Integrated nonlinear optimization of bioprocesses via linear programming

Abstract

The problem of integrated design and control of bioprocess plants is considered. A pre®iously presented optimization approach for biochemical systems based on linear ( programming and modeling using the power law formalism the Indirect Optimization ) Method, IOM is extended. This method is enhanced in order to take into account both static and dynamic measures, and its use for the optimization of the integrated design of a bioprocess is illustrated. The chosen case study is a wastewater treatment plant, a bioprocess which typically presents controllability problems in real practice due to bad design methodologies. After defining an objecti®e function reflecting both in®estment ( ) costs and '' paracosts'' such as stability, flexibility, and controllability , a set of constraints determined by the system components and technical and economical factors is defined. A comparison of the results obtained with this new method and with a global optimization method re®eals that, in both cases, significant impro®ements in both controllability and cost reduction are achie®ed, although the global method yields somewhat better impro®ements. The ad®antages and limitations of both methods are e®aluated, concluding that the IOM, through its incorporation to a dynamic process simulator, can be successfully used to obtain, in a quick, inexpensi®e and interacti®e way, near-optimal integrated designs for bioprocess plants. IntroductionThe proper design and operation of any microbial-based biotechnological process requires the quantitative description of the variables relevant for the system's kinetics. Once this information is available, it will be possible to derive an optimal process design and to attain its optimal operation. However, the nonlinear nature of these processes has impaired Ž such optimizations Vagners, 1983;Heinrich and Schuster, . 1996 . In order to circumvent these difficulties chemical and biochemical engineers have developed strategies to minimize or even avoid nonlinearities. Focusing on specific properties of chemical networks and by using prudent approximations, different techniques and approaches have been developed within the field of process engineering, which permits the process improvement through the right choice of operating Ž parameters Stephanopoulos, 1998;Stephanopoulos et al., . 1998 . Correspondence concerning this article should be addressed to N. V. Torres.One approach that fully acknowledges the nonlinearities, yet ultimately leads to linear optimization tasks, is based on a modeling framework called Biochemical Systems Theory Ž . Savageau 1969a,b; Voit, 2000 . The hallmark of this theory is the approximation of rate laws and other processes with products of power-law functions. Mathematically, this type of representation is very convenient and solidly grounded in Taylor's theory of approximating functions with polynomials. The Biochemical System Theory framework offers some choices for the formulation of biochemical systems, among which the most relevant for our present purposes is the S-sys-Ž...

A modified iterative IOM approach for optimization of biochemical systems

“…Like the previous sensitivities, the logarithmic gains should have low values (less than 10 in absolute value) (Vera et al, 2003b).…”

“…Much research has been directed toward the development of model-based optimization strategies, including the mathematical foundations of such approaches (Voit, 1992;Regan et al, 1993;Hatzimanikatis et al, 1996aHatzimanikatis et al, , 1996bTorres et al, 1996Torres et al, , 1997Petkov and Maranas, 1997;Voit and Del Signore, 2001;Torres and Voit, 2002;Marín-Sanguino and Torres, 2003;Vera et al, _____________________ 2003a;Chang and Sahinidis, 2005) and their application to some processes (Heinrich et al, 1991;Hatzimanikatis et al, 1998;Torres, 2000, 2002;Alvarez-Vasquez et al, 2000;Vera et al, 2003b;Sevilla et al, 2005). One successful approach to the optimization of biochemical systems is the indirect optimization method (IOM) (Torres et al, 1996(Torres et al, , 1997Voit, 1992;Marín-Sanguino and Torres, 2003;Vera et al, 2003a), which is based on the approximation of the original nonlinear differential equation models describing the biochemical process as an S-system or a GMA system.…”

Biochemical Systems Theory: A Review

“…e IOM method was later extended to take static as well as dynamic features into account and to facilitate the optimization of bioprocesses with efficient methods of linear programming [638]. Xu corrected the approximation error by proposing a �modi�ed IOM� with a �agrangian analysis, where the objective function includes an extra term that compares the derivatives of the metabolite concentrations with respect to the enzyme activities in the original and the S-system model [639].…”

Towards Model Predictive Control on Anaerobic Digestion Process

“…The complex nature of the AD system provides difficulty for modelling the process and, consequently, there are several causes of inconsistency between the process model and real AD systems. This is mainly due to lack of in depth process knowledge as well as (1) Limited number of process interactions being modelled, (2) Models which do not take into account full indirect effects, (3) Selection of variables which mainly affect inventory, (4) Assumptions on the rate of change of some process effects, (5) Assumptions on the scale of some unmeasured parameters, (6) No sensitivity analysis conducted on numerical solutions, (7) and Hybrid models for model improvement.…”

“…In order to control a microbial process such as AD requires quantitative description of variables relevant for the systems kinetics. The availability of such information enables optimal process design for obtaining optimal control [6]. Nonetheless the non-linear nature of such processes does not permit this being possible; therefore approximations are made by developers aiming to choose the operating parameters that enable process improvement.…”