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Reactive Transport in Heterogeneous Porous Media Under Different Peclet Numbers

<p>In our recent paper &ldquo;Reactive Transport in Heterogeneous Porous Media Under Different Peclet Numbers&ldquo;, we study the synergistic effects of the Peclet number and the length scale of medium heterogeneity on the evolution of bimolecular reactive transport between mobile and immobile species. We performed a suite of numerical simulations at the Darcy scale that quantify the instantaneous, irreversible bimolecular reaction , under various transport conditions (Peclet numbers) and porous media configurations (correlation lengths).</p> <p>&nbsp;</p> <p><strong>Numerical Methods</strong></p> <p>We used the following steps to obtain the results:</p> <p>1. Generation of the hydraulic conductivity fields &ndash; we used a widely tested sequential Gaussian simulator (G&oacute;mez-Hern&aacute;ndez &amp; Journel, 1993). The software is written in C and available to&nbsp;download via&nbsp;<a href="https://wiki.52north.org/AI_GEOSTATS/SWGCOSIM3D">https://wiki.52north.org/AI_GEOSTATS/SWGCOSIM3D</a>.&nbsp;In the file &lsquo;real20.mat&rsquo;, we show an example of the generated 20 realizations, from the software, for&nbsp;<span class="math-tex">\(\ell\)</span>=1&nbsp;,<span class="math-tex">\(\sigma^2\)</span>=1.&nbsp;</p> <p>2. Determination of the flow field &ndash; we solve the Darcy equation (for each of the hydraulic conductivity fields), using an open-source code MRST (Lie, 2016). The software is available to download via&nbsp;<a href="https://www.sintef.no/projectweb/mrst/">https://www.sintef.no/projectweb/mrst/</a>. In the file &lsquo;real20_solutions.mat&rsquo;, we show the flow field solutions (for the different realizations from &lsquo;real20.mat&rsquo;) under different Peclet numbers. For each realization and Peclet, we store the solution of the velocity components (first column), the velocity magnitude (second column) and the hydraulic conductivity field (third column).</p> <p>3.&nbsp;Chemical transport &ndash; was modeled through the Langevin equation, where movement by advection and diffusion were taken into account. Chemical reaction between the different chemical species was modeled via the reaction-radius approach (Edery, Porta, Guadagnini, Scher, &amp; Berkowitz, 2016).</p> <p><br> <strong>Results</strong></p> <p>The data of the published figures can be download from the following files:</p> <p><strong>Fig2.txt</strong> -- processed simulation results shown in Figure 2.</p> <p><strong>Fig3.txt</strong> -- processed simulation results shown in Figure 3a,b.</p> <p><strong>Fig4.txt </strong>-- processed simulation results shown in Figure 4.</p> <p><strong>Fig5.txt </strong>-- processed simulation results shown in Figure 5.</p> <p><strong>FigS1.png </strong>--&nbsp;First and second statistical moments of the generated conductivity fields, for different correlation lengths. The left axis displays the first moment of the generated fields (ln(K)), and the right axis shows the second moment (ln)). The small circles represent individual realizations, and the large circles indicate the mean value among realizations.</p> <p><strong>FigS2.png </strong>--&nbsp;Sensitivity analysis of the power law parameters (a) &nbsp;&nbsp;and (b) &nbsp;(see equation (1) in the main text), among realizations; mean values are represented by gray circles, and the standard deviations by the vertical black lines. (c) and (d) show the standard deviations of (a) and (b), respectively, in percentage. Note that among the different realizations, the standard deviation does not exceed 3%.&nbsp;</p> <p>&nbsp;</p> <p><strong>References</strong></p> <p>[1] Edery, Y., Porta, G. M., Guadagnini, A., Scher, H., &amp; Berkowitz, B. (2016). Characterization of Bimolecular Reactive Transport in Heterogeneous Porous Media. Transport in Porous Media. https://doi.org/10.1007/s11242-016-0684-0</p> <p>[2] G&oacute;mez-Hern&aacute;ndez, J. J., &amp; Journel, A. G. (1993). Joint Sequential Simulation of MultiGaussian Fields. https://doi.org/10.1007/978-94-011-1739-5_8</p> <p>[3] Lie, K.-A. (2016). User Guide for the MATLAB Reservoir Simulation Toolbox (MRST). In A. Soares (Ed.), An Introduction to Reservoir Simulation Using MATLAB. Oslo, Norway: SINTEF ICT, Department of Applied Mathematics.&nbsp;</p> <p>&nbsp;</p> <p>&nbsp;</p>