We use a lattice Boltzmann algorithm for liquid-gas coexistence to investigate the steady-state interface profile of a droplet held between two shearing walls. The algorithm solves the hydrodynamic equations of motion for the system. Partial wetting at the walls is implemented to agree with Cahn theory. This allows us to investigate the processes which lead to the motion of the three-phase contact line. We confirm that the profiles are a function of the capillary number and a finite-size analysis shows the emergence of a dynamic contact angle, which can be defined in a region where the interfacial curvature tends to zero.

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Two methods are presented for predicting critical oil rate for bottomwater coning in anisotropic, homogeneous formations with the well completed from the top of the formation. The first method is based on an analytical solution where Muskat's assumption of uniform flux at the wellbore has been replaced by 'that of an infinitely conductive wellbore. The potential distribution in the oil zone, however, is assumed unperturbed by the water cone. The method is derived from a general solution of the time-dependent diffusivity equation for compressible, single-phase flow in the steady-state limit. We show that very little difference exists between our solution and Muskat's. The deviation from simulation results is caused by the cone influence on potential distribution.The second method is based on a large number of simulation runs with a general numerical reservoir model, with more than 50 critical rates determined. The results are combined in an equation for the isotropic case and in a single diagram for the anisotropic case. The correlation is valid for dimensionless radii between 0.5 and 50 and shows a rapid change in critical rate for values below five. Within the accuracy of numerical modeling results, Wheatley's theory is shown to predict the correct critical rates closely for all well penetrations in the dimensionless radius range from 2 to 50.

Recovery from an oil zone underlying a gas cap, overlying an aquifer, or sandwiched between gas and water can be improved by repressing the coning problem through horizontal-well drainage. Literature methods to predict coning behavior are limited to steady-state flow conditions and determination of the critical rate. The results in this paper are based on new semianalytical solutions for time development of a gas or water cone and of simultaneous gas and water cones in an anisotropic infinite reservoir with a horizontal well placed in the oil column. The solutions are derived by a moving-boundary method with gravity equilibrium assumed in the cones. For the gas-cone case, the semianalytical results are presented as a single dimensionless curve (time to breakthrough vs. rate) and as a simple analytical expression for dimensionless rates > l!J. For the simultaneous gas-and water-cone case, the results are given in two dimensionless sets of curves: one for the optimum vertical well placement and one for the corresponding time to breakthrough, both as functions of rate with the density contrast as a parameter. The validity of the results has been extensively tested by a general numerical simulation model. Sample calculations with reservoir data from the Troll field and comparison with test data from the Helder field demonstrate how the theory can be used to estimate the time to cone breakthrough and its sensitivity to the uncertainties in reservoir parameters.

The cross section for elastic scattering of photons on a static Coulomb potential, Delbruck scattering, is calculated in the lowest-order Born approximation. Using conventional Feynman techniques and gauge invariance we obtain expressions for the real and imaginary parts of the scattering amplitude for polarized photons. These rather complicated expressions contain multidimensional integrals which have been evaluated partly by analytical and partly by numerical methods, and Delbriick amplitudes have been obtained for various scattering angles and for photon energies o varying from zero to several GeV. The results confirm earlier calculations at very low energies (o ( 1 MeV), confirm the imaginary parts but disagree with the real parts previously obtained by Ehlotzky and Sheppey for o < 20 MeV, and confirm the high-energy results of Cheng and Wu to lowest order. A comparison with some recent experiments is shown.