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Analytical solutions of 2D cresting models using the hodograph method (1994)

McCarthy, J. F.

Springer

Transport in porous media 15 (1994), S. 251-269

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ISSN: 1573-1634

Keywords: Hodograph method ; 2D cresting models ; gas and water cresting

Source: Springer Online Journal Archives 1860-2000

Topics: Geosciences , Technology

Notes: Abstract Three new applications of the hodograph method to the problem of gas and water cresting towards horizontal wells are presented: (1) A numerical technique, based on the hodograph method, is used to find the shape of the oil/water interface and values of critical heights for the problem of water cresting towards a horizontal well beneath an impermeable plane. (2) By correct implementation of the boundary conditions in the lateral edge drive model, a hodograph solution is found for which the water crest tends to a horizontal asymptote far from the well, rather than tending towards a parabolic curve as in previous approaches. The solution yields integral representations for the lengths of boundary segments and enables an explicit expression for the critical rate to be derived in terms of the distance to the constant potential boundary. (3) The problem of simultaneous gas and water cresting towards a horizontal well in a thin oil column reservoir is solved using the hodograph method, providing shapes of the free interfaces and an expression for the optimal placement of the well with respect to the interfaces.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00613281

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A statistical mechanical model of solidification (1995)

Yang, Y. S. ; Blake, N. ; Abbott, T. B. ; [et al.]

Chichester : Wiley-Blackwell

Communications in Numerical Methods in Engineering 11 (1995), S. 805-812

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ISSN: 1069-8299

Keywords: solidification ; dendritic growth ; probabilistic modelling ; Engineering ; Engineering General

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Mathematics , Technology

Notes: A model of solidification is developed from a statistical mechanics basis that incorporates nucleation of columnar and equiaxed grains, thermal and solute diffusion, and latent heat of the phase change. The model is applied to the solidification of austenitic steel. The dendritic growth of columnar and equiaxed grains is simulated, including the segregation of solute ahead of the solid-liquid interface. The irregular branched morphology of the solid forms in a manner analogous to dendritic morphologies that arise from constitutional undercooling in real materials. There is competition between columnar and equiaxed growth. When growing grains approach, the solute layer and the thermal field act to prevent them overlapping.

Additional Material: 5 Ill.