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VII. Transport in Layered Soil

VII. Transport in Layered Soil

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irreversible) retention [see Eqs. (19) and (23)] to describe solute behavior

in each layer of a multilayered soil profile. Different simulations were

conducted to evaluate the importance of soil layer stratification and adsorption characteristics on the shape and position of effluent concentration distributions



_ from



~ soil profiles.

For the linear case, a retardation factor R [ R = 1 + p K d / O ;see Eq. (29)]

represents the magnitude of retention for each layer and is represented by

R 1 , R 2 , etc. (Selim et al., 1977). Solid lines in Fig. 27 are simulated BTC

results from columns in which the solute passed first through L1 and then

L 2 ; open circles are calculated results of solute flow in the opposite

direction. The dashed lines are for the homogeneous cases wherein L = L1

or L = L2 and these cases have the appropriate retardation factors, R1 or

R 2 , respectively. As expected, the BTCs for the two-layered cases lie

between the homogeneous cases R1 and R2 (dashed lines). The retardation

factor R1 equals one and represents a nonreactive solute whereas R2 equals

10. Increasing L2 (or decreasing L,) causes the breakthrough curves to

move to the right toward the homogeneous R2 case. The most striking

result in Fig. 27 is the failure of the order of soil layers to influence the

shape or position of the effluent concentration distribution. Based on these

results, a layered soil profile could be regarded as homogeneous with an

average retardation factor used to calculate emuent concentration distributions. An average retardation factor R for N-layered soil can simply be

obtained from













Figure 27. Simulated effluent concentration distribution for two-layered soils with retardation factors R, and RZ (linear sorption) and varying lengths L , and Lz. Solid lines are

simulations wherein layer 1 with R, is first encountered, whereas open circles are for flow in

the reverse direction. Dashed curves are for homogeneous soils. From Selim et al. (1977),

with permission.


3 79

BTCs identical to those in Fig. 27 were obtained using the solution to the

convention-dispersion Eq. (7) presented by Lindstrom et al. (1967) and an

average retardation factor. This averaging procedure [Eq. (65)] can also be

used to describe the BTCs from a soil profile composed of three or more

layers (see Selim et al., 1977). However, if solute distribution within the

profile is desired, the use of an average retardation factor is no longer valid

and the problem must be treated as a multilayered case.

The nonlinear (Freundlich) equilibrium and first-order kinetic retention

were also considered for a two-layered soil column with L1= L2 = 0.5L

(Selim ef al., 1977). The BTCs were identical regardless of the sequence of

soil layers (not shown in Fig. 27). This is a significant conclusion and can be

used to simplify field problems involving solute movement through nonhomogeneous field soils under steady water-saturated flow conditions. Unlike

the linear adsorption cases, an average retardation factor R for nonlinear

adsorption cannot be obtained, because of the dependency of R on the

solute concentration C.



Selim et al. (1977) simulated solute transport through water-unsaturated

multilayered soil profiles, in which a steady, vertically downward water

flow (q = constant) was considered. A soil profile was assumed to consist of

two distinct layers, sand and clay, each having equal lengths, and was

underlain by a water table at a depth L = 100 cm. The case for which the

water table was at great depth (z 4 m) was also considered. When a

constant flux was assumed, the steady state 0 and water suction (h)

distributions for a sand-clay and a clay-sand soil profile were calculated

(see Fig. 28 for the clay-sand case). Solute concentration versus pore

volume of effluent (collected at a 100-cm depth) for a nonreactive and

reactive solute having linear (equilibrium) retention is shown in Fig. 29. As

expected, similar BTC results for the nonreactive solute for sand-clay or

clay-sand soil profiles were obtained. In contrast, BTCs for the reactive

solute show a distinct separation, with lower retardation factors for the soil

profiles having a water table at z = 100 cm than at z + m. This observation

is consistent for the sand-clay as well as clay-sand profiles. Due to the

higher water contents in the soil profiles, wherein the water table was at

x = 100, the retardation factor R is less in comparison to the case for which

the water table was at great depth ( z + m).

If the water content distributions were considered uniform, with an

average water content within each individual layer (see Fig. 28), the

problem of solute transport and retention through unsaturated multilayered soil profiles can be significantly simplified, as discussed in the


3 80

Water Suction h, cm

40 60 80 100




Water Suction h, cm


5 2o

















0 0.1 0.2 0.3 0.4 0.5




0.1 0.2 0.3 0.4 0.5

Water Content e,cm3/cm3

Water Content 8,cm 31cm 3

Figure 28. Simulated water content 0 and water suction h versus depth in a clay-sand

profile having a water table at (A) 100-cm depth and (B) great depth. From Selim et al.

(1977), with permission.

previous section. The open circles in Fig. 29 are calculated results of

concentration distributions for the reactive and nonreactive solutes when

an average water content within each layer was used. These results show

that, for all unsaturated profiles considered, the use of average water

contents (open circles) provided concentration distributions identical to

those obtained when the actual water content distributions were used

(dashed and solid lines). Thus, when a steady water flux is maintained



0" 0.6



water table

at x = 1 0 0 c m













v I v,

Figure 29. Simulated effluent concentration distribution for reactive and nonreactive

solute in an unsaturated clay-sand profile. Open circles are simulations based on average

water content 0 for each soil layer. From Selim et al. (1977), with permission.



through the profile, BTCs of reactive and nonreactive solutes at a given

location in the soil profile can be predicted with average water contents

within unsaturated soil layers. Based on the above results we can conclude

that average microhydrologic characteristics for a soil layer can be used to

describe the movement of solutes leaving a multilayered soil profile. This

conclusion supports the assumption made earlier that uniform soil water

content can be used to represent each soil layer in order to simplify the

solute transport problem. However, such a simplifying approach was not

applicable for the general case of transient water flow conditions of unsaturated multilayered soils. As illustrated by Selim (1978), the transport of

reactive, as well as nonreactive, solutes through multilayered soils, for

transient water flow, was significantly influenced by the order in which the

soil layers were stratified.


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3 82


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3 83

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Abscission, corn, 209-210, 227

Absorption matrix, fingerprinting crop

varieties, 89

Acid exchange, deposition on forested soils,


Acid-neutralizing capacity (ANC), deposition

on forested soils, 4-6

forest soils, 12, 16, 18.24, 36,39

Acidic deposition on forested soils, 1-3.


chemical factors

cation exchange, 19-29

hydrogen budgets, 38-40

mineral weathering, 35-38

nitrate retention, 29-32

soil organisms, 40-42

soil pH, 15-19

sulfate retention, 29, 32-35

future research, 63-65

physical factors

canopy interactions, 7-9

hydrology, 11-15

soil horizons, 9-11

soil acidification, 3-6

soil change studies

intensity-type changes, 44-48

leaching, 48-56,61-63

measurement, 42-43

seasonal variations, 59-61

uptake, 56-59,61-63

Acidification, soil, see Acidic deposition on

forested soils

Activity coefficient

inorganics in soils, 368

surface complexation models, 234-235,


Adaptation, corn, 206-207,214,222

Adjustable parameters, surface complexation

models, 236-237


acidic deposition on forested soils, 33,


chemical transport through soil

processes, 161-165.169, 171-175

solute transport, field studies of,

182-185, 188

inorganics in soils, 332, 340

ion exchange, 369,372-376

kinetic retention models, 345-347,


layered soil, 378-379

multiple-reaction models, 351, 358-359

surface complexation models

competitive adsorption reactions,


description, 235,235-238.241.


inorganic anion adsorption, 289-307

metal ion adsorption, 274-289

organic ligand adsorption, 308-312

protonation-dissociation reactions, 5 1,


Adsorption density, surface complexation

models, 283

Adsorption envelopes, surface complexation

models, 289,301,308-309

Adsorption isotherm models, chemical

transport through soil, 161

Adsorptive additivity, surface complexation

models, 278

Air pollution, acidic deposition on forested

soils, 63


corn, 208,211-212,227

fingerprinting crop varieties, 98, 105

Alumino hydroxy sulfate, acidic deposition on

forested soils, 33-34


acidic deposition on forested soils

chemical factors, 16, 19-29.31.34-35

future research, 63

hydrogen budgets, 40

mineral weathering, 37-38

physical factors, 14-15

soil change studies, 43,45-46.58-59,



Aluminum (conrinued)

soil organisms, 42

inorganics in soils, 352-353

surface complexation models, 276,278,


toxicity, acidic deposition on forested soils,


Aluminum oxide

acidic deposition on forested soils, 32-34

inorganics in soils, 351

surface complexation models, 237

inorganic anion adsorption, 289-291,


metal ion adsorption, 275, 279

organic ligand adsorption, 308

protonation-dissociation reactions,


Aluminum trihydroxide, acidic deposition on

forested soils, 22, 26

Amino acids

fingerprinting crop varieties, 89

surface complexation models, 308,310

Amplification, fingerprinting crop varieties,


Anatase, surface complexation models, 252,


Anion exchange, acidic deposition on forested

soils, 34


acidic deposition on forested soils, 55-56,


inorganics in soils, 350

surface complexation models, 242,244,


competitive adsorption reactions,


inorganic anion adsorption, 289-307

Antibodies, fingerprinting crop varieties, 89

Antigens, fingerprinting crop varieties, 89

Apparent dispersivity, chemical transport

through soil, 181-182

Apples, fingerprinting crop varieties, 94, 97

Arsenate, surface complexation models,


Arsenic, surface complexation models, 291,


Arsenite, surface complexation models, 305,


Artificial selection, corn, 222

Asymptotic dispersion models, chemical

transport through soil, 151-154

Atrazine, chemical transport through soil,

184, 187-188

Autoradiograms, fingerprinting crop varieties,



Back-crossing, fingerprinting crop varieties,

108, 112,121-122

Barley, fingerprinting crop varieties, 94,

113-114, 123

Base cations, acidic deposition on forested


chemical factors, 28, 31.36-37

soil change studies, 54,57, 61

Base saturation (BS), acidic deposition on

forested soils, 19-20.26

Bicarbonate salts, acidic deposition on

forested soils, 20

Bidentate metal complex, surface

complexation models, 241, 247,281,

290,295, 308

Biological transformation, chemical transport

through soil, 168-169

Block inheritance, corn, 211

Boehmite, surface complexation models, 250,


Borate, surface complexation models,


Boron, surface complexation models, 243.


Boundary conditions, inorganics in soils,


Branching habit, corn, 219,221,226

Brassicas, fingerprinting crop varieties, 123,


Breakthrough curves, inorganics in soils

ion exchange, 376,378-379

layered soil, 381

multiple-reaction models, 352, 356,


Bromide, chemical transport through soil,

176, 178,183-185,187

Buffer capacity, acidic deposition on forested

soils, 18-19

Buffering mechanisms, acidic deposition on

forested soils, 16, 35

Buffering ranges, acidic deposition on

forested soils, 20, 26, 31,40, 66

Bulk density, inorganics in soils, 332, 334




inorganics in soils

ion exchange, 368, 375-376

kinetic retention models, 342

multiple-reaction models, 350-351,


transport equations, 339-340

surface complexation models

competitive adsorption reactions,


computer codes, 319

metal ion adsorption, 278,282,285,



acidic deposition on forested soils

chemical factors, 17.20-21,24,26,28

mineral weathering, 36-37

physical factors, 7 , 9

soil change studies, 45, 52,54,56-62

deficiency, acidic deposition on forested

soils, 29

inorganics in soils, 367-373, 376

surface complexation models, 282,285,


Calcium carbonate, surface complexation

models, 285, 305

Calcium nitrate, surface complexation

models, 285-286

Canopy, acidic deposition on forested soils,


Capacitance density, surface complexation

models, 236,238

Capacity changes, acidic deposition on

forested soils

leaching, 48-56

uptake, 56-59

Capacity factors, acidic deposition on forested

soils, 5-6, 66


acidic deposition on forested soils, 9, 30,

4 1-42

surface complexation models, 315

Carbon dioxide, acidic deposition on forested

soils, 18

Carbonate, surface complexation models, 315,


Carbonic acid, deposition on forested soils, 3,


forest soils, 16, 18-19, 27-28


Cation exchange

acidic deposition on forested soils, 66

chemical factors, 19-29, 31,38

soil change studies, 42,45,55.57,


inorganics in soils, 369-372

Cation exchange capacity, acidic deposition

on forested soils, 16, 37


inorganics in soils, 350,367-368, 375

surface complexation models, 242, 244,


competitive adsorption reactions, 312,


metal ion adsorption, 282,286

Celery, fingerprinting crop varieties, 124-125

Charge balance, surface complexation

models, 236,245-246

Charge-potential relations, surface

complexation models, 240,245, 250

Chemical mass flux laws, chemical transport

through soil, 145-154

Chemical phase concentrations, chemical

transport through soil, 144-145

Chemical speciation models, 319

Chemical transport through soil, 142-143,


field regime

dispersion, 193-194

preferential Row, 192

rate processes, 193

history, 194-195

processes, 143-144

chemical mass flux laws, 145-154

chemical phase concentrations, 144-145

concentrations, 160-161

convection-dispersion, 154-156

dispersion transport, 169-171

interphase mass transfer laws, 161-167

mass conservation law, 144

react ions, 167- I69

solute adsorption, 171-175

transfer function models, 156-160

solute transport, field studies of, 175-176

indices of solute disperion, 189-191

mean solute velocity, 176-179

preferential flow, 185-188

scale of heterogeneity, 189

solute adsorption, 182-185

solute dispersion, 179-182

CHEMTRAN, inorganics in soils, 367-368




chemical transport through soil, 176,181,

183-184, 186

surface complexation models, 266

Chromate, surface complexation models,



fingerprinting crop varieties

characters, 89,95-96,98

discrimination, 110

usage, 123,125

inorganics in soils, 367

Chromium, inorganics in soils, 340,



corn, 207-209,214,219,227

chromosome 4,210-212.227

fingerprinting crop varieties, 102, 124, 126

Citrate, surface complexation models, 304,


Clay minerals

inorganics in soils, 332

surface complexation models, 320

inorganic anion adsorption, 289-291,


metal ion adsorption, 275,277

protonation-dissociation reactions,


Climate, acidic deposition on forested soils,


Clones, fingerprinting crop varieties,


Cloudwater, acidic deposition on forested

soils, 7-8


inorganics in soils, 339, 375-376

surface complexation models, 278, 286,


Coleoptile isozymes, fingerprinting crop

varieties, 112-113, 115

Competitive adsorption reactions, surface

complexation models, 312-318

Competitive transport models, inorganics in

soils, 376

Complementary DNA, fingerprinting crop

varieties, 99-100

Computer codes, surface complexation

models, 319-320

Computer programs, surface complexation

models, 279,290,297,319-320, see


Concentration, inorganics in soils, 369, 380

Concentration outflow, chemical transport

through soil, 172

Concentration-depth curves, chemical

transport through soil, 169

Concentration-time curves, chemical

transport through soil, 169

Condensation, corn, 209,228

Conditional equilibrium constants, surface

complexation models, 236,238-240,


competitive adsorption reactions, 316-3 17

inorganic anion adsorption, 290,297,300,


metal ion adsorption, 275, 279

organic ligand adsorption, 308

protonation-dissociation reactions, 25 1,


Constant capacitance model, 234,320

competitive adsorption reactions, 312,


computer codes, 319

description, 238-240,242-249

inorganic anion adsorption, 289-297

metal ion adsorption, 274-279

organic ligand adsorption, 308-310

protonation-dissociation reactions,



chemical transport through soil, 193-195

processes, 147-151,156,159-160,


solute transport, field studies of, 178,


inorganics in soils, 334

Convection-dispersion model, chemical

transport through soil, 152-156,166,

176, 189

Convective-dispersive equation, inorganics

in soils

equilibrium retention models, 337

ion exchange, 367,369-370, 373

kinetic retention models, 347

layered soil, 379

multiple-reaction models, 351-352,355,


transport equations, 335-336

Convective-dispersive flux, chemical

transport through soil, 154-156, 158,

161, 195

Convective-lognormal transfer function,

chemical transport through soil,


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VII. Transport in Layered Soil

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