1. Solute Transport in Soils and Salinity16
Hillel, pp
Solute Transport in Soils and Salinity

2. Solute Transport in Soils
The transport of soluble chemicals in soils is very important for a range environmental and agricultural issues.
Typical sources of contamination?
Large amounts of water-soluble chemicals are applied for agricultural, industrial, construction, and transportation with the intent of using them in uppermost soil zone (e.g., fertilizers, salts on roads).
In many cases these chemicals are transported to greater depths (beyond the root zone), which not only makes them ineffective for their original intended use, but leads to contamination of natural resources (drinking water) and the environment.
Accidental releases of chemicals (leaky tanks, landfills, chemical pits, etc.) resulting contaminant plumes that migrate through soils.

3. Solute Transport in Soils
The transport of solutes through porous media is coupled with the flow of water. The convective streams of flowing soil water carry salts and other constituents.
Self-diffusion of constituents in the liquid phase is another mechanism of transport in soils.
Solutes interact with the soil matrix through adsorption and desorption, they may precipitate whenever their solubility is exceeded, and they may react among themselves.

4. Mechanisms for Solute Transport in Soil
Convective Transport (Jc):
Convective transport is the passive transport of dissolved constituents with the flowing water. In this case, water and the solutes move at the same average rate:
Darcy Velocity
Jc is the solute flux c is the volume averaged solute concentration Jw is the water flux density or Darcy velocity
The water flux density Jw represents the flow velocity averaged over an entire cross sectional area.

5. Mechanisms for Solute Transport in Soil
Convective Transport (Jc) - Continued:
Because convection occurs in the liquid phase only, we use the mean apparent velocity or pore water velocity (v) to estimate solute travel or arrival times:
Therefore solute flux may also be characterized as:

6. Mechanisms for Solute Transport in Soil
Convective Transport (Jc) - Example:
The annual drainage rate below a rooting zone is 0.5 m/yr and the average water content between the bottom of the rooting zone and the water table located 10 m below is 0.2 m3/m3.
Find the time required to transport nitrate from the bottom of the root zone to ground water.
First we calculate pore water velocity according to:
The time required for nitrates to reach the groundwater by convective transport is simply:
What happens in practice with heterogeneous pathways?

7. Mechanisms for Solute Transport in Soil
Diffusive Transport (Jd):
Diffusive transport is a spontaneous process resulting from random thermal motion, collisions, and deflections of dissolved molecules. The net effect of this process tends towards equalization of spatial differences in concentration, where solutes diffuse from locations with higher to locations with lower concentration.
Concentration Gradient is the Driving Force
The rate of diffusion (Jd) in bulk water at rest is given by Fick's Law:
Diffusion Coefficient in Bulk Water

8. Mechanisms for Solute Transport in Soil
Diffusive Transport (Jd) - Continued:
In unsaturated soils, empty voids and solid particles form barriers to liquid diffusion – we thus introduce an apparent diffusivity Ds [L2/t].
The apparent liquid diffusivity is a function of the available path for diffusion determined by tortuosity T(q) defined by the geometry of the soil (i.e., soil texture and structure), and volumetric water content q.
A relationship between bulk water D0 and apparent soil-liquid diffusivity Ds is given by Jury et al. [1991]:
n is the porosity
The diffusive flux of solutes in an unsaturated soil is thus given as:

9. Mechanisms for Solute Transport in Soil
Dispersive Transport (Jh):
Differences in flow velocities at the pore scale due to different pore sizes and shapes cause solutes to be transported at different rates and thus lead to mixing, or dispersion, of an incoming solution within an antecedent solution.

10. Mechanisms for Solute Transport in Soil
Dispersive Transport (Jh):
Mixing in soil pore networks

11. Mechanisms for Solute Transport in Soil
Dispersive Transport (Jh):
The process is macroscopically similar to mixing by diffusion (thermal motion); however, it is passive, i.e. not driven by concentration gradients, and is entirely dependent on the flow of water.
The solute flux due to mechanical, or hydrodynamic, dispersion (Jh) is described by an equation similar to Fick's Law for diffusion:
Hydrodynamic Dispersion Coefficient [L2/t]
The Hydrodynamic Dispersion Coefficient is dependent on the interstitial pore water flow velocity v [L/t], and on the dispersivity l [L] of the soil which is a function of pore sizes and shapes.

12. Mechanisms for Solute Transport in Soil
Dispersive Transport (Jh) - Continued:
The Hydrodynamic Dispersion Coefficient is given as:
a and n are empirical parameters, with n commonly assumed to equal 1. This means we have a linear relationship between dispersion coefficient and average pore water velocity.
Diffusion and Hydrodynamic Dispersion are similar from macroscopic point of view.
Therefore it is common to combine the Diffusion and Dispersion coefficients, assuming that they are additive.
The resulting coefficient is called Diffusion-Dispersion Coefficient De, and is a function of average pore water velocity and volumetric water content.

13. Hydrodynamic dispersion
The Hydrodynamic Dispersion Coefficient is given as:

14. Hydrodynamic dispersion
The Hydrodynamic Dispersion Coefficient is given as:
(a) Longitudinal dispersion coefficient vs. pore water velocity for (b) different size distributions of sand (Klotz et al., 1980).

15. Effect of scale and heterogeneity

16. The Convection-Dispersion Equation (CDE)
The total flux of dissolved solutes in soil Js is the result of combined transport by convection, diffusion, and dispersion. Js may be described by the Convection- Dispersion Model:
Js is the total mass of solute transported to a unit cross-sectional area of soil per unit time Jw is the Darcy Flux or Darcy Velocity c is the volume averaged solute concentration De is the Diffusion-Dispersion Coefficient c/x is the spatial solute gradient (Note that the partial derivative indicates that the gradient may also vary with time)
De is commonly dominated by the dispersion process under most flow conditions.

17. The Convection-Dispersion Equation (CDE)
Conservation of mass during transport through the soil profile is invoked (continuity) with above equation to obtain a general equation for one-dimensional solute transport:
q.c is the mass of solutes in concentration.
We may also consider changes in the mass of solute adsorbed onto the solid soil matrix given by rbs, where rb is the soil bulk density and s is the adsorbed concentration in terms of mass of solute per mass of soil. The modified continuity equation including the adsorbed solute is given as:

18. The Convection-Dispersion Equation (CDE)
The mass of the adsorbed solute can often be related to its concentration in the solution by an adsorption isotherm. In its simplest form, s and c are assumed to be related by a linear (or linearized) equilibrium isotherm given by:
kd is Distribution Coefficient
In practice, adsorption isotherms are not linear – requiring either the use of complex expressions or linearization

19. The Convection-Dispersion Equation (CDE)
If we assume steady state water flow in a homogeneous soil profile such that Jw and q are constant in time and space, and a linear adsorption isotherm, the previous equation reduces to the well-known Convection-Dispersion Equation (CDE):
RETARDATION FACTOR
SOIL-SOLUTE INTERACTIONS
DIFFUSION- DISPERSION
CONVECTION
R=1 (kd=0) no interactions between soil and solutes R<1 Ion Exclusion R>1 Chemical Reaction - Adsorption

20. Column Break Through Curve (BTC) Experiments

21. Column Break Through Curve (BTC) Experiments
Laboratory experiments are commonly applied for analysis and characterization of solute transport phenomena.
Typical Laboratory Setup:
Chemical Analyses EC

22. Column Break Through Curve (BTC) Experiments
A plot of the outflow concentration measured at the bottom of the column versus time is known as a chemical or solute breakthrough curve (BTC).
It is convenient to plot the results in the form of relative concentration of the effluent c(L,t)/c0 versus dimensionless time T*=vt/L, which is also equal to the number of displaced pore volumes.
Narrow Solute Pulse
Break Through Curve

23. BTC’s - Piston Displacement
Dependent on the mixing scenario we receive different shapes of BTC’s.
If we consider the transport of an inert and nonadsorbing chemical (R=1) through a partially-saturated, constant q soil column of length L, without dispersion (D=0) the interface between the resident solution and the displacing solution is planar and abrupt.
The interface between the invading and the antecedent solutions acts like a displacing piston moving through the soil at a velocity of v. Hence, the "piston" reaches the outlet at vt=L, T*=1, or one pore volume of applied eluant.

24. BTC’s - Longitudinal Dispersion
When dispersion is not negligible (D>0), and R=1, the interface between the solutions (the leading edge of the "piston") spreads. The larger the flow velocity (v), the larger the value of D, which in turn, controls the extent of spread.
The uniform distribution is related to normal distributed pore sizes of this particular soil.
Note that in absence of interactions between soil and solute the areas A and B are always equal regardless of the shape of the curve.
It is customary to express the relationship between flow velocity, column length (L) and D in a dimensionless form known as the Peclet Number P:

25. BTC’s - Longitudinal Dispersion

26. BTC’s - Longitudinal Dispersion
For media with two distinct pore spaces (e.g., aggregated or macroporous soils) we have a bimodal pore size and pore water velocity distribution.
The areas A and B are equal in size if R=1 (no soil-solute interactions).

27. BTC’s - Adsorption and Exclusion
Solute Exclusion and Chemical Reaction:
When R>1 (chemical adsorption) the BTC is retarded and appears at the column outlet later than for R=1.
When R<1, the BTC is shifted to the left of T*=1 and applied solutes appear at the bottom of the column "earlier" than in other scenarios. This case may represent a situation of solute exclusion or the presence of immobile (stagnant) water regions which reduce the mean flow path, thereby increasing the effective velocity (v).

28. BTC’s - Adsorption and Exclusion
Solute Exclusion and Chemical Reaction:
Chloride and Tritium BTC for Columbia Silt Loam are good examples for Solute Exclusion and Chemical Reaction.
Cl ions are repulsed by the negatively charged particle surfaces, therefore the BTC is shifted to the left of one pore volume.
Tritium is absorbed and exchanged in the soil therefore the BTC is shifted to the right of one pore volume.

29. CDE in the field
Measured and calculated solute and water content profiles for: (a) qi=0.005 m3/m3 and water flux was 29 cm/hr; (b) qi=0.005 m3/m3 and water flux was 4.89 cm/hr; (c) measured profiles for two values of qi (Wood and Davidson, 1975).

30. Water and solute movement in unsaturated soil
Simultaneous water and solute movement in unsaturated soil (De Smedt and Wierenga, 1978).

31. Water and solute movement in unsaturated soil

32. Analytical Solutions for the CDE
Transport of a Solute Pulse Through Soil:
A narrow pulse of solute having concentration c0 is added to the inlet of a column with zero initial concentration at t=0, we seek a solution for the effluent concentration at x=L for subsequent times. The boundary conditions are given by:
The solution is given by Jury et al. [1991]:
A is the “pulse width”, A=c0Dt. Note that R in the original equation of Jury et al. was taken as R=1.

33. Analytical Solutions for the CDE
D becomes larger (for constant L and v, this means a smaller Peclet number P), the pulse becomes more and more spread

34. Analytical Solutions for the CDE
Step Application of Solute Into Infinite (and Finite) Length Soil Columns:
A group of analytical solutions applicable to a variety of initial and boundary conditions for solute front passage through a finite length soil column was presented by van Genuchten and Wierenga (1986). Their solutions consider absorbing solutes, i.e., having a retardation factor R>1.
Considering a column with uniform initial or resident concentration ci under steady flow replaced at t=0 with a solution of constant concentration (c0) the initial and boundary conditions are given by:
An analytical solution for solute concentration distribution in a column is given by:

35. Analytical Solutions for the CDE
Complimentary Error Function erfc:
For a complete evaluation of erfc(u) we use the identity erfc(u)=1-erf(u) and approximate erfc(u) for 0≤u< by the following rational approximation (Abramowitz and Stegun, 1964):
The error involved in this approximation is e(u)≤3x10-7
COEFFICIENTS
This approximation applies only to 0 ≤ u .
For u < 0 we take advantage of the symmetry in erf(-u)=-erf(u):

36. Transport parameter estimation
Estimation of solute transport parameters – experiments, measured BTC, model  parameters.
Different experiments and BC – lab #3 next week (saturated, steady state flow, EC measurements).

37. Salt balance and salinity
Salts are a common and necessary component of the soil, and many salts (e.g., nitrate and potassium) are essential plant nutrients. Soil salinity is a measure of the total amount of soluble salts in the soil.
As salinity levels increase, plants extract water less easily, aggravating water stress conditions.
High soil salinity can also cause nutrient imbalances that result in the accumulation of toxic elements.

38. SOIL SALINITY Sources for Soil Salinity: Weathering of bedrock
Inorganic fertilizers
Soil amendments (e.g., composts and manures)
Irrigation water.
High salt concentrations in the groundwater
Salts applied to deice highways

39. SOIL SALINITY
Salt-affected plants are stunted with dark green leaves which, in some cases, are thicker and more succulent than normal.
In woody species, high soil salinity may lead to leaf burn and defoliation.
Grasses also appear dark green and stunted with leaf burn symptoms.
Salinity tolerance is influenced by many plant, soil, and environmental factors and their interrelationships.
Generally, fruits, vegetables, and ornamentals are more salt sensitive than forage or field crops.
In addition, certain varieties, cultivars, or rootstalks may tolerate higher salt levels than others.

40. SOIL SALINITY General guidelines for plant response to soil salinity:
Salinity tolerance of common field crops in Utah:

41. SOIL SALINITY
Salt affected soils in the US:

42. SOIL SALINITY Salt Balance Equation:
The concept of a salt balance follows closely the soil water balance. Because evapotranspiration removes no salts, and plants remove negligible amounts, a simple form of the salt balance equation for an irrigated area may be given as:
I is irrigation P is precipitation D is deep drainage DW is change in soil water storage during the observation period ci are the respective salt concentrations
For an annual salt balance the term DW may often be neglected, as seasonal inputs approximate seasonal outflow. Note also that we have neglected changes in the solid phase (csDS) resulting from dissolution and precipitation of salts.

43. SOIL SALINITY
The salt balance concept has been used for monitoring salinity trends over long periods in large-scale irrigation projects as well as in individual fields. Based on this concept, several tools for salinity control have been developed. The leaching of excess salts from the root zone is one example.

44. SOIL SALINITY Leaching Requirement:
The leaching requirement is a salinity management tool which allows poor-quality irrigation water to be used without excessive accumulation of salts in the rooting zone.
This concept is particularly useful in arid regions where rainfall is insufficient for leaching of the profile.
The basic idea is to apply irrigation in an amount greater than evapotranspiration, or more than the crop needs, such that a fraction of the water will flow downward past the root zone and carry with it excess salts.
The leaching fraction for steady-state conditions may be calculated as:
D is deep drainage I is irrigation EC electrical conductivity of the irrigation and drainage water

45. SOIL SALINITY
The leaching fraction states that if the maximum allowable concentration in drainage water is five times that of the irrigation water, then 1/5 of the irrigation water must drain.
This can be developed further by using the water balance to express the drainage as: D=I+P-Et, and thus the amount of irrigation water (of cI) needed to maintain the concentration of the drainage at cD is:
The equation also shows how the amount needed for leaching is reduced by increased precipitation (P).

46. Salinity Profiles with Plant Water Uptake
SOIL SALINITY
Salinity increases with depth as water is being continually withdrawn by plants, leaving dissolved salts behind. The root system may experience the entire range of concentrations from that of irrigation water (cI) at the top, to that of drainage water (cD) at the bottom of the root zone
Salinity Profiles with Plant Water Uptake
Such irrigation practices may be sustained only where the water table is sufficiently deep, and where an efficient drainage system is functional.

47. SOIL SALINITY
Salinity Profiles Under Steady State Flow Conditions – Example:
High frequency irrigation of concentration cI at a rate of JW=-i0 was applied to a crop having a constant and uniform water uptake per unit volume of soil per unit time: u=Et/L where L is the depth of the root zone.
This constant uptake rate yields a steady-state flux which diminishes with depth according to: JW(z)=-i0-Et(z/L), for L<z<0. Assuming a "piston" type convective flow, the solute flux is JC=JWcI=-i0cI which by conservation of solute mass must be equal to JW(z)c(z). The depth-dependent concentration is thus:

48. SOIL SALINITY Example - Continued:
Defining the leaching fraction as: fL=(drainage rate)/(irrigation rate)=(i0-Et)/i0 enables us to express c(z) as a function of fL

49. Other effects of salinity
Enhanced susceptibility to erosion due to surface sealing and dispersion
Road surface deterioration due to irrigation seepage and salinity

50. SOIL SALINITY
Saline stream at the end of summer:

51. Resident vs. Flux Concentrations
Resident concentration - Cr is the mass of solutes per mass of soil.
The flux concentration, cf, is the ratio of solute mass flux (Js) and water flux (Jw), i.e., cf=Js/Jw.
Under steady state:
An alternative representation: For D/vL<1 the difference between the two types of solute concentration is negligible

52. The Convection-Dispersion Equation (CDE)
kd is Distribution Coefficient
In practice, adsorption isotherms are not linear – requiring either the use of complex expressions or linearization
Adsorption and desorption isotherms for Fluometuron on Cobb sand (Wood and Davidson, 1975).