Batch process physical model

The importance of modeling batch processing systems forces a review of the mathematical analysis needed to set up and solve the models. The mathematical definition of physical problems involves (1) identification, (2) expression of the problem in mathematical language, (3) finding a solution, and (4) evaluating the solution. The completion of these steps in the order established determines whether a solution can be attained. The problem must be identified before one spends time setting up equations these and the initial and boundary conditions that define the problem must be well established before a solution is attempted then a solution can be obtained and evaluated. 

The fermentation process can be performed batch-wise or continuously at a given temperature and time. The broth is further processed to remove the desired chemical. Figure 11-11 shows a schematic and an abstracted physical model of a fermenter with the liquid phase as the control region. 

Unsteady-state or dynamic simulation accounts for process transients, from an initial state to a final state. Dynamic models for complex chemical processes typically consist of large systems of ordinary differential equations and algebraic equations. Therefore, dynamic process simulation is computationally intensive. Dynamic simulators typically contain three units (i) thermodynamic and physical properties packages, (ii) unit operation models, (hi) numerical solvers. Dynamic simulation is used for batch process design and development, control strategy development, control system check-out, the optimization of plant operations, process reliability/availability/safety studies, process improvement, process start-up and shutdown. There are countless dynamic process simulators available on the market. One of them has the commercial name Hysis [2.3]. 

Model concept in a batch process helps in understanding its hierarchical structure, and is specified in Part 1 of ISA 88. This structure will assist in dividing the systems into smaller parts. In line with the standard. Fig. VI/3.1.2-1 shows the various model types. Fig. Vl/3.1.2-1 A (or Fig. 1 of ISA 88) shows how the entire process has been divided into smaller parts for analysis of the system. As shown, the process is subdivided into process stage, process action, etc. This is a process model of batch process. The entire process can be divided in terms of models in three ways, viz. physical model, procedural model, and control activity model, as shown in Fig. VI/3.1.2-IB. Therefore, it is better to start the discussion on the three types one by one. 

The recipe model is hierarchical, the degree of details depending of the level of the physical model at which the recipe is specified. The standards for batch process automation define four major categories of recipes (Fig. 3) ... 

For APIs, limits are set on chemical purity, mean particle size, PSD, and other appropriate physical attributes by the biobatch model for clinical evaluation. The term biobatch refers to the regulatory requirement of identifying a particular batch, normally a pilot scale batch used in clinical trials, as the defining standard for physical and chemical attributes that must be reproduced at the manufacturing scale to be acceptable for sale. The critical process attributes (CPAs), once established, must be met on scale-up to the manufacturing facility. In addition, the process must be operated within the ranges established as critical process parameters (CPPs). Development of a crystallization process must include determination of realistic and reproducible ranges for both the CPPs and the CPAs. 

Batch kinetic studies at various initial Cr concentrations were also used to obtain adsorption and desorption second-order rate coefficients. A strong dependence of the rate coefficients on the initial input concentration was observed, thus Cr BTC were difficult to model because of transient Cr concentrations during transport (Fig. 10-6). Fluhler and Selim (1986) suggested that physically controlled processes were unlikely to be responsible for Cr retention since this soil has little, if any, aggregation. Low peak concentrations and extensive tailing during Cr desorption were believed to be the result of slow chemical reactions of Cr on soil surfaces exhibiting multiple types of reaction sites. 

In this paper we will discuss the application of a general batch reactor model that considers the reaction kinetics, heats of reaction, heat transfer properties of the reactor, physical properties of the reactants and the products, to predict 1) The concentration profile of the products, thus enabling process optimization 2) Temperature profile during the reaction, which provides a way to avoid conditions that lead to a thermal runaway 3) Temperature profile of the jacket fluid while maintaining a preset reactor temperature 4) Total pressure in the reactor, gas flow rates and partial pressure of different components. The model would also allow continuous addition of materials of different composition at different rates of addition. 

The sulfite oxidation rate in hold tanks of antipollution scrubbers is central to flue gas desulfurization technology. The accurate description of the rate of disappearance of sulfite slurry particles (from the scrubber liquor) bears upon both process selection and economics. This article will describe a mathematical model for a semi-batch, stirred tank reactor in which S(IV) anions, sulfite and bisulfite, are reacted with dissolved oxygen gas at saturation. Experimental work to secure several physical parameters and to verify the... 

As discussed earlier, the analytical solutions for the CSD for a batch or semibatch crystallizer are difficult to obtain unless both the initial condition for the CSD and appropriate kinetic models for nucleation and growth are known. An example of such an analytical solution—simple yet not overly restrictive—was given by Nyvlt (1991). It is assumed that the process, in which both external seeding and nucleation take place, occurs at constant supersaturation (G = constant, Bq = constant) in an ideally mixed crystallizer. An additional assumption of size-independent growth allows one to rewrite the time-dependent moments, Eqs. (10.12)-(I0.15), in terms of the physical properties such as the total number (A), length (L), surface area A), and mass of... 

---