代写CENG0006: Project – Benzene Production帮做R编程

CENG0006: Project - Benzene Production

Prepare a report (pdf) and submit it via TurnItIn including a copy of the GAMS (.gms) codes for Q1(b), Q2 and Q3, and gPROMS (.gpj) code for Q4 in the report. The report (including the codes) should be up to 12 pages long including figures and tables. To include the GAMS and gPROMS codes in the report, copy it in the text format and then paste it into the word processor document used for preparing the report. Do not copy the GAMS and gPROMS codes as images or screenshots.

Do copy the GAMS/gPROMS codes (.gms/.gpj files) and paste into the report in the text format, for example:	Correct
variables x(i); equations mass_balance(j) mass balances; mass_balance(j) .. sum(i,a(j,i)*x(i)) =e= b(j); model MassBalance /all/; solve MassBalance using CNS;

Do not copy the GAMS/gPROMS codes (.gms/.gpj) as images/screenshots, for example the following image/screenshot format is not acceptable and you will lose marks if you submit it in this format:	Incorrect

Each question carries marks distributed as shown [  ].

Cyclohexane, a precursor of nylon, can be manufactured from benzene, and benzene can be produced by deyhdroalkylation of toluene. A simplified process flowsheet for the production of benzene from toluene is shown in Figure 1. Feed (stream 1) containing toluene and hydrogen is mixed with the recycle (stream 9) to give the inlet (stream 2) to the reactor, where the following irreversible reactions take place:

C7H8  + H2  → C6H6  + CH4                                   (First reaction)

2C6H6  → C12H10  + H2                                            (Second reaction)

In the first reaction a fraction of the toluene is converted to benzene and in the second reaction, which is a side reaction, a small fraction of the benzene produced in the first reaction is converted to biphenyl, which is a by-product. Stream 3 leaving the reactor contains all the components that appear in the first and second reactions. Stream 3 then enters Separator-1 where it is separated into streams 4 and 5. To avoid build-up of CH4, purge (stream 4) is used to get rid of CH4  by using Separator-1, but some quantity of other components also gets purged along with CH4. Stream 5 enters separator-2 where it is separated into streams 6 and 7. Stream 6 enters Separator-3 and gets separated into streams 8 and 9. Stream 7 is the product stream (mainly containing benzene).   Stream 8 mainly contains the by-product, biphenyl, and stream 9 is the recycle stream (mainly containing the unreacted raw materials).

Figure 1. Benzene production process

PART A: Steady-State System

Q1: Process flowsheeting with recycle

Let the subscript. i denote the components such that:

The feed stream consists of:

(kmols hr-1)

C7H8                               5000

H2                                   7000

Reactor

For each component i

where σij = stoichiometric coefficient for component i in reaction j

νj = extent of reaction for reaction j

C7H8 + H2 → C6H6 + CH4	ν1 = 3500 kmol hr-1
2C6H6 → C12H10 + H2	ν2 = 70 kmol hr-1

Separators

Let αi  denote the split fractions for the separators such that:

	Separator-1 For stream 3 going to stream 4	Separator-2 For stream 5 going to stream 7	Seprator-3 For stream 6 going to stream 8
α 1	0.01	0.01	0.01
α2	0.90	0.01	0.01
α3	0.01	0.90	0.01
α4	0.90	0.01	0.01
α5	0.01	0.01	0.95

(a)  Write the mass balance for this problem and submit it as a part of the report. [5]

(b) Equation Oriented Process Flowsheeting - using GAMS as a modelling tool: Formulate this problem in GAMS and solve it using the CNS solver. Provide the GAMS (.gms) code in the report. [20]

(c)  Sensitivity analysis: Once you have solved the problem in part b above, analyse and discuss the effect of the parameter, the amount of H2 entering in the feed (stream 1) and also the effect of the parameter, the amount of H2  being purged in stream 4 on the remaining component flowrates in the flow sheet. For example, is the amount or purity of the product affected, do the overall flowrates change, does the amount of H2  purged etc. Note that for the analysis and discussion you may want to consider that higher component flowrates will require bigger  sized equipments for the unit operations, higher product purity will result in higher selling price of the product, and the lower amount of H2  purged will result in lower waste and costs, etc. The values of the parameters to change for carrying out the sensitivity analysis have to be chosen by you. GAMS (.gms) code for this part is not required. [10]

Q2: Linear Programming for Optimisation of the Benzene Production

The product value is given by £1000 per kmol of benzene in stream 7 with a penalty of £5 per kmol of the remaining components. The feed cost is given by £150 per kmol of stream 1. The processing costs of mixer, reactor, separator-1, separator-2 and separator-3 are given by £0.1, £0.2, £0.15, £0.15 and £0.15 per kmol of the inlet flowrates to these units, respectively.

For this question, ignore the feed stream component flowrates given in Q1 and instead assume that molar feed composition is C7H8  = 30% and H2  = 70%.

(a)  The objective is to maximize profit where profit is given by product (stream 7) value minus feed (stream 1) cost and processing costs of the five units; product (stream 7) value is the selling price of benzene in stream 7 minus the penalties due to the presence of other components in stream 7. Due to environmental regulations a maximum of 4800 kmols/hr of H2   and  3500 kmols/hr of CH4  can be purged in stream 4. Set this problem as a Linear Programming problem and provide the formulation in 1-2 pages in the report. Solve it by using GAMS. Use ‘SETS’, ‘PARAMETERS’ and ‘TABLE’ features wherever possible in the GAMS input file. The input file must also contain adequate comment  statements for ease of understanding. In the report, provide values of the profit (in £/hr), feed (stream 1) component flowrates (in kmols/hr), product (stream 7) component flowrates (in kmols/hr), and H2  and CH4  flowrates in the purge (stream 4). Provide the GAMS (.gms) code in the report. [15]

(b) Multi-objective optimisation: Consider a situation where in addition to the maximisation of profit in part a, there is also another objective function given by the environmental impact that is to be minimised; assume that the environmental impact is given by the summation of the flowrates of H2 and CH4  in stream 4. Formulate this problem as a multi-objective optimisation problem and solve it using the epsilon-constraints method to analyse the trade-offs between profit and environmental impact. Use a starting value of epsilon of 8300, remove the constraints on flowrates of H2  and CH4  in stream 4 that were given in part a, and then increase the value of epsilon and extents of reaction by in each iteration as follows:

Iteration number	Epsilon	ν1	ν2
0	8300	3500	70
1	9130	3850	77
2	9960	4200	84
3	10790	4550	91
4	11620	4900	98
5	12450	5250	105

Carry out the iterations as above, and provide and discuss the trade-off curve. Provide the GAMS (.gms) code in the report. [10]

PART B: Dynamic System

Dynamic Model of Separator-2

Consider the following Ordinary Differential Equations model for Separator-2. For simplicity, consider that only two components, benzene and biphenyl, are involved where benzene is the light component and biphenyl is the heavy component.

The vapour-liquid equilibrium in the column is given by the following algebraic equation:

where, x k  denotes the liquid mole fraction of the light component at tray k (k = 1,2,…,5) and y k  represents the vapour mole fraction of light component above the tray k; the reboiler is considered as the 1st  tray and the condenser is considered as the 5th tray. L and V are liquid and vapor molar flow rates, which are assumed to remain constant for each tray. The values of the constant parameters are given as: Hc = 30 mol, Hr = 30 mol, Ht = 20 mol, β = 5, L = 27.3755 mol min-1, V = 32.3755 mol min-1, Lf   = 10 mol min-1, xf   = 0.5. Note that Hc, Hr, Ht, β , Lf and xf represent condenser holdup, reboiler holdup, tray holdup, relative volatility, feed flow rate and feed composition, respectively.

Q3: Steady-state operation: Assume that separator-2 is operating at steady-state, i.e., ODE equations (1)-

(3) and can be replaced by the following algebraic equations:

0 = (L + Lf)(x2 —  x1) + V(x1 —  y1)                                                                                                           (7)

0 = (L + Lf)(x3 —  x2) + V(y1 — y2)                                                                                                           (8)

0 = Lfxf  + Lx4 — (L + Lf)x3  + V(y2 —  y3)                                                                                                 (9)

0 = L(x5  —  x4) + V(y3  —  y4)                                                                                                                    (10)

0 = V(y4  —  x5)                                                                                                                                           (11)

Solve these nonlinear algebraic equations using the CNS solver in GAMS. Discuss the importance of initial guess, i.e., the starting point in the solution of nonlinear algebraic equations and your observations for this problem. Provide the GAMS (.gms) code in the report. [20]

Q4: Dynamic operation:

(a)  Solve the ODE model given by equations (1)-(6) using gPROMS. Provide and discuss the profiles of

x k  as a function of t. Solve the model for t = [0, 40], x1 (t=0)  = 0.05, x2(t=0)  = 0.1872, x3 (t=0) = 0.4702, x4(t=0) = 0.7917, x5 (t=0) = 0.95. Provide the gPROMS code (.gPJ) in the report. [10]

(b)  Sensitivity analysis: analyse and discuss the effect of Lf  and  xf  and on x k, by changing the values

Lf  and  xf  (the values have to be chosen by you) and simulating the model in gPROMS to obtain the profiles of xk. The gPROMS code for this part is not required. [10]