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CE/ENVE 320 – Vadose Zone Hydrology/Soil Physics Spring 2004 Copyright © Markus Tuller and Dani Or 2002-2004 Solute Transport in Soils and Salinity 16.

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Presentation on theme: "CE/ENVE 320 – Vadose Zone Hydrology/Soil Physics Spring 2004 Copyright © Markus Tuller and Dani Or 2002-2004 Solute Transport in Soils and Salinity 16."— Presentation transcript:

1 CE/ENVE 320 – Vadose Zone Hydrology/Soil Physics Spring 2004 Copyright © Markus Tuller and Dani Or Solute Transport in Soils and Salinity 16 Hillel, pp

2 Copyright© Markus Tuller and Dani Or 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? 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). 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. 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. Accidental releases of chemicals (leaky tanks, landfills, chemical pits, etc.) resulting contaminant plumes that migrate through soils.

3 Copyright© Markus Tuller and Dani Or 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. 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. 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. 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 Copyright© Markus Tuller and Dani Or Mechanisms for Solute Transport in Soil 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: Convective Transport (J c ): Darcy Velocity J c is the solute flux c is the volume averaged solute concentration J w is the water flux density or Darcy velocity The water flux density J w represents the flow velocity averaged over an entire cross sectional area.

5 Copyright© Markus Tuller and Dani Or Mechanisms for Solute Transport in Soil 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: Convective Transport (J c ) - Continued: Therefore solute flux may also be characterized as:

6 Copyright© Markus Tuller and Dani Or Mechanisms for Solute Transport in Soil 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 m 3 /m 3. Find the time required to transport nitrate from the bottom of the root zone to ground water. Convective Transport (J c ) - Example: 1.First we calculate pore water velocity according to: 2.The time required for nitrates to reach the groundwater by convective transport is simply: What happens in practice with heterogeneous pathways?

7 Copyright© Markus Tuller and Dani Or Mechanisms for Solute Transport in Soil 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. Diffusive Transport (J d ): Concentration Gradient is the Driving Force The rate of diffusion (J d ) in bulk water at rest is given by Fick's Law: Diffusion Coefficient in Bulk Water

8 Copyright© Markus Tuller and Dani Or Mechanisms for Solute Transport in Soil  In unsaturated soils, empty voids and solid particles form barriers to liquid diffusion – we thus introduce an apparent diffusivity D s [L 2 /t].  The apparent liquid diffusivity is a function of the available path for diffusion determined by tortuosity T(  ) defined by the geometry of the soil (i.e., soil texture and structure), and volumetric water content .  A relationship between bulk water D 0 and apparent soil-liquid diffusivity D s is given by Jury et al. [1991]: Diffusive Transport (J d ) - Continued: n is the porosity The diffusive flux of solutes in an unsaturated soil is thus given as:

9 Copyright© Markus Tuller and Dani Or Mechanisms for Solute Transport in Soil 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. Dispersive Transport (J h ):

10 Copyright© Markus Tuller and Dani Or Mechanisms for Solute Transport in Soil Mixing in soil pore networks Dispersive Transport (J h ):

11 Copyright© Markus Tuller and Dani Or Mechanisms for Solute Transport in Soil 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 (J h ) is described by an equation similar to Fick's Law for diffusion: Dispersive Transport (J h ): Hydrodynamic Dispersion Coefficient [L 2 /t] The Hydrodynamic Dispersion Coefficient is dependent on the interstitial pore water flow velocity v [L/t], and on the dispersivity [L] of the soil which is a function of pore sizes and shapes.

12 Copyright© Markus Tuller and Dani Or Mechanisms for Solute Transport in Soil The Hydrodynamic Dispersion Coefficient is given as: Dispersive Transport (J h ) - Continued: 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 D e, and is a function of average pore water velocity and volumetric water content. 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.

13 Copyright© Markus Tuller and Dani Or Hydrodynamic dispersion The Hydrodynamic Dispersion Coefficient is given as:

14 Copyright© Markus Tuller and Dani Or 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 Copyright© Markus Tuller and Dani Or Effect of scale and heterogeneity

16 Copyright© Markus Tuller and Dani Or The Convection-Dispersion Equation (CDE) The total flux of dissolved solutes in soil J s is the result of combined transport by convection, diffusion, and dispersion. J s may be described by the Convection- Dispersion Model: D e is commonly dominated by the dispersion process under most flow conditions. J s is the total mass of solute transported to a unit cross-sectional area of soil per unit time J w is the Darcy Flux or Darcy Velocity c is the volume averaged solute concentration D e 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)

17 Copyright© Markus Tuller and Dani Or 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:   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  b s, where  b 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 Copyright© Markus Tuller and Dani Or 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: k d is Distribution Coefficient In practice, adsorption isotherms are not linear – requiring either the use of complex expressions or linearization

19 Copyright© Markus Tuller and Dani Or The Convection-Dispersion Equation (CDE) If we assume steady state water flow in a homogeneous soil profile such that J w and  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 (k d =0) no interactions between soil and solutes R 1 Chemical Reaction - Adsorption

20 CE/ENVE 320 – Vadose Zone Hydrology/Soil Physics Spring 2004 Copyright © Markus Tuller and Dani Or Column Break Through Curve (BTC) Experiments

21 Copyright© Markus Tuller and Dani Or 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 Copyright© Markus Tuller and Dani Or 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)/c 0 versus dimensionless time T*=vt/L, which is also equal to the number of displaced pore volumes. Break Through Curve Narrow Solute Pulse

23 Copyright© Markus Tuller and Dani Or 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  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 Copyright© Markus Tuller and Dani Or 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 Copyright© Markus Tuller and Dani Or BTC’s - Longitudinal Dispersion

26 Copyright© Markus Tuller and Dani Or 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 Copyright© Markus Tuller and Dani Or BTC’s - Adsorption and Exclusion Solute Exclusion and Chemical Reaction: 1)When R>1 (chemical adsorption) the BTC is retarded and appears at the column outlet later than for R=1. 2)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 Copyright© Markus Tuller and Dani Or 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 Copyright© Markus Tuller and Dani Or CDE in the field Measured and calculated solute and water content profiles for: (a)  i =0.005 m 3 /m 3 and water flux was 29 cm/hr; (b)  i=0.005 m 3 /m 3 and water flux was 4.89 cm/hr; (c) measured profiles for two values of  i (Wood and Davidson, 1975).

30 Copyright© Markus Tuller and Dani Or Water and solute movement in unsaturated soil Simultaneous water and solute movement in unsaturated soil (De Smedt and Wierenga, 1978).

31 Copyright© Markus Tuller and Dani Or Water and solute movement in unsaturated soil

32 Copyright© Markus Tuller and Dani Or Analytical Solutions for the CDE Transport of a Solute Pulse Through Soil: A narrow pulse of solute having concentration c 0 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=c 0  t. Note that R in the original equation of Jury et al. was taken as R=1.

33 Copyright© Markus Tuller and Dani Or 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 Copyright© Markus Tuller and Dani Or 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 c i under steady flow replaced at t=0 with a solution of constant concentration (c 0 ) the initial and boundary conditions are given by: An analytical solution for solute concentration distribution in a column is given by:

35 Copyright© Markus Tuller and Dani Or 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  (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 Copyright© Markus Tuller and Dani Or 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 Copyright© Markus Tuller and Dani Or 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. 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. 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. High soil salinity can also cause nutrient imbalances that result in the accumulation of toxic elements.

38 Copyright© Markus Tuller and Dani Or SOIL SALINITY Sources for Soil Salinity: Weathering of bedrockWeathering of bedrock Inorganic fertilizersInorganic fertilizers Soil amendments (e.g., composts and manures)Soil amendments (e.g., composts and manures) Irrigation water.Irrigation water. High salt concentrations in the groundwaterHigh salt concentrations in the groundwater Salts applied to deice highwaysSalts applied to deice highways

39 Copyright© Markus Tuller and Dani Or SOIL SALINITY Salt-affected plants are stunted with dark green leaves which, in some cases, are thicker and more succulent than normal. 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. In woody species, high soil salinity may lead to leaf burn and defoliation. Grasses also appear dark green and stunted with leaf burn symptoms. 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. 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. 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. In addition, certain varieties, cultivars, or rootstalks may tolerate higher salt levels than others.

40 Copyright© Markus Tuller and Dani Or SOIL SALINITY General guidelines for plant response to soil salinity: Salinity tolerance of common field crops in Utah:

41 Copyright© Markus Tuller and Dani Or SOIL SALINITY Salt affected soils in the US:

42 Copyright© Markus Tuller and Dani Or I is irrigation P is precipitation D is deep drainage  W is change in soil water storage during the observation period c i are the respective salt concentrations 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: For an annual salt balance the term  W may often be neglected, as seasonal inputs approximate seasonal outflow. Note also that we have neglected changes in the solid phase (c s  S) resulting from dissolution and precipitation of salts.

43 Copyright© Markus Tuller and Dani Or 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 Copyright© Markus Tuller and Dani Or 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 Copyright© Markus Tuller and Dani Or 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 c I ) needed to maintain the concentration of the drainage at c D is: The equation also shows how the amount needed for leaching is reduced by increased precipitation (P).

46 Copyright© Markus Tuller and Dani Or 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 (c I ) at the top, to that of drainage water (c D ) at the bottom of the root zone Such irrigation practices may be sustained only where the water table is sufficiently deep, and where an efficient drainage system is functional. Salinity Profiles with Plant Water Uptake

47 Copyright© Markus Tuller and Dani Or SOIL SALINITY Salinity Profiles Under Steady State Flow Conditions – Example: High frequency irrigation of concentration c I at a rate of J W =-i 0 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: J W (z)=-i 0 -Et(z/L), for L

48 Copyright© Markus Tuller and Dani Or SOIL SALINITY Example - Continued: Defining the leaching fraction as: f L =(drainage rate)/(irrigation rate)=(i 0 -Et)/i 0 enables us to express c(z) as a function of f L

49 Copyright© Markus Tuller and Dani Or Other effects of salinity Enhanced susceptibility to erosion due to surface sealing and dispersion Road surface deterioration due to irrigation seepage and salinity

50 Copyright© Markus Tuller and Dani Or SOIL SALINITY Saline stream at the end of summer:

51 Copyright© Markus Tuller and Dani Or Resident vs. Flux Concentrations  Resident concentration - C r is the mass of solutes per mass of soil.  The flux concentration, c f, is the ratio of solute mass flux (J s ) and water flux (Jw), i.e., c f =J s /J w.  Under steady state:  An alternative representation: For D/vL<1 the difference between the two types of solute concentration is negligible

52 Copyright© Markus Tuller and Dani Or The Convection-Dispersion Equation (CDE) k d 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).


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