Upload
amie-nichols
View
214
Download
0
Embed Size (px)
DESCRIPTION
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
Citation preview
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.
play movie
Steam Flood Simulation