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Numerical simulation of salt transport in vertical boreholes

Technical Report ·
OSTI ID:6987567
;

A finite difference study is made of the problem of salt transport in vertical boreholes. A rectangular cavity initially filled with fresh water is chosen to represent the vertical wellbores. The top of the rectangle is always supplied with saturated salt water and the bottom with fresh water. The problem is formulated in terms of three simultaneous nonlinear partial differential equations: salt concentration, vorticity and stream function. The Alternating Direction Implicit method (ADI) is chosen to solve the concentration and vorticity formulations. The method of Successive Over Relaxation (SOR) is used to solve the stream function relation. The instability problems associated with high Grashof numbers are overcome by using the second upwind differencing technique. Three dimensionless flow parameters are considered in the finite difference solutions: (1) the ratio of gravity to viscous forces referred to as Grashof number, Gr; (2) the ratio of viscous to diffusion forces known as Schmidt number, Sc; and, the cavity length to width ratio, L. A Nusselt number correlation is derived from the numerical method. This correlation is found to be dependent on the length to width ratio of the cavity, L, only. A steady state rate of salt transport is computed from the Nusselt number for various rectangular cavities. 15 tables, 32 figures.

Research Organization:
Texas Univ., Austin (USA). Dept. of Petroleum Engineering
DOE Contract Number:
W-7405-ENG-26
OSTI ID:
6987567
Report Number(s):
Y/OWI/SUB-4082/3
Country of Publication:
United States
Language:
English

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54 ENVIRONMENTAL SCIENCES
BOREHOLES
CAVITIES
CONVECTION
DIFFERENTIAL EQUATIONS
DIFFUSION
ENERGY TRANSFER
ENVIRONMENTAL TRANSPORT
EQUATIONS
FINITE DIFFERENCE METHOD
GEOLOGIC DEPOSITS
GRASHOF NUMBER
HEAT TRANSFER
ITERATIVE METHODS
MANAGEMENT
MASS TRANSFER
MATHEMATICAL MODELS
NATURAL CONVECTION
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
NUSSELT NUMBER
RADIOACTIVE WASTE STORAGE
RADIONUCLIDE MIGRATION
SALT DEPOSITS
STORAGE
WASTE MANAGEMENT
WASTE STORAGE