David D. McLean

Biodiesel production from waste cooking oil: 1. Process design and technological assessment

Four different continuous process flowsheets for biodiesel production from virgin vegetable oil or waste cooking oil under alkaline or acidic conditions on a commercial scale were developed. Detailed operating conditions and equipment designs for each process were obtained. A technological assessment of these four processes was carried out to evaluate their technical benefits and limitations. Analysis showed that the alkali-catalyzed process using virgin vegetable oil as the raw material required the fewest and smallest process equipment units but at a higher raw material cost than the other processes. The use of waste cooking oil to produce biodiesel reduced the raw material cost. The acid-catalyzed process using waste cooking oil proved to be technically feasible with less complexity than the alkali-catalyzed process using waste cooking oil, thereby making it a competitive alternative to commercial biodiesel production by the alkali-catalyzed process.

Optimization and sensitivity analysis for multiresponse parameter estimation in systems of ordinary differential equations

Abstract Methodology for the simultaneous solution of ordinary differential equations (ODEs) and associated parametric sensitivity equations using the Decoupled Direct Method (DDM) is presented with respect to its applicability to multiresponse parameter estimation for systems described by nonlinear ordinary differential equations. The DDM is extended to provide second order sensitivity coefficients and incorporated in multiresponse parameter estimation algorithms utilizing a modified Newton scheme as well as a hybrid Newton/Gauss—Newton optimization algorithm. Significant improvements in performance are observed with use of both the second order sensitivities and hybrid optimization method. In this work, our extension of the DDM to evaluate second order sensitivities and development of new hybrid estimation techniques provide ways to minimize the well-known drawbacks normally associated with second-order optimization methods and expand the possibility of realizing their benefits, particularly for multiresponse parameter estimation in systems of ODEs. The Decoupled Direct Method (DDM) for the simultaneous solution of ODEs and the associated first order parametric sensitivity equations was extended to include solution of the second order parametric sensitivity equations. The extended DDM was then used to develop a full Newton scheme for multiresponse parameter estimation in systems of ODEs. A hybrid method was also developed which allowed switching between this Newton scheme and a generalized Gauss—Newton scheme. The switching procedure was based on the magnitude of the Bates—Watts convergence criterion (Bates and Watts, 1985). Both methods were compared to a generalized Gauss—Newton method and also to a hybrid method which incorporated the DGW update method and the generalized Gauss—Newton method. This latter method was based on a modification of the single reponse nonlinear least squares algorithm of Dennis et al. (1981). In comparing the four estimation methods as applied to four test examples it was observed that methods which incorporated second order sensitivity coefficients in the evaluation of the Hessian matrix were more robust and reliable. The modified full Newton method and the hybrid (Newton/Gauss-Newton) method successfully converged despite problems with high correlation between parameters, large residuals and poor initial estimates. The use of a hybrid method incorporating the DGW update formula to estimate the Hessian matrix was also observed to be robust but not to the extent observed for the full second order methods. Of the two methods employing second order sensitivities, the new hybrid method was significantly more efficient. There are well known drawbacks to requiring second-order derivatives in parameter estimation algorithms. Additional coding for calculating the derivatives, increased computational time and storage are prime factors which increase dramatically with the size of the problem. Some of these problems can be circumvented. For example, the use of symbolic computation packages greatly reduced the amount of coding required. In fact, with packages such as MAPLE, only coding of the model equations was required. Our extension of the DDM to evaluate second-order sensitivities and development of new hybrid estimation techniques provide ways to minimize these drawbacks and expand the possibility of realizing the benefits of second order methods, particularly for multirepsonse parameter estimation in systems of ODEs. It is clear that the efficient and accurate evaluation of second order sensitivity coefficients enhances convergence. In addition, this allows evaluation of the extent of nonlinearity that the model experiences upon variation of the model parameters. In particular, we are currently exploring for the evaluation of curvature measures similar to those developed by Bates and Watts (1985) for complex nonlinear multiresponse regression models. Such curvature measures have been shown to be useful diagnostic tools in nonlinear regression analysis for single responses. As a final, supplemental comment, we note that many of the problems in multiresponse parameter estimation arise as a consequence of limitations in the model building strategy. In particular, starting with too large or complex a model form with limited information in the data inevitably leads to problems in estimation. We strongly recommend beginning with a simplified model with informative data, collected from carefully designed experiments, followed by subsequent modification of the model and further data collection until an adequate fit is achieved. Suitable transformation of the parameters can also improve the estimation. With such a strategy, a simple first order estimation method will usually suffice. Nevertheless, situations do arise where second order methods are required making hybrid methods like those developed here valuable.

Singularities in Multiresponse Modelling

Care is required when analysing multiple response data if misleading results are to be avoided. Box et al. [4] have warned of errors in analysis resulting from linear relationships among the response data, and have provided a detection procedure. This is effective for most situations; however, we have encountered two cases that require additional consideration. This paper extends the work of Box et al. to include these cases. The key issue is the detection of singularities in the multiresponse dispersion matrix, and a procedure for this is presented. The situation is also discussed in which linear dependencies in the data may be ignored to advantage. Illustrations are from chemical kinetics investigations.

Further support for fed-batch production of gellulases

SummaryNew data for the fed-batch production of cellulases usingTrichoderma reesei Rut. C-30 give additional motivation for this mode of culture as a result of simultaneously high enzyme titres (31 IU FPA/mL), productivities (160 IU FPA L−1 h−1) and yields (477 IU FPA/g cellulose). These results also indicate a strong potential for even further improvements through the optimization of feeding policies.

Development of a mathematical model describing the enzymatic degradation of biomedical polyurethanes. 1. Background, rationale and model formulation

Abstract Of the various polymers used in medical devices, polyurethanes have been relatively successful due to their acceptable mechanical and biological properties. However, concerns have arisen in recent years regarding the biostability of polyurethanes when exposed to the harsh environment of the human body. Lysosomal enzymes released from inflammatory cells have been proposed as important mediators in the degradation of biomedical polyurethanes. If polyurethanes are to be developed which resist the rigors of implantation, a clear understanding of the degradative processes will be required. Unfortunately, the exact mechanism of enzymatic degradation of polyurethanes remains poorly defined. Consequently, a computer model was proposed as a tool for elucidating, simulating and distinguishing between a variety of mechanisms of degradation. Although the enzymatic environment at the site of an in-vivo implant is very complex, the model was first developed to represent the in-vitro degradation of a poly(ester-urea-urethane) by a single hydrolytic enzyme, cholesterol esterase. The processes of polyurethane surface dynamics, enzyme adsorption and inactivation, solvolytic and enzymatic degradation of the polyurethane, and degradation of products in solution were all described by the model. Possible breakdown products were also proposed. Parameter values and starting conditions were estimated from existing literature and the model was solved for various conditions which were considered experimentally relevant. Factors such as the rate of enzyme inactivation, the susceptibility of specific polyurethane bonds, the rates of in-solution degradation and the mobility of the polyurethane surface all had a marked effect on the extent of degradation and the type and amount of breakdown products in solution. Model development and preliminary simulations are presented.

Impact of model structure on the performance of dynamic data reconciliation

Dynamic data reconciliation (DDR) is a technique used to estimate the true values of process variables when plant measurements are corrupted by measurement noise. DDR integrates information from both measurements and process models such that the reconciled values become more reliable and better represent the current state of the process. Process models play a key role in the performance of DDR. Empirical or black-box models are identified and used in the DDR when phenomenological models are unavailable, impractical to obtain, or whose solutions require excessive computation time for real-time applications. Black-box models usually have higher degree of uncertainty and use a wide variety of structures. This article examines the impact of model structure on the performance of DDR, and more importantly, on the performance of controllers when the DDR is embedded inside feedback control loops. Simulation results of a binary distillation column demonstrated that the model structure can have a major impact on the performance of DDR. The DDR using simple linear models can successfully attenuate the noise propagation; however, further significant improvement of DDR performance can be achieved if more advanced models, such as nonlinear models, are used.

CLOSED-LOOP DATA RECONCILIATION FOR THE CONTROL OF A BINARY DISTILLATION COLUMN

ABSTRACT Data reconciliation is a procedure that makes use of process models along with process measurements to give more precise and consistent estimates for process variables. Data reconciliation has been traditionally used to provide a more representative set of data to calculate steady-state inventories and process yields. For dynamic systems, the use of data reconciliation is relatively nascent. This article examines the potential use of data reconciliation in closed-loop control as a filter to attenuate the noise in measurements of the controlled variables so that the controllers can access more accurate sets of data. Data reconciliation filters were implemented in simulations of a PID control system for a binary distillation column. Results showed that data reconciliation could efficiently reduce the propagation of measurement noise in control loops, so that the overall performance of the controller is enhanced.

USE OF AN AUTOASSOCIATIVE NEURAL NETWORK FOR DYNAMIC DATA RECONCILIATION

Abstract The technique of dynamic data reconciliation has been previously studied in the literature and shown to be an effective tool to better estimate the true values of process variables by using information from both measured values and process models. Real-time implementation of dynamic data reconciliation involves solving complex optimization problem, leading to large computation time. This paper presents a study on the use of a dynamic Autoassociative Neural Network (AANN) for dynamic data reconciliation. Once trained, the AANN can be directly used for online signal validation. Closed-loop performance of the AANN for both linear and nonlinear processes was evaluated using simulations of two storage tank processes. The AANN provided accurate estimates of measured values for the two processes studied in this investigation.