18-Env-A6 Solid Waste Engineering and Management · May 2013

Question 17 of 17: Break-Even Price for Diverted Paper

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

National Examination, May 2013 — 04-Env-A6 / 18-Env-A6, Solid Waste Engineering and Management. 3 hours duration, closed book, one letter-sized aid sheet permitted. All 17 questions constitute a complete paper (100 marks total).

Reference texts: Tchobanoglous, Theisen & Vigil, Integrated Solid Waste Management: Engineering Principles and Management Issues; Vesilind, Worrell & Reinhart, Solid Waste Engineering; Davis & Cornwell, Introduction to Environmental Engineering (6th ed.); CCME, Guidance Document on Landfill Gas Management.

Check: several questions on this paper (Q1, Q13, Q14, Q17) supply an incomplete data set and explicitly invite the candidate to "make and state" assumptions. Every assumed value below is called out where it is introduced and is chosen from standard solid-waste-engineering practice; the governing METHOD, not the specific assumed number, is what the exam is testing.

Question 17: Break-Even Price for Diverted Paper (6 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. Incinerator feed 400 t/d MSW; 20% reduction in paper/cardboard reaching the incinerator due to source separation; NG cost \$0.40/m³; paper energy content 16,300 kJ/kg; NG energy content 37,300 kJ/m³.

Find. The minimum price per tonne the municipality must receive for the diverted paper to exactly offset the extra natural-gas cost (break-even).

Energy make-up balance: natural gas replaces exactly the heating value lost from the diverted paper so steam output is unchanged.

Approach. Compute the mass of paper actually diverted from the incinerator, convert its lost heating value to an equivalent natural-gas volume and cost, then divide that cost by the diverted paper tonnage to get the break-even price.

Check: this question does not state what fraction of the 400 t/d feed is paper/cardboard. Reusing this paper's own Q15 waste-composition analysis (Table 1: paper = 45% by mass) is the only composition data the exam supplies, and is assumed to represent this city's incinerator feed.

Paper mass diverted from the incinerator. $$m_{paper,in} = 400\times0.45 = 180\ \text{t/d}, \qquad m_{diverted} = 0.20\times180 = \boxed{36\ \text{t/d}}$$
Heating value lost, and natural gas needed to replace it. $$\Delta E = 36{,}000\ \text{kg/d}\times16{,}300\ \text{kJ/kg} = 5.868\times10^{8}\ \text{kJ/d}$$ $$V_{NG} = \dfrac{5.868\times10^{8}}{37{,}300} = \boxed{15{,}732\ \text{m}^3/\text{d}}$$
Extra natural-gas cost, and break-even paper price. $$C_{NG} = 15{,}732\ \text{m}^3/\text{d}\times\$0.40/\text{m}^3 = \$6{,}293/\text{d}$$ $$\text{Price}_{paper} = \dfrac{\$6{,}293/\text{d}}{36\ \text{t/d}} = \boxed{\$175/\text{tonne}}$$

Quantity	Value
Paper diverted from incinerator	36 t/d
Extra natural-gas required	15,732 m³/d
Extra natural-gas cost	\$6,293/d
Break-even paper price	≈\$175/tonne

Topic: Fuel-substitution economics at a waste-to-energy facility.

Key relations: Break-even price = (make-up fuel cost) ÷ (mass of the substituted fuel diverted); make-up fuel volume = lost heating value ÷ make-up fuel's own heating value.

Why this works: The facility must supply the same total heat input to hold steam output constant; whatever heating value the diverted paper no longer contributes must come from an equivalent amount of purchased natural gas, so the paper's "worth" to the facility (and therefore its break-even recycling price) is exactly the avoided-fuel cost per tonne.

Common pitfall: using the full 400 t/d feed (or the full 180 t/d paper stream) instead of only the 36 t/d actually diverted when dividing the natural-gas cost to get a price per tonne — the break-even price is per tonne of paper actually removed, not per tonne processed.

Source: Tchobanoglous, Theisen & Vigil, Integrated Solid Waste Management, Ch. 14 (thermal conversion/energy recovery economics).

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