Groundwater Contaminant Transport Calculation: |
Chemical injected during a finite time period. Compute concentration as a function of time and distance or back-calculate injected concentration. Advection, dispersion, and retardation. |

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**Topics on this page**: Introduction Equations
Applications Variable
Definitions Property Data Error Messages References

**Introduction
**
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This calculation simulates one-dimensional (*x*-direction) transport of a chemical
in a confined groundwater aquifer. It is also valid for transport in an unconfined
aquifer if the head gradient (*dh/dx*) is nearly constant. There are two
common boundary conditions for chemical transport: One is a step (i.e. continuous)
injection of chemical - the chemical is added at *x=0* from time *t=0* to *t=T*.
The other common boundary condition is a pulse input where a mass of chemical is added
instantaneously at *x=0*. This web page uses the first boundary condition
though a pulse input can be simulated by using a short injection time *T*.
The calculation solves for concentration at whatever time and distance is desired by the
user.

The calculation includes advection, dispersion, and retardation.
Advection is chemical movement via groundwater flow due to the groundwater hydraulic (i.e.
head) gradient. Dispersion is the longitudinal (forward and backward) spreading of
the contaminant. If there were no dispersion, all of the contaminant would travel at
the mean chemical velocity. With dispersion, some chemical travels faster and some
slower than the mean velocity; the chemical "spreads out." Retardation
causes the mean chemical velocity to be slower than the groundwater velocity. If
your chemical exhibits no dispersion, set both the dispersivity (*a*) and diffusion
coefficient (*D**) to zero. If the chemical is not retarded, then uncheck the
retardation check box or use the chemical drop-down menu to select "User enters *K _{oc}*"
and set

**Equations****
**
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**Governing Equation and Boundary Conditions**

The governing equation for one-dimensional chemical transport in groundwater with
advection, dispersion, and retardation is (Van Genuchten and Alves, 1982):

**Solution**

The solution to the governing equation and boundary conditions shown above is (Van
Genuchten and Alves, 1982):

erfc( ) is called the "complementary error function." Our calculation uses the most accurate numerical representation of erfc( ) given in Abramowitz and Stegun (1972, eqn 7.1.26).

**Applications**
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The following graphs were developed to demonstrate effects of dispersion for
trichloroethylene (TCE) in a sandy aquifer as predicted by the calculation. The
following data were used:

*C _{o} = 10,000 mg/l, d = 1.6 g/cm^{3}, dh/dx = -0.007 m/m, D* =
0, f_{oc} = 0.1%,*
Click for variable definitions

K = 0.001 cm/s, K_{oc} = 100 cm^{3}/g, n = 35%, n_{e} = 25%.

Therefore,

Two injection durations were used: *T=1,000,000 days* in Figure 1 and *T=100
days* in Figure 2. For Figure 1, *T* was selected large enough to
simulate an infinite duration injection. In both figures, the concentration front
occurs at *x = V _{c} t = 16.6 m* when

Figure 1. TCE concentration profile at 1000 days for an injection of duration 1,000,000 days

Figure 2. TCE concentration profile at 1000 days for an injection of duration 100 days.

**Variable Definitions
**
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The variables used on this web page are:

* a* = dispersivity [L]. Varies from 0.1 to 100 m.
Field and laboratory tests have indicated that

** Property Data
**
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Table of Soil Properties

Soil Type |
HydraulicConductivity K (cm/s) |
TotalPorosity n (%) |
EffectivePorosity n _{e} (%) |
BulkDensity d (g/cm ^{3}) |

Clayey | 10^{-9} - 10^{-6} |
40-60 | 0-5 | 1.2-1.8 |

Silty | 10^{-7} - 10^{-3} |
35-50 | 3-20 | 1.1-1.8 |

Sandy | 10^{-5} - 10^{-1} |
20-50 | 10-35 | 1.3-1.9 |

Gravelly | 10^{-1} - 10^{2} |
25-40 | 12-30 | 1.6-2.1 |

Table of Organic Carbon Partition Coefficient, K_{oc}

Chemical |
K_{oc} (cm^{3}/g) |
Chemical |
K_{oc} (cm^{3}/g) |

Benzene | 20-400 | Pyrene | 2000-200,000 |

Ethyl Benzene | 90-1500 | Tetrachloroethylene | 100-3000 |

Dichloroethane | 10-250 | Trichloroethylene | 20-500 |

Naphthalene | 100-2500 |

**Error Messages given by calculation
**
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** "Certain inputs must be > 0."** No
computations.

** "Certain inputs must be >= 0."** No
computations.

** "n, n_{e} , and f_{oc} must be <= 100%."**
No computations. Total porosity, effective porosity, and soil organic carbon cannot
exceed 100%.

** "n_{e} must be <= n."** No
computations. Effective porosity cannot exceed total porosity.

** "C_{o} cannot be determined" **or

**
References **
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Abramowitz, M. and I. A. Stegun. 1972. Handbook of Mathematical Functions. Dover Publications, Inc.

Coduto, D. P. 1994. Foundation Design Principles and Practices. Prentice Hall, Inc.

Fetter, C. W. 1993. Contaminant Hydrogeology. Macmillan Pub. Co.

Freeze, R. A. and J. A. Cherry. 1979. Groundwater. Prentice Hall, Inc.

Hillel, D. H. 1982. Introduction to Soil Physics. Academic Press, Inc.

Ingebritsen, S. E. and W. E. Sanford. 1998. Groundwater in Geologic Processes. Cambridge University Press.

Lyman, W. J. Adsorption coefficient for soils and sediments. __In__
Handbook of Chemical Property Estimation Methods. Lyman, W. J., W. F. Reehl, and D.
H. Rosenblatt, eds. McGraw-Hill Book Co. 1982. pp. 4-1 thru 4-33.

Sanders, L. L. 1998. A Manual of Field Hydrogeology. Prentice Hall, Inc..

Van Genuchten, M. Th. and W. J. Alves. 1982. Analytical Solutions of the One-Dimensional Convective-Dispersive Solute Transport Equation. United States Department of Agriculture, Agricultural Research Service, Technical Bulletin 1661.

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