Vertical equilibrium with sub-scale analytical methods for geological CO2 sequestration

Abstract

Large-scale implementation of geological CO 2 sequestration requires quantification of risk and leakage potential. One potentially important leakage pathway for the injected CO 2 involves existing oil and gas wells. Wells are particularly important in North America, where more than a century of drilling has created millions of oil and gas wells. Models of CO 2 injection and leakage will involve large uncertainties in parameters associated with wells, and therefore a probabilistic framework is required. These models must be able to capture both the large-scale CO 2 plume associated with the injection and the small-scale leakage problem associated with localized flow along wells. Within a typical simulation domain, many hundreds of wells may exist. One effective modeling strategy combines both numerical and analytical models with a specific set of simplifying assumptions to produce an efficient numerical-analytical hybrid model. The model solves a set of governing equations derived by vertical averaging with assumptions of a macroscopic sharp interface and vertical equilibrium. These equations are solved numerically on a relatively coarse grid, with an analytical model embedded to solve for wellbore flow occurring at the sub-gridblock scale. This vertical equilibrium with sub-scale analytical method (VESA) combines the flexibility of a numerical method, allowing for heterogeneous and geologically complex systems, with the efficiency and accuracy of an analytical method, thereby eliminating expensive grid refinement for sub-scale features. Through a series of benchmark problems, we show that VESA compares well with traditional numerical simulations and to a semi-analytical model which applies to appropriately simple systems. We believe that the VESA model provides the necessary accuracy and efficiency for applications of risk analysis in many CO 2 sequestration problems.

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

“…Conversely, most research codes used in the literature to study CO 2 migration are based on a simple IMPES or sequential-splitting method and are not publicly available. In particular, the VESA code [26], which to the best of our knowledge is the most general code reported in the literature, uses a nonstandard nonconservative version of IMPES, but nevertheless seems to work rather well.…”

“…The validity of the simplifying assumptions underlying VE models has been studied both with respect to spatial [20] and temporal [21] scales, and the utility of VE models is thoroughly discussed in, e.g., [22,23]. Early studies focused on VE models with a sharpinterface assumption [24][25][26], and models that only account for the basic effects of buoyant migration were successfully used to simulate long-term migration in the Utsira [27] and Johansen [28] aquifers. Later, the class of VE models has been extended to incorporate most of the flow effects that are pertinent to large-scale migration, including compressibility [29], convective dissolution [30,31], capillary fringe [32], small-scale caprock topography variations [33][34][35], various hysteretic effects [36][37][38], multiple geological layers [39,40], and heat transfer [41].…”

A simulation workflow for large-scale CO2 storage in the Norwegian North Sea

“…The simplest models are formulated both in terms of h and S and discretized and solved using a sequential splitting method to give high computational efficiency. The more sophisticated methods are, unlike most other VE models reported in recent literature [7,8,9,10,11], formulated in terms of S using the black-oil framework that is standard in the petroleum industry. To ensure maximum robustness, the models are discretized and solved using a fully-implicit solver [12,13] as implemented in leading commercial reservoir simulators (e.g., including standard techniques to safeguard the time steps).…”

An iterative global pressure solution for the semi-analytical simulation of geological carbon sequestration

“…Additional assumptions made by this model include: 1) Aquifers exhibit horizontal flow; 2) Capillary pressure is negligible resulting in a sharp fluid interface; 3) CO 2 plume thickness at any given location is assumed to be the maximum plume thickness from all sources in the aquifer; 4) Pressure response from sources and sinks are superimposed in each aquifer; and 5) the injectivity of the formation remains constant. Several of these processes are important [9,11,13,15,17,22,26] and should be included [6,16,23,39] when model accuracy is more important that efficiency (e.g. during final project design).…”

“…However, because it does not require the linearization of the pressure solution, Equations (9-12) and (14)(15)(16)(17)(18)(19) are not used in conjunction with IGPS. Two additional parameters are implemented when applying this modification to ensure time step convergence stability.…”