Mordechai Shacham

Statistical analysis of linear and nonlinear correlation of the Arrhenius equation constants

Abstract Engineers must often use correlations that were developed before statistical analysis and verification of the correlation became a routine procedure. In this paper, we use modern statistical techniques to compare the traditional linear regression technique with the modern nonlinear regression as applied to the Arrhenius equation. The objective of the comparison is to determine whether there are basic flaws with the technique used in the past and whether these flaws may render the constants published in the literature untrustworthy. It is concluded that linear regression, when applied to the Arrhenius expression, is in principle not inferior to nonlinear regression and if the relative error in the data is distributed normally, it can even be superior. Nevertheless, if insufficient data were used for calculation of the constants and/or the experimental data were interpolated or smoothed, the accuracy of the published correlation is unpredictable.

The SROV program for data analysis and regression model identification

Abstract A new stepwise regression program (SROV) for the construction of optimal (stable and of highest possible accuracy) regression models comprised of linear combination of independent variables and their non-linear functions is described. The program uses for regression QR decomposition based on Gram–Schmidth orthogonalization, which is highly resilient to numerical error propagation. Variables are selected to enter the regression model according to their level of correlation with the dependent variable and they are removed from further consideration when their residual information gets below the noise level. The use of this program is demonstrated in two examples. In both examples the program identifies an optimal and stable regression model and several sub-optimal models. The existence of sub-optimal models provides additional insight regarding the relationships that exist between the explanatory variables, between the explanatory variables and the dependent variable and information on model related uncertainties caused by sample size and experimental error.

An improved memory method for the solution of a nonlinear equation

Abstract A new method, the improved memory method, for the solution of a nonlinear equation is introduced. This method is compared with several widely used solution methods by solving 15 test problems from different chemical engineering application areas. It is shown that the proposed method requires the smallest number of function (or derivative) evaluations to achieve the solution. A new algorithm for stopping the iterations is introduced. This algorithm stops the iterations when the true error is reduced for the first time below the desired error tolerance.

Comparing software for the solution of systems of nonlinear algebraic equations arising in chemical engineering

Abstract Five codes for solving systems of nonlinear equations, which are available in the literature, are compared using 10 test problems. The test problems are representative of a variety of areas in chemical engineering. In the comparison, robustness and reliability of the programs are emphasized, but information regarding their effectiveness is also given. The results of this study give the chemical engineer clear guidelines concerning the method that should be used for solving a particular problem.

Meaningful wind chill indicators derived from heat transfer principles

The wind chill index (WCI) and the more widely used wind chill equivalent temperature represent an attempt to combine several weather-related variables (temperature, wind velocity and solar radiation) into a single index which can indicate human comfort. Since its introduction in 1945, the WCI has been criticized mainly on the ground that the underlying model does not comply with modern heat transfer theory. In spite of that, the WCI, “calibrated” to human comfort, has proven to be successful in predicting discomfort and tolerance of man to the cold. Nevertheless, neither the WCI nor the wind chill equivalent temperature can be actually measured and, therefore, without the additional ‘calibration’ they are meaningless. In this study we have shown that the WCI represents the instantaneous rate of heat loss from bare skin at the moment of exposure to the cold, and as such, it correlates reasonably well with measurable variables that represent a feeling of cold. Two new wind chill indicators have been introduced: exposed skin temperature and maximum exposure time. These indicators yield more information than the WCI provides, are measurable, have physical meaning and are based on established heat transfer principles.

Pipeline Network Design and Synthesis

Publisher Summary A pipeline network is a collection of elements such as pipes, compressors, pumps, valves, regulators, heaters, tanks, and reservoirs interconnected in a specific way. Pipeline networks constitute major bulk carriers for crude oil, natural gas, water, and petroleum products. Networks of pipes and valves form an integral part of pressure-relieving and fire–water systems designed to handle contingencies in the operation of process units. The behavior of the network is governed by two factors: the specific characteristics of the elements and the connection of these elements. The first factor is determined by the physical laws and the second by the topology of the network. The simplest form of network synthesis involves a single input and a single output—the problem of optimal routing of a pipeline. Another form involves a tree—the synthesis of a gathering or distribution network. The chapter assesses the status of the relevant technology with particular reference to formulation of problems and methods of solution. It is concerned with the previous technical literature of the last few years. It also discusses some digital computation methods of designing pipeline networks.

Considering precision of data in reduction of dimensionality and PCA

Abstract Reduction of dimensionality of the data space in process data analysis is considered. A new stepwise collinearity diagnostic (SCD) procedure is presented, which employs indicators based on the estimated signal-to-noise ratio in the data in order to measure the collinearity between the variables. The SCD procedure selects a maximal subset of non-collinear variables and identifies the corresponding collinear subsets of variables. Using SCD, the dimension of the data space is reduced to the dimension of the maximal non-collinear subset. In process monitoring applications, the data associated with the surplus variables can be used for distinguishing between process and sensor failures. Two examples, which demonstrate the advantages of the proposed method over principal component analysis (PCA), are presented.

Open architecture modelling and simulation in process hazard assessment

Abstract Dynamic modelling and simulation of a chemical process in emergency conditions is considered. Such modelling and simulation often requires rapid implementation of model changes by the process engineer followed by simulation runs. A simulator with an open architecture structure is presented where the model components (equations) are stored in an object-oriented form in a database, enabling rapid and easy modification of the model. A general-purpose numerical solver is used for solving the model and plotting the pertinent results. An example is presented, where the use of the proposed simulator enables a rapid identification of the right strategy to prevent development of runaway temperature conditions in a reactor.

A method for evaluation of mass transfer coefficients in the different regions of air lift reactors

Abstract The present state of the art in the experimental determination of mass transfer coefficient in Air Lift Reactors is reviewed. A Criterion which allows to decide whether the assumption of perfect mixing of the liquid phase is valid was experimentally verified. For the cases where such assumption does not hold, a new method that renders local values of K L a in each of the regions of the reactor (riser, downcomer and gas separator) is presented. The model is based on a fluid dynamic structred model of the system.

Considering precision of experimental data in construction of optimal regression models

Construction of optimal (stable and of highest possible accuracy) regression models comprising of linear combination of independent variables and their non-linear functions is considered. It is shown that estimates of the experimental error, which are most often available for engineers and experimental scientists, are useful for identifying the set of variables to be included in an optimal regression model. Two diagnostical indicators, which are based on experimental error estimates, are incorporated in an orthogonalized-variable-based stepwise regression (SROV) procedure. The use of this procedure, followed by regression diagnostics, is demonstrated in two examples. In the first example, a stable polynomial model for heat capacity is obtained, which is ten times more accurate than the correlation published in the literature. In the second example, it is shown that omission of important variables related to reaction conditions prevents reliable modeling of the product properties.