This paper describes a 25‐year project in which we defined problem solving, identified effective methods for developing students' skill in problem solving, implemented a series of four required courses to develop the skill, and evaluated the effectiveness of the program. Four research projects are summarized in which we identified which teaching methods failed to develop problem solving skill and which methods were successful in developing the skills. We found that students need both comprehension of Chemical Engineering and what we call general problem solving skill to solve problems successfully. We identified 37 general problem solving skills. We use 120 hours of workshops spread over four required courses to develop the skills. Each skill is built (using content‐independent activities), bridged (to apply the skill in the content‐specific domain of Chemical Engineering) and extended (to use the skill in other contexts and contents and in everyday life). The tests and examinations of process skills, TEPS, that assess the degree to which the students can apply the skills are described. We illustrate how self‐assessment was used.

Experimental data for a fixed-bed reactor were obtained for the reaction of sucrose to give glucose plus fructose using the enzyme invertase which was immobilized by covalently binding it to a polymer matrix adsorbed in the pores of alumina. A mathematical model, which included external film mass transfer, internal pore diffusion, axial dispersion, and enzymatic reaction with both substrate and product inhibition, was used to predict the performance of the fixed-bed reactor over a wide range of operating variables. The tortuosity factor for pore diffusion was measured separately for use in the model. Hence, external and internal pore diffusion effects were known and it was necessary to obtain only the activity of the immobilized enzyme from the experimental reactor data. Comparisons of the experimental data and the theoretical predictions from the model indicated a 70% loss of the native invertase activity constant resulting from the immobilization and a 32% decrease for the Michaelis constant and the product and substrate inhibition constants.

Flow rate measurements in a steady-state process are reconciled by weighted least squares so that the conservation laws are obeyed. A projection matrix is constructed which can be used to decompose the linear problem into the solution of two subproblems, by first removing each balance around process units with an unmeasured component flow rate. The remaining measured flow rates are reconciled, and the unmeasured flow rates can then be obtained from the solution of the conservation equations. The basic case contains constraints which are linear in the component and the total flow rates. The method is extended to cases with bilinear constraints, involving unknown parameters such as split fractions.Chi-square and normal statistics are used to test for overall gross measurement errors, for gross error in each node imbalance which is fully measured, and for each measurement adjustment. C. M. CROWE SCOPETo monitor the performance of a chemical process, we require balanced component and total flow rates in the process streams. These flows can be calculated from judiciously chosen measurements of concentrations, temperatures and total flow rates; but since these measurements are subject to random error, the conservation laws will in general be violated.The basic case considered here is linear in that it is assumed that whenever a concentration or temperature in a stream is measured, so is the total flow rate. Then the component or enthalpy flow can be calculated and used as the raw measurement data. These data are adjusted (reconciled), and the unmeasured flow rates are estimated so that the weighted sum of squares of the adjustments is a minimum and the conservation laws are obeyed. This restriction is then relaxed to allow the inclusion of bilinear constraints, which contain unknown parameters, multiplied by measured quantities.The computational effort can be minimized if a reduced set of balance equations can be obtained from the original balances, such that the reduced set involves no unmeasured flow rate but a maximum number of measured flow rates. This was accomplished originally by Vaclavek (1969b), and later by Mah et al. (1976) and Romagnoli and Stephanopoulos (1981) by algorithms which iteratively eliminate balances involving unmeasured feed or product flow rates and merge two balances with a common unmeasured flow rate. These workers assumed that a stream was either unmeasured or completely measured, an assumption not made here.The approach here is to define a projection matrix which can be directly constructed and which effectively blanks out the unmeasured quantities in producing this reduced set of balances.

Statistical testing prouides a tool for engineers and operators to judge the validity

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Flow rate and concentration measurements in a steady state process are reconciled by weighted least squares so that the conservation laws and other constraints are obeyed. Two projection matrices are constructed in turn, in order to decompose the problem into three subproblems to be solved in sequence. The first matrix eliminates all unmeasured component flow rates and concentrations from the equations; the second then removes the unmeasured total flow rates. The adjustments to component flow rates are iteratively determined, starting with guessed values of unmeasured total flow rates.Chi-square and normal test statistics are derived by linearizing the equations, to allow detection of gross errors in imbalances and adjustments of measurements. C. M. CROWE Department of Chemical EngineeringMcMaster University Hamilton, Ontario, Canada L8S 4L7 SCOPEThe cornerstone for monitoringplant performance is a set of steady state balances for component and total flow rates. Such flow rates are normally obtained from measurements of total flow rates and of concentrations, which are subject to random and sometimes gross errors, and thus in general violate conservation laws. The measurements should be reconciled, in some "best" sense, to obey those laws and any other constraints that are required to be enforced.The linear case, where it is assumed that the total flow rate is measured in any stream in which a concentration is measured, was discussed by Crowe et al., (1983). In this paper, that assumption is omitted so that the balance equations contain products of unknowns and thus are nonlinear (actually bilinear).Conflict with conservation laws can only arise in sections of the process where measurements have been made in all streams in a balance equation. Thus previous work by Vaclavek (1969), Mah et al. (1976), and Romagnoli and Stephanopoulos (198 1) was directed to devising path-tracing or combinatorial algorithms for efficiently finding a maximal set of sections of the process with redundant measurements -the reduced balance scheme (RBS). Unfortunately, such searches must be done separately for each component, or each element in the case of reactions. Crowe et al. (1983) proposed a constructive method of finding the RBS by a projection matrix that effectively blanked out all unmeasured flows in the linear case.The approach here is to extend the technique of Crowe et al. to the nonlinear case by constructing two successive projection matrices. The first eliminates all unmeasured component flow rates and concentrations; the second then eliminates the unmeasured total flow rates from the balance equations. The original problem is thus divided into three sequentially solved subproblems. Guesses of the unmeasured total flow rates are used to solve for the adjustments to component flow rates. These guesses are iteratively updated in the second subproblem until convergence is achieved. Then those unmeasured component flow rates that are determinable are found in the third subproblem.Gross errors in the measurements can arise fro...