Today, simulation is an accepted way of studying various processes that are practised in the chemical and biochemical industries, including processes to control air and water pollution. These processes may be a single-unit opera-tion or involve an entire plant. Simulaopera-tion may be carried out to study the behaviour of these unit operations or the plant as such without fabricating any equipment or the entire plant. Therefore, there is no real loss or damage to the real world (i.e. life, equipment or even the environment). However, simulation studies can be used to predict such losses.
The engineering of process systems, now called ‘process systems engi-neering’, was initially qualitative in nature. With time, it has evolved and is now founded on engineering sciences, computer-aided tools and system-theoretical methodologies (Stephanopoulos and Reklaitis 2011).
Computers have helped in solving complex problems involving systems of non-linear equations, optimisation problems, partial differential equa-tions etc. This has helped in the development of an integrated approach to process design. The effect of environmental issues, choice of the con-troller, process safety and the like on the economic design of a process plant can now be considered. It has been made possible only by the use of simulation.
Simulation is the representation of the behaviour or characteristics of a real system by using a system of mathematical equations, which may be either linear or non-linear algebraic equations, in the form of inequalities and ordinary or partial differential equations. Often, the equations are diffi-cult to solve analytically and hence are solved numerically using a computer.
Therefore, ‘simulation’ is frequently referred to as ‘numerical simulation’ or
‘computer simulation’.
1.1 Chemical Processes
The first step in simulation is to represent the process in terms of mathemati-cal equations; however, the physimathemati-cal process may be so complex that it would be impossible to formulate it in terms of mathematical equations. The pro-cesses used in chemical industries are complex in nature. Classroom problems
are simplified representations of these complex processes. They are repeated so many times that the students accept the descriptions as the final versions of the representations of the processes by the set of equations. For example, Poiseuille’s equation, taught in lower-level classes, seems to be the only equa-tion to describe the flow behaviour in a pipe until one realises that not all the fluids are Newtonian. Thus, the flow is not always laminar; it may also be ‘tur-bulent’. The tubes may be short, for which ‘end effects’ have to be considered.
The physical representation of a process requires understanding all those phenomena which characterise it. These phenomena should be expressed in terms of mathematical equations using known laws of physics. A detailed description of a process will result in a large set of mathematical equations.
This enhances the degree of difficulty in solving these equations.
As aforementioned, the chemical processes are complex in nature. Even a single-unit operation might be too complicated to describe. Let us under-stand why it is so through the following examples.
1.1.1 Unit Process: Fixed Bed
Fixed beds find many applications in chemical, biochemical and environ-mental engineering. These are used as reactors, absorbers, distillation col-umns and many more. Let us consider a fixed bed in which a fluid enters from the bottom of the column through a distributor (Figure 1.1). The pres-sure drop due to a single particle can be determined from the drag force
Flow around particles Wake
FIGURE 1.1 Fixed bed.
3 Introduction to Modelling and Simulation
obtained by knowing the flow field around a single particle. One such relationship is Stokes’ law, which describes the drag force on a sphere at a very low Reynolds number. However, it is still not clear as to how to use this information to determine the pressure drop across a bed of particles. Let us examine the complexities present in a fixed bed.
1. Not all fixed beds contain the same types of particles. Various types of packing are used in industrial applications.
2. All particles are not of the same shape and size. Variation in shape and size is observed.
3. The particles (or packing) may not have the same orientation.
The inter-particle distance may be different.
4. The fluid entering the column flows through the interstitial space, which is not the same around all the particles. Therefore, the drag force for each particle will be different.
5. The fluid velocity near the distributor will not be uniform. The fluid enters the bed through many holes and then spreads.
6. In the case of shallow beds, the fluid may not spread due to insuf-ficient height of the beds (i.e. the flow is not fully developed).
The behaviour of shallow beds is different from that of typical fixed beds.
7. The fluid velocity in fixed beds exhibits radial variation. The fluid velocity is minimum adjacent to the wall and is maximum at the centre.
8. The flow regime may be laminar, transition or turbulent. All fixed beds may exhibit these regimes at various conditions.
9. The change from laminar to transition and from transition to turbu-lent flow regime occurs be at different Reynolds numbers depending on the shape of the particle.
10. In the case of a reaction, the flow rate may change in the axial direc-tion due to a change in the volume.
11. The volume of a gas depends on temperature and pressure. Thus, varying the temperature results in a change in the gas flow rate along the column.
12. If the packing height is high, the pressure of the gases decreases with increasing bed height. It also results in an axial variation of the flow rate.
13. Since the properties of the gas depend on temperature and pres-sure, the flow regimes may change at elevated temperatures and pressures. As a result, fixed beds operating at elevated tempera-tures and pressures behave differently from those operating at ambient conditions.
There may be many more factors which have not been mentioned here.
The complexities mentioned above have been tackled by researchers either by using average properties (e.g. porosity) or by specifying certain proper-ties (e.g. packing factors). Computational fluid dynamics (CFD) simulation may be carried out to consider many of the complexities, but even for a small variation in the definition of the problem, the CFD simulation must be car-ried out again. Parameters such as ‘superficial velocity’ have been used in various correlations. Superficial velocity is the fluid velocity considering that the column does not have any solids in it. Thus, superficial fluid velocity is hypothetical but is being used without much discussion; this is because of the need to find a way to describe the hydrodynamic behaviour of the fixed bed. Due to the wide range of operating conditions and geometrical param-eters, various models and correlations for flow in fixed beds are reported in the literature. It is not an easy task to propose a universal equation to define the pressure drop in fixed beds.
Let us now look at an example of an entire plant and examine its complexity.
1.1.2 Sulphuric Acid Plant
Sulphuric acid is manufactured industrially using a source of sulphur as a raw material. A schematic flow diagram of the process is given in Figure 1.2.
In a typical sulphuric acid plant, sulphur is burnt in excess of air to pro-duce sulphur dioxide, which is converted to sulphur trioxide in a four-stage fixed-bed reactor. After each stage in the fixed bed, the gases are passed through heat exchangers to cool to a desired temperature and then sent to the next stage. The outlet gases from the fourth stage of the fixed bed are cooled and sent to the absorption column, where the sulphur trioxide
Air
Sulphur
O2 SO2
SO3+SO2
dil. H2SO4
con. H2SO4 Gases Heatexchanger
Sulphur burner
O2
SO3 Heatexchanger SO2
Two-stage
reactor Absorber Two-stage Absorber
reactor
FIGURE 1.2 Sulphuric acid plant.
5 Introduction to Modelling and Simulation
gets absorbed into 98% sulphuric acid. This absorption column is also a fixed bed. The recent trend is to use two absorption columns (Figure 1.2).
The gases leaving the second stage of the fixed-bed reactor are sent to the first absorber. The unabsorbed gases leaving the absorber are sent to the third stage of the reactor. The gases from the fourth stage are sent to the second absorber. This process is called the double conversion double absorption (DCDA) process.
The other units present in the sulphuric acid plant are storage tanks, sul-phur burners, heat exchangers, waste heat boilers, pumps, and compressors.
Several different types of equipment and several similar kinds of equipment, but of different sizes, are used in a process plant, as is seen in the case of a sulphuric acid plant. A mathematical description of the process is thus much more complicated than that of a single unit.
Several fixed-bed reactors and absorbers are thus used in this process.
If a set of equations is used to describe the behaviour of a certain fixed bed, then a similar set of equations can be used to describe all other fixed beds.
However, the operating conditions and the reactions in each fixed bed may be different, resulting in different behaviours. Each fixed bed can be consid-ered a sub-model of a model for the entire plant.
Sub-models cannot always be solved independently. The four-stage reactor, absorbers and a network of heat exchangers are arranged in such a manner that this portion of the plant involves a recycle stream which is unknown.
The recycle stream is chosen to minimise the cost of production. Increasing the recycle stream reduces the conversion and hence increases the size of the absorbers. An increased bed height results in an increased outlet tempera-ture from the fixed-bed reactor, but at the same time it reduces equilibrium conversion.
1.1.3 Complex Nature of Chemical Processes
Most chemical processes are complex in nature as they exhibit non-linear and non-equilibrium behaviour. This complexity is due to simultaneous and often coupled momentum-, heat- and mass-transfer phenomena and kinetic processes taking place at different scales. The bubbles and drops have dimensions ranging from 10−3 to 10−4 m. The catalyst particles are much smaller, ranging from 10−9 to 10−6 m (Charpentier 2009). Various geometrical dimensions of the reactor may be of the order of a few metres. At a differ-ent scale, the physical phenomena governing a process are differdiffer-ent. This multiscale nature of chemical processes makes them even more complex.
Charpentier (2010) proposed a triplet ‘molecular processes–product– process engineering (3PE)’ integrated multiscale approach for chemical product design and manufacturing.
The demands of a product vary with time. The process industry should be able to handle this problem. Fluctuations in product demand and supply of the raw materials have forced process engineers to address this problem.
Supply chain management and time scheduling of multiple products are some of the problems that have been addressed recently, resulting in strat-egies meant to increase profits and handle uncertainties. Today, with the help of simulation studies, chemical engineers are able to tackle more com-plex problems.
1.2 What Is Simulation?
A mathematical model to capture the behaviour of a process plant may be formulated. It may involve several algebraic and ordinary and partial dif-ferential equations. It is not always possible to obtain an analytical solution to a mathematical model. However, it is possible to obtain a numerical solu-tion using a suitable numerical technique. Can solving a set of equasolu-tions be called ‘simulation’?
Simulation is the process of analysing a whole process or a part of it, using the set of equations describing it. The purpose of the analysis may include optimising operating conditions, analysing the effect of input variation on the properties of the output stream or troubleshooting a prob-lem in the process. Simulation studies thus involve several parameters and studying the effects of these variables on the solution (i.e. response of the process). Korn (2007) states, ‘Simulation is experimentation with the models’.
Problems can be divided into two types. When the inputs to the process are known and the output variables are to be determined, the problem is called a ‘rating problem’. The problem can be solved by solving the model equations directly. For example, for a given configuration of a heat exchanger, the geometry of the heat exchanger, as well as the flow rate and physical properties of the process fluid and heating–cooling fluid, is known. The requirement is to determine the output temperature of the process fluid or the flow rate of the cooling–heating liquid. The other type of problem is called a ‘design problem’. The outputs of the system are the desired values, and one must determine the input variables which pro-vide the desired output. This class of problem can be solved by inverting the model equations (Charpentier 2010). The solution methodology consists of treating the problem as an ‘optimisation problem’. In the case of design of a heat exchanger, geometrical parameters – such as tube length, tube diameter, number of tubes, shell diameter, baffle spacing and flow rate of the cooling–heating fluid – are to be determined if the flow rate and input and output temperatures of the process fluid are known. A number of solu-tions can be obtained; however, the desired solution is that which is most economical. The solution of the model equation is obtained by using opti-misation techniques.
7 Introduction to Modelling and Simulation
1.2.1 Types of Simulation
Simulations can be classified into various types based on the type of model used. Models may be steady-state or dynamic, deterministic or stochastic, or continuous or discrete events. The formulation of the problem, the types of variables and equations, and the solution methodology in each simulation type may be different.
1.2.1.1 Steady-State Simulation
Many processes work in continuous mode. The variables and parameters remain constant and do not change with time. When the laws of conser-vation of mass, energy or momentum are applied, the accumulation term remains zero. The latter represents the variation of mass, energy or momen-tum with time. The differential equations thus obtained do not have any temporal derivative. The model equations are simple since ‘time’ is not pres-ent in these equations. However, the steady-state simulations are not capable of predicting the dynamic behaviour of the process.
1.2.1.2 Dynamic Simulation
A process industry consists of processes which operate under batch or contin-uous mode. Batch processes are of a dynamic nature. Reactions are carried out in batch reactors to achieve the desired selectivity in a cost-effective manner.
Many separation processes such as adsorbers and regenerators also operate in batch mode. Start-up and shutdown of a unit operating continuously also constitute a dynamic process. The design of process control systems requires knowledge of the dynamic response of the process to disturbances. These aspects cannot be studied by steady-state simulations. A simulation study that considers time as a parameter is called ‘dynamic simulation’. Dynamic simulation studies can be used to obtain optimum operating conditions for a process. The time needed for the start-up and shutdown of a process can be minimised. A safe, feasible and economical procedure for process start-up and shutdown can be developed using dynamic simulation.
Dynamic simulation–based systems can be used to train plant personnel.
Plant operators become familiar with the behaviour of unit operations and control systems. After training, they quickly respond to the changing behav-iour of the system and take appropriate action. These systems can be used to verify the responses of the operators. The learning process can be carried out even in the absence of an instructor.
1.2.1.3 Stochastic Simulation (Monte Carlo Simulation)
Several models do not consider the random nature of the phenomena and do not involve random variables. Instead, they use the average proper-ties. For example, transfer processes in fluidised beds may be modelled
without considering the particle velocity. Such models are called ‘determin-istic models’. If a simulation model involves random variables, it is called a ‘stochastic model’. Simulation studies using such a model are known as
‘stochastic simulation’. This allows the use of more basic laws of physics.
Simulation based on deterministic models directly provides average proper-ties, and the results of stochastic simulation are averaged to get them. This type of simulation is also known as ‘Monte Carlo simulation’.
1.2.1.4 Discrete-Event Simulation
Many variables change continuously. The conduction in a slab at constant wall temperature is a continuous process. The conduction may be a steady-state or even unsteady-steady-state process. There are several events which take place suddenly at a particular time. For example, the arrival of particles on the wall of a fluidised bed is of a discrete nature. Addition of reactants into a fed-batch reactor may take place only at fixed times. This process is also discrete in nature. Discrete-event simulation usually involves random vari-ables. The mathematical description involves discrete varivari-ables.
1.2.1.5 Molecular Simulation
To understand the processes at the molecular level and their relationship with the macroscale processes, the model must consider the effect of the mol-ecule on the process. Molecular dynamic simulations that consider the veloc-ity of each molecule, the charges on a single molecule and the forces between all molecules have been carried out to predict many physical properties such as coefficient of thermal expansion, surface tension, viscosity, vapour– liquid equilibria and liquid–liquid equilibria (Gupta 2003). Such simulations can help in studying diffusion at the nanoscale, or the development of new drugs, enzymes and biocatalysts. However, molecular simulations are time consuming, requiring extensive computational power. At present, super-computers are used to carry out molecular simulation.
Note that the classification discussed here is very broad. Simulation to han-dle a large system of equations in cases of increased degrees of complexity is continuously being attempted. The methodologies to solve the equations are also being refined day by day. A few decades ago, solving a momentum balance equation in the case of a steady state and three dimensions was con-sidered extremely difficult, even numerically. Today, it is a reality and being simulated using dedicated CFD software such as FLUENT, STAR-CD and COSMOL Multiphysics.
1.2.2 Applications of Simulation in Chemical Engineering
Simulation is an important tool for chemical and process engineers. It is used at various steps, including plant design, plant operation, troubleshoot-ing, shutdown and start-up operations. Simulation is based on a model or
9 Introduction to Modelling and Simulation
a set of sub-models. Many processes are so complex that the traditional method of changing a variable at a time and studying its effect on other parameters experimentally is not possible. However, it is possible using simulation studies. Some of the wide areas of application in which simula-tion plays an important role are discussed in this secsimula-tion.
1.2.2.1 Process Synthesis
Before commissioning a new process plant, a techno-economic feasibil-ity study is carried out. If only laboratory data are available, a pilot plant is
Before commissioning a new process plant, a techno-economic feasibil-ity study is carried out. If only laboratory data are available, a pilot plant is