22-Mec-B2 Environmental Control in Buildings · May 2015

Question 8 of 8: Ideal R-134a vapour-compression chiller, and refrigerant environmental concerns

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

Notes on this paper

Paper format. Professional Engineers of Ontario / EGBC annual examination, 07-Mec-B2 (now 22-Mec-B2) Environmental Control in Buildings, May 2015 sitting. Three hours, open book. Eight problems of 20 points each; the candidate is instructed to solve five and to nominate on the cover of the first workbook which five are to be graded. Psychrometric charts and a pressure–enthalpy diagram for the refrigerant are appended to the paper, and candidates are expected to bring an environmental-control text and steam tables. Instruction 1 invites the candidate to submit a clear statement of any interpretation assumptions with the answer — that latitude is used explicitly below wherever the printed data are redundant or incomplete.

All eight problems are worked here. Every psychrometric state has been recomputed from the ASHRAE formulation for saturation vapour pressure rather than scaled off a chart, so the numbers below are tighter than a graphical solution would be; chart-quality agreement (about $\pm 0.2$ K in temperature and $\pm 0.0002$ kg/kg in humidity ratio) is all that an examiner expects, and a candidate reading the appended charts should reproduce every answer to within that band.

Reference texts for this subject.

W. P. Jones, Air Conditioning Engineering, 5th ed., Butterworth-Heinemann — the standard reference for this examination code; Ch. 2–3 (psychrometry), Ch. 6 (cooling loads), Ch. 10 (cooling towers), Ch. 15 (fans and duct design).
McQuiston, Parker & Spitler, Heating, Ventilating and Air Conditioning: Analysis and Design, 6th ed., Wiley — Ch. 3 (moist air), Ch. 8 (energy estimating and degree-day methods), Ch. 12–13 (fluid flow, fans and duct design).
ASHRAE Handbook – Fundamentals (2021) — Ch. 1 (psychrometrics), Ch. 21 (fans and duct design), Ch. 25–27 (heat, air and moisture transfer in the envelope), Ch. 30 (refrigerant properties).
Moran, Shapiro, Boettner & Bailey, Fundamentals of Engineering Thermodynamics, 9th ed., Wiley — Ch. 10 (vapour-compression refrigeration and heat pumps).
ANSI/ASHRAE Standard 62.1, Ventilation for Acceptable Indoor Air Quality, and ANSI/ASHRAE Standard 55, Thermal Environmental Conditions for Human Occupancy.
Canadian frame: National Building Code of Canada 2020 (Part 6, and Appendix C for design temperatures and degree-days), National Energy Code of Canada for Buildings 2020, Health Canada Residential Indoor Air Quality Guidelines, and Environment and Climate Change Canada Canadian Climate Normals.

Psychrometric relations used throughout. At barometric pressure $p$ with saturation vapour pressure $p_{ws}(t)$ from the ASHRAE correlation, the humidity ratio, specific enthalpy and humid volume of moist air are

$$W = 0.621945\,\frac{\phi\,p_{ws}(t)}{p - \phi\,p_{ws}(t)}, \qquad h = 1.006\,t + W\,(2501 + 1.86\,t), \qquad v = \frac{0.287042\,(t + 273.15)\,(1 + 1.6078\,W)}{p}$$

with $h$ in kJ per kg of dry air, $t$ in $\,{}^{\circ}$C and $p$ in kPa. In inch-pound units the enthalpy becomes $h = 0.240\,t + W\,(1061 + 0.444\,t)$ Btu per lb of dry air with $t$ in $\,{}^{\circ}$F. Wet-bulb temperatures are obtained by solving the adiabatic-saturation equation, not by eye. Mixing two air streams is exact in moisture and in enthalpy, so $W$ and $h$ of the mixture are the mass-weighted averages and the mixed dry bulb follows from them; weighting the dry bulb directly is the usual shortcut and differs here by about $0.01$ K.

Question 8: Ideal R-134a vapour-compression chiller, and refrigerant environmental concerns (20 marks: 15 + 5)

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.

(a) The ideal cycle

Given. An ideal (standard) vapour-compression cycle: saturated vapour leaves the evaporator, compression is isentropic, saturated liquid leaves the condenser, and expansion through the valve is isenthalpic. Pressure drops in the heat exchangers and lines are neglected.

Given data
Quantity	Symbol	Value
Refrigerant	—	R-134a
Evaporating temperature	$t_{evap}$	35 °F (1.67 °C)
Condensing temperature	$t_{cond}$	125 °F (51.67 °C)
Refrigerating capacity	$\dot{Q}_e$	20 tons (240000 Btu/h, 70.34 kW)

Find. The evaporator and condenser pressures, the refrigerant mass flow rate, the COP, and a comparison with the Carnot COP between the same two temperatures.

The ideal cycle on the R-134a pressure–enthalpy diagram. 1–2 is isentropic compression from saturated vapour to the condensing pressure, 2–3 condensation to saturated liquid, 3–4 isenthalpic expansion through the valve, and 4–1 evaporation back to saturated vapour.

Approach. Read the saturation pressures and the state enthalpies from the R-134a tables (or the appended p–h diagram), follow the four ideal processes round the cycle to get the specific refrigerating effect and the specific compressor work, and scale by the required capacity to obtain the mass flow.

Saturation pressures. From the R-134a saturation table,$$p_{evap} = p_{sat}(35\,{}^{\circ}\text{F}) = 310.9 \text{ kPa} = \boxed{45.1 \text{ psia}}$$$$p_{cond} = p_{sat}(125\,{}^{\circ}\text{F}) = 1374 \text{ kPa} = \boxed{199.3 \text{ psia}}$$ a pressure ratio of $4.42$, comfortably within single-stage territory.
State 1 — saturated vapour leaving the evaporator.$$h_1 = h_g(35\,{}^{\circ}\text{F}) = 399.57 \text{ kJ/kg}, \qquad s_1 = 1.7262 \text{ kJ/kg}\cdot\text{K}$$
State 2 — isentropic compression to the condenser pressure. Following $s_2 = s_1$ into the superheat region at $1374$ kPa gives$$h_2 = 430.46 \text{ kJ/kg} \quad\text{at}\quad t_2 = 134.4\,{}^{\circ}\text{F}$$ so the discharge is superheated about $5.2$ K above the condensing temperature — a modest and realistic discharge temperature for R-134a.
States 3 and 4 — condensation and expansion. Saturated liquid leaves the condenser and the expansion valve is isenthalpic:$$h_3 = h_f(125\,{}^{\circ}\text{F}) = 274.22 \text{ kJ/kg}, \qquad h_4 = h_3 = 274.22 \text{ kJ/kg}$$
Specific effects and COP. Round the cycle,$$q_e = h_1 - h_4 = 399.57 - 274.22 = 125.35 \text{ kJ/kg}$$$$w_c = h_2 - h_1 = 430.46 - 399.57 = 30.89 \text{ kJ/kg}$$$$\text{COP} = \frac{q_e}{w_c} = \frac{125.35}{30.89} = \boxed{4.058}$$ As a check the condenser must reject $q_c = h_2 - h_3 = 156.24$ kJ/kg, and indeed $q_e + w_c = 125.35 + 30.89 = 156.24$ kJ/kg.
Refrigerant mass flow rate. One ton of refrigeration is 3.5169 kW, so 20 tons is $70.34$ kW and$$\dot{m} = \frac{\dot{Q}_e}{q_e} = \frac{70.337}{125.35} = \boxed{0.5611 \text{ kg/s}}$$ which is $74.2$ lb/min, or $4453$ lb/h. The compressor then absorbs $\dot{m}\,w_c = 17.33$ kW ($23.2$ hp) and the condenser rejects $\dot{m}\,q_c = 87.67$ kW.
Comparison with the Carnot cycle. Between the same two temperatures, expressed absolutely ($T_e = 274.82$ K, $T_c = 324.82$ K),$$\text{COP}_{Carnot} = \frac{T_e}{T_c - T_e} = \frac{274.82}{324.82 - 274.82} = 5.496$$ so the ideal vapour-compression cycle achieves$$\frac{\text{COP}}{\text{COP}_{Carnot}} = \frac{4.058}{5.496} = \boxed{0.738 \;=\; 73.8\ \%}$$ of the Carnot value. The shortfall is not inefficiency in any avoidable sense: it is the price of the two irreversibilities that are built into the standard cycle, namely the throttling valve (which replaces a reversible expander and destroys the work it could have recovered) and the superheat horn on the compression line (which pushes the discharge above the condensing temperature). A real machine, with isentropic compressor efficiency around 70% and finite temperature differences in both heat exchangers, would deliver perhaps 2.5–3.0 rather than $4.06$.

(b) Primary environmental concerns with refrigerants

Four concerns dominate, and they are best kept distinct because they call for different responses. Stratospheric ozone depletion was the original driver: chlorine and bromine released from CFCs and HCFCs catalyse ozone destruction, and the Montreal Protocol, implemented in Canada through the Ozone-depleting Substances and Halocarbon Alternatives Regulations under CEPA, has phased out CFCs entirely and is completing the phase-out of HCFCs such as R-22. R-134a, the refrigerant in this problem, contains no chlorine and has zero ozone depletion potential, which is precisely why it replaced R-12.

Direct global warming is now the binding constraint. R-134a has a 100-year global warming potential of about 1430, so every kilogram leaked is equivalent to roughly 1.4 tonnes of CO₂. The Kigali Amendment to the Montreal Protocol, which Canada has ratified, imposes a stepwise phase-down of HFC consumption, and Canadian regulations already restrict high-GWP refrigerants in new equipment. The industry response is the move to low-GWP alternatives — HFO blends such as R-1234yf and R-513A, and the natural refrigerants ammonia (R-717), CO₂ (R-744) and hydrocarbons — each of which trades the GWP problem for toxicity, pressure or flammability issues that must then be managed by design and by code.

Indirect emissions are usually the larger term and are easy to overlook: the electricity the compressor consumes over the machine's life typically dominates the direct leakage contribution. The total equivalent warming impact (TEWI) framework adds the two together, and it is why a modest gain in COP can outweigh a large reduction in refrigerant GWP. In this cycle the compressor draws 17.3 kW continuously; over 4000 operating hours a year that is roughly 69333 kWh, and on a fossil-fired grid the associated emissions would exceed the direct effect of leaking the entire charge.

Containment, safety and end-of-life complete the picture. Leakage is the mechanism by which every direct impact is realised, so Canadian regulation requires leak testing, record-keeping, certified technicians and the recovery rather than venting of refrigerant at servicing and decommissioning. Safety classification under ASHRAE Standard 34 and the machinery-room requirements of ASHRAE Standard 15 govern toxicity and flammability — the reason ammonia, for all its thermodynamic and environmental merit, is confined to industrial plant rooms. Some newer HFOs also break down in the atmosphere to trifluoroacetic acid, a persistent compound now under active study. Good engineering practice therefore means specifying the lowest-GWP refrigerant compatible with the safety class the occupancy allows, minimising the charge, designing for tightness, and treating efficiency as an environmental measure in its own right.

Final results
Quantity	Symbol	Result
Evaporator pressure	$p_{evap}$	45.1 psia (310.9 kPa)
Condenser pressure	$p_{cond}$	199.3 psia (1374 kPa)
Refrigerating effect	$q_e$	125.35 kJ/kg
Compressor work	$w_c$	30.89 kJ/kg
Refrigerant mass flow rate	$\dot{m}$	0.5611 kg/s (74.2 lb/min, 4453 lb/h)
Compressor power	$\dot{W}_c$	17.33 kW (23.2 hp)
Condenser heat rejection	$\dot{Q}_c$	87.67 kW
Cycle COP	COP	4.058
Carnot COP between the same temperatures	$\text{COP}_{Carnot}$	5.496
Fraction of Carnot achieved	—	73.8%

Topic. The standard vapour-compression cycle, and its position relative to the Carnot limit.

Key relations. $q_e = h_1 - h_4$; $w_c = h_2 - h_1$ with $s_2 = s_1$; $q_c = h_2 - h_3$; $h_4 = h_3$ (isenthalpic throttling); $\text{COP} = q_e/w_c$; $\dot{m} = \dot{Q}_e/q_e$; $\text{COP}_{Carnot} = T_e/(T_c - T_e)$ with absolute temperatures. One ton of refrigeration = 12 000 Btu/h = 3.5169 kW.

Why this works. The whole cycle analysis reduces to reading four enthalpies, because each of the four components is a steady-flow device with one energy interaction: the evaporator and condenser exchange heat at constant pressure, the compressor does work with no heat transfer, and the valve does neither, so its enthalpy is unchanged. The Carnot comparison is instructive rather than decorative — it separates what is thermodynamically unavoidable given the two temperature levels from what the particular cycle configuration costs. Here the 26% shortfall is attributable almost entirely to the throttling valve and the superheat horn, which is why real improvements come from raising the evaporating temperature and lowering the condensing temperature rather than from chasing component efficiency.

Common pitfall. Using Celsius or Fahrenheit rather than absolute temperatures in the Carnot expression — with °C it would give 0.03 instead of 5.496. Also common are assuming the compression ends at saturated vapour rather than superheated (which would understate the work), and forgetting that the throttling process conserves enthalpy, not entropy.

Source. Moran, Shapiro, Boettner & Bailey, Fundamentals of Engineering Thermodynamics, 9th ed., Ch. 10 (vapour-compression refrigeration); ASHRAE Handbook – Fundamentals (2021) Ch. 2 and Ch. 30 (thermophysical properties of refrigerants); ASHRAE Standards 15 and 34; Environment and Climate Change Canada, Ozone-depleting Substances and Halocarbon Alternatives Regulations (SOR/2016-137).

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