Multiphase flow and reactive transport benchmark for radioactive waste disposal

Abstract

Abstract Compacted bentonite is part of the multi-barrier system of radioactive waste repositories. The assessment of the long-term performance of the barrier requires using reactive transport models. Here we present a multiphase flow and reactive transport benchmark for radioactive waste disposal. The numerical model deals with a 1D column of unsaturated bentonite through which water, dry air and $${\hbox {CO}_{2{(g)}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>CO</mml:mtext> <mml:mrow> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>g</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:msub> </mml:math> may flow and with the following reactions; aqueous complexation, calcite and gypsum dissolution/precipitation, cation exchange and gas dissolution. INVERSE-FADES-CORE V2, $$\hbox {DuMu}^X$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mtext>DuMu</mml:mtext> <mml:mi>X</mml:mi> </mml:msup> </mml:math> , TOUGHREACT and iCP were benchmarked with 6 test cases of increasing complexity, starting with conservative tracer transport under variably unsaturated conditions and ending with water flow, gas diffusion, minerals and cation exchange. The solutions of all codes exhibit similar trends. Small discrepancies are found in conservative tracer transport due to differences in hydrodynamic dispersion. Computed $${\hbox {CO}_{2{(g)}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>CO</mml:mtext> <mml:mrow> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>g</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:msub> </mml:math> pressures agree when a sufficiently refined grid is used. Small discrepancies in $${\hbox {CO}_{2{(g)}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>CO</mml:mtext> <mml:mrow> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>g</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:msub> </mml:math> and pH are found near the no-flow boundary at early times which vanish later. Discrepancies are due differences in the formulations used for gas flow at nearly water-saturated conditions. Computed $${\hbox {CO}_{2{(g)}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>CO</mml:mtext> <mml:mrow> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>g</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:msub> </mml:math> pressures show a fluctuation between $$10^{-4}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> </mml:math> and $$10^{-3}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:math> years which slows down the in-diffusion of $${\hbox {CO}_{2{(g)}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>CO</mml:mtext> <mml:mrow> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>g</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:msub> </mml:math> . This fluctuation is associated with chemical reactions involving $${\hbox {CO}_{2}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>CO</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> </mml:math> . There are discrepancies in solute concentrations due to differences in the Debye–Hückel (DH) formulation. They are overcome when all codes use the same DH formulation. The results of this benchmark will contribute to increase the confidence on multiphase reactive transport models for radioactive waste disposal.