Using statistical design procedures an initial‐rate study of the oxidation of propylene over a silica‐supported bismuth molybdate catalyst was carried out using a differential‐bed reactor over the following range of conditions: temperatures from 350 to 390°C, oxygen and propylene concentrations from 1.0 to 8.0 mmol/L. Among the models considered a Redox Steady‐State Model (with half‐order oxygen concentration) involving oxygen adsorption and reaction with propylene from the gas phase was found to provide the best fit to the data.

Some cases of the motion of two miscible fluids in uniform linear models are discussed. There is no bulk flow through the models, and the convection currents are caused solely by density gradients. Horizontal, vertical and inclined positions of the models are treated separately. Analytical formulas for the motion of a narrow transition zone between the fluids are obtained and compared with measurements, and the limitations are discussed. Observations of the ultimate stabilizing effect of diffusion on the motion are compared with the theory. It is shown that fluid motion in an inclined model with a constant rate of bulk flow can be directly deduced from the cases discussed, provided the viscosity ratio is small. Introduction In some reservoirs, convection currents caused by variations in the fluid densities may be significant. For practical purposes it may be desirable either to minimize the effect, particularly in miscible displacement, or to maximize the effect as in some schemes for the production of heavy crude oils by combustion. Experiments by Craig, et al, have shown the effectiveness of gravity in reducing the efficiency of a miscible displacement when the mixed zone between the displacing and displaced fluids is narrow compared with the height of the system. The presence of a board transition zone from one fluid to the other has been shown by Perkins, et al, to nullify considerably the influence of a difference in density. Indeed, the theoretical discussion given by Perrine has shown that when the transition zone exceeds a certain critical length the efficiency approaches 100 per cent. Many additional results have been published on miscible and immiscible displacements which show the importance of density difference and also mobility ratio. The aim of the present paper is to discuss some cases of gravity segregation of miscible fluids in linear models such as are often used in the laboratory to evaluate recovery processes, and to supply additional experimental evidence in support of the conclusions. An attempt is made to calculate simply the magnitude of the fluid motion caused by density gradients and mobility ratios, and to quantify the modifications in the fluid motion produced by the combined effect of molecular and convective dispersion. However, it should be pointed out that the uniform permeability of the models and the use of only a single pair of fluids (whereas several pairs of fluids may be employed in a recovery scheme) severely restricts direct conclusions about natural reservoirs. For conciseness, the motion generated by density gradients is emphasized for the case of no bulk flow through the models. This is not a drastic limitation because, as shown in Appendix A, a fluid motion with a constant bulk flow through any linear model is equivalent to a fluid motion with no bulk flow in the same model inclined at a different angle to the horizontal, provided only that the density is a linear function of the viscosity of the fluid mixture. HORIZONTAL MODEL In this case the model is assumed to have a rectangular cross-section with a horizontal breadth b, vertical height h and a great length L. Throughout the paper it will be assumed that x-axis points along the length, the y-axis along the width and the z-axis along the height. Thus, in the present case the x, y plane is horizontal. Initially, the transition zone between the fluids is assumed to be thin and parallel to the y, z plane. An example of this situation in a practical problem arises in a scheme for using air for cushion gas in the storage of fuel gas in aquifers. With the passage of time the denser fluid sinks and spreads along the bottom of the model while the lighter fluid rises. The interface extends from the top plane of the model to the bottom. Experiments have shown that for practical purposes this interface may be treated as a plane surface at all times. The surface is significantly curved, however, for viscosity ratios greater than about 10. Other complications arise with large viscosity ratios because of the nonlinear dependence of the viscosity on the composition of the mixture, so that the simple results given here are restricted to fairly low viscosity ratios. SPEJ P. 95^

A sequential design strategy was used to direct an experimental kinetic study of propylene oxidation over bismuth molybdate. Two statistical criteria were used to design experiments. The first is a joint criterion for the dual problem of model discrimination and parameter estimation which was proposed by Hill et al. (1968), but which to the best of our knowledge has not been tested in an experimental program. Using this joint criterion design, it was demonstrated that both the objectives of model discrimination and precise parameter estimation were effectively accomplished. After model discrimination had been achieved, a design strategy for further improvement in parameter precision was found, as expected, to be effective for that purpose.

Rates of oxidation of toluene were measured as a function of temperature and reactant concentration. A fixed bed reactor was operated at low conversions over the following range of conditions, 300°C to 350°C., 1 × 10−3 to 15 × 10−3 moles oxygen per litre of gas, and 1 × 10−3 to 6 × 10−3 moles toluene per litre of gas. The rate data for the oxidation of toluene were correlated by the following equation, which is based on a model by Hinshelwood. The values of k, obtained agree with those reported previously for naphthalene oxidation(1). It is concluded that the Hinshelwood model is a useful one for this type of reaction, and within the limits of available data provides a satisfactory interpretation.

Introduction The general application of Darcy's law to natural rocks has already been challenged in the literature. The evidence shows that the permeability as calculated from the Darcy equation can be a function of the pressure drop and the salt concentration of the water phase. Most explanations for aberrant behavior involve clays and their properties and have been qualitatively satisfactory. Recently, however, Odeh revived the theoretical views of Yuster. Since Yuster's concept implies a fundamental error in using Darcy's relationship for two-phase flow, and not merely that conditions may limit its use, Odeh's experimental support arouses considerable interest. However, Odeh's work as presented is thought to be inadequate. He has omitted important information about his materials and procedures; therefore, acceptance of his conclusions should be withheld. Since a clay effect is possible, Odeh should have been allowed space to present a more detailed account of the rocks which he used and the precautions which he took to avoid confounding the effects of clay and fluid circulation. In addition, it follows from Odeh's discussion that the oil relative permeability should increase as the viscosity ratio increases. Odeh presents data corroborating this deduction. It also follows that the oil relative permeability should decrease as the viscosity ratio of oil to water decreases. However, our results show that a high relative permeability, when once attained by using a viscous oil, may be maintained when that oil is replaced by an oil of much lower viscosity.