to the authorsof the many excellent papers contributed during the past decade that are notmentioned here. History of Simulation In the broadest sense, reservoir simulation has been practiced since thebeginning of petroleum engineering. By the late 1940's, the potential ofreservoir simulation was recognized and several companies embarked on thedevelopment of both analog and numerical models to enhance the existinganalytical solutions, material balances, and ID Buckley-Leverett displacementcalculations. By the late 1950's, major commitments to fundamental research on thenumerical solution of flow equations began to bear fruit. The results werecrude, but certainly useful, computer programs for simulating reservoirs. Theseprograms represented a major advance and used the solution of sets offinite-difference equations to describe 2D and 3D, transient, multiphase flowin heterogeneous-porous media. For the first time, reservoir engineers couldsolve complex problems. The driving force for development of numerical-simulation systems was theability to predict the future performance of a reservoir under various "whatif" conditions so that better reservoir-management decisions could be made. This force still drives the use of reservoir simulation today. Current businessincentives for virtually all reservoir-simulation applications fall into one ormore of the following categories: economics; credibility and reliability;decision-making; arbitration and unitization; performance monitoring;nonelective studies resulting from safety, environmental, or regulatoryconcerns; and communications and personnel utilization.2 Throughout the 1960's, reservoir-simulation development was devoted largelyto three-phase, black-oil reservoir problems. Recovery methods that weresimulated included pressure depletion and various forms of pressuremaintenance. Many computer programs were developed to address most of thegeneral reservoir problems encountered. These programs operated on mainframecomputers and used decks of cards for input. During the 1970's, the picture changed remarkably because of theproliferation of research in EOR processes, advances in numerical-solutiontechniques, and the decreased size and increased speed of computers. Mathematical simulators were developed that extended beyond conventionalprimary and secondary recovery into such areas as chemical flooding, steamflooding, and in-situ combustion. Research during this period resulted insignificant advances in characterizing the physics of hydrocarbon displacementsunder the influences of temperature, chemical agents, and complexmulticomponent phase behavior. Simulators had to reflect chemical adsorptionand degradation, reaction kinetics, interfacial-tension-reduction effects, andmore complex equilibrium phase behavior. The range of reservoir-simulation application continued to expand during the1980's. Reservoir description, finally becoming a major topic on its own, advanced to the use of geostatistics to describe heterogeneities and to providereservoir definition not expressed in reservoir models. The technology to modelnaturally fractured reservoirs, including compositional effects, was alsodeveloped, with extensions into the simulation of hydraulic fracturing andhorizontal wells. and application to such complex processes as reservoirmonitoring.

Reservoir simulators are highly complex computer programs and are often treated as “black boxes” that act on standardized input formats. In part, this is due to the closed-source nature of commercial offerings commonly used in industry, but even when the source-code is available, modification of a fully featured simulator can be a daunting task: A reservoir simulation problem, when fully specified, can have a great number of parameters and functional relationships that are tightly coupled together in most implementations. This is an obstacle to workflows that go beyond forecasting and into optimization, parameter fitting and sensitivity analysis where the solution quantity of interest should be paired with gradients taken with respect to forces and parameters. The monolithic design of typical reservoir simulation codes cannot be separated from the technical and mathematical choices made when discretizing the governing equations: The implicitness required to handle pressure changes and strong coupling between different solution variables means that the Jacobian of the governing equations must be implemented with respect to the primary variables: An error-prone process when done manually, and highly time-consuming when considering coupled systems. Automatic differentiation (AD) is a common cure to this problem that can generate Jacobians, but often comes at a severe cost in runtime performance. A more practical issue is that high computational performance for simulation problems relevant to modern geoenergy operations necessitates implementation in a compiled language while optimization and history matching workflows that integrate many data sources are most naturally expressed in high-level scripting languages. We describe the design of JutulDarcy, an open-source porous media simulator written in the Julia language. JutulDarcy is designed from the ground up with extensibility and computation of sensitivities in mind, starting from the assumption that high-performance automatic differentiation enables us to radically rethink the way simulators are designed. Highlights of this design include arbitrary execution graphs for the equation terms, in which dependence relationships can be re-configured on the fly, easy coupling of models, computation of sensitivities with respect to all model parameters through an adjoint method with a parameter declaration system, and an assembly process with performance that can exceed that of compiled simulators with hand-coded Jacobians. We validate the simulator on a number of standard test cases (immiscible, black-oil, CO2 and compositional flow) and demonstrate MPI parallel performance on multi-million cell models. In addition, we offer a frank assessment of the relative strengths and weaknesses of the Julia programming language for scientific computing.

This paper describes application of Project INTERSECT, a next generation highly scalable reservoir simulator on real large scale field models. High resolution reservoir simulation is required to better define and describe fluid flow and enable improved field development and tactical operational planning. Massively parallel computing techniques overcome limitations of problem size and space resolution. This paper demonstrates that large-scale simulation models can be performed on commodity hardware taking advantage of evolution in multicpu hardware architecture and software engineering. This allows both geologists and reservoir engineers to include more realistic geologic and engineering detail for better and more reliable production optimization. Intense computer simulation is essential for effective reservoir management. The advances in reservoir characterization techniques and the industry drive towards the ‘smart oilfield’ with rapid model updates will require more efficient model processing to achieve timely field operational decisions. Parallel reservoir simulators have the potential to solve larger, more realistic problems than previously possible. The size and application of reservoir simulation problems have been limited by the availability of computing hardware, reservoir simulation architecture and of solution methods for solving large-scale heterogeneous problems. The next generation reservoir simulator demonstrates that key modeling challenges has been overcome by a software architecture and capability to model more realistic subsurface and surface models. Applications of the new reservoir simulator illustrates how typical reservoir engineering options such as local grid refinement, local grid coarsening, multilateral wells and aquifer modeling affect the overall parallel performance and scalability using highly heterogeneous large-scale models. Application of new modeling techniques highlight increased accuracy of modeling results and more reliable field development planning and reservoir management decisions.

Sequential Fully Implicit (SFI) schemes have been proposed as an alternative to the Fully Implicit Method (FIM). A significant advantage of SFI is that one can employ scalable strategies to the flow and transport problems. However, the primary disadvantage of using SFI compared with FIM is the fact that the splitting errors induced by the decoupling operator, which separates the pressure from the saturation(s), can lead to serious convergence difficulties of the overall nonlinear problem. Thus, it is important to quantify the coupling strength in an adaptive manner in both space and time. We present criteria that localize the computational cells where the pressure and saturation solutions are tightly coupled. The approach is using terms in the FIM Jacobian matrix, we quantify the sensitivity of the mass and volume-balance equations to changes in the pressure and the saturations. We identify three criteria that provide a measure of the coupling strength across the equations and variables. The standard CFL stability criteria, which are based entirely on the saturation equations, are a subset of the new criteria. Here, the pressure equation is solved using Algebraic MultiGrid (AMG), or a multiscale solver, such as the Multiscale Restricted-Smooth Basis (MsRSB) approach. The transport equations are then solved using a fixed total-velocity. These ‘coupling strength’ criteria are used to identify the cells where the pressure-saturation coupling is strong. The applicability of the derived coupling-strength criteria is tested using several test cases. The first test is using a gravitational immiscible dead-oil lock-exchange under a unit mobility ratio and large differences in density. For this case, the SFI algorithm fails to converge to the fully coupled solution due to the large splitting errors. Introducing a fully coupled solution stage on the local subdomains as an additional correction step restores nonlinear convergence. Detailed analysis of the ‘coupling strength’ criteria indicates that the criteria related to the sensitivity of the mass balance to changes in the pressure and the sensitivity of the volume balance to changes in the saturations are the most important ones to satisfy. Other test cases include an alternate gas-water-gas injection in a top layer of the SPE 10 test case and an injection-production scenario in a three-dimensional reservoir with layered lognormally distributed permeability. We propose novel criteria to estimate the strength of coupling between pressure and saturation. These CFL-like numbers are used to identify the cells that require fully implicit treatment in the nonlinear solution strategy. These criteria can also be used to improve the nonlinear convergence rates of Adaptive Implicit Methods (AIM).

13 - Reservoir Simulation

Produced water (PW) is one of the byproducts from gas and gas-condensate production in many gas fields in the Gulf of Thailand. One method to dispose the PW is to inject into shallow aquifer through injection wells. The advantages of this method are high disposal capacity, potential harmful fluids are permanently removed from direct human and indirect food chain, interaction and to prevent generation of byproducts from the treatment process. In this study, the most suitable formations sand units A and B in M field in the Gulf of Thailand was selected. The reasons are high porosity, permeability and reservoir volume. Two wells were used to inject the PW into shallow aquifers, located above the producing formation. In this study, a 3D reservoir simulator ECLIPSE 100 is used to perform reservoir model construction and performance prediction. The reservoir simulation models of targeted sand units were constructed based on structural map, well logging data and special core analysis data. Initial reservoir conditions and fluid properties were input to complete the models. After initializing the homogeneous model (HM), Channel-I and Channel-II models were generated to introduce heterogeneity. Under the three models a number of simulation cases were run at different initial well injection rates with single and both well injection options in order to investigate injection capacity and performance. The impact of different well injection rates on injection capacity and performances were investigated. In addition, under intermittent injection the gain of injection performance (IP) was also investigated. Finally, the best sand candidate in terms of maximum cumulative injection volume was recommended.

Recently, use of parallel machines in reservoir simulation has received considerable attention from the petroleum industry. This paper presents parallelization of a 3D compositional, equation-of-state reservoir simulator on the CM-5 and KSR-1. To the best of our knowledge, this is the first time that the parallelization of a compositional reservoir simulator has been performed on both the CM-5 and KSR-1. For new users of the CM-5 machines, the software and hardware of CM-5 architecture is presented, as well as details of the parallelization techniques. For example, domain decomposition, I/O's, phase equilibrium computations, and well model are described. The parallelism techniques on the KSR-1 are presented with the emphasis on the porting of the phase equilibrium calculation. The performance of each machine is evaluated by showing the speedup on different sets of processing nodes. Two test problems were used to explore the capability of the parallelized version of the code; one is a waterflood problem and the other is a CO2 multiple contact miscible flood, both in a West Texas oil field. These field problems were run on 1, 2, 4, 8, 16, and 32 processors to get insight into the locations of communication bottlenecks, generally occurring in the programming with distributed memory machines. The problems of latency and bandwidth which are associated with communication efficiency of the CM-5 are also addressed.

Hysteresis effects of three-phase relative permeabilities on black-oil reservoir simulation under WAG injection protocols

An efficient, non-iterative flash calculation algorithm has been developed for equation of state (EOS) compositional reservoir simulation problems. In this algorithm, the flash calculation is carried out by solving two sets of linear equations. The solution of these equations is the mole number of each component in each phase. The phase saturation can thus be obtained without solving the Rachford-Rice equation1. Tests against many PVT data sets show that the new approach gives the same results as those computed by the fugacity iteration based on the EOS. However, the computation time is reduced significantly. A series of reservoir simulations has been conducted by an EOS compositional reservoir simulator, UTCOMP, with this new flash approach. Comparisons are made with those performed by UTCOMP with a rigorous fugacity iteration of the Peng-Robinson5 EOS. The results obtained by these two methods are in very good agreement. However, a considerable reduction of the CPU time is generally accompanied by using the new approach. For the runs in which an immiscible displacement process takes place in the reservoir, the computational burden in the phase behavior calculations is reduced by around 90%. Correspondingly, the reduction of the total simulation time is as much as 65%. Besides, it is found that the number of components used affects on the CPU time of the simulations much less with the new approach. These observations may lead to the time used for an EOS compositional reservoir simulations with the new approach being comparable to a black-oil simulation without sacrificing computational accuracy. Also in this work an attempt is made to employ the non-iterative approach as a tool for providing the initial guess for the rigorous EOS iteration. A considerable reduction of the CPU time is still observed.

New fully implicit formulations for the multicomponent surfactant-polymer flooding reservoir simulation

A Preconditioned Adaptive Implicit Method for Reservoirs with Surface Facilities Thomas J. Byer; Thomas J. Byer Stanford U. Search for other works by this author on: This Site Google Scholar Michael G. Edwards; Michael G. Edwards Stanford U. Search for other works by this author on: This Site Google Scholar Khalid Aziz Khalid Aziz Stanford U. Search for other works by this author on: This Site Google Scholar Paper presented at the SPE Reservoir Simulation Symposium, Houston, Texas, February 1999. Paper Number: SPE-51895-MS https://doi.org/10.2118/51895-MS Published: February 14 1999 Cite View This Citation Add to Citation Manager Share Icon Share Twitter LinkedIn Get Permissions Search Site Citation Byer, Thomas J., Edwards, Michael G., and Khalid Aziz. "A Preconditioned Adaptive Implicit Method for Reservoirs with Surface Facilities." Paper presented at the SPE Reservoir Simulation Symposium, Houston, Texas, February 1999. doi: https://doi.org/10.2118/51895-MS Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex Search Dropdown Menu nav search search input Search input auto suggest search filter All ContentAll ProceedingsSociety of Petroleum Engineers (SPE)SPE Reservoir Simulation Conference Search Advanced Search This paper was prepared for presentation at the 1999 SPE Reservoir Simulation Symposium held in Houston, Texas, 14-17 February 1999. Keywords: facility model, upstream oil & gas, implicit formulation, reservoir simulation, cpu time, preconditioner, subdomain, spe 51895, artificial intelligence, convergence Subjects: Reservoir Simulation This content is only available via PDF. 1999. Society of Petroleum Engineers You can access this article if you purchase or spend a download.