Coupled semi-analytical solution for CO2 injection-induced surface uplift and caprock deflection

This study focuses on a specific problem related to the surface uplift induced by the injection of CO2 at depth. The adopted methodology includes the development of a mathematical model that incorporates the deformable behaviour of storage media and the flow of two immiscible fluids (CO2 and water) within the aquifers while the surface rock or caprock layer is modelled as a thin plate. Governing equations are solved for the axisymmetric flexural deflection due to a constant rate of injection of CO2. Comparison of the results with the surface uplift measurements (In Salah project), show good agreement. The results show that this semi-analytical solution is capable of capturing the pressure build-up during the very early stage of injection, resulting in a high rate of surface uplift. Compared to a FEM simulation, the calculation time required using the semi-analytical solution is very short; it can be employed as a preliminary design tool for risk assessment using parameters such as the injection rate, porosity, rock properties and geological structures. This semi-analytical solution provides a convenient way to estimate the influence of high injection rates of CO2 on the surface uplift. The methodology in this development can easily incorporate other pressure distributions; thus advances in hydrology researches can also benefit this approach. CO2 into deep aquifers is considered as a hydromechanical coupled process [8]. High rates (>1Mt/year) of injection of CO2 into an aquifer could result in an abrupt fluid pressure build-up within the injection area [9]. This increase in fluid pressure leads to deformation of the aquifer and the sealing caprock. Induced strain may propagate to the surface [10] and can also cause variations in the porosity resulting in alterations in the hydraulic properties such as permeability. As a consequence, the state of fluid overpressure changes further. Employing a hydromechanical coupling technique can help estimate the surface or caprock deformation more accurately. Rutqvist [8] estimated the surface uplift at In Salah using a simple analytical solution according to [11]. The uplift is overestimated because of various assumptions such as a unique layer of the reservoir, 1-dimentional geometry and a uniformly distributed overpressure. This can be accepted as a very preliminary approximation on the order of magnitude of uplift. In reality, the contact between the rock layers is often curved, which tends to prevent the induced strain from propagating to the surface. Furthermore the uplift is highly dependant on the state of the overpressure as previously stated. It is important to incorporate the temporal and spatial evolution of the overpressure in order to determine the magnitude of the uplift. Selvadurai [12, 13] has derived a convenient mathematical model for determining the surface uplift and caprock vertical deformation respectively. By taking in account bending effects, the axisymmetric flexural deflections of the surface layer and caprock layer have been deduced analytically. Nevertheless a flat overpressure within the injection zone is assumed in the study, which could be refined. Vilarrasa et al. [14] has derived expressions for fluid overpressure distributions from two analytical solutions proposed by Nordbotten et al. [15] and Dentz and Tartakovsky [16]. The overpressure predicted by both approaches displays a more realistic distribution and has the same order of magnitude as numerical simulations after accounting for CO2 compressibility and viscosity [14]. The goal of this paper is to assess the surface uplift and caprock deformation by deriving a semi-analytical solution, which takes a more realistic evolution of overpressures into account. First, a mathematical analysis of the pressurization-induced displacement is given. This is followed by the incorporation of the real distribution of overpressure. After proposing several numerical simulations using the semi-analytical analysis, the solution is employed to estimate the surface uplift observed at the In Salah project as an illustrative example. 2. CAPROCK DEFORMATION DUE TO PRESSURIZATION 2.1. Embedded plate approach Selvadurai [13] has proposed a straightforward analytical approximation to estimate the primary caprock deformation due to constant injection-induced uniformly distributed overpressures over a circular region located under the caprock layer. The proposed system consists of an overburden region and a storage unit with a primary caprock in between. CO2 is injected into an mmetre-thick injection zone within a storage unit with a distance l to the primary caprock (Figure 1). The injection zone can be situated just below the primary caprock (l=m/2). Injection of fluids at a constant rate through a vertical injection well causes radial pressurization in the injection zone, the so-called discshaped pressurized zone. The approach assumes that (i) the caprock is oriented horizontally and embedded between an overburden region and a storage region, (ii) the caprock layer is considered as a thin plate and (iii) it behaves elastically. The assumption of a thin plate applied here is justified by its thickness in relation to the dimension (radius) of the pressurized zone [17]. Both overburden and storage regions are modelled as halfspace regions and an isotropic elastic model is applied to these regions. The embedded caprock layer exhibits flexural behaviour that is governed by the Germain-Poisson-Kirchhoff thin plate theory [17]. The governing equation is written in polar coordinates with the Laplace operator 2 2 2 1 d d dr r dr ∇ = +  :