GWB Online Academy

Dissolution and Precipitation

General Form of Built-in Rate Law

• r is the mineral’s dissolution rate (mol s–1)

• As is the surface area of the mineral (cm2)

• k+ is the intrinsic rate constant (in mol cm–2 s–1)

• aj, mj = activity or concentration of promoting or inhibiting species

• Pj = species’ power (+ is promoting, – is inhibiting)

• Q and K are the activity product and equilibrium constant for the dissolution reaction

( | ) 1jj

Ps j j

Qr A k a mK

• Supply specific surface area (cm2 g–1) and rate constant (mol cm–2 s–1) for each kinetic mineral.

• Set rate constant (k+) directly or via activation energy EA (J mol–1) and pre-exponential factor A (mol cm–2 s–1) for Arrhenius equation

where R is gas constant, TK absolute temperature.

A KE RTk Ae

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 cm2 per cm3 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?

0 20 40 60 80 100

0

2

4

6

X position (m)

SiO2(aq)

(mg kg–1)

t = 30 yrinlet

equilibrium

0 20 40 60 80 100

0

.0002

.0004

X position (m)

Quartz dissolution

rate(vol% yr–1)

t = 30 yr

Relaxation times

• Silica in fluid

• Quartz in aquifer

• Where Ceq = equilibrium conc. (mol cm–3) AS/V = surface area/fluid volume (cm–1) k+ = intrinsic rate constant (mol cm–2 s–1) Xqtz = vol. fraction quartz MV = quartz mole volume (cm3 mol–1)

• E.g., Lasaga and Rye (1993)

2SiO (aq) ( / )0.1 year

eq

S

CA V k

5

( / )

10 year

qtzqtz

S V

XA V M k

.001 .01 .1 1 10

0

.0002

.0004

Time (yr)

Quartz dissolution

rate(vol% yr–1)

x = 5 m

“Stationary state”

RelaxationτSiO2(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 AS = Surface area/fluid volume (cm2 cm–3) k+ = Intrinsic rate constant (mol cm–2 s–1) ai = Activity of a catalyzing/inhibiting species Pi = Species’ power L = Length scale of interest (cm) Ceq = Equilibrium concentration (mol cm–3) vx = Fluid velocity (cm s–1)

• A good reference: Knapp (1989) GCA 53, 1955-1964.

iPS i

i

eq x

A k a LDa

C v

0 20 40 60 80 100

0

2

4

6

X position (m)

SiO2(aq)

(mg kg–1)

vx = 10 000 m yr–1

10 m yr–1

100 m yr–1

1000 m yr–1

330 m yr–1

Da

0 20 40 60 80 100

0

.0002

.0004

X position (m)

Quartz dissolution

rate(vol% yr–1)

vx = 10 000 m yr–1

10 m yr–1100 m yr–1

1000 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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