MATLAB reactor

Using Matlab the volume and the heat transfer area of the reactors are deduced as follows ... 

It is advisable to graph and inspect the reaction more closely at the entrance of the reactor. After a few experiments with Vend = 0.1, 0.04, and 0.01, we have set the desired final volume to Vend = 0.01 m3 in Figure 4.4, which is drawn by the MATLAB command fixedbedreactf.003,160,1200,1030,.01,15,0,1) . ... 

We can validate our formulas and code against the earlier computed conversion rate of 72.64% at the end of the tubular reactor for the Damkohler number Da = 1.4 and Pe = 15.0 by running conversionDa(15,0.7264) with the inputs Pe = 15 and the conversion rate percent = 0.7264 (= xa) in MATLAB. This call computes the Damkohler number Da = 1.4007 correctly to within 0.05%. 

In this section we have presented and solved the BVPs associated with the diffusion and reaction that take place in the pores of a porous catalyst pellet. The results were expressed graphically in terms of the effectiveness factor rj versus the Thiele modulus d> for two cases One with negligible external mass and heat transfer resistances, i.e., when Sh and Nu —> oo, and another with finite Sh and Nu values. This problem is very important in the design of fixed-bed catalytic reactors. The sample results presented here have shown that for exothermal reactions multiple steady states may occur over a range of Thiele moduli d>. Efficient numerical techniques have been presented as MATLAB programs that solve singular two-point boundary value problems. 

Develop the model equations and MATLAB code for solving the problem of a packed bed reactor which is packed with porous catalyst pellets that catalyze a first-order exothermic reaction with 2 = 1.8, 7 = 1.1, and (3 = 1.1. Use a dimensionless feed concentration and reactor length, as well as Sh = 250.0 and Nu = 10.0. 

Choose a reaction from the literature that is similar to the reaction of this reactor, such as catalytic hydrogenation, and perform the above computations using MATLAB to obtain the concentrations, temperatures, and effectiveness factor profiles along the length of the reactor. 

The effectiveness factors at each point along the length of the reactor are calculated for the key components methane and carbon dioxide by using either the dusty gas model or one of our simplified models (A) and (B). The dusty gas model gives rise to more complicated two point boundary value differential equations (BVPs) for the catalyst pellets. These are solved in MATLAB via bvp4c or bvp4cf singhouseqr. m as done in Chapter 5. 

The catalyst pellet boundary value differential equations (7.172) and (7.173) can be solved via MATLAB using bvp4c or bvp4cf singhouseqr as practiced in Chapter 5. The reactor model DEs (7.166) and (7.180) to (7.182) can be solved via MATLAB s standard IVP solvers ode.. . The reactor model equations and the catalyst pellet equations used to compute the effectiveness factors rjj are all coupled. 

Numerically the heterogeneous model involves I VPs for the reactor and BVPs for the catalyst pellets. These problems can be solved as before via MATLAB. 

Develop a model for an industrial riser reactor FCC unit. Collect the necessary data and develop the MATLAB code needed to design the unit from your model. 

The effectiveness of the proposed approach has been tested in simulation by considering a jacketed batch reactor in which the phenol-formaldehyde reaction presented in Chap. 2 takes place. The complete system of differential equations given by the 13 mass balances presented in Sect. 2.4 has been simulated in the MATLAB/SIMULINK environment. 

Figure 2.11 gives a Matlab program that performs these sizing calculations. Results for the base case feedrate, a 50% conversion, and a 320 K reactor temperature yield a coolant exit temperature of 314 K and a log-mean temperature difference of 13.5 K. The heat transfer area of the coil is 81.44 m2, compared to a jacket area of 63.4 m2. The vessel... 

It is quite easy to use the fsolve function in Matlab to solve for the four unknowns. Figure 2.14 gives a program that solves for the four reactor compositions given reactor temperature, reactor volume, feed conditions and kinetics. 

The Matlab program given in Figure 2.19 solves these nonlinear simultaneous equations for given reactor volume, temperature, and feeds. Figure 2.20 gives results... 

Figure 2.61 Matlab program for design of reactor-stripper process.

Figure 3.1 gives a Matlab program that sizes the reactor given the conversion, reactor temperature, feed conditions, coolant properties, and kinetic parameters. Then the coefficients of the linear model are evaluated, and the poles and zeros of the openloop transfer function are calculated. If any of the poles have positive real parts, the system is openloop-unstable. 

Figure 3.36 Matlab program for reactor-column simulation.

Figure 3.45 gives a Matlab program for the nonlinear simulation of the autorefrigerated reactor. The specific case is the 90% conversion with a cooling water temperature in the condenser of 317 K. The reactor volume is 1.68 m3, and the reactor temperature TR is 353 K. The condenser area is 19.9 m2, and the condenser temperature Tc is 331 K. The temperature differential driving force is 331 - 317 = 14 K to transfer 0.237 MW. 

Figure 3.45 Matlab program for autorefrigerated reactor simulation.

Figure 4.2 Matlab program for batch reactor simulation.

Figure 4.40 Matlab program for fed-batch hydrogenation reactor.

Figure 4.43 gives a Matlab program for the simulation of this fed-batch reactor. 

Figure 5.6 gives a Matlab program for a non-adiabatic tubular reactor. The reactor inlet temperature is assumed to be the same as the steam temperature (Tst = Tjn = All K in the... 

The dynamics and control of a number of tubular reactor systems have been studied in this chapter. Both adiabatic and cooled tubular reactors have been explored in both isolation and a plantwide environment. Ideal systems have been studied using Matlab programs. Real chemical systems have been studied using Aspen Dynamics. 

Using the symbolic calculation engine available in Matlab ,2 we obtained the following description of the intermediate dynamics of the reactor-condenser process ... 

When using an ordinary differential equation (ODE) solver such as POLYMATH or MATLAB, it is usually easier to leave the mole balances, rate laws, and concentrations as separate equations rather than combining them into a single equation as we did to obtain an analytical solution. Writing She equations separately leaves it to the computer to combine them and produce a solution. The formulations for a packed-bed reactor with pressure drop and a semibatch reactor are given below for two elementary reactions. 

For the case of isothermal operafion with no pressure drop, we were able to obtain an analytical solution, given by equation B, which gives the reactor volume necessary to achieve a conversion X for a gas-phase reaction carried out isothermaliy in a PFR, However, in the majority of situations, analytical solutions to the ordinary differential equations appearing in (he combine step are not possible. Consequently, we include POLYMATH, or some other ODE solver such as MATLAB, in our menu in that it makes obtaining solutions to the differential equations much more palatable, ... 

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