Rainer Helmig

Martin Schneider, Kilian Weishaupt, Dennis Gläser et al.

A discretization is proposed for models coupling free flow with anisotropic porous medium flow. Our approach employs a staggered grid finite volume method for the Navier-Stokes equations in the free flow subdomain and a MPFA finite volume method to solve Darcy flow in the porous medium. After appropriate spatial refinement in the free flow domain, the degrees of freedom are conveniently located to allow for a natural coupling of the two discretization schemes. In turn, we automatically obtain a more accurate description of the flow field surrounding the porous medium. Numerical experiments highlight the stability and applicability of the scheme in the presence of anisotropy and show good agreement with existing methods, verifying our approach.

Shubhangi Gupta, Barbara I. Wohlmuth, Rainer Helmig

We present an extrapolation-based semi-implicit multirate time stepping (MRT) scheme and a compound-fast MRT scheme for a naturally partitioned, multi-time-scale hydro-geomechanical hydrate reservoir model. We evaluate the performance of the two MRT methods compared to an iteratively coupled solution scheme and discuss their advantages and disadvantages. The performance of the two MRT methods is evaluated in terms of speed-up and accuracy by comparison to an iteratively coupled solution scheme. We observe that the extrapolation-based semi-implicit method gives a higher speed-up but is strongly dependent on the relative time scales of the latent (slow) and active (fast) components. On the other hand, the compound-fast method is more robust and less sensitive to the relative time scales, but gives lower speed up as compared to the semi-implicit method, especially when the relative time scales of the active and latent components are comparable.

Ettore Vidotto, Martin Schneider, Rainer Helmig et al.

In this paper, we present a fast streamline-based numerical method for the two-phase flow equations in high-rate flooding scenarios for incompressible fluids in heterogeneous and anisotropic porous media. A fractional flow formulation is adopted and a discontinuous Galerkin method (DG) is employed to solve the pressure equation. Capillary effects can be neglected in high-rate flooding scenarios. This allows us to present an improved streamline approach in combination with the one-dimensional front tracking method to solve the transport equation. To handle the high computational costs of the DG approximation, domain decomposition is applied combined with an algebraic multigrid preconditioner to solve the linear system. Special care at the interior interfaces is required and the streamline tracer has to include a dynamic communication strategy. The method is validated in various two- and three-dimensional tests, where comparisons of the solutions in terms of approximation of flow front propagation with standard fully-implicit finite volume methods are provided.

Shubhangi Gupta, Christian Deusner, Matthias Haeckel et al.

Natural gas hydrates are considered a potential resource for gas production on industrial scales. Gas hydrates contribute to the strength and stiffness of the hydrate-bearing sediments. During gas production, the geomechanical stability of the sediment is compromised. Due to the potential geotechnical risks and process management issues, the mechanical behavior of the gas hydrate-bearing sediments needs to be carefully considered. In this study, we describe a coupling concept that simplifies the mathematical description of the complex interactions occuring during gas production by isolating the effects of sediment deformation and hydrate phase changes. Central to this coupling concept is the assumption that the soil grains form the load-bearing solid skeleton, while the gas hydrate enhances the mechanical properties of this skeleton. We focus on testing this coupling concept in capturing the overall impact of geomechanics on gas production behavior though numerical simulation of a high-pressure isotropic compression experiment combined with methane hydrate formation and dissociation. We consider a linear-elastic stress-strain relationship because it is uniquely defined and easy to calibrate. Since, in reality, the geomechanical response of the hydrate bearing sediment is typically inelastic and is characterized by a significant shear-volumetric coupling, we control the experiment very carefully in order to keep the sample deformations small and well within the assumptions of poro-elasticity. The closely co-ordinated experimental and numerical procedures enable us to validate the proposed simplified geomechanics-to-flow coupling, and set an important precursor towards enhancing our coupled hydro-geomechanical hydrate reservoir simulator with more suitable elasto-plastic constitutive models.

Shubhangi Gupta, Rainer Helmig, Barbara Wohlmuth

We present a hydro-geomechanical model for subsurface methane hydrate systems. Our model considers kinetic hydrate phase change and non-isothermal, multi-phase, multi-component flow in elastically deforming soils. The model accounts for the effects of hydrate phase change and pore pressure changes on the mechanical properties of the soil, and also for the effect of soil deformation on the fluid-solid interaction properties relevant to reaction and transport processes (e.g., permeability, capillary pressure, reaction surface area). We discuss a 'cause-effect' based decoupling strategy for the model and present our numerical discretization and solution scheme. We then identify the important model components and couplings which are most vital for a hydro-geomechanical hydrate simulator, namely, 1) dissociation kinetics, 2) hydrate phase change coupled with non-isothermal two phase two component flow, 3) two phase flow coupled with linear elasticity (poroelasticity coupling), and finally 4) hydrate phase change coupled with poroelasticity (kinetics-poroelasticity coupling) and present numerical examples where, for each example, one of the aforementioned model components/couplings is isolated. A special emphasis is laid on the kinetics-poroelasticity coupling. We also present a more complex 3D example based on a subsurface hydrate reservoir which is destabilized through depressurization using a low pressure gas well. In this example, we simulate the melting of hydrate, methane gas generation, and the resulting ground subsidence and stress build-up in the vicinity of the well.