GATE Chemical Engineering Plant Design and Economics Syllabus

Plant Design and Economics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Plant Design and Economics in GATE Chemical Engineering, not a summary of it.

1. 1

   Principles of Process Economics and Cost Estimation

   7 topics

   • Depreciation and Total Annualized Cost
   • Cost Indices
   • Rate of Return
   • Payback Period
   • Discounted Cash Flow
   • Optimization in Process Design
   • Sizing of Chemical Engineering Equipments
     • Heat Exchangers
     • Multistage Contactors

Plant Design and Economics flashcards for GATE Chemical Engineering

18 of 50 cards from the Plant Design and Economics deck — real questions with worked answers.

1. Define depreciation in the context of plant economics.

   Depreciation is the gradual reduction in the value of a physical asset (equipment, buildings) over its useful life due to wear, tear, deterioration and obsolescence. It is treated as an annual cost charged against income to recover the capital invested.

2. State the straight-line method formula for annual depreciation, $d$.

   $$d = \frac{V - V_s}{n}$$ where $V$ is the original (installed) value, $V_s$ is the salvage value, and $n$ is the service (useful) life in years.

3. In the straight-line method, what is the book value (asset value) after $a$ years?

   $$V_a = V - a\,d = V - a\left(\frac{V - V_s}{n}\right)$$ where $d$ is the annual depreciation charge.

4. State the declining-balance (fixed-percentage) method. What is the book value after $a$ years?

   A constant fraction $f$ of the current book value is charged each year. Book value after $a$ years: $$V_a = V(1-f)^{a}$$ and the salvage value gives $V_s = V(1-f)^{n}$, so $f = 1-\left(\frac{V_s}{V}\right)^{1/n}$.

5. What is the double-declining-balance (DDB) depreciation factor?

   The DDB method uses a fixed fraction $f = \frac{2}{n}$ (twice the straight-line rate) applied to the current book value, where $n$ is the service life.

6. State the sum-of-the-years-digits (SYD) depreciation charge for year $a$ (asset age $a$).

   $$d_a = \frac{(n - a + 1)}{\sum_{k=1}^{n} k}\,(V - V_s) = \frac{2(n-a+1)}{n(n+1)}\,(V - V_s)$$ It is an accelerated method giving larger charges early in life.

7. State the sinking-fund method formula for the uniform annual deposit $R$.

   $$R = (V - V_s)\,\frac{i}{(1+i)^{n} - 1}$$ where $i$ is the interest rate. The fund plus interest accumulates to the depreciable value $(V - V_s)$ over $n$ years.

8. Define Total Annualized Cost (TAC) of a process plant.

   TAC is the sum of the annualized capital (fixed) cost and the annual operating cost: $$\text{TAC} = \text{(Capital cost} \times \text{Capital Recovery Factor)} + \text{Annual Operating Cost}$$ It places one-time and recurring costs on a common yearly basis for design comparison.

9. Write the Capital Recovery Factor (CRF) used to annualize capital cost.

   $$\text{CRF} = \frac{i(1+i)^{n}}{(1+i)^{n} - 1}$$ where $i$ is the interest rate and $n$ the project life. Annualized capital cost $=$ Capital $\times$ CRF.

10. What is the purpose of a cost index, and how is it used to update equipment cost?

    A cost index converts a cost from a past date to its equivalent present cost, accounting for inflation/price changes: $$\text{Cost}_{2} = \text{Cost}_{1}\times\frac{\text{Index}_{2}}{\text{Index}_{1}}$$

11. Name the common cost indices used in chemical engineering.

    Marshall and Swift (M&S) equipment cost index, Chemical Engineering Plant Cost Index (CEPCI), Nelson-Farrar Refinery construction index, and the Engineering News-Record (ENR) construction cost index.

12. State the six-tenths-rule (capacity-cost / power law) for equipment cost scaling.

    $$\frac{C_2}{C_1} = \left(\frac{Q_2}{Q_1}\right)^{n}$$ where $Q$ is capacity/size. The typical exponent is $n \approx 0.6$, hence 'six-tenths rule'; it captures economy of scale.

13. Define Return on Investment (ROI) / Rate of Return.

    $$\text{ROI} = \frac{\text{Annual net profit}}{\text{Total capital investment}}\times 100\%$$ It measures the annual earning power of the invested capital, often based on net (after-tax) profit.

14. What is the difference between rate of return based on gross profit vs. net profit?

    Gross-profit ROI uses profit before income taxes; net-profit ROI uses profit after taxes. Net profit $=$ gross profit $\times (1 - t)$ where $t$ is the tax rate, giving a lower, more conservative ROI.

15. Define the Payback Period (payout time).

    The payback period is the time required for the cumulative net cash inflows to equal the original fixed-capital investment: $$\text{Payback period} = \frac{\text{Fixed-capital investment}}{\text{Annual cash flow (profit} + \text{depreciation)}}$$

16. In payback period calculation, why is depreciation added back to net profit?

    Depreciation is a non-cash bookkeeping expense; it is subtracted to compute profit but does not represent an actual cash outflow. The annual cash flow recovering the investment is therefore net profit plus depreciation.

17. What is a key limitation of the simple payback period method?

    It ignores the time value of money and disregards all cash flows occurring after the payback point, so it does not measure overall profitability—only the speed of capital recovery.

18. Define the Discounted Cash Flow Rate of Return (DCFRR) / internal rate of return.

    DCFRR is the discount (interest) rate $i$ at which the net present value of all project cash flows equals zero: $$\sum_{j=0}^{n}\frac{CF_j}{(1+i)^{j}} = 0$$ i.e. discounted inflows equal the investment.

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