Vertically-integrated dual-porosity and dual-permeability models for CO2 sequestration in
fractured reservoirs
Bo Guo, Karl Bandilla, Yiheng Tao, Michael Celia
Department of Civil and Environmental Engineering, Princeton University
Abstract
Analysis of geological storage of carbon dioxide (CO2) in deep saline aquifers requires
computationally efficient mathematical models to accurately predict the pressure evolution and the
injected CO2 plume migration. The subsurface system of CO2 injection into saline aquifers can be
modeled as a two-phase flow system, with a non-wetting less dense (supercritical) CO2 phase and a
denser brine as the wetting phase. One type of simplified model can be developed by integrating the
three-dimensional governing equations in the vertical dimension. The dimension reduction resulting
from vertical integration leads to a very computationally efficient model; we refer to these as
vertically-integrated models. In the past decade, a range of vertically-integrated models have been
developed and applied to field-scale modeling of CO2 injection, migration and leakage (e.g.,
Nordbotten and Celia, 2006; Hesse et al, 2007, 2008; Gasda et al., 2009, 2012; Juanes et al., 2010;
Macminn et al., 2010; Golding et al., 2011; Celia et al., 2011). Almost all of those models are based
on the vertical equilibrium assumption, which assumes that the CO2 and brine segregate rapidly in
the vertical direction due to strong buoyancy, and each of the fluid phases is always in pressure
(hydrostatic) equilibrium. Vertical equilibrium is a fairly strong assumption, and may not be
satisfied, especially for injection formations with low vertical permeability or heterogeneous
formations with a wide range of permeabilities. For these systems, buoyant segregation times are
typically large, and the vertical equilibrium assumption is not appropriate. Recently, Guo et al.
(2014) used the idea of multi-scale modeling for vertically integrated models (Nordbotten and
Celia, 2012) to introduce the concept of dynamic reconstruction for the CO2-brine system. That
dynamic reconstruction approach includes vertical two-phase flow dynamics of both CO2 and brine,
with those dynamics represented as one-dimensional fine-scale problems within the verticallyintegrated framework. As such, this version of the vertically integrated model does not rely on the
vertical equilibrium assumption.
These concepts associated with vertically integrated models may be applied to two-phase (CO2 and
brine) flows in fractured rock systems. To date, such vertically-integrated models have not been
developed for fractured reservoirs. The CO2 injection into a fractured reservoir involves two
different characteristic time scales, one for buoyant segregation in the fractures and a second for the
fluid dynamics in the matrix. The high permeability of the fractures leads to fast buoyant
segregation of CO2 and brine in the vertical direction within the fractures, and therefore the vertical
equilibrium model is likely to be applicable. Flow in the matrix is typically much slower and
involves longer time scales for segregation; thus the vertical equilibrium approach is unlikely to
apply in the matrix.
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In this paper, we treat the fractured reservoir as a dual continuum and develop a hybrid verticallyintegrated model, with different vertically-integrated approaches used in the fracture (continuum)
and the matrix (continuum), based on the different buoyant segregation time scales. We use a
vertical equilibrium model for the fracture domain and explore different model options for the
matrix domain, including the classical dual-porosity model that treats the matrix as a source/sink
term for the fracture as well as other more advanced models that explicitly account for the twophase flow dynamics of the CO2 and brine in the vertical direction within the context of a vertically
integrated model. A corresponding vertically-integrated mass transfer function is derived and used
to model the mass exchange between the fracture and the matrix domains. We adopt different mass
transfer functions, taken from the literature, and compare results from this hybrid model with a full
multi-dimensional model in terms of both model accuracy and computational efficiency.
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