SME
Process Design · Problem type
Economic potential of the input–output structure
Use this for “A plant makes 100 kmol/h of product worth $40 per kmol from 105 kmol/h of feed at $25, 8000 h a year. What is its economic potential?”
Chart
EPₕ = VP − CF
4,000 − 2,625 = 1,375
The flows in add and the flows out take away: EPₕ = 1,375.
Product rate ṅP = 100 kmol/h
Product price pP = 40 $/kmol
Feed rate ṅF = 105 kmol/h
Feed price pF = 25 $/kmol
Operating time per year t = 8,000 h
Economic potential per year EP = $11,000,000
This is an example. Type your own values to start a new problem.
VP ($/h)
=
ṅP (kmol/h)
×
pP ($/kmol)
CF ($/h)
=
ṅF (kmol/h)
×
pF ($/kmol)
$
EP
=
(
VP ($/h)
−
CF ($/h)
)
×
t (h)
EPₕ
Economic potential per hour
calculated · $/h
Formulas
VP = ṅP × pP
4,000 = 100 × 40
CF = ṅF × pF
2,625 = 105 × 25
EPₕ = VP − CF
1,375 = 4,000 − 2,625
EP
=
EPₕ
×
t
11,000,000 = 1,375 × 8,000
Assumptions
•
Economic potential (EP) is product value minus raw-material cost, before any equipment, energy or labor cost.
•
Prices are per kmol; flows are steady over the hours the plant runs each year.
•
A negative EP ends the design here: no later level can make the plant pay.
•
ṅP and ṅF come from the overall balance and the reaction’s stoichiometry; the page doesn’t check them.
Step-by-step
WE KNOW
ṅP = 100 kmol/h, pP = 40 $/kmol, ṅF = 105 kmol/h, pF = 25 $/kmol, t = 8,000 h
FIND
product value (VP), feed cost (CF), economic potential per hour (EPₕ), economic potential per year (EP)
Step 1 · Find product value (VP)
Use VP = ṅP × pP
Product made each hour times its price.
VP = 100 × 40
VP = 4,000 $/h
Step 2 · Find feed cost (CF)
Use CF = ṅF × pF
Feed bought each hour times its price.
CF = 105 × 25
CF = 2,625 $/h
Step 3 · Find economic potential per hour (EPₕ)
Use EPₕ = VP − CF
What the products earn minus what the feeds cost, each hour; below 0, the process cannot pay.
EPₕ = 4,000 − 2,625
EPₕ = 1,375 $/h
Step 4 · Find economic potential per year (EP)
Use EP = EPₕ × t
Each hour’s margin times the hours the plant runs in one year.
EP = 1,375 × 8,000
EP = $11,000,000
Check
Put the numbers back in. Both sides should match.
4,000 = 100 × 40 ✓
2,625 = 105 × 25 ✓
1,375 = 4,000 − 2,625 ✓
11,000,000 = 1,375 × 8,000 ✓
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