The Double Constraint Inversion Methodology by Wouter Zijl Florimond De Smedt Mustafa El-Rawy & Okke Batelaan

Author:Wouter Zijl, Florimond De Smedt, Mustafa El-Rawy & Okke Batelaan
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

3.8 Boundary Conditions “Upside Down”

Suppose that we consider a problem in which only flux boundary conditions are imposed. Such types of problems are frequently considered in petroleum reservoir simulations, where the fluids (water, oil, gas) are contained in a closed reservoir and flow is caused only by production and injection wells. Provided that the volumetric balance “production rate equals injection rate” (Eq. 2.​3) is honored, the flux model results in a well-posed problem. For a specified conductivity field, the fluxes and head gradients can be determined everywhere in the flow field, while the head is known up to a constant. However, some, not all, numerical methods for solving the system of algebraic equations perform better if in one point the head is specified. In the double constraint method, this means that for the flux model, all production/injection rates are imposed except for one well (the “upside-down well”) where the well head is imposed. In that case, the head run is based on imposed well heads, except for the “upside-down well,” where the volumetric flow rate is imposed. Similar types of problems may be encountered in hydrogeology. Below we analyze the consequences of such a deviation from the original flux model and head model principle.

We simplify the analysis for an isotropic medium for which we minimize a modified version of Darcy residual Eq. 3.3.

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