IORSim: A Mathematical Workflow for Field-Scale Geochemistry Simulations in Porous Media
Authors: Feldmann Felix , Nødland Oddbjørn , Sagen Jan , Antonsen Børre , Sira Terje , Vinningland Jan Ludvig , Moe Robert , Hiorth Aksel 
Published: June 2024

Abstract
Reservoir modeling consists of two key components: the reproduction of the historical performance and the prediction of the future reservoir performance. Industry-standard reservoir simulators must run fast on enormous and possibly unstructured grids while yet guaranteeing a reasonable representation of physical and chemical processes. However, computational demands limit simulators in capturing involved physical and geochemical mechanisms, especially when chemical reactions interfere with reservoir flow. This paper presents a mathematical workflow, implemented in IORSim, that makes it possible to add geochemical calculations to porous media flow simulators without access to the source code of the original host simulator. An industry-standard reservoir simulator calculates velocity fields of the fluid phases (e.g., water, oil, and gas), while IORSim calculates the transport and reaction of geochemical components. Depending on the simulation mode, the geochemical solver estimates updated relative and/or capillary pressure curves to modify the global fluid flow. As one of the key innovations of the coupling mechanism, IORSim uses a sorting algorithm to permute the grid cells along flow directions. Instead of solving an over-dimensionalized global matrix calling a Newton–Raphson solver, the geochemical software tool treats the species balance as a set of local nonlinear problems. Moreover, IORSim applies basis swapping and splay tree techniques to accelerate geochemical computations in complex full-field reservoir models. The presented work introduces the mathematical IORSim concept, verifies the chemical species advection, and demonstrates the IORSim computation efficiency. After validating the geochemical solver against reference software, IORSim is used to investigate the impact of seawater injection on the NCS Ekofisk reservoir chemistry.

Article Highlights

The IORSim sorting algorithm decouples the nonlinear geochemical reaction calculations into recurring one-dimensional problems to assure numerical stability and computation efficiency. To the best of our knowledge, this work presents the mathematical concept, implementation, and application of topological sorting for the first time on (industry) field-scale problems.

IORSim combines topological sorting with basis swapping and splay trees to significantly reduce computation times. Moreover, a high-speed forward simulation mode was developed to allow the post-advection of chemical components to visualize species distribution, water chemistry, and mineral interactions. If the geochemical reactions interfere with the fluid flow, the IORSim backward mode uses relative permeability curves to update the global fluid flow at each time step.

We validate the implemented topological scheme on a reservoir grid, show the computation efficiency, and compare the impact of explicit, implicit, and grid refinement on numerical dispersion.

The decoupled flow simulator and geochemical reaction calculations allow seamless integration of full-field reservoir models that contain complex geological structures, a large number of wells, and long production histories.

The computation capabilities of IORSim are demonstrated by simulating and reproducing the impact of seawater injection in the southern segment of the giant Ekofisk field (more than 50 years of injection and production history). IORSim shows that seawater injection changed the Ekofisk mineralogy and impacted the produced water chemistry. In the investigated Ekofisk case, seawater promoted calcite dissolution and led to the precipitation of magnesite and anhydrite. Moreover, surface complexation modeling revealed that sulfate is adsorbed on the calcite surface.