Opening the Black Box: A Critical and Comparative Investigation of Solvers and Methods in Conventional and Next-generation Reservoir Simulators
Authors: Temizel Cenk , Hancioglu Baris , Purwar Suryansh , Dursun Serkan , Tek Suleyman 
Published: April 2020

Abstract
The term "next-generation" has been used related to reservoir simulation within the industry for almost a decade. This paper discusses factors that make next-generation simulators more special and effective than well-known previous methods by outlining the basis as well as the differences between the methods. The conventional reservoir simulator discussed makes use of the fully implicit (FI) and implicit in pressure / explicit in saturation (IMPES) methods. Fully implicit methods are more stable than explicit methods; however, more core memory and computation effort per time step are required when using fully implicit methods. Time truncation errors encountered when large time steps are used and the difficulties with implementation of higher order methods to reduce spatial truncation are some of the drawbacks of fully implicit formulations. Krylov subspace algorithms are the sole option for linear system solvers.
The next-generation simulator discussed uses a relaxed volume balance approach, which is better than a mass balance formulation because the volume balance is a local error, and does not accumulate over time. The volume balance is simply the difference between the fluid volume and the pore volume in each grid block in the model, and is the primary convergence criteria in a volume balance model. A review and systematic comparison of solvers and solution methods is provided, such as finite difference methods (FDMs) and finite element methods (FEMs). Finally, the results of runs conducted on the SPE CSP 9 from both "conventional" and next-generation simulators are provided along with a comparison of processing times.

Introduction
The potential of reservoir simulation was realized in the mid-1940s and the first reservoir simulators were developed in the 1950s. Analysis methods that supplement reservoir simulation include well testing, field observation, laboratory tests, field pilot tests, simple mathematical analyses, and extrapolation from the performance of other reservoirs. Two kinds of simulators predate numerical reservoir simulation: electric analogs and scaled physical models. As electric analog models are outmoded, focus within the industry has been on fluid-flow simulators (Mattax and Dalton 1990).
The validity of a reservoir simulation model is tested using history matching. The reservoir simulation results are compared with real field data as it becomes available. The smart field concept provides the opportunity for real-time collection of field performance data, and real-time history matching is achieved using automated workflows.
Numerical simulation is a convenient tool used for production forecasting, thus helping make correct reservoir management decisions. Traditional finite difference (FD) simulators dominate both theoretical and practical work in reservoir simulation. Conventional FD simulation is underpinned by three physical concepts: conservation of mass, isothermal fluid phase behavior, and the Darcy approximation of fluid flow through porous media. Thermal simulators (most commonly used for heavy crude oil applications) also permit conservation of energy, allowing temperatures to change within the reservoir.