deletions | additions       diff --git a/Geological model1.tex b/Geological model1.tex  index af0cad4..129ff7c 100644  --- a/Geological model1.tex  +++ b/Geological model1.tex 
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\subsection{Geological model}  We consider an idealized geometry and physical model to describe the sedimentary sequence of the St. Lawrence Lowlands. The geological model consists of a tabular succession of six horizontal layers corresponding to the Lorraine group, Utica shales, Trenton group, Beekmantown group, Cairnside formation, Covey Hill formation and the Grenville basement. The grid size is 1000 x 1500 $m^2$ with a cell size is 1 x 1 $m^2$, leading to a total of 1.5 million cells. For each cell, 12 parameters ($K_{dry},K_s,K_f,\phi,G_s,\rho_s,\rho_f,\tau,\eta,\kappa,Q,f_0$) characterize the medium.\\ medium.  A sequential Gaussian simulation (SGS) framework is used to modify the geological model in order to obtain a more realistic model, especially at the layer transitions. First, for each layer, we compute the mean ($\mu$) and the standard deviation ($\sigma$) of the physical properties ($V_{clay},V_{calcite},V_{quartz},V_{dolomite},\phi,\rho$) derived from log data available in well A196. Distribution of the physical properties are then obtained by simple kriging under Gaussian hypothesis and used for compute the model parameters as the following:\\  the dry-rock bulk modulus ($K_{dry}$) is estimated using inverse Gassmann's equation \citep{Carcione2007}:  \begin{equation}  
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\begin{equation}   \tau = \phi^{1-m},   \end{equation}  where $m$ is the cementation factor.\\ factor.  The brine properties are obtained by using the equations given in \citet{Batzle1992}. The pressure and temperature dependent bulk modulus ($K_f$), density ($\rho_f$) and viscosity ($\eta_f$) of the CO$_2$ are determined from the thermodynamic properties obtained from NIST’s online chemistry webBook \citep{Lemmon2014}. Permeabilities ($\kappa$) are taken from \citet{TranNgoc2014}.\\ \citet{TranNgoc2014}.  The velocity fields for the stochastic and for the classical block models are shown in Fig \ref{fig:mstochvsblock}. Fig.~\ref{fig:mstochvsblock}.