General Form of Built-in Rate Law r is the mineral’s dissolution rate (mol s –1 ) A s is the surface area of the mineral (cm 2 ) k + is the intrinsic rate constant (in mol cm –2 s –1 ) a j, m j = activity or concentration of promoting or inhibiting species P j = species’ power (+ is promoting, – is inhibiting) Q and K are the activity product and equilibrium constant for the dissolution reaction

Supply specific surface area (cm 2 g –1 ) and rate constant (mol cm –2 s –1 ) for each kinetic mineral. Set rate constant (k + ) directly or via activation energy E A (J mol –1 ) and pre- exponential factor A (mol cm –2 s –1 ) for Arrhenius equation where R is gas constant, T K absolute temperature. Built-in Rate Law

Mineral Nucleation In order for a new mineral to precipitate, it must have nuclei on which to grow. React uses a simple description of nucleation. The user specifies: A nucleus density (keyword nucleus; the surface area on which the mineral can grow, in cm 2 per cm 3 of fluid). A critical saturation index (keyword critSI ; log Q/K = 0, by default) above which the nuclei are available.

Modeling Strategy It is neither practical nor possible to describe all chemical reactions with kinetics. Chemical reactions may be divided into three groups Reactions that proceed quickly over the time span of the calculation  equilibrium model. Reactions that proceed negligibly over the calculation  suppressed reaction. Reactions that proceed slowly but measurably  kinetic law.

Task 1 — Quartz Dissolution Rainwater infiltrates an aquifer composed of quartz only. Quartz dissolves into flowing water according to a kinetic rate law. What controls distribution of dissolution reaction, dissolved silica?

X position (m) SiO 2 (aq) (mg kg –1 ) t = 30 yr inlet equilibrium

X position (m) Quartz dissolution rate (vol% yr –1 ) t = 30 yr

Relaxation times Silica in fluid Quartz in aquifer Where C eq = equilibrium conc. (mol cm –3 ) A S /V = surface area/fluid volume (cm –1 ) k + = intrinsic rate constant (mol cm –2 s –1 ) X qtz = vol. fraction quartz M V = quartz mole volume (cm 3 mol –1 ) E.g., Lasaga and Rye (1993)

Time (yr) Quartz dissolution rate (vol% yr –1 ) x = 5 m “Stationary state” Relaxation τ SiO2(aq) ≈ 1 month Delay log scale

Damköhler Number Da represents rate at which a component reacts chemically relative to the rate at which it is transported by advection. In a one-component system, where A S = Surface area/fluid volume (cm 2 cm –3 ) k + = Intrinsic rate constant (mol cm –2 s –1 ) a i = Activity of a catalyzing/inhibiting species P i = Species’ power L= Length scale of interest (cm) C eq = Equilibrium concentration (mol cm –3 ) v x = Fluid velocity (cm s –1 ) A good reference: Knapp (1989) GCA 53,

X position (m) SiO 2 (aq) (mg kg –1 ) v x = m yr –1 10 m yr –1 100 m yr – m yr –1 330 m yr –1 Da

X position (m) Quartz dissolution rate (vol% yr –1 ) v x = m yr –1 10 m yr –1 100 m yr – m yr –1 330 m yr –1 Da

Lessons from Damköhler Small Da: Use a lumped parameter simulation (“box model”). Large Da: Local equilibrium assumption/model (“LEA” or “LEM”). Else: Reactive transport simulation.

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