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ECMOR XV - 15th European Conference on the Mathematics of Oil Recovery
- Conference date: 29 Aug 2016 - 01 Sep 2016
- Location: Amsterdam, Netherlands
- ISBN: 978-94-6282-193-4
- Published: 29 August 2016
161 - 163 of 163 results
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Block-preconditioned Krylov Methods for Coupled Multiphase Reservoir Flow and Geomechanics
Authors S. Klevtsov, N. Castelletto, J.A. White and H.A. TchelepiThe present work focuses on numerical solution of partial differential equations coupling multiphase flow and mechanical processes in geological formations. The balance equations are discretized using finite volume and finite element techniques. A backward implicit time integration scheme is selected. Linearization of the system of nonlinear algebraic equations produces a Jacobian matrix characterized by block structure due to the coupled nature of mass and momentum balance equations. Based upon approximate block-factorization of the Jacobian, we propose a two-stage preconditioner for fully implicit simulation. Generalized Constrained Pressure Residual approach is used to construct a pressure-displacement system, involving the unknowns characterized by long range error components. Specifically, in the first stage elliptic components of the coupled problem are tackled, with the reduced system being solved by the fixed-stress block-partitioned algorithm recently advanced in the context of single-phase poromechanics. Once pressure and displacement degrees of freedom have been updated, a second stage preconditioner is applied to deal with the other unknowns, namely saturations. Note that, from an algebraic standpoint, both CPR and fixed-stress strategies are built on particular choices of sparse Schur complement approximations, which combine algebraic and physically-based arguments. Numerical results are presented to illustrate performance and robustness of the proposed preconditioner.
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Algebraic Dynamic Multilevel (ADM) Method for Immiscible Multiphase Flow in Heterogeneous Porous Media with Capillarity
Authors M.C. Cusini, C. van Kruijsdijk and H. HajibeygiAn algebraic dynamic multilevel method (ADM) is developed for fully-implicit (FIM) simulations of multiphase flow in heterogeneous porous media with strong non-linear physics. The fine-scale resolution is defined based on the heterogeneous geological one. Then, ADM constructs a space-time adaptive FIM system on a dynamically defined multilevel nested grid. The multilevel resolution is defined using an error estimate criterion, aiming to minimize the accuracy-cost trade-off. ADM is algebraically described by employing sequences of adaptive multilevel restriction and prolongation operators. Finite-volume conservative restriction operators are considered whereas different choices for prolongation operators are employed for different unknowns. The ADM method is applied to challenging heterogeneous test cases with strong nonlinear heterogeneous capillary effects. It is illustrated that ADM provides accurate solution by employing only a fraction of the total number of fine-scale grid cells. ADM is an important advancement for multiscale methods because it solves for all coupled unknowns (here, both pressure and saturation) simultaneously on arbitrary adaptive multilevel grids. At the same time, it is a significant step forward in the application of dynamic local grid refinement techniques to heterogeneous formations without relying on upscaled coarse-scale quantities.
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Mechanisms of Formation of Natural Hydrogen Reservoirs in Thermal Aquifers - Impact of Bacteria and Gas Bubble Dynamics
Authors M. Panfilov, S. Zaleski and C. JosserandUnderground hydrogen reservoirs, whose existence has been confirmed recently by geologists all over the world, represent a new source of renewable energy. Hydrogen is formed as the product of reaction of serpentinization between ferromagnesian minerals of the Mantle and water in the offshore zones of subduction or in continental zones at considerable depth beneath hydrothermal aquifers. Initially dissolved in water, hydrogen can create free gas bubbles when the local concentration of H2 dissolved in water exceeds the equilibrium value. The bubbles raise up and create the gas cap of free hydrogen. This process is significantly influenced by methanogen bacteria inhibiting in aquifers and consuming hydrogen for their metabolism. The reactions initiated by bacteria leads to the appearance of other volatile components as methane. The dimension, the form of the gas cap and the concentration of hydrogen and methane determine the efficiency of gas production and the energy potential of the reservoir. In the present paper we develop the conceptual mathematical model of gas cap formation in hydrogen reservoir. The bacterial activity is described by the equation of population dynamics with specific kinetic functions obtained by the authors by treating experimental data. The formation of free gas is modelled in terms of the formation of oversaturated nuclei, their growth and simultaneous motion of isolated bubbles. As far as the bubbles grow, they stick together and create continuous free gas. Thus, the hydrogen motion consists of two stages: (i) the motion of isolated bubbles, controlled by the equations of ganglion dynamics; and (ii) the motion of continuous gas through water, governed by Darcy’s law. The bubble growth is ensured by the mass exchange with hydrogen dissolved in water, which involves a non-equilibrium in the average hydrogen concentrations. Such a problem of hydrogen raising is solved analytically in simplified situation without bacteria. The problem can be reduced to a system of nonlinear hyperbolic equations, which has either continuous or discontinuous solutions (shock waves) depending on the degree of the non-equilibrium. Multiples deformations of the shocks under gas raising are described. The impact of bacteria is studied numerically by using the open source Basilisk (developed by D’Alembert Institute). We have revealed non trivial scenarios of the appearance of piece-wise constant traveling waves, or auto-oscillations caused by the nonlinear population dynamics. The result obtained enables us to give estimation to the characteristic time of gas cap formation and the evolution of its composition in time.
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