A PROJECT ON SIMULATION dynamic response response of Batch R eactor’ ‘To study the dynamic
Submitted by Dipak D shah (080190105056) Pratik M patel (080190105046) Mahesh B Dhaduk (080190105009) Pruthviraj V Chauhan (0801901050201)
Under guidance by Girish vegad (assistant professor of Gec valsad)
Bachelor of engineering In chemical engineering
Government Engineering College, Valsad-39600
INDEX SR NO. 1 2 3 4 5 6
SUBJECT Problem statement Introduction Process description model development and algorithm Result & conclusion References
PAGE NUMBER 3 3 4 6 12 12
PROBLEM
STATEMENT
To study the dynamic response of continuous stirred tank bioreactor
INTRODUCTION In batch reactor a given amount of material is introduced first and no material is fed to or collected as the reaction proceeds. After a certain period of time,the operation is stopped and the product is withdrawn.Then the batch product is sometimes further treated in order to achieve the required product purity to satisfy the commercial requirements and relavant regulatory authorities. For large-scale production, continuous processing is almost alwas economically beneficial to batch processing.However, there are many industries in which batch processing is consistently used in manufacture of relatively small volume high value added products.The inherent flexibility offered by batch mode of operation allows us to produce different materials,using the same equipment ,thereby redusing the initial investement.The batch processing is also preferred when the product is highly sensitive and regulated,as in the food and pharmaceutical industries.If something is made in a batch reactor,it can be tested and certified by batch, and from a regulatory point of view,it is easier to deal with. The following cases are efficiently handled by the batch mode of operation. (i)Slow reaction are frequently best handled in batch processing. To accelerate some slow reactions,the temperature and pressure,which are must easier to control in the batch units,are adjusted.(ii)Solids are are easy to mix and handle in a batch process. (iii)Oxygen from the air may interface with the reation.Some reactions with air may be explosive. Air is difficult to exclude completely from the continuous flow system and batch processes are usually used to operate under such condition. Although the batch reactor is vary flexible, its operation and product quality control are usually difficult.Batch processes are inherently transient in nature (no steady state) and this behavior leads to operation under a wide range of condition. However ,a realistic dynamic procs model can be used as a diagnostic tool to identify the operating problems.Also remember that an efficient controller can maximize the yield of desired product. In the present study,we will develop a mathematical model for a batch reactor. The dynamic simulation of the process model wll also be included in our study. It is recognized that the control of a batch reactor system provides an interasting challenge in that the system has no steady state. Although our objective is not to design an advance controller, we are interasted to 1 observed the closed-loop process responce by implementing a convetional proportional integral (PI) controller. 3
PROCESS
DESCRIPTION
Consider a batch reactor shown in figure.The reactor is filled with reactant and then sealed.The contents of the reactor are heated up to the reaction temperature with saturated steam supplied to jacket at temperature T s. Consider steam is collected in a steam trap. The reaction mixture is contiuously stirred at a fixed rpm.The reactor is fitted with a cooling coil through which chilled water is [assed and the exothermic heat is removed to move the system temperature along a predetermined desired temperature-time trajectory.To follow the prescribed trajectory,both heating and cooling of the process unit is necessary.
Consider the following consecutive reactions that take place in the reactor k
k
A1→B 2→C It is assumed that A→B has the second order kinetics,where as B→C has fierst order kinetics.In this batch operation, B is the desired product.If the reaction goes on for a long time,the yield of undesired waste C will be high.Again if we stop the reaction too early,the convection of A may be vary low.In both situations the yield of desired product B are low.Therefore,there is an optimum time when we can stop the operation and get the maximum amount of desired product.This is known as batch time.
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MODEL
DEVELOPMENT AND ALGORITHM
Assumptions We make the following assumptions to develop the process model. -Both the chemical reactions occurred in the example, batch reactor,are exothermic. -The reactor is well-insulated such that there is negligible heat exchange in between the reactor and the external environment.Some part of the cooling water and steam supply lines, which are exposed to the environment,are also insulated. -The inlet and outlet temperatures do not vary much due to a sufficient rapid flow rate of the coolant steam.Therefore,an average water coolent temperature T c is used in the mathematical model. -The condensed steam is discharge at its saturation temperature(no subcooling). -We assume constant volume(V) reactor with constant mixture capacity (C p). Note that here the volume refers to the volume of reaction mixture, not the volume of reactor -The reactor contents are perfectly mixed and do not exhibit significance gradients of species concentration or temperature in any part of the reactor. -The overall heat transfer coefficient for heating jacket U j is assumed constant but the overall heat transfer coefficient for cooling coil U c is assumed to be a function of the coolent flow rate Fc as: 0.8
1/Uc = 1/4550F c
= 1/10.8
(3.1)
Model development The basis of most of reactor modelling is a set of fundamental balance equations.These equations are mathematical statement of physical laws that that require conservation of mass, energy, momentum ,and quantities of particular chemical species.The basic equation is: [Rate of accumulation within the system]=[Rate of flow in to the system]-[Rate of flow out of system]+[Rate of generation by chemical reaction within the system] (3.2) More simply,
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[Rate of accumulation within the system]=Net rate of flow into the system] +[Rate of generation by chemical reaction within the system] (3.3) In SI system,all the terms in the above equation (3.2) and (3.3) have the unit of kilo-mole per second(kmole/s) or kilograme per second (kg/s) for mass balance and kilo-joule per second(kj/s) for energy balance.
Total continuity Equation In the batch operation,Net flow rate of mass in to reactor=0 Rate of generation of mass within the reactor=0 and Rate of accumulation of mass within the reactor=d(ρV)/dt Since ρ is the mixture density and V is the mixture volume, and ρV beomes the total mass inside the reactor.Substituting all these terms in equation (3.30,we get the total continuity equation as: d(ρV)/dt =0
(3.4)
We have assumed that V is constant and therefore according to total continuity equation, ρ remains unchanged (constsnt).
Component contiuity Equations For component A(reactant) In the component balance equation for species A, Net flow rate of component A into reactor=0, Rate of generation of component A by chemical reaction=-(-r A)v, and =(rA)v,and Rate of accumulation of component A within the reactor= dN A /dt By conection, (-r A) is the rate of disappearance of species A;r A is the rate of formation of A.Here,NA represent the number of moles of species A in the system at time t.Now Equation (3.3) gives the following form of species A as: dNA /dt = -(-rA)v
(3.5)
that is, 7
1/V dNA /dt =d(NA /V)/dt =dCA /dt
(3.6)
Where, CA is the concentration of species A.Since the reaction A kinetics,so 2
(-rA) = k 1CA
k 1
→ B has second-order
(3.7)
Where K1 represent the reaction rate constant.Substitution of Equation (3.7) in to Equation (3.6) gives 2
dCA /dt = - k 1CA
This is the component contiuity or mass balance equation for species A For component B (desired product) Net flow rate of component B into reactor=0, Rate of generation of component B by chemical reaction=-(-r B)v Rate of accumulation of component A within the reactor= dN B /dt Here (-rB) is the rate of disappearance of species B andN B denotes the number of moles of species B in the system at time t. After rearranging Equation (3.3) for the case of component B, we obtain dNB /dt = -(-rB)v Based on the specified reaction as stated earlier,we can write 2
2
(-rB) = k 2CB - k 1CA
Where CB is the concentration of species B and K 2 denotes the reaction rate constant.Substituting Equation (3.10) in to Equation(3.9),finally we get 2
dCB /dt =k 2CA - k 1CB This is the component contiuity Equation for species B.
Reaction rate Constant Common sence and chemical intuition suggest that the higher the temperature (T),the faster a given chemical will proceed.Quantatively this relationship between the rate of reaction and its temperature is determinate by Arrhenius equation.According to the Arrhenius law,the reaction 2 rate constant ,k ( also known as specific reaction rate constant) is expressed by K= α exp(-E/RT)
(3.12) 8
Where, α=frequency factor or pre-exponential factor E=activation energy R=universal gas constant The exponential temperature-dependant function in the kinetic Equation (3.12) represents one of the severe nonlinier in chemical engineering systems.For the sample batch reactor,the Arrhenius equation gives the following forms: K1 = α10 exp(-E1 /RT)
(3.13)
K2 = α20 exp(-E2 /RT)
(3.14)
The two above equationhave been used in the component continuity and energy balance equations.
Energy balance equation For the concerned batch reactor,Equation (3.3) can be expressed in terms of energy as: [Rate of energy accumulation]=[Net rate of energy input]+[Rate of energy added by exothermic chemical reactions] (3.15) Now, Net rate of energy input=[Rate of heat input from the heating jacket to the reactor]-[Rate of heat output from the reactor to the cooling coil] =U jA j(Ts-T) – UcAc(T-Tc) Here, A j and Ac are the heat transfer areas of the heating jacket and the cooling coil respectively. Since we have assumed that the reactor is well insulated and ,therefore,no heat exchange in between the reactor and the environment is accounted. Again,rate of energy added by the exothermic reactions =∑
()() 2
=(-H1)k 1 C AV+(-H2)k 2 CBV k
k
Clearly ,n=2 The subscript 1 and 2 are used for the reaction A 1 → B and B 1 → C respectively.Here, (-∆H1) and (-∆H2) are the exothermic heats of reaction for the two reaction.It is well-known that the heat of reaction is negative for the exothermic reaction and positive for th endothermic reaction.
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Now,the rate of accumulation of energy=d( ρVh)/dt =ρVCp dT/dt Here ρ,V, Cp all are constrains,and h is enthalpy (C p T).Substituting all these energy terms in equation (3.5) we obtain the following form: 2
ρVCp dT/dt =(-H1)k 1 C AV+(-H2)k 2 CBV + U jA j(Ts-T) – UcAc(T-Tc)
(3.16)
Rearranging, 2
dT/dt=(- H1)/ ρCp. k 1 C
H2)/ ρCp .k 2 CB + U jA j/ ρVCp (Ts-T)- UcAc / ρVCp (T-Tc) (3.17)
A +(-
This is the energy balance equation for the sample batch reactor.
Algorithm Now we will discuss the control of the example batch reactor under the assumption that some of the basic control theories are familier to the reader. The control of a batch reactor system is a great challenge because the system has no steady state. From figure it is clear that the cooling rate is controlled by manipulating the water flow rate (F c) through the cooling coil.Again, the control of the heating rate is accomplished by regulatin the steam pressure, and hence,the steam temperature (T s) simultaneously to regulate the reactor temperature(T). In order to achieve a maximum yield of desired product, it is always necessary to create a reaction-friendly environment in the reactor.For the present case, the set point temperature in the reactor should be changed precisely and the dynamc set point is given as a desired temperaturetime trajectory -3
Td(t) = 54 +71 exp(-2.5 × 10 t)
(3.18)
In general practice,one output variable(here T) is controlled using a single manipulated variable (say T s). If we use another variable F c (or Uc since they are easily correlated according to Equation (3.1))simultaneously to derive T,the control system will be over-determined.A way of soling this difficulty is to introduce a single parametric variable u,defined in the following manner. Ts = (Ts, max – Ts min)u + Ts ,min Uc = (Uc, min – Uc, max)u +Uc, max
(3.19) (3.20)
Where the maximum and minimum values of T s and Uc are choosen from or safety limits.Clearl,u=0 represents the maximum cooling of the system and u=1,maximum heating. This
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Parametric variable is used as a single manipulated variable in the prescribed batch control problem. After substituting Equation (3.19) and (3.20) in to equation (3.17) and rearrangeing,we obtain dT/dt = γ1k 1CA + γ2k 2CB +(a1+a2T) +(b1+b2T) u
(3.21)
where γ1= (-H1)/ ρ Cp
(3.22)
γ2=(-H2)/ ρ Cp
(3.23)
a1=( U jA jTs mi + Uc, max AcTc / ρ Cp V
(3.24)
a2=-(U jA j +Uc, max Ac)/ ρ Cp V
(3.25)
b1=[ U jA j (Ts, max – Ts min) – (Uc, max – Uc, min)]
(3.26)
b2=(Uc, max – Uc, min) Ac/ ρ Cp V
(3.27)
Now ucan be obtained by employing algorithm. Here, a classical PI controller will be implemented to regulate the temperature in the batch reactor. The PI controller equation is U(t) = us +Kc (e(t) + 1/гi ∫
e(t) dt)
(3.28)
Where us is the controllers bais signal, K c the proportional gain, гi the integral time constant (tuning parameter)and the error to controller e(t) =T d – T(t). The values of the tuning 0 -1 parameter are arbitrarily chosen as: K c C and гi= 360 (s)
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RESULT
AND CONCLUSION
We have developed a mathematical model for a batch reactor.The reactor is inherently transient in nature and the modelling equations are strongly nonlinear. The model structure consist of mass balance,energy balance and reaction rate equations. In oerder to carry out the closed loop simulation experiment,the process simulator is developed with solving the coupled model equations.
REFERENCES Amiya k jana , page no 39 to 51
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