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Stochastic inversion workflow using the gradual deformation in order to predict and monitor the CO\(_2\) flow within a saline aquifer

Due to budget constraints, CCS in deep saline aquifers is often carried out using only one injector well and one control well, which seriously limits infering the dynamics of the CO_2 plume. In such case, monitoring of the plume of CO_2 only rely on geological assumptions or indirect data. In this paper, we present a new two-step stochastic \(P\)- and \(S\)-wave, density and porosity inversion approach that allows reliable monitoring of CO_2 plume using time-lapse VSP. In the first step, we compute several sets of stochastic models of the elastic properties using conventional sequential Gaussian cosimulations. Each realization within a set of static models are then iteratively combined together using a modified gradual deformation optimization technique with the difference between computed and observed raw traces as objective function. In the second step, this statics models serves as input for a CO_2 injection history matching using the same modified gradual deformation scheme. At each gradual deformation step the CO_2 injection is simulated and the corresponding full-wave traces are computed and compared to the observed data. The method has been tested on a synthetic heterogeneous saline aquifer model mimicking the environment of the CO_2 CCS pilot in Becancour area, Quebec. The results show that the set of optimized models of \(P\)- and \(S\)-wave, density and porosity showed an improved structural similarity with the reference models compared to conventional simulations.

One of the major challenges limiting large-scale deployment of Carbon Capture and Storage (CCS) operations is the issue of evaluating and forecasting the fate of CO_2 in deep rock formations. The characteristics of the reservoir determine from the very beginning the design and operational conditions of most of the CCS chain. Indeed, having a comprehensive knowledge of the physical characteristics of the storage site is crucial to determine the optimal rate of CO_2 injection, which influences the rate of capture, as well as the parameters of a proper monitoring strategy. Let us recall that monitoring is an essential component of any CCS project and that most, if not all, jurisdictions require more or less elaborated monitoring, verification and accounting (MVA) programs (e.g. European CCS directive).

A common task in CCS projects is thus to monitor the spatial distribution of CO_2 over time. However, the spatial distribution of the CO_2 plume that is estimated through monitoring is often inconsistent, to varying degrees, with model-based simulations (Ramirez et al., 2013). This is mainly due to the lack or sparseness of direct measurements of petrophysical properties of the reservoir, to the low spatial coverage of geophysical surveys, to the underlying resolution of inversion techniques and to uncertainties that limits the understanding of the subsurface and therefore the ability to produce accurate reservoir models allowing reliable forecast of the CO_2 plume.

The process of optimizing a reservoir model to fit dynamic data is commonly known as history matching and is extensively used in the oil and gas industry. In conventional history matching, the target variables are reservoir engineering properties such as pressure, water-cut, rate of production of oil, and the like, all involving at least one injector and one pumping well. In CO_2 storage projects, such well configuration is not conceivable (pumping is not done) and only one injector well is usually available. In this context, only indirect data have the spatial coverage and the potential to improve the estimation of the CO_2 plume within the deep saline aquifers.

History matching requires the knowledge, at least in the stochastic sense, of the spatial distribution of the static properties of the reservoir (porosity, permeability). Due to the geological complexity and the scarcity of direct observations (i.e. well data), probabilistic methods appear to be the most suitable choice to build a reliable reservoir model. In addition, it is established that seismic measurements are well suited to constrain static reservoir property modeling as they provide indirect but correlated and spatially extensive information about reservoir properties (Doyen, 2007).

The estimation of static parameters from seismic data is a complex, ill-conditioned, nonlinear inverse problem due principally to the limited bandwidth and resolution of the seismic data, to noise, to measurement errors, and to the assumptions underlying to forward models (Tarantola, 2005). Seismic inverse problems may be developed following deterministic or probabilistic approaches and can be divided into two main categories: (1) multiple step inversion methods and (2) stochastic inversion methods (Grana et al., 2012).

In multiple step inversion methods, the problem of estimating reservoir properties from seismic data is split into two or more subproblems; elastic properties are first derived from partial stacked seismic data through elastic inversion; then, reservoir properties are classified by statistical techniques, such as Bayesian classification (Avseth et al., 2001; Mukerji et al., 2001; Buland et al., 2003).

Iterative stochastic inversion methodologies solve the seismic inverse problem using deterministic or stochastic optimization techniques. First, a set of equivalent earth models is simulated using a stochastic algorithm based on prior information usually from available well log data and a spatial continuity pattern (e.g. variogram, training image) to create fine-scale reservoir models (Bosch et al., 2009) . Then suitable rock-physics transforms are applied to generate the corresponding volumes of the elastic properties. Finally, synthetic seismic volumes are computed and compared to real seismic data to evaluate the mismatch. Several optimization methods exist to infer the elastic properties based on the measured traces. González et al. (2008) performed a trace-by-trace deterministic optimization, Bosch et al. (2009) proposed an iterative optimization based on Newton’s method; Markov chain Monte Carlo approach has been used successfully for the stochastic exploration of the model space (Eidsvik et al., 2004; Larsen et al., 2006; Gunning et al., 2007; Rimstad et al., 2010; Ulvmoen et al., 2010; Hansen et al., 2012). Grana et al. (2012) show the efficiency of the probability perturbation method (Caers et al., 2006) to estimate fine-scale reservoir models in a stochastic inversion. A multidimensional scaling technique was successfully applied by Azevedo et al. (2013) to asses how the parameter model space is explored by global elastic inversion algorithm.

In addition to the static information and in order to evaluate the performance of the reservoir in terms of CO_2 storage, reservoirs models need to be constrained by dynamic data obtained from the CO_2 injection operations. To be meaningful, reservoir models must match the observed dynamic behavior of the reservoir within some interval of tolerance. History matching is also an ill-posed problem and can be solved using the same algorithms as the one used for estimating the static properties, but then involving the injection data and forward fluid flow modeling.

In this paper we propose a stochastic inversion workflow using a modified gradual deformation parametrization method (Roggero et al., 1998) as a stochastic optimization technique that integrates geophysical and geological logs, seismic reflection data and CO_2 flow simulations in order to analyze and monitor the CO_2 injection and its propagation within a saline aquifer. This paper is organized as follows. In the first section, we focus on each step of the seismic inversion algorithm. The second section presents an the application of the approach to characterize a synthetic reservoir for the CO_2 injection in the St. Lawrence Lowlands, Quebec, Canada.

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