W. G. Laidlaw

Sensitivity of drainage and imbibition to pore structures as revealed by computer simulation of displacement process

Abstract This work concerns the effects of the properties of porous media on two phase fluid displacement at slow rates. These properties include the size frequency distributions, shape and connectivity of pores and throats, the size correlation of directly connected throats and pores and the spatial arrangement of pores and throats in porous media. Computer simulations using 3-dimensional networks of pores and throats were used to determine the effects of these properties on the form of primary and secondary drainage curves, imbibition curves and scanning loops of a capillary pressure diagram. The application of the results is in deriving information about the structure of a porous medium from capillary pressure curves and understanding how predictions about the form of relative permeability curves can be made from capillary pressure curves. The concepts of finite and infinite throat and pore controlled domains are applied during the filling and emptying of a network. These concepts are then combined with considerations of the accessibility of network sites to non-wetting phase or wetting phase sources and sinks to provide information about the amounts and distribution of continuous and discontinuous wetting phase (wp) and non-wetting phase (nwp) at any stage of a displacement. The distribution of fluids Is strictly controlled by the domains. It is shown that recognition of the types, abundance and distribution of domains provides a fundamental basis for understanding boundary effects, differences in tortuosity in porous systems containing two immiscible phases, breakthrough pressures, and saturations, differences in nwp withdrawal efficiency between uncorrelated and correlated pore-throat size models, differences in hysteresis between drainage and imbibition and differences in the shapes of capillary pressure and relative permeability curves for various types of porous structures.

On the application of the variational principle to a type of nonlinear ’’Schrödinger equation’’

’’Schrodinger equations’’ in which the potential of the ’’Hamiltonian’’ H (φ) =H0+V (φ) depends on the first order density σσ− have received some attention in recent literature. The direct variation of the functional <φ‖H (φ) ‖φ≳/<φ‖φ≳ does not lead to the eigenequation H (φ) φ=eφ. A variational functional J (φ) is proposed which has the form J (φ) =H (φ) −(q/q+1) V(q)(φ), q being the degree in φφ*. The functional j (φ) leads to solutions of the eigenequation H (φ) φ=eφ and, provided the potential Vq(φ) fulfil <φ‖V(q)(φ) ‖φ≳? (q+1) < (q+1) <φ‖V‖φ≳, its expectation value is bounded by the lowest exact eigenvalue E0, i.e., <σ‖J (φ) ‖φ≳?E0.

Simulated annealing statics computation using an order-based energy function

The residual statics problem in seismic data analysis is treated by introducing an optimization function that emphasizes the coherence of neighboring common depth point (CDP) gathers within a nonlinear simulated annealing technique. This optimization criterion contrasts with stack power optimization which only considers the coherence between traces within a single CDP. Emphasizing coherence between CDPs removes many of the phase space degeneracies that result from stack‐power based optimization techniques. We have applied the method to both synthetic and real data sets, and initial results display significant improvement over the input data in the coherence of reflections, even in structurally complex areas.

Thermal conditioning in Bactrocera tryoni eggs (Diptera: Tephritidae) following hot-water immersion

Abstract Bactrocera tryoni Froggatt eggs were immersed in hot water to determine egg mortality. Eggs were either immersed in water at a constant temperature, or experienced changing temperature at a specified rate of increase and from a specified start temperature. Comparison of the estimated lethal time for 99% kill (LT 99 ) of eggs experiencing different treatments allowed thermal conditioning to be identified and quantified. Conditioning depended on the temperature and duration of treatment, being a maximum near 38°C. Most conditioning appeared to occur during the early part of the exposure to a given temperature. Exposure to lethal temperatures (≥42°C) as a target temperature of 46 or 48°C was approached, contributed significantly to the mortality if the rate of heating was relatively slow. Calculations of egg survival in a mathematical model of the conditioning and lethal thermal responses, correlated well with experimental values in terms of both trends and magnitudes of LT 99 values. The thermal conditions, prior to disinfestation treatment, influence the response to subsequent heat treatment and thus have implications for the specification of postharvest quarantine treatments which are often expressed in terms of a fruit centre target temperature. This does not take into account of the influence of temperatures and exposure times in the range 32–42°C which can have a very significant effect on the time required to reach high levels of mortality. An efficacious treatment may be the combination of a lethal stress and a particular heating rate which falls within a band, bounded by rates of heating that are too slow or too fast. The use of models will assist in the identification of promising treatments while avoiding extensive in-fruit testing.

Residual statics estimation using the genetic algorithm

An optimization problem as complex as residual statics estimation in seismic image processing requires novel techniques. One interesting technique, the genetic algorithm, is based loosely on the optimization process forming the basis of biological evolution. The objective of this paper is to examine this algorithm’s applicability to residual statics estimation and present three new ingredients that help the algorithm successfully resolve residual statics. These three ingredients include (1) breaking the population into subpopulations with restricted breeding between the subpopulations, (2) localizing the search, to varying degrees, about the uncorrected input stack, and (3) modifying the optimization function to take account of CDP‐dependent structural features. Introducing subpopulations has the effect of enhancing the search when the volume of phase space being searched is large and limited information is given about where the algorithm should concentrate its efforts. Subpopulations work well initially,...

Perturbation Theory for Intermolecular Forces Including Exchange

Generalized solutions to the Eisenschitz and London perturbation equations are derived. It is pointed out that the results obtained in the formalisms proposed by Hirschfelder (HAV), by Hirschfelder and Silbey, by Murrell and Shaw, and by Musher and Amos are special cases of the generalized treatment.

Applications of the Quantum‐Mechanical Green's Functions to the Study of Chemical Reactions. II

Starting from a field theoretical representation of chemical reactions, the rate equation is developed in terms of the quantum mechanical Greens functions. The equation is valid for non‐Markowian behavior and the approximations that are necessary in order to obtain the conventional (Markowian) rate equation are investigated. The effect of finite collision times is also discussed.

A lattice model of foam flow in porous media: A percolation approach

Because fluid flow in porous media is opaque to most observational techniques simulations of the processes occurring in porous media have become important. Typical reservoir simulations treat the flow as taking place in some averaged (Darcy-scale) medium but simulations can also be carried out at the level of the network of pores and throats of the porous medium. We report the results of a pore-scale investigation of mechanisms for the alteration of mobility by foam lamella blockage in a network of these spaces and channels of porous media. Saturation and relative permeability curves are obtained using well-known power-law expressions of percolation theory and a rescaling of the percolation parameter readily permits a number of lamella-blocking mechanisms to be treated. An explanation of the shift in breakthrough gas saturation and the deformation of the shape of permeabilityvs saturation curves upon introduction of foam is provided for a variety of blocking mechanisms. The qualitatively different features seen in experimental studies of modification of gas mobility by foam can be rationalized using only two parameters which characterize the throat-size at which blockage commences and the degree of blockage.

A comparison of several cooling schedules for simulated annealing implemented on a residual statics problem

A study of several cooling schedules for the simulated annealing optimization algorithm, as applied to a residual statics problem in seismic data processing, is undertaken and discussed. A variety of schedules which depend on user-controlled parameters and an adaptive annealing schedule which depends on the system itself are considered. The algorithm, with each schedule implemented in turn, is tested on a residual statics estimation where the optimization function is a coherence function between adjacent common depth point (CDP) gathers. Results of this study suggest the usefulness of a hybrid cooling schedule to reduce the number of cycles. Constrained adaptive annealing schedule offers a viable alternative.

Fluid topology for invasion percolation in 3-D lattices

A computer algorithm for the displacement of one fluid by another in three-dimensional pore-throat network models of porous media allows the determination of fluid characteristics and distributions at any point in the displacement process. The flowing fluids are found to form two closely intertwined networks with very few regions of space containing only one fluid. Further, the fraction of dead-end invader, i.e. the ratio of the fraction of nonflowing to flowing pores is essentially constant throughout a process. The dendritic character of trapped, i.e. disconnected fluid is dependent on the degree of pore-throat correlation in the network. As a result, a given pore filled with one of the fluids is likely to have at least one neighbor filled with another fluid. Our observations imply that (1) fillable pores are very likely to be filled, and (2) clusters are not compact. The latter provides a ready explanation for the ease with which so-called oil ganglia are broken up rather than moved.