Process Flow Sheet Optimisation Using Gams Lab Report

The question must be solved through the use of progamming language called GAMS. All input and output must be included so that I know the code 100% works.

OPTIMISATION:
REFINERY WALKTHROUGH
Sales Price
Costs
($24/bbl)
Gasoline
($36/bbl)
Crude Oil 1
Kerosene
($24/bbl)
REFINERY
Crude Oil 2
Fuel Oil
($21/bbl)
($15/bbl)
Residual
($10/bbl)
Volume Percentage Yield Maximum allowable
production bbl/day
Crude Oil 1 Crude Oil 2
Gasoline
80
44
24000
Kerosene
5
10
2000
Fuel Oil
10
36
6000
Residual
5
10
Processing cost ($/bbl)
0.5
1
Let:
X1 = bbl/day of Crude Oil 1
X2 = bbl/day of Crude Oil 2
X3 = bbl/day Gasoline
X4 = bbl/day of Kerosene
x5 = bbl/day of Fuel Oil
X6 = bbl/ day Residual Oil
bbl means barrel
• Profit = Income – Raw Material Cost – Process cost
• Income = 36 X3 + 24 X4 + 21 X5 + 10 X6
• Raw Material Cost = 24 X1 + 15 X2
• Processing Cost = 0.5 X1 + X2
• X3 = 0.8 X1 + 0.44 X2
• X4 = 0.05 X1 + 0.1 X2
• X5 = 0.1 X1 + 0.36 X2
• X6 = 0.05 X1 + 0.1 X2
Mass Balances for
each product.
Income is the
addition of the
price of the
products
multiplied by the
amount of that
specific fuel.
Substitute Values for X3 to X6 into Income equation:
Income = 36(0.8 X1 + 0.44X2) + 24(0.05X1 + 0.1X2) +
21(0.1 X1 + 0.36 X2) + 10(0.05 X1 + 0.1 X2)
Simplify Income equation in terms of X1 and X2 and then subtract
raw material costs and processing costs to get final profit
equation:
Profit = f(x) = 8.1X1 + 10.8X2.
Inequality constraints:
• Gasoline: X3 ≤ 24000; 0.80 X1 + 0.44 X2 ≤ 24000
• Kerosene: X4≤ 2000; 0.05 X1 + 0.10 X2≤ 2000
• Fuel oil: X5≤ 6000; 0.10 X1 +0.36 X2 ≤ 6000
Note: There are no constraints here for residual oil because
there is no limit to the maximal allowable production.
Non-negativity Restrictions
• X1≥ 0
• X2 ≥ 0
Plot constraints in x1-x2 plane
Determine the feasible region (blue area – see graph on next
slide). In this case, the plotted constraints have ‘less than or
equal to’ signs therefore, the feasible region must be an area
below all 3 lines. The non negativity constraints prevent the
lines from going below 0.
Feasible Region for Refinery Problem
60,000
50,000
Crude Oil 2 (x2)
40,000
30,000
20,000
10,000
0
0
10,000
20,000
30,000
40,000
Crude Oil 1 (x1)
50,000
60,000
70,000
Optimum value will occur at one of the corners of the feasible
region.
(0, 16,667): f(x) = $180,000
(15,000, 12,500): f(x) = $256,500
(26,200, 6,900): f(x) = $286,700
(30,000, 0): f(x) = $243,000
Therefore maximum profit is $286,700 at point (26,200, 6,900)
Question – 1: Process Flowsheet Optimisation by using GAMS
Consider the following flowsheet of a gas phase reaction for the production of methanol:
Feed
Product
2
3
1
Mixer
Reactor
Separator-1
4
5
6
Separator-2
Purge
7
Fig. 1. Process flowsheet
The component mole fractions of the feed stream are given by:
CO2
CH4
CO
H
HO
CH3OH
N2
0.1
0.05
0.184
0.59
0.008
0
0.068
The following equations should be used.
Reactor
For each componenti
Flowout(i) = Flowin(i) – vol
where 0y=stoichiometric coefficient for component i in reaction j
v;= extent of reaction for reaction j
CO + 2H2 + CH3OH
CO2 + H2CO + H2O
vi = 1280 kmol/hr
v2 = 360 kmol/hr
Separator 1
Assume all CO2, CH4, CO, H2 and N2 go into stream 5. 99% of H20 and 96% of CH3OH go into the
product stream.
Separator 2
10% of stream 5 is purged in stream 7.
The product value is given by £1000 per kmol of stream 4 and the feed cost is given by £1.5 per kmol
of stream 1. The processing costs of mixer, reactor, separator-1 and separator-2 are given by £0.1, £0.2,
£0.15 and £0.15 per kmol of the inlet flowrates to these equipments respectively.
The objective is to maximize profit where profit is given by product (stream 4) value minus feed (stream
1) cost and processing costs of the four equipments. Due to environmental regulations a maximum of
200 kmols/hr of CO2 and 5.5 kmols/hr of CH3OH can be purged in stream 7. Set this problem as a
Linear Programming problem and provide the formulation in 1-2 pages in the report.
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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 4) component flowrates (in kmols/hr), and CO2 and CH3OH flowrates in
the purge (stream 7).
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