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WRRCTMR No.55 Numerical Modelling of Liquid Waste Injection into Porous Media Saturated with Density-Stratified Fluid: A Progress Report

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Title: WRRCTMR No.55 Numerical Modelling of Liquid Waste Injection into Porous Media Saturated with Density-Stratified Fluid: A Progress Report
Authors: Wheatcraft, Stephen W.
LC Subject Headings: Groundwater flow -- Mathematical models.
Sewage disposal in the ground -- Mathematical models.
Issue Date: Dec 1977
Publisher: Water Resources Research Center, University of Hawaii at Manoa
Citation: Wheatcraft SW. 1977. Numerical modelling of liquid waste injection into porous media saturated with density-stratified fluid: a progress report. Honolulu (HI): Water Resources Research Center, University of Hawaii at Manoa. WRRC technical memorandum report, 55.
Series/Report no.: WRRC Technical Memorandum Reports
Abstract: Waste effluent injected into an aquifer saturated with denser ambient
brackish or salt water experiences a buoyant lift. As a result, the effluent
migrates both outward from the well and upward in response to the combined
effects of injection head and buoyant force. After the injection
process has begun, several phenomena can affect the density, shape, and
distribution in space and time of the resulting buoyant plume. The most
important of these include convection and mechanical dispersion and molecular
Previous sandbox and Hele-Shaw laboratory modelling work have provided
a basic qualitative understanding of buoyant plume movement in a porous
medium. However, these laboratory models cannot correctly simulate dispersion
phenomena which may have significant effects on buoyant plume movement
and distribution. Consequently, it is necessary to mathematically model
the problem using coupled sets of partial differential equations which take
into account the effects of dispersion and diffusion, as well as convection.
For this problem, there are four unknowns (density, concentration, velocity,
and pressure), requiring four equations. The four governing equations are:
a motion equation (Darcy's law), a continuity equation, a dispersion equation,
and an equation of state. In addition, boundary and initial conditions
must be stipulated. In this study, two sets of boundary conditions
are used: the first consists of conditions identical to those in the sandbox
model studies, and the second models the geology of a specific prototype
area. The resulting governing equations and boundary and initial conditions
are numerically solved by both the finite difference and the finite element
methods. Finally, the numerical models are calibrated with the results of
the sandbox model studies mentioned previously.
This report describes in detail formulation of the governing equations
and the initial and boundary conditions, and preliminary finite difference
modelling work completed to date.
Sponsor: U.S. Department of the Interior OWRT Project NO. A-071-HI Grant/Contract No. 14-34-0001-7026
Pages/Duration: v + 23 pages
Appears in Collections:WRRC Technical Memorandum Reports

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