A meshfree generalized finite difference method for solution mining processes
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A meshfree generalized finite difference method for solution mining processes Isabel Michel1
· Tobias Seifarth1
· Jörg Kuhnert1
· Pratik Suchde1
Received: 30 January 2020 / Revised: 23 July 2020 / Accepted: 19 August 2020 © The Author(s) 2020
Abstract Experimental and field investigations for solution mining processes have improved intensely in recent years. Due to today’s computing capacities, three-dimensional simulations of potential salt solution caverns can further enhance the understanding of these processes. They serve as a “virtual prototype” of a projected site and support planning in reasonable time. In this contribution, we present a meshfree generalized finite difference method (GFDM) based on a cloud of numerical points that is able to simulate solution mining processes on microscopic and macroscopic scales, which differ significantly in both the spatial and temporal scales. Focusing on anticipated industrial requirements, Lagrangian and Eulerian formulations including an Arbitrary Lagrangian–Eulerian (ALE) approach are considered. Keywords Meshfree methods · Generalized finite difference method · Lagrangian formulation · Arbitrary Lagrangian– Eulerian formulation · Solution mining
1 Introduction The basic motivation of this research is to provide a method that is able to simulate the long-term development of a salt cavern during a double-well solution mining process. Solution mining is used to extract underground water-soluble minerals such as salt and potash. A double-well convection process has been a preferred choice for solution mining due to its large recovery rate [2,33]. As the name suggests, this involves the use of two boreholes or wells for the extraction process: an injection well and a recovery or extraction well. For the extraction of salt, freshwater is pumped into a salt deposit through the first “injection” well. Salt present in the cavern dissolves in the water to produce a saturated brine solution. This is then extracted at the second “extraction” well. A schematic of this process is shown in Fig. 1. The main direction of dissolution is vertical, which is controlled by alternate lifting of the injection and the extraction well. Electronic supplementary material The online version of this article (https://doi.org/10.1007/s40571-020-00353-2) contains supplementary material, which is available to authorized users.
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Isabel Michel [email protected]
In this work, we focus on modeling of the fluid flow involved in such a double-well solution mining procedure, including the formation of the salt–water solution. An essential aspect of this is to accurately model the long-term geometrical evolution of the salt cavern. This is needed to steer the actual process of solution mining, in terms of, for example, determining when and at what rate the injection and extraction wells are raised. However, numerically modeling this is very challenging, as it is a highly dynamic threedimensional process involving different spatial and temporal scales. Over the timescale of several
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