Page 84 - Academic Press Encyclopedia of Physical Science and Technology 3rd Chemical Engineering

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Encyclopedia of Physical Science and Technology EN002E-49 May 17, 2001 20:13

48 Batch Processing

to tasks on the basis of achieving the best performance. matical description of the process can be formulated. At
That program could be the starting point for a more de- this stage, the equations do not constitute a model; they
tailed short-term planning analysis. only interpret the principles in mathematical form. Next,
the important characteristics of the problem are identified,
and the mathematical formulation is simplified, justifying
VI. OPTIMIZATION
the approximations with physical arguments. The result-
ing equations constitute a model. Though the description
Production costs depend on the cost of the manufacturing
of large-scale processes is complex, the model postulated
equipment involved. The batch times t(i) determine the
must contain the essence of the process in its simplest
sizes of the batch units; the longer these times, the larger
form; it must be expressed by a set of equations whose
is the holdup storage needed to keep the stock of reactants
solution can be obtained and be useful for process simu-
and products used in the next batch. The semicontinuous
lation. Complications can be added to simple models as
times t( j) may be reduced to decrease the total batch cy-
needed; beginning with a model that is too complex causes
cle, at the expense of increasing the size and the cost of the
confusion and unnecessary work. The depth of physical
semicontinuous units. The reduction of storage and reactor
knowledge determines the type of modeling that can be
sizes may result in an economic advantage. Studies of this
formulated; two types are common, as described in the
sort are completed during the design of the plant to mini-
following subsections.
mize capital investment. Any reduction in the downtimes
t(k) also improves the economics. Though this analysis
may seem simple, it indicates the importance of consid- A. Defined Modeling
ering the specific circumstances ruling batch processes.
Definedmodelingisapplicabletoprocesseswhereonecan
Every case is different and may involve additional com-
associate sufficient measurable inputs and outputs with
plexity. For example, production costs could be reduced
each physical change taking place in the system. In most
by decreasing cycle time if the operation did not result
cases, the inputs and outputs can be related through a set of
in additional costs caused by secondary unfavorable reac-
nonlinear ordinary (ODEs) or partial differential (PDEs)
tions. It can be inferred from the above considerations that
equations. Modeling is the determination of the equations
in batch processing there are opportunities for the analysis
and boundary conditions that define the system in space
of alternatives that may well pay back the time and efforts
and time. Simulation results from the solution and numer-
invested. Some concepts of optimal design may be useful,
ical evaluation of the model. The equations are set by es-
recognizing that formal optimization may be too expen-
tablishing mass and energy balance and/or applying other
sive; that is, a generalized expression for batch plant opti-
pertinent physical laws. Modeling problems of this type
mization problems may not be applicable to actual cases,
are common in engineering practice. A typical case is that
since the cases to be analyzed are too specific.
of modeling a batch chemical reactor. Then one material
balance equation per component is required in addition to
VII. SIMULATION defining the inventory change of each component and the
energy with time. Two varieties of defined modeling are
Experience has been the only requirement for running common:
many processes. However, there is economic incentive
for modeling and simulating industrial processes since, 1. Transport phenomena modeling. This type of mod-
when technology is understood on some theoretical basis, eling is applicable when the process is well understood
it is likely that process operating efficiency and economic and quantification is possible using physical laws such
yields will be improved. Modeling of batch processes has as the heat, momentum, or diffusion transport equations
attracted considerable attention because of the need to de- or others. These cases can be analyzed with principles of
termine the changes occurring and to follow them with transport phenomena and the laws governing the physico-
time. A model consists of a set of mathematical equations chemical changes of matter. Transport phenomena models
and proper boundary conditions that are capable of simu- apply to many cases of heat conduction or mass diffu-
lating a plant or a section of a plant. It can also be used for sion or to the flow of fluids under laminar flow conditions.
process prediction and control. A model must be simple Equivalent principles can be used for other problems, such
enough to be understood; it must be suitable for predict- as the mathematical theory of elasticity for the analysis
ing the behavior of the system it intends to simulate; and of mechanical, thermal, or pressure stress and strain in
it must not be trivial to the extent that its predictions are beams, plates, or solids.
grossly inaccurate. The first step in the theoretical anal- 2. Empiricalmodeling.Whenthemodelistoocomplex
ysis is understanding the physicochemical principles that or some defined knowledge is missing, approximations of
rule the transformations taking place. Then the mathe- theory are used to implement the theoretical arguments.