L.T. Fan

Graph-theoretic approach to process synthesis: axioms and theorems

Abstract An innovative approach, based on both graph theory and combinatorial techniques has been proposed for facilitating the synthesis of a process system. In contrast to other general purpose mathematical programming methods, this innovative approach is designed to cope with the spscificities of a process system: it represents the structure of a process system by a unique bipartite graph, termed a P-graph, and captures not only the syntactic but also the semantic contents of the process system. An axiom system underlying the approach has been constructed to define the combinatorially feasible process structures. This axiom system is based on a given set of specificatios for the process synthesis problem. Such specifications include the types of operating units and the raw materials, products, by-products, and a variety of waste associated with these operating units. All feasible structures of the process system are embedded in the maximal structure, from which individual solution-structures can be extracted subject to various technical, environmental, economic, and societal constraints. Various theorems have been derived from the axiom system to ensure that this approach is mathematically rigorous, thereby rendering it possible to develop efficient process synthesis methods on the basis of a rigorous mathematical foundation. Examples are presented to highlight the significance and efficacy of the present approach.

Graph-theoretic approach to process synthesis: Polynomial algorithm for maximal structure generation

Abstract The maximal structure, which can be expressed as a process graph (P-graph), is the union of all combinatorially feasible process structures of a synthesis problem. This is analogous to the conventionally used term “superstructure” which has not yet been defined mathematically, and thus, cannot be analyzed mathematically. Since a mathematical programming method of process synthesis requires a mathematical model, as its input, based on the super or maximal structure, generating this structure is a problem of fundamental importance. Algorithm MSG, presented here, appears to be the first published algorithm for generation of the maximal structure. This algorithm is efficient because its complexity is polynomial. It is, therefore, advantageous for solving large industrial process synthesis problems. The mathematical basis of maximal structure, the proof of all statements and validation of algorithm MSG are also presented.

Recent developments in solids mixing

Abstract This review covers the major development in solids mixing since 1976. The publications on the subject have been divided into three major categories: characterization of states of solids mixtures, rates and mechanisms of solids mixing processes, and design and scale-up of mixers or blenders. Possible future work has been proposed.

Hydrodynamic characteristics of fluidization in liquid-solid tapered beds

Hydrodynamic characteristics of fluidization in conical or tapered beds differ from those in columnar beds due to the variation of superficial velocity in the axial direction of the beds. In the former, fixed and fluidized regions could coexist and the sharp peaking of the pressure drop could occur, thereby giving rise to a remarkable pressure drop-flow rate hysteresis loop at incipient fluidization. To explore these unique properties, a series of experiments was carried out in liquid-solid tapered fluidized beds with various tapering angles. Detailed visual observations of fluid and particle behavior and measurements of the pressure drops have led to the identification of five flow regimes. The tapering angle of the beds has been found to dramatically affect the beds behavior. Other hydrodynamic characteristics determined experimentally included the maximum pressure drop, minimum velocity of partial fluidization, minimum velocity of full fluidization, maximum velocity of partial defluidization, and maximum velocity of full defluidization. Models have been proposed to quantify the hydrodynamic characteristics of liquid-solid tapered fluidized beds. The results predicted by the models compare favorably with experimental data. Naturally, the models are applicable to liquid-solid columnar fluidized beds corresponding to the tapered beds with a tapering angle of zero.

Downstream process synthesis for biochemical production of butanol, ethanol, and acetone from grains: generation of optimal and near-optimal flowsheets with conventional operating units.

Manufacturing butanol, ethanol, and acetone through grain fermentation has been attracting increasing research interest. In the production of these chemicals from fermentation, the cost of product recovery constitutes the major portion of the total production cost. Developing cost‐effective flowsheets for the downstream processing is, therefore, crucial to enhancing the economic viability of this manufacturing method. The present work is concerned with the synthesis of such a process that minimizes the cost of the downstream processing. At the outset, a wide variety of processing equipment and unit operations, i.e., operating units, is selected for possible inclusion in the process. Subsequently, the exactly defined superstructure with minimal complexity, termed maximal structure, is constructed from these operating units with the rigorous and highly efficient graph‐theoretic method for process synthesis based on process graphs (P‐graphs). Finally, the optimal and near‐optimal flowsheets in terms of cost are identified.

Process network synthesis: Problem definition

Analyses of network problems have yielded mathematically and practically significant results. Naturally, it should be of substantial interest to extend such results to a general class of network problems where the structure of any system can be represented by a directed bipartite graph containing two types of vertices; the model for one of them is nonlinear. This class of problems is frequently encountered in the design of process systems for carrying out transformation of chemical or material species through physical, chemical, or biological means. General-purpose mathematical programming methods have failed so far to solve large-scale network problems involved in the design of such systems. This paper is intended to define this class of network problems, i.e., the problems of process network synthesis, and to elucidate the unique features of these problems.

Graph-theoretical identification of pathways for biochemical reactions

A rigorous method for identifying biochemical reaction or metabolic pathways through its systematic synthesis has been established. The current method for synthesizing networks of metabolic pathways follows the general framework of a highly exacting combinatorial method. The method is capable of generating not only all combinatorially independent, feasible reaction networks only once, but also those combinations of independent pathways. A case study involving the conversion of glucose to pyruvate with 14 elementary reactions illustrates the efficiency and efficacy of the method. All the results have been obtained with a PC (Pentium-III 550 MHz, 256 MB RAM) within 1 s.

Modelling and simulation of a continuous fluidized-bed dryer

Abstract A fairly rigorous mechanistic model of a continuous fluidized-bed dryer has been developed. It depicts the dynamic interactions between gaseous and solid phases in detail. The performance of the dryer has been simulated numerically based on the model. The effects of the operating parameters on the performance characteristics of the dryer have been investigated. These parameters include the superficial gas velocity, the inlet temperature of the drying gas, the mean residence time of solids and the dryer-wall temperature. The results of simulation based on the present model are compared with those based on an existing model. This comparison shows that the former is a substantial improvement over the latter.

Modeling adsorption in liquid—solid fluidized beds

Abstract Under certain conditions, the breakthrough time in a fluidized-bed adsorber is considerably shorter than that in a comparable fixed-bed adsorber. This phenomenon is probably due to the appreciable macroscale or axial mixing occurring in the solid and liquid phases of the fluidized bed. An axial dispersion model has been adapted to characterize the fluidized-bed adsorber. The model takes into account the effects of axial mixing in the solid and liquid phases, mass transfer resistance in the laminar fluid boundary surrounding an individual adsorbent particle, and diffusional resistance within the particle. The model has been solved numerically to simulate the performance of a laboratory-scale adsorber. The results of the simulation closely represent experimental observations over wide ranges of the influent flow rate, fluidized-bed height and adsorbent particle size.

Generation of light hydrocarbons through Fischer―Tropsch synthesis: Identification of potentially dominant catalytic pathways via the graph―theoretic method and energetic analysis

Abstract The Fischer–Tropsch synthesis (FTS) for the production of widely distributed hydrocarbons through the catalytic hydrogenation of carbon monoxide (CO) has been intensively and extensively explored. This is attributable to its immense theoretical as well as practical importance. Naturally, such exploration would be greatly facilitated if the feasible or dominant catalytic pathways (mechanisms) of FTS can be determined. The stoichiometrically feasible and independent catalytic pathways (IPis) of FTS have been exhaustively identified via the rigorous graph–theoretic method based on P-graphs (process graphs). The most extensive set of elementary reactions available, which numbers 26, has yielded 24 IPis in less than 1xa0s on a PC. The plausibly dominant pathways have been selected from the stoichiometrically feasible pathways through the analysis of their activation energies. Naturally, the dominant pathway or pathways need ultimately be discriminated among these plausibly dominant pathways via various means, e.g., in situ spectroscopic measurements of intermediates.