Hi!
1)Can I use the STANMOD package for fime metal particle ( colloidal) particles through soil medium?
2)What are the limitations of STANMOD package?
harendra
fine particles
STANMOD
Software package
Evaluating Solute Transport in Porous Media Using Analytical Solutions of the Convection-Dispersion Equation
STANMOD (STudio of ANalytical MODels) is a Windows based computer software package for evaluating solute transport in porous media using analytical solutions of the convection-dispersion solute transport equation. Version 1.0 of STANMOD includes the following models for one-dimensional transport problems: CXTFIT 2.0 [Toride et al., 1995], CFITM [van Genuchten, 1980], CFITIM [van Genuchten, 1981], and CHAIN [van Genuchten, 1985]. Version 2.0 of STANMOD, to be released in the spring of 2000, will also include the models 3DADE [Leij and Bradford, 1994] and N3DADE [Leij and Toride, 1997] for two- and three-dimensional transport problems.
CXTFIT
The software package includes a modified and updated version of the CXTFIT code of Toride et al. [1995] for estimating solute transport parameters using a nonlinear least-squares parameter optimization method. This code may be used to solve the inverse problem by fitting a variety of analytical solutions of theoretical transport models, based upon the one-dimensional convection-dispersion equation (CDE), to experimental results. The program may also be used to solve the direct or forward problem to determine concentrations as a function of time and/or position. Three different one-dimensional transport models are considered: (i) the conventional equilibrium CDE; (ii) the chemical and physical nonequilibrium CDEs; and (iii) a stochastic stream tube model based upon the local-scale equilibrium or nonequilibrium CDE.
CFITM
STANMOD also comes with an updated version of the CFITM code of van Genuchten [1980] for analyzing observed column effluent data using analytical solutions of the one-dimensional equilibrium convective-dispersive transport equations. The code considers analytical solutions for both semi-finite and finite columns. The model provides an easy to use, efficient and accurate means of determining various transport parameters by optimizing observed column effluent data. CFITM represents a simple alternative to the much more comprehensive, but also more complex, CXTFIT model.
CFITIM
STANMOD also contains an updated version of the CFITIM code of van Genuchten [1981] for analyzing observed column effluent data using analytical solutions of the one-dimensional equilibrium and nonequilibrium convective-dispersive transport equations. The code involves analytical solutions for semi-finite columns. The nonequilibrium solutions consider the two-region dual-porosity (bi-continuum) flow model for physical nonequilibrium and the one-site or two-site sorption models for chemical nonequilibrium. The model provides an easy to use, efficient and accurate means of determining various transport parameters by optimizing column effluent data.
CHAIN
In addition, STANMOD 1.0 includes the modified and updated CHAIN code of van Genuchten [1985] for analyzing the convective-dispersive transport of solutes involved in sequential first-order decay reactions. Examples are the migration of radionuclides in which the chain members form first-order decay reactions, and the simultaneous movement of various interacting nitrogen or organic species.
3DADE
STANMOD 2.0 will include the 3DADE code of Leij and Bradford [1994] for evaluating analytical solutions for two- and three-dimensional equilibrium solute transport in the subsurface. The analytical solutions assume steady unidirectional water flow in porous media having uniform flow and transport properties. The transport equation contains terms accounting for solute movement by convection and dispersion, as well as for solute retardation, first-order decay, and zero-order production. The 3DADE code can be used to solve the direct problem, i.e., the concentration is calculated as a function of time and space for specified model parameters, and the indirect (inverse) problem in which the program estimates selected transport parameters by fitting one of the analytical solutions to specified experimental data.
N3DADE
Finally, STANMOD 2.0 will incorporate the N3DADE code of Leij and Toride [1997] for evaluating analytical solutions two- and three-dimensional nonequilibrium solute transport in porous media. The analytical solutions pertain to multi-dimensional solute transport during steady unidirectional water flow in porous media in systems of semi-infinite length in the longitudinal direction, and of infinite length in the transverse direction. The solutions can be applied also to one- and two-dimensional problems. The flow and transport properties of the medium are again assumed to be macroscopically uniform. Nonequilibrium solute transfer can occur between two domains in either the liquid phase (physical nonequilibrium) or the absorbed phase (chemical nonequilibrium). The transport equation contains terms accounting for solute movement by advection and dispersion, as well as for solute retardation, first-order decay, and zero-order production.
Test Examples distributed with the model:
STANMOD is installed with numerous examples that are divided into eight groups (workspaces): CFITM, CFITIM, CHAIN, Direct, Inverse, Stochast, 3DADE, and N3DADE. The first three workspaces CFITM, CFITIM, and CHAIN contain examples of the corresponding models. The next three workspaces Direct, Inverse, and Stochast contain examples of the direct, inverse, and stochastic problems solved with the CXTFIT model. The last two workspaces 3DADE and N3DADE contain examples of the 3DADE and N3DADE models. Users are advised to select an example closest to their particular problem, copy this example and then simply modify the input data.
Examples of the CFITM model
1. The transport of chromium through a sand, a semi-infinite system.
2. The transport of chromium through a sand, a finite system.
Examples of the CFITIM model
1. A generated data set using the assumption of physical non-equilibrium solute transport
2. The movement of tritiated water through a Glendale clay loam in a 30-cm long column. The nonequilibrium transport model with five fitted parameters (P, R, ??, ?Ä, and the dimensionless pulse time, T0).
3. The movement of tritiated water through a Glendale clay loam in a 30-cm long column. The linear equilibrium adsorption model with three fitted parameters (P, R, and T0) was used.
Examples of the CHAIN model
1. The transport of the three-species nitrification chain (NH4+ - NH2- - NH3-).
2. The transport of the radionuclide decay chain (238Pu - 234U - 230Th - 226Ra).
Examples of the CXTFIT model:
a) Direct problems:
1. The first-order physical nonequilibrium model to calculate concentrations in the mobile and immobile phases as a function of time at a depth of 50 cm for a 2-d pulse input at the soil surface. Four different combinations of the mobile water content (?? = ?ám/?á = 0.25, 0.5, 0.75, and 0.99) and the transfer rate (?ç = 0.2, 1, 5, 1000) are used
2. Ditto with five different fractions of sorption sites (f = 0, 0.25, 0.5, 0.75, 1) that equilibrate with the mobile region are used.
3. Example illustrating the effect of the first-order decay constant, ?Ý (=0, 0.25, 0.5, 1 d-1) on solute distribution.
4. Example calculatiing flux (cf) concentrations for two values of the Peclet number, P (= 2, 10) as a function of relative distance when solute-free water is applied to a soil having a stepwise initial resident distribution.
5. Ditto for and resident (cr) concentration
6. Example showing the effects of the first-order mass transfer rate coefficient, ???n(= 0.08, 0.2, 10, 1000 d-1), on breakthrough curves in terms of the flux-averaged concentration, as a result of applying a Dirac delta input function to an initially solute free soil.
7. Example calculating breakthrough curves according to the two-site nonequilibrium CDE for four values of the fraction of sorption sites (f = 0, 0.3, 0.7, and 0.999). Value of 0.08 for the first-order mass transfer rate, ???z?nwere used.
8. Ditto with the value of and 0.2 d-1 for the first-order mass transfer rate, ???z?nwere used.
9. Examples calculating breakthrough curves using different sets of R, ??, and f values in the two-site nonequilibrium CDE for Dirac delta input and pulse input, respectively.
10. Example involving a direct problem using deterministic nonequilibrium transport as described by an initial value problem. The case calculates equilibrium and nonequilibrium resident concentrations and total concentration profiles at T = 1 for three values of the partitioning coefficient ?? (= 0.1, 0.5, and 0.9).
11. Examples demonstrating the effect of the first-order decay coefficient ?Ý (= 0, 0.1, 0.2, 0.35) on Picloram movement through Norge loam using either a pulse or step input, respectively, and assuming applicability of the equilibrium CDE.
12. Example demonstrating the effect of the dimensionless mass transfer coefficient ?ç (= 0.001, 0.28, 0.7, 1.7, 2.8, 7.0, 1000000) on calculated effluent curves for 2,4,5-T movement through Glendale clay loam using the two-region physical nonequilibrium CDE model).
13. Example demonstrating the effect of the dimensionless partitioning coefficient ?? (= 0.2, 0.35, 0.5, 0.65, 0.80, 0.99) on calculated effluent curves from, and spatial concentration distributions in, an aggregated sorbing medium, respectively, assuming two-region physical nonequilibrium transport.
14. Examples demonstrating the effect of the retardation factor R (= 1.0, 1.75, 2.5, 3.5, and 5.0) on calculated effluent curves from, and spatial concentration distributions in, an aggregated sorbing medium, respectively, again assuming two-region physical nonequilibrium transport.
15. Example calculating solute concentration versus time and distance for an aggregated sorbing medium, respectively, assuming two-region physical nonequilibrium model, as affected by the dimensionless mass transfer coefficient ?ç (= 0.02, 0.2, 0.5, 1.5, 7.5, 1000).
16. Example demonstrating the effect of the Peclet number P (= 5, 15, 40, 100, 10000) on calculated effluent curves from, and spatial concentration distribution in, an aggregated sorbing medium, respectively, assuming two-region physical nonequilibrium transport.
b) Stochastic problems:
1. Examples calculating field-scale resident concentrations, cr, versus depth resulting from the instantaneous application of a solute to the surface as a BVP (variable mass) and an IVP (constant mass).
2. Examples calculating field-scale resident concentrations versus depth as a result of a pulse-type solute application of constant duration.
3. Example demonstrating the effect of variability in the pore-water velocity, v, on the field-scale resident concentration profile and the distribution of the variance for cr in the horizontal plane. This example calculates the mean resident concentration and its variance as a function of depth at t = 3 d for three values of ??v (=0.1, 0.3, 0.5) as a result of a 2-d solute application to a solute-free soil.
4. Examples calculating the breakthrough curves for three types of field-scale concentration modes.
5. Example demonstrating the effect of correlation (?âvKd = -1, 0, +1) between the pore-water velocity, v, and the distribution coefficient, Kd, on calculated field-scale resident concentration, cr, profiles. Field-scale concentrations at t = 5 d resulting from a Dirac delta input at t = 0 are calculated versus depth for either perfect or no correlation between v and Kd.
6. Examples calculating field-scale resident and total concentrations, respectively, assuming stochastic nonequilibrium solute transport. Examples assume a negatively correlated v and Kd (?âvKd = -1) using three values of the mass transfer coefficient ?ç.
c) Inverse problems:
1) The pore-water velocity, v, and dispersion coefficient, D, are estimated from breakthrough curves measured at three different depths (11, 17, and 23 cm) with four-electrode electric conductivity sensors. Breakthrough curves were a result of (a) continuous application of a 0.001 M NaCl solution to an initially solute-free saturated sand, and (b) leaching with solute free water during unsaturated conditions, respectively.
2) Two examples of nonequilibrium solute transport consider transport of tritiated water and boron, respectively, through Glendale clay loam in a 30-cm long column. In both examples parameters of the non-equilibrium transport model were optimized against effluent curves.
3) The stochastic option of CXTFIT, together with parameter estimation, is demonstrated with two examples. The first example pertains to resident concentrations in a 0.64-ha field to which a bromide pulse was applied for 1.69 d followed by leaching with solute-free water [Jury et al., 1982]. The stream tube model was used to estimate the mean pore-water velocity <v>, the mean dispersion coefficient <D>, and their standard deviations ??v and ??D, respectively. The second example demonstrates the estimation of parameters in the stream tube model for reactive transport using a hypothetical data set. The standard deviation, ??Kd, and the coefficient of correlation between v, and Kd, i.e., ?âvKd, were fitted to the hypothetical data, while keeping <v>, ??v, and <Kd> constant.
Examples of the 3DADE model
1) Example calculating steady-state concentration profiles for a diffuse solute source in one quadrant of the soil surface.
2) Examples calculating transient concentration profiles for transport from a rectangular solute source at the surface using either a first- or third-type boundary condition.
3) Example calculating transient concentration profiles for transport from a parallelepipedal initial distribution.
4) Example calculating transient concentration profiles for transport from a circular solute source at the surface using a third-type boundary condition.
5) Example that considers (similarly to Example1) solute application in one quadrant of the soil surface. The parameters R, Dx, and Dy (retardation factor, and dispersion coefficients in the x- and y-directions, respectively) are fitted using a breakthrough curve at a specified position and the steady-state profile at a selected transect.
6) Example involving the estimation of the parameters R, ?Ý?z?n?Ü?z?nDx, Dy, and Dz (retardation factor, first-order rate coefficient for decay, zero-order rate coefficient for production, and dispersion coefficients in the x-, y- and z-directions, respectively) for solute transport from a parallelepipedal initial distribution. Breakthrough curves at ten positions along the x coordinate and two transverse profiles were used for the problem.
7) Example that concerns the application of a solute pulse from a circular area at the soil surface. Parameters t0, Dx, and Dr (pulse time, and dispersion coefficients in the x- and r-directions, respectively) were estimated using concentrations at several spatial locations at a specific time.
Examples of the N3DADE model
1) Examples calculating breakthrough curves at a depth of 50 cm and the flux-averaged spatial concentration distribution for instantaneous solute application from a disk having radius of 2.5 cm at the soil surface. The problem involves a circular geometry.
2) Example that pertains to flux-averaged concentration profiles resulting from the continuous application of solute to a rectangular surface area (-2.5 < y < 2.5, -2.5 < z < 2.5). It calculates equilibrium, nonequilibrium and total concentrations versus longitudinal distance at three different times, and in the transverse plane at two longitudinal positions.
3) Example that considers an initial value problem (rectangular) with solute initially located in the regions 5 < x < 15 (c = 1) and 25 < x < 35 (c = 0.5) for 15 < y < 25 and -100 < z < 100.
4) Example, which also pertains to an initial value problem (in this case spherical), assumes that the solute has initially a maximum value at the point given by x=5, y=0, and z=5, and that the solute concentration decreases exponentially from the maximum.
5) Example involving solute production in a cylindrical region of the soil (0 < x < 10 and 0 < r < 2.5). The problem is modeled as a production value problem (PVP) with a heaviside function for the longitudinal and transversal directions, with production in the equilibrium phase equal to 0.5, and in the nonequilibrium phase equal to 1.
Software package
Evaluating Solute Transport in Porous Media Using Analytical Solutions of the Convection-Dispersion Equation
STANMOD (STudio of ANalytical MODels) is a Windows based computer software package for evaluating solute transport in porous media using analytical solutions of the convection-dispersion solute transport equation. Version 1.0 of STANMOD includes the following models for one-dimensional transport problems: CXTFIT 2.0 [Toride et al., 1995], CFITM [van Genuchten, 1980], CFITIM [van Genuchten, 1981], and CHAIN [van Genuchten, 1985]. Version 2.0 of STANMOD, to be released in the spring of 2000, will also include the models 3DADE [Leij and Bradford, 1994] and N3DADE [Leij and Toride, 1997] for two- and three-dimensional transport problems.
CXTFIT
The software package includes a modified and updated version of the CXTFIT code of Toride et al. [1995] for estimating solute transport parameters using a nonlinear least-squares parameter optimization method. This code may be used to solve the inverse problem by fitting a variety of analytical solutions of theoretical transport models, based upon the one-dimensional convection-dispersion equation (CDE), to experimental results. The program may also be used to solve the direct or forward problem to determine concentrations as a function of time and/or position. Three different one-dimensional transport models are considered: (i) the conventional equilibrium CDE; (ii) the chemical and physical nonequilibrium CDEs; and (iii) a stochastic stream tube model based upon the local-scale equilibrium or nonequilibrium CDE.
CFITM
STANMOD also comes with an updated version of the CFITM code of van Genuchten [1980] for analyzing observed column effluent data using analytical solutions of the one-dimensional equilibrium convective-dispersive transport equations. The code considers analytical solutions for both semi-finite and finite columns. The model provides an easy to use, efficient and accurate means of determining various transport parameters by optimizing observed column effluent data. CFITM represents a simple alternative to the much more comprehensive, but also more complex, CXTFIT model.
CFITIM
STANMOD also contains an updated version of the CFITIM code of van Genuchten [1981] for analyzing observed column effluent data using analytical solutions of the one-dimensional equilibrium and nonequilibrium convective-dispersive transport equations. The code involves analytical solutions for semi-finite columns. The nonequilibrium solutions consider the two-region dual-porosity (bi-continuum) flow model for physical nonequilibrium and the one-site or two-site sorption models for chemical nonequilibrium. The model provides an easy to use, efficient and accurate means of determining various transport parameters by optimizing column effluent data.
CHAIN
In addition, STANMOD 1.0 includes the modified and updated CHAIN code of van Genuchten [1985] for analyzing the convective-dispersive transport of solutes involved in sequential first-order decay reactions. Examples are the migration of radionuclides in which the chain members form first-order decay reactions, and the simultaneous movement of various interacting nitrogen or organic species.
3DADE
STANMOD 2.0 will include the 3DADE code of Leij and Bradford [1994] for evaluating analytical solutions for two- and three-dimensional equilibrium solute transport in the subsurface. The analytical solutions assume steady unidirectional water flow in porous media having uniform flow and transport properties. The transport equation contains terms accounting for solute movement by convection and dispersion, as well as for solute retardation, first-order decay, and zero-order production. The 3DADE code can be used to solve the direct problem, i.e., the concentration is calculated as a function of time and space for specified model parameters, and the indirect (inverse) problem in which the program estimates selected transport parameters by fitting one of the analytical solutions to specified experimental data.
N3DADE
Finally, STANMOD 2.0 will incorporate the N3DADE code of Leij and Toride [1997] for evaluating analytical solutions two- and three-dimensional nonequilibrium solute transport in porous media. The analytical solutions pertain to multi-dimensional solute transport during steady unidirectional water flow in porous media in systems of semi-infinite length in the longitudinal direction, and of infinite length in the transverse direction. The solutions can be applied also to one- and two-dimensional problems. The flow and transport properties of the medium are again assumed to be macroscopically uniform. Nonequilibrium solute transfer can occur between two domains in either the liquid phase (physical nonequilibrium) or the absorbed phase (chemical nonequilibrium). The transport equation contains terms accounting for solute movement by advection and dispersion, as well as for solute retardation, first-order decay, and zero-order production.
Test Examples distributed with the model:
STANMOD is installed with numerous examples that are divided into eight groups (workspaces): CFITM, CFITIM, CHAIN, Direct, Inverse, Stochast, 3DADE, and N3DADE. The first three workspaces CFITM, CFITIM, and CHAIN contain examples of the corresponding models. The next three workspaces Direct, Inverse, and Stochast contain examples of the direct, inverse, and stochastic problems solved with the CXTFIT model. The last two workspaces 3DADE and N3DADE contain examples of the 3DADE and N3DADE models. Users are advised to select an example closest to their particular problem, copy this example and then simply modify the input data.
Examples of the CFITM model
1. The transport of chromium through a sand, a semi-infinite system.
2. The transport of chromium through a sand, a finite system.
Examples of the CFITIM model
1. A generated data set using the assumption of physical non-equilibrium solute transport
2. The movement of tritiated water through a Glendale clay loam in a 30-cm long column. The nonequilibrium transport model with five fitted parameters (P, R, ??, ?Ä, and the dimensionless pulse time, T0).
3. The movement of tritiated water through a Glendale clay loam in a 30-cm long column. The linear equilibrium adsorption model with three fitted parameters (P, R, and T0) was used.
Examples of the CHAIN model
1. The transport of the three-species nitrification chain (NH4+ - NH2- - NH3-).
2. The transport of the radionuclide decay chain (238Pu - 234U - 230Th - 226Ra).
Examples of the CXTFIT model:
a) Direct problems:
1. The first-order physical nonequilibrium model to calculate concentrations in the mobile and immobile phases as a function of time at a depth of 50 cm for a 2-d pulse input at the soil surface. Four different combinations of the mobile water content (?? = ?ám/?á = 0.25, 0.5, 0.75, and 0.99) and the transfer rate (?ç = 0.2, 1, 5, 1000) are used
2. Ditto with five different fractions of sorption sites (f = 0, 0.25, 0.5, 0.75, 1) that equilibrate with the mobile region are used.
3. Example illustrating the effect of the first-order decay constant, ?Ý (=0, 0.25, 0.5, 1 d-1) on solute distribution.
4. Example calculatiing flux (cf) concentrations for two values of the Peclet number, P (= 2, 10) as a function of relative distance when solute-free water is applied to a soil having a stepwise initial resident distribution.
5. Ditto for and resident (cr) concentration
6. Example showing the effects of the first-order mass transfer rate coefficient, ???n(= 0.08, 0.2, 10, 1000 d-1), on breakthrough curves in terms of the flux-averaged concentration, as a result of applying a Dirac delta input function to an initially solute free soil.
7. Example calculating breakthrough curves according to the two-site nonequilibrium CDE for four values of the fraction of sorption sites (f = 0, 0.3, 0.7, and 0.999). Value of 0.08 for the first-order mass transfer rate, ???z?nwere used.
8. Ditto with the value of and 0.2 d-1 for the first-order mass transfer rate, ???z?nwere used.
9. Examples calculating breakthrough curves using different sets of R, ??, and f values in the two-site nonequilibrium CDE for Dirac delta input and pulse input, respectively.
10. Example involving a direct problem using deterministic nonequilibrium transport as described by an initial value problem. The case calculates equilibrium and nonequilibrium resident concentrations and total concentration profiles at T = 1 for three values of the partitioning coefficient ?? (= 0.1, 0.5, and 0.9).
11. Examples demonstrating the effect of the first-order decay coefficient ?Ý (= 0, 0.1, 0.2, 0.35) on Picloram movement through Norge loam using either a pulse or step input, respectively, and assuming applicability of the equilibrium CDE.
12. Example demonstrating the effect of the dimensionless mass transfer coefficient ?ç (= 0.001, 0.28, 0.7, 1.7, 2.8, 7.0, 1000000) on calculated effluent curves for 2,4,5-T movement through Glendale clay loam using the two-region physical nonequilibrium CDE model).
13. Example demonstrating the effect of the dimensionless partitioning coefficient ?? (= 0.2, 0.35, 0.5, 0.65, 0.80, 0.99) on calculated effluent curves from, and spatial concentration distributions in, an aggregated sorbing medium, respectively, assuming two-region physical nonequilibrium transport.
14. Examples demonstrating the effect of the retardation factor R (= 1.0, 1.75, 2.5, 3.5, and 5.0) on calculated effluent curves from, and spatial concentration distributions in, an aggregated sorbing medium, respectively, again assuming two-region physical nonequilibrium transport.
15. Example calculating solute concentration versus time and distance for an aggregated sorbing medium, respectively, assuming two-region physical nonequilibrium model, as affected by the dimensionless mass transfer coefficient ?ç (= 0.02, 0.2, 0.5, 1.5, 7.5, 1000).
16. Example demonstrating the effect of the Peclet number P (= 5, 15, 40, 100, 10000) on calculated effluent curves from, and spatial concentration distribution in, an aggregated sorbing medium, respectively, assuming two-region physical nonequilibrium transport.
b) Stochastic problems:
1. Examples calculating field-scale resident concentrations, cr, versus depth resulting from the instantaneous application of a solute to the surface as a BVP (variable mass) and an IVP (constant mass).
2. Examples calculating field-scale resident concentrations versus depth as a result of a pulse-type solute application of constant duration.
3. Example demonstrating the effect of variability in the pore-water velocity, v, on the field-scale resident concentration profile and the distribution of the variance for cr in the horizontal plane. This example calculates the mean resident concentration and its variance as a function of depth at t = 3 d for three values of ??v (=0.1, 0.3, 0.5) as a result of a 2-d solute application to a solute-free soil.
4. Examples calculating the breakthrough curves for three types of field-scale concentration modes.
5. Example demonstrating the effect of correlation (?âvKd = -1, 0, +1) between the pore-water velocity, v, and the distribution coefficient, Kd, on calculated field-scale resident concentration, cr, profiles. Field-scale concentrations at t = 5 d resulting from a Dirac delta input at t = 0 are calculated versus depth for either perfect or no correlation between v and Kd.
6. Examples calculating field-scale resident and total concentrations, respectively, assuming stochastic nonequilibrium solute transport. Examples assume a negatively correlated v and Kd (?âvKd = -1) using three values of the mass transfer coefficient ?ç.
c) Inverse problems:
1) The pore-water velocity, v, and dispersion coefficient, D, are estimated from breakthrough curves measured at three different depths (11, 17, and 23 cm) with four-electrode electric conductivity sensors. Breakthrough curves were a result of (a) continuous application of a 0.001 M NaCl solution to an initially solute-free saturated sand, and (b) leaching with solute free water during unsaturated conditions, respectively.
2) Two examples of nonequilibrium solute transport consider transport of tritiated water and boron, respectively, through Glendale clay loam in a 30-cm long column. In both examples parameters of the non-equilibrium transport model were optimized against effluent curves.
3) The stochastic option of CXTFIT, together with parameter estimation, is demonstrated with two examples. The first example pertains to resident concentrations in a 0.64-ha field to which a bromide pulse was applied for 1.69 d followed by leaching with solute-free water [Jury et al., 1982]. The stream tube model was used to estimate the mean pore-water velocity <v>, the mean dispersion coefficient <D>, and their standard deviations ??v and ??D, respectively. The second example demonstrates the estimation of parameters in the stream tube model for reactive transport using a hypothetical data set. The standard deviation, ??Kd, and the coefficient of correlation between v, and Kd, i.e., ?âvKd, were fitted to the hypothetical data, while keeping <v>, ??v, and <Kd> constant.
Examples of the 3DADE model
1) Example calculating steady-state concentration profiles for a diffuse solute source in one quadrant of the soil surface.
2) Examples calculating transient concentration profiles for transport from a rectangular solute source at the surface using either a first- or third-type boundary condition.
3) Example calculating transient concentration profiles for transport from a parallelepipedal initial distribution.
4) Example calculating transient concentration profiles for transport from a circular solute source at the surface using a third-type boundary condition.
5) Example that considers (similarly to Example1) solute application in one quadrant of the soil surface. The parameters R, Dx, and Dy (retardation factor, and dispersion coefficients in the x- and y-directions, respectively) are fitted using a breakthrough curve at a specified position and the steady-state profile at a selected transect.
6) Example involving the estimation of the parameters R, ?Ý?z?n?Ü?z?nDx, Dy, and Dz (retardation factor, first-order rate coefficient for decay, zero-order rate coefficient for production, and dispersion coefficients in the x-, y- and z-directions, respectively) for solute transport from a parallelepipedal initial distribution. Breakthrough curves at ten positions along the x coordinate and two transverse profiles were used for the problem.
7) Example that concerns the application of a solute pulse from a circular area at the soil surface. Parameters t0, Dx, and Dr (pulse time, and dispersion coefficients in the x- and r-directions, respectively) were estimated using concentrations at several spatial locations at a specific time.
Examples of the N3DADE model
1) Examples calculating breakthrough curves at a depth of 50 cm and the flux-averaged spatial concentration distribution for instantaneous solute application from a disk having radius of 2.5 cm at the soil surface. The problem involves a circular geometry.
2) Example that pertains to flux-averaged concentration profiles resulting from the continuous application of solute to a rectangular surface area (-2.5 < y < 2.5, -2.5 < z < 2.5). It calculates equilibrium, nonequilibrium and total concentrations versus longitudinal distance at three different times, and in the transverse plane at two longitudinal positions.
3) Example that considers an initial value problem (rectangular) with solute initially located in the regions 5 < x < 15 (c = 1) and 25 < x < 35 (c = 0.5) for 15 < y < 25 and -100 < z < 100.
4) Example, which also pertains to an initial value problem (in this case spherical), assumes that the solute has initially a maximum value at the point given by x=5, y=0, and z=5, and that the solute concentration decreases exponentially from the maximum.
5) Example involving solute production in a cylindrical region of the soil (0 < x < 10 and 0 < r < 2.5). The problem is modeled as a production value problem (PVP) with a heaviside function for the longitudinal and transversal directions, with production in the equilibrium phase equal to 0.5, and in the nonequilibrium phase equal to 1.