Experiments on buoyancy-driven instability ahead of a dissolution front in a porous rock

Fluid-rock reactions are of great interest in many engineered geological storage and disposal systems where the long term integrity of the system is key, and where fluid seepage through a permeable rock may lead to reaction and convective transport of material through the formation. If an unsaturated fluid displaces formation fluid in equilibrium with a reactive porous medium, a reaction front develops, across which the invading fluid becomes saturated with the soluble matrix material. Depending on the composition of the invading fluid, it may initially be less dense than the formation fluid, but following reaction it may become denser than the formation fluid. If the invading fluid displaces the formation fluid downwards through the porous layer, the reaction front may then be stabilized by buoyancy, but a Rayleigh-Taylor type instability can develop at the interface between the reacted fluid and the original formation fluid ahead of the reaction front. We present a series of new analog experiments of this process by injecting aqueous sugar solutions into a porous layer containing saturated salt solution, salt powder, and glass ballotini. As an analog of a reaction front, a dissolution front develops as the aqueous sugar solution dissolves the salt powder and becomes denser than the saturated salt solution. The buoyancy instability then leads to a growing finger interface. If the buoyancy speed of the fluid, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>u</a:mi><a:mi>B</a:mi></a:msub></a:math>, is smaller than <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:msub><b:mi>u</b:mi><b:mi>F</b:mi></b:msub><b:mo>−</b:mo><b:msub><b:mi>u</b:mi><b:mi>R</b:mi></b:msub></b:mrow></b:math>, where the speed of the advancing fluid-fluid front is <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi>u</c:mi><c:mi>F</c:mi></c:msub></c:math> and the speed of the dissolution front is <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:msub><d:mi>u</d:mi><d:mi>R</d:mi></d:msub></d:math> then the instability grows as if the system were unconfined. However, if <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:msub><e:mi>u</e:mi><e:mi>B</e:mi></e:msub><e:mo>&gt;</e:mo><e:msub><e:mi>u</e:mi><e:mi>F</e:mi></e:msub><e:mo>−</e:mo><e:msub><e:mi>u</e:mi><e:mi>R</e:mi></e:msub></e:mrow></e:math>, then the supply of fluid at the dissolution front limits the growth of the instability. We present an idealised model for the speed of the non-linear buoyancy-driven fingers, and we consider the implications of our results for the long term integrity of a number of geological storage systems.