Jude T. Sommerfeld

Relationship between growth in gross domestic product (GDP) and growth in the chemical engineering literature in five different countries

Data were compiled and linearly correlated on the growth in the gross domestic product (GDP) with the academic chemical engineering literature over a recent 26-year period for five different English-speaking countries, namely, the United States, Canada, Great Britain, India and Australia. The publication figures were also scaled to the total number of chemical engineering schools in the country; furthermore, all of these data were normalized from zero to unity, using the figures for the most recent year (1996) as the denominators, and then correlated against each other in linear fashion. Resulting confidence levels were in excess of 99% for each of the individual five countries, as well as for the entire set of normalized data for all of the countries.

Discrete-Event Simulation in the Design of Textile Finishing Processes

The General Purpose Simulation System (GPSS) was used to model and perform a discrete-event simulation of a large textile finishing mill, producing a variety of woven and knit fabrics for sheeting and mens and womens apparel. This model was validated with actual mill operating data. Simulations were made to determine the effects of market demands, maintenance practices, quality control policies, and total production on equipment and manpower utilization, work-in-process, inventory, and total processing time. For this particular mill, the numbers of dye machines represented the primary bottleneck in increasing mill capacity, and the effect of adding more such machines on capacity was studied in further simulations.

Maximum leakage times through puncture holes for process vessels of various shapes

Abstract In this work, equations are developed for the drainage of vessels of different geometrical shapes through a side leak. From these equations, the maxima in the leakage times, divided by the time required to drain the full vessel from its bottom as a function of the side leak elevation, are determined. Five different geometric shapes are considered here — spheres, cylinders, cones, paraboloids and ellipsoids. The equations and ma- xima for the latter three configurations have not previously appeared in the literature.

Elliptic integral solutions for the kinetics of autocatalytic termolecular reactions with reactive intermediate species

Abstract The kinetics of an autocatalytic termolecular reaction with overall stoichiometry of A + B → C + D was investigated. It is assumed that each of the three components A, B and C dissociate into reactive intermediate species, with equilibrium always established in all three cases. The rate-limiting step is then assumed to be the reaction between the intermediates formed from A and B, respectively, catalyzed by the reactive intermediate formed from product C. Integration of the differential equation describing the chemical kinetics of this process was performed for various special cases of initial reactant concentrations—stoichiometric and non-stoichiometric. The analytical solution in the latter case incorporates incomplete elliptic integrals of the first kind. Numerical values of reaction times may then be readily computed with the aid of various extensive compilations of elliptic integrals.

Elliptic integral solutions for fluid discharge rates from punctured horizontal cylindrical vessels

Abstract The problem of determining fluid discharge rates from the side (as opposed to the bottom) of punctured cylindrical and spherical vessels was recently addressed by Crowl1. Both vertical and horizontal cylindrical configurations were examined. Analytical solutions to the spherical and vertical cylindrical problems were obtained in rather straightforward fashion. However, the geometry is considerably more complex in the case of the horizontal cylindrical configuration. Crowl does not present an analytical solution to this more complicated problem, but employs numerical methods in order to integrate the governing differential material balance equation. The purpose of this communication is to present a direct analytical solution to the problem of side drainage from a punctured horizontal cylindrical vessel with the use of elliptic integrals, values of which are tabulated in numerous mathematical handbooks2–4. Because of their inherently greater accuracy, analytical solutions can serve as standards or benchmarks against which to check the reliability of numerical solutions and, in addition, are generally readily programmable on computers and/or spreadsheets.

Discrete‐event simulation in wastewater treatment

Abstract This paper illustrates the utility of discrete‐event simulation in the analysis and design of wastewater treatment plants. Specifically, the application of the General‐Purpose Simulation System (GPSS) to investigation of the batch operation of a poultry processing wastewater treatment plant, featuring sequencing batch reactors (SBRs), is described. The SBR process represents an innovative use of a classical biological process for which there is a great deal of theoretical data but limited experimental data available. Batch processing of industrial wastewaters is an alternative technology being explored due to more stringent discharge requirements and lower maintenance costs. The process is also easily adaptable to new demands because the equipment can be operated in several different modes. This simulation utilized several process configurations to obtain maximum usage of each individual unit. The numbers of the following items were varied: primary anaerobic reactors, aerobic reactors and dewater...

Process dynamics for overflow devices of rectangular, circular, parabolic and triangular shape — loss prevention applications

The problem of unsteady-state liquid flow across overflow devices of various shapes has been investigated. Dimensionless efflux times to evacuate a given amount of liquid from an upstream vessel or basin through an overflow conduit or weir as a function of dimensionless height of the liquid crest were computed for four specific overflow device shapes: rectangular, circular, parabolic and triangular. Analytical expressions were developed for this purpose in all cases except circular. Generalized comparison charts were developed for the cases of (1) equal flow areas of the overflow devices and (2) equal maximum flow capacities. Two examples illustrating application of the equations and charts developed in this paper to loss prevention scenarios are also presented.

Flow equations for parabolic and elliptical weirs

Abstract Steady‐state flow across parabolic and elliptical weirs is addressed. This situation may arise in the cases of actual flow through such cross‐sections, as in an overflow pipe in the side of a vessel, through saturator troughs as employed in the textile finishing industry, or across weirs of these shapes. An exact analytical solution is found in the parabolic case. Specifically, the volumetric flowrate of fluid across a parabolic weir is shown to be directly proportional to the square of the liquid crest height; this result may be useful in certain process or environmental control applications. The solution for the elliptical configuration is a generalization of that presented earlier by Stevens (1957) in his classical paper on circular weirs. Whether the cross‐section is elliptical or circular, the resulting solutions contain the same types of elliptic integrals.

Fluid discharge resulting from puncture of spherical process vessels

Abstract Risk analysis associated with incidents of puncture or rupture of process vessels generally requires estimation of actual or average fluid discharge rates resulting from such an incident. Most formulas developed to date for fluid discharge rates from vessels generally assume that the flow opening is located at the bottom of the vessel; this is undoubtedly due to the previously predominant interest in computing time requirements for gravity drainage of process or storage vessels. An accidental puncture however, such as resulting from a moving vehicle, can occur at almost any elevation. Hence, from a risk analysis point of view, it would be useful to have formulas which would estimate fluid discharge amounts and rates from a flow opening at any arbitrary elevation. In this article, the differential and algebraic equations governing liquid discharge from an opening at any point on the surface of a spherical vessel are solved. This solution is then generalized in terms of dimension-less efflux times, liquid volumes and average release rates as functions of dimensionless elevations.

Non-Linear Gasoline Tanks and Gauges

In this article, the dynamic equations describing the behaviour of the liquid level in a gasoline tank, as typically found on a conventional passenger car, are developed for a variety of geometric tank shapes. Generalized solutions to these equations are then presented for a number of specific such shapes, and these results are compared with actual data taken on an American passenger automobile.