Order No: FOS 70

Version: 2.01 (February 1996)

Price: **Contact igwmc@mines.edu for more info **

VERTPAK-1 is a package of eight analytical solutions covering fluid flow, rock deformation and solute transport in fractured and unfractured porous media. The following analytical solutions are included:

BAREN: Double-porosity analytical solution for transient well flow in a fractured confined aquifer as given by Barenblatt et al. (1960). The solution describes radial flow to a pumping well fully penetrating a fractured confined aquifer of infinite lateral extent. Prior to pumping, the piezometric surface is horizontal. Fracture permeability is isotropic and homogeneous while the permeability of the porous rock matrix is negligible. Storage is assumed to take place in the porous matrix only.

GIBMAC: Plane strain and axi-symmetric consolidation of a semi-infinite fully- saturated homogeneous, isotropic soil medium with a free drainage top boundary condition (McNamee and Gibson, 1960). The model is based on the description of the dissipation of excess pore pressure and settlement of a semi-infinite soil medium subject to a uniform strip or cylindrical load. The model allows the use of either a cartesian or a radial coordinate system. The soil medium obeys linear stress- strain and velocity-pressure gradient relationships.

GRINRH: Transient flow to a partially penetrating well in a confined reservoir with a single horizontal fracture (Gringarten, 1971). This analytical solution describes axi-symmetric flow to a well pumping at a constant rate from a confined aquifer containing a single horizontal fracture of finite thickness. The model can be used to simulate: 1) a single, plane (zero thickness) horizontal fracture; 2) partial penetration of the producing formation; and 3) limited flow entry throughout a producing interval. The model assumes that the reservoir is horizontal, homogeneous and anisotropic, with different radial and vertical permeabilities. The fully penetrating well is represented as a line sink. A single horizontal fracture of constant radius is centered at the well.

GRINRV: Transient flow to a well fully penetrating a confined reservoir and intercepting the center of a vertical fracture (Gringarten et al., 1974). The model is based on two-dimensional planar flow. The fracture has zero thickness and full penetration of the reservoir. The model can be used to simulate: 1) flow when a uniform flux boundary condition is present over the length of the fracture, and 2) flow in case of infinite conductivity (uniform pressure) in the fracture. The reservoir. The model assumes that the reservoir is horizontal, homogeneous and isotropic and of infinite lateral extent. The fully penetrating well is represented as a line sink.

HART: Thermoelastic deformation in the form of elastic behavior of an infinite medium subject to a line heat source (Nowacki, 1962). The axi-symmetric model describes the temperature stress and displacement fields invoked by an infinitely long line heat source. Both the thermal and mechanical properties of the medium are isotropic, while the mechanical behavior is linear elastic. The heat source is either constant or exponentially decaying.

LESTER: Analytical solution of the one-dimensional dispersive-advective solute transport equation describing the distribution of concentrations for a three-component radionuclide chain in a semi-infinite porous medium (Letter et al., 1975). A material flux boundary condition is specified at the inlet with a decaying step-release function. The medium properties and flow velocity are constant.

STRELT: Transient well flow in a dual porosity confined aquifer (Streltsova- Adams, 1978). The model describes transient radial flow to a pumping well fully penetrating a fractured aquifer of infinite lateral extent. The permeability of the rock matrix is negligible compared with fracture permeability; fluid storage in the fractures is included.

TANG: Advective and dispersive solute transport along a single planar fracture with diffusion into adjacent rock matrix (Tang et al., 1981). The fluid flow velocity is constant. The solute may be subject to first-order decay, adsorption on the fracture-rock mass interface, and adsorption within the rock mass. The fluid flow and solute motion is one-dimensional along the fracture, and the solute motion in the rock matrix is one-dimensional perpendicular to the fracture. Fluid flow velocity in the rock mass is zero.

The programs run in batch mode. For each program, example data sets are provided, which can be copied and edited with a text editor for individual problems. Results are saved in text files. The VERTPAK-1 package is distributed on a HD DOS formatted disk containing source code, executable image, and example data sets. The user's manual includes installation instructions and program documentation.

**SYSTEM REQUIREMENTS**

- Intel 80i86 based computer
- 640 Kb RAM
- DOS 2.1 or higher
- about 1 Mb free disk space

*Authors: Intera Environmental Consultants, Inc. (Austin, TX)
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