Fully-implicit simulation of vertical-equilibrium models with hysteresis and capillary fringe

Abstract

Geological carbon storage represents a new and substantial challenge for the subsurface geosciences. To increase understanding and make good engineering decisions, containment processes and large-scale storage operations must be simulated in a thousand year perspective. A hierarchy of models of increasing computational complexity for analysis and simulation of large-scale CO 2 storage has been implemented as a separate module of the opensource Matlab Reservoir Simulation Toolbox (MRST). This paper describes a general family of two-scale models available in this module. The models consist of two-dimensional flow equations formulated in terms of effective quantities obtained from hydrostatic reconstructions of vertical pressure and saturation distributions. The corresponding formulation is fully implicit and is the first to give a massconservative treatment and include general (non-linearized) CO 2 properties. In particular, the models account for compressibility, dissolution, and hysteresis effects in the finescale capillary and relative permeability functions and can be used to accurately and efficiently study the combined large-scale and long-term effects of structural, residual, and solubility trapping.

Robust simulation of sharp-interface models for fast estimation of CO2 trapping capacity in large-scale aquifer systems

“…Likewise, the S-formulation is a more natural starting point when extending the vertical equilibrium model to black-oil type models or including physical effects like compressibility and hysteresis. A more detailed discussion of hysteresis is given in [50].…”

“…Apart from capillary fringe, which is discussed in [50], our models incorporate the physical effects discussed by Gasda et al [30], but the formulation and notation will follow that of standard black-oil models used in the petroleum industry (see Appendix B) to make similarities and differences with models implemented in standard simulators as clear as possible. The effects discussed in this section can be divided in two categories.…”

“…This enables the users to easily perform sensitivity studies or formulate efficient strategies for rigorous mathematical optimization of large-scale injection strategies [6,7,48,49]. In [50], we discuss how the framework can be extended to account for smooth transitions (capillary fringe) between pure CO 2 and brine. We also show how inclusion of more advanced flow physics naturally leads to pressure-dependence and hysteretic effects in the vertically-integrated relative permeabilities and capillary pressure and suggest implementation choices we think are important to make flexible and efficient VE simulators.…”

A Simulation Workflow for Large-scale CO2 Storage in the Norwegian North Sea

“…In addition, each cell in the grid contains information of the petrophysical properties in the volume that lies below it in the 3D representation of the aquifer. The computational methods that will be discussed in the following can be roughly divided into two classes: (i) methods that do not utilize temporal information to identify the potential for structural trapping [4], and (ii) methods for estimating the outcomes of injection operations in a long-term, large-scale perspective by simulating the combined effects of structural, residual, and solubility trapping in a vertically averaged sense [5,6]. The methods are designed to fit together as part of a multi-fidelity tool-chain supporting the flexibility in resolution required of simulations used for decision support.…”

Spill-point analysis and structural trapping capacity in saline aquifers using MRST-co2lab

“…These methods have later been combined with simulation tools based on an assumption of vertical equilibrium [2,3] to provide a comprehensive toolbox for optimizing injection strategies and simulating large-scale containment in a thousand-year perspective [4,5,6].…”