Environmental Engineering Reference
In-Depth Information
1
M
∞
/M
o
=0.01
M
∞
/M
o
=0.03
0.8
M
∞
/M
o
=0.05
0.6
0.4
M
/M
o
=0.1
∞
M
∞
/M
o
=0.3
0.2
M
∞
/M
o
=0.5
M
∞
/M
o
=0.9
0
0.00001 0.0001 0.001 0.01 0.1 1
Dt/a
2
FIGURE 10.4
Fractional release (M
t
/M
∞
) into a fixed bath as a function of a dimensionless
parameter Dt/a
2
and fractional solubility (M
∞
/M
o
) modified from Garrabrants.
201
a fixed bath.
216
Figure 10.4 shows the fractional release (i.e., the release with chang-
ing time relative to the release at infinite time) for a constituent released into a fixed
bath. Parameters that determine the rate of release include the fractional solubility
(i.e., the ratio between the amounts of constituent soluble in the fixed bath to the
total amount) and a dimensionless parameter determined as the observed diffusivity
(D) multiplied by the contact time (t) and divided by the square of the particle radius
(a).
If the 90% fractional release (M
t
/M
∞
= 0.9) is assumed to represent equilibrium
and a constituent is known to have a fractional solubility in the liquid phase of 5%
(M
∞
/M
o
= 0.05), the minimum value of the dimensionless parameter Dt/a
2
that will
attain equilibrium is 0.005. Thus, extraction of particles sized using the TCLP
maximum (2a = 9.5 mm) would require a minimum of approximately 300 hours to
establish equilibrium of constituents with a mid-range diffusivity (D = 10
-13
m
2
/s).
Particle-size reduction to 0.6 mm (2a = 0.6 mm) would accelerate the release process
to a minimum of 14 hours. Of course, this first-order analysis assumes that diffusion
is the rate-limiting process and that all particles are of the same diameter.
10.4.4.4
Liquid-to-Solid Ratio
The amount of liquid relative to the mass of solid dictates the controlling mechanism
of release as detailed in the discussion of infiltration rates (see Section 10.3.2.2).
Leaching tests designed to obtain equilibrium or steady-state release usually consist
of batch extractions at L/S ratios in the range of 5 to 20 mL/g of dry material (e.g.,
TCLP, ANC, SR003.1). At these L/S ratios, the release of highly soluble species
(e.g., Na
+
, K
+
, Cl
-
) is assumed to be limited by the solid content (availability-limited),
while the release of sparingly soluble species may be constrained by solubility in
the liquid phase. Equilibrium at L/S ratios below 5 mL/g are used in some leaching
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