Based on the following information for the Dimethyl Ether $($DME$)$ process design, answer questions $1$ to $3.$

Background

The plant is capable of producing $50,000$ metric tons of DME per year of $99\mathrm{.}5\%$ purity via the catalytic dehydration of methanol over an acid zeolite catalyst. The goal is to design a grassroots facility, which safely and efficiently produces DME.

DME is used primarily as a propellant. DME is miscible with most organic solvents and it has a high solubility in water. Recently, the use of DME as a fuel additive for diesel engines has been investigated due to its high volatility $($desired for cold starting$)$ and high cetane number.

Dimethyl Ether Production Reactions

The production of DME is via the catalytic dehydration of methanol over an amorphous alumina catalyst treated with $10\mathrm{.}2\%$ silica. A methanol conversion of about $80\%$ is achieved in the reactor. DME is produced by the following reaction:

$2C{H}_{3}OH>C{H}_{3}OC{H}_3+H_{2}O$

In the temperature range of normal operation, there are no significant side reactions, and the equilibrium conversion for pure methanol feed exceeds $92\%.$ Therefore, the reactor is kinetically controlled in the temperature range of normal operation.

Process Description

The process flow diagram for Unit $200$ is shown in Figure $1\mathrm{.}1.$ The essential operations in the process are the preheating of the raw material $($nearly pure methanol$),$ reacting methanol to form DME, product separation, contaminant separation, and methanol separation and recycle.

Fresh methanol, Stream $1,$ is combined with recycled reactant, Stream $13,$ and vaporized prior to being sent to a fixed bed reactor, operating between $250C$ and $400C.$ The single pass conversion in the reactor must be limited to $80\%$ due to equipment constraints. The reactor effluent, Stream $7,$ is then cooled prior to being sent to the first of two distillation columns, DME product is taken overhead from the first column $T-201.$ The second column T$-202$ separates water from the unreacted methanol. The methanol is recycled back to the front end of the process $($Stream $13),$ while the water $($stream $15)$ is sent to waste treatment to remove trace amounts of organic compounds.

Appendix I contains all required and pertinent process system information: the PFD is shown in Figure $1\mathrm{.}1$; stream table indicating current operation is given as Table $1\mathrm{.}1$; the utility summary is in Table $1\mathrm{.}2$; and equipment information is given in Table $1\mathrm{.}3.$

Page$|2$

Question $1$

$30$ marks

Using the pertinent equipment information given in Table $1\mathrm{.}3$ in Appendix $1,$ determine the bare module cost, $,{?}^{,of},$ the following equipment for the year $2022$:

$($i$)$ The distillation column T$-202.$ The cost of the tower and trays are calculated separately and then added together to obtain the total cost of a distillation column.

$[10$ marks$]$

$($ii$)$ The heat exchanger E$-202.$

$[5$ marks$]$

$($iii$)$ The reactor R$-201.$

$[5$ marks$]$

$($iv$)$ The pump P$-203$ A$/$B$.$

$[5$ marks$]$

$($v$)$ The vessel V$-201.$

$[5$ marks$]$

Question $2$

$40$ marks

The process and equipment information given in Tables I$\mathrm{.}1-1\mathrm{.}5$ in Appendix I can be used to estimate the overall cost of manufacturing of the Dimethyl Ether product.

Calculate;

$($i$)$ The annual cost of operating labor, $Co,$ to operate the Dimethyl Ether process plant. The current cost for a chemical plant operator is $$72,\frac{000}{y}$ r$?$

$[5$ marks$]$

$($ii$)$ The cost of the raw material, $C_{RM}.$

$[5$ marks$]$

$($iii$)$ The cost of utilities CuT.

$[10$ marks$]$

$($iv$)$ The cost of manufacturing $($without depreciation$)$ for the chemical plant. The Dimethyl Ether process plant for which a capital cost analysis estimates the fixed capital investment to be $$1,240,000$ while the cost of waste treatment is $$716,025.$

$[10$ marks$]$

$($v$)$ The cost of manufacturing cost $($in $\frac{\text{\$}}{k}g)$ of the Dimethyl Ether produced. Justify the difference, if any, between the selling price and the manufacturing price.

$[10$ marks$]$

NOTE:

All the data for the purchased cost of equipment were obtained from a survey of equipment manufacturers during the period May to September of $2022,$ so an average value of the CEPCI of $797\mathrm{.}6$ over this period should be used when accounting for inflation.

Annual operating hours: stream factor of $95\%(8322$ operating hours$).$

The current cost for a chemical plant operator is $$72,\frac{000}{?}$ year.

Pagel$3$