Energy Accounting, Thermodynamics and Performance Metrics

Introduction

Energy management in industry begins with a reliable account of where energy enters a system, how it is converted, where it is used, and where it is lost or rejected. Thermodynamics supplies the physical laws needed to construct this account; performance metrics convert physical measurements into indicators that support engineering decisions. Together, these tools help engineers reduce operating cost, improve reliability, lower emissions, and justify investment in efficient equipment.

An energy account is not merely a list of utility bills. It is a quantified model of an industrial system. A useful account must define the system boundary, select a time period, identify energy carriers, measure flows consistently, and reconcile inputs with outputs. The same principles apply to a boiler, furnace, compressor station, production line, building, or complete plant.

Learning Objectives

By the end of this chapter, the reader should be able to:

1. Define system boundaries and prepare mass and energy balances.
2. Apply the first and second laws of thermodynamics to industrial equipment.
3. Distinguish energy efficiency from exergy efficiency.
4. Use heat-transfer principles to interpret industrial losses.
5. Construct load profiles and calculate specific energy consumption.
6. Develop energy performance indicators and benchmark performance responsibly.
7. Interpret and prepare Sankey diagrams.
8. Evaluate measurement, accounting, and implementation limitations.

1. Energy Accounting and System Boundaries

Energy accounting is the systematic measurement and reconciliation of energy inputs, useful outputs, stored energy, and losses. The analyst must first define the boundary. A control-volume boundary surrounds equipment through which mass and energy may cross. A closed-system boundary permits energy transfer but no mass transfer. A whole-plant boundary may include fuel, electricity, steam, compressed air, water, products, waste, and exported utilities.

The choice of boundary affects the result. For example, the efficiency of an electric motor may exclude transmission losses, whereas a production-line efficiency may include the motor, drive, and process equipment. Comparisons are meaningful only when boundaries, operating conditions, and reporting periods are comparable.

Energy carriers and units

Common industrial energy carriers include electricity, natural gas, fuel oil, coal, steam, hot water, compressed air, and recovered heat. The SI unit of energy is the joule (J). Practical units include kWh, MJ, GJ, and therms. Electrical energy is related to power by:

where E is energy, P is power, and t is time. If P is in kW and t is in hours, E is in kWh. The conversion 1 kWh = 3.6 MJ is exact.

Fuel energy must be identified as higher heating value (HHV) or lower heating value (LHV). HHV includes the latent heat recovered when water vapor in combustion products condenses; LHV does not. A performance comparison must use the same basis throughout.

First-law energy balance

For a control volume, the general rate balance is:

Here E_cv is energy stored in the control volume (J), ṁ is mass flow rate (kg/s), h is specific enthalpy (J/kg), V is velocity (m/s), g is gravitational acceleration (m/s²), z is elevation (m), Q̇ is heat transfer into the system (W), and Ẇ is work done by the system (W). The equation assumes a clearly defined control volume and consistent sign convention. Kinetic and potential terms may be neglected only when they are small relative to enthalpy and work terms.

For steady operation, storage is zero. For a device with negligible changes in kinetic and potential energy:

For a simple process with no work output, this often becomes useful heat input equals enthalpy increase plus losses. In plant accounting, an equivalent energy-balance form is:

This identity is an accounting statement, not a claim that all losses have the same physical cause. “Loss” may include stack heat, radiation, leakage, rejected cooling water, unmeasured consumption, or measurement error.

Mass balance

For a control volume:

At steady state, total mass entering equals total mass leaving. Component balances are required when composition changes, as in combustion, drying, evaporation, or chemical processing. Energy and mass balances should be reconciled together: an unexplained energy discrepancy may result from an incorrect mass flow, temperature, fuel composition, or production record.

2. Thermodynamic Foundations

The first law

The first law expresses conservation of energy. Energy changes form but cannot be created or destroyed. Heat and work are modes of energy transfer, not properties stored in a system. Internal energy, enthalpy, and entropy are properties; heat and work depend on the path.

For a closed system:

where ∆U is the change in internal energy, Q is heat supplied to the system, and W is work done by the system. This sign convention must be stated because some texts define work input as positive.

For steady-flow equipment, enthalpy is convenient because it includes flow work:

where h is specific enthalpy, u is specific internal energy, p is pressure, and v is specific volume. For incompressible liquids over moderate temperature ranges, a useful approximation is ∆h ≈ c_p∆T, where c_p is specific heat capacity.

The second law

The first law does not indicate whether a process is possible or how much useful work can be obtained. The second law introduces directionality and irreversibility. For a control volume, the entropy rate balance is:

where S_cv is entropy (J/K), s is specific entropy (J/kg·K), Q̇_j is heat transfer at boundary temperature T_j (K), and Ṡ_gen is entropy generation (W/K). The second law requires Ṡ_gen ≥ 0. Equality applies only to an ideal reversible process; real processes generate entropy through friction, finite temperature differences, mixing, throttling, electrical resistance, and unrestrained expansion.

A heat engine operating between a high temperature T_H and a low temperature T_L has a maximum reversible efficiency:

Temperatures must be absolute temperatures in kelvin. The Carnot value is a theoretical upper limit, not a practical prediction, because real engines have irreversibilities and finite-rate heat transfer.

3. Efficiency, Effectiveness and Exergy

Energy efficiency

A general energy efficiency is:

The numerator must be defined carefully. For a boiler, useful output may be the enthalpy increase of steam relative to feedwater. For a motor, it is shaft power. For a furnace, it may be heat transferred to the product rather than heat contained in hot exhaust gases.

Efficiency can be expressed as a percentage, but it is meaningful only when the input and output are on compatible energy bases and measured over the same period. A boiler may show high energy efficiency while still wasting high-quality heat at a temperature suitable for power generation.

Exergy

Exergy is the maximum theoretical useful work obtainable as a system comes to equilibrium with a specified environment. Unlike energy, exergy is not conserved; it is destroyed by irreversibility. Exergy analysis therefore identifies not only how much energy is lost, but also how valuable that energy is.

For a stream, neglecting kinetic and potential terms, physical exergy relative to an environment at T₀ and p₀ is commonly written:

where ex_ph is specific physical exergy (J/kg), h₀ and s₀ are properties at the reference environment, and T₀ is reference temperature (K). Chemical exergy may be important for fuels and reactive mixtures. Exergy destruction is related to entropy generation by the Gouy–Stodola relation:

where Ė_D is exergy destruction (W). This equation assumes a uniform, fixed reference environment.

Exergy efficiency is:

A furnace may have a high first-law efficiency because most fuel energy leaves with the product, yet a lower exergy efficiency because fuel chemical exergy is degraded into low-temperature heat. This distinction helps prioritize improvements: reducing a large quantity of low-temperature heat may be less valuable than preventing a smaller destruction of high-temperature or high-pressure exergy.

4. Heat Transfer and Industrial Losses

Heat transfer occurs by conduction, convection, and radiation. In real equipment, these mechanisms often occur simultaneously.

For one-dimensional conduction through a plane wall:

where k is thermal conductivity (W/m·K), A is area (m²), L is wall thickness (m), and T₁ and T₂ are surface temperatures (K or °C differences). The equation assumes steady one-dimensional conduction, constant k, and negligible contact resistance.

Convective heat transfer is represented by:

where h is the convection coefficient (W/m²·K), T_s is surface temperature, and T_∞ is bulk-fluid temperature. The coefficient depends on geometry, fluid properties, velocity, and flow regime.

Thermal radiation from an idealized surface is described by:

where ε is emissivity, σ is the Stefan–Boltzmann constant, and absolute temperatures are required. Radiation becomes particularly important at furnace temperatures because of the fourth-power dependence.

Industrial heat losses include poorly insulated surfaces, open furnace doors, hot product discharge, flue gases, steam leaks, condensate losses, cooling-water rejection, and heat exchanger fouling. Insulation reduces conduction and surface temperature, but it must be selected for temperature, moisture, mechanical durability, fire safety, and access requirements. Insulation can also conceal corrosion under insulation, so inspection planning is essential.

5. Load Profiles and Demand Analysis

A load profile shows demand as a function of time. It reveals operating schedules, start-up peaks, idle consumption, cycling, and opportunities for control. For electrical systems, average demand over an interval is:

Peak demand is the maximum measured interval demand. Demand charges may depend on a utility-defined interval, such as 15 or 30 minutes, rather than on instantaneous power.

The load factor is:

A low load factor indicates that equipment operates near peak only briefly or that production is highly variable. Improving load factor may involve scheduling, sequencing large motors, storage, demand response, or avoiding simultaneous start-up—not merely reducing total kWh.

Thermal loads should be represented using suitable intervals because temperature dynamics and storage affect demand. A heat-treatment furnace, for example, may draw high power during warm-up and lower power during holding. A short measurement period during the holding phase would misrepresent its energy performance.

6. Specific Energy Consumption and Performance Indicators

Specific energy consumption (SEC) normalizes energy by an output measure:

Typical units include kWh/t, GJ/t, MJ per batch, or kWh per component. The denominator must be clearly defined: saleable product is generally more useful than total throughput when scrap is significant.

Energy performance indicators (EnPIs) may include:

• total energy use per month;
• energy cost per unit product;
• electricity intensity in kWh/t;
• fuel intensity in GJ/t;
• peak demand in kW;
• boiler efficiency;
• compressed-air leakage rate;
• energy use per operating hour; and
• carbon emissions per unit product.

A useful EnPI is specific, measurable, normalized when necessary, and linked to an operational decision. Weather, product mix, production rate, raw-material moisture, ambient temperature, and equipment condition may require normalization. A simple regression model can be written as:

where E is energy use, P is production, HDD and CDD are heating- and cooling-degree indicators, β terms are fitted coefficients, and ε is unexplained variation. Regression is useful only when data are sufficient, variables are physically meaningful, and model residuals are examined. Correlation does not prove that a variable causes energy use.

Benchmarking

Internal benchmarking compares similar machines, shifts, lines, or periods within one organization. External benchmarking compares facilities with comparable technology, products, climate, and operating constraints. Benchmarking must account for boundary definitions, product quality, utilization, age, maintenance, and environmental conditions. A target copied from a different process may encourage unsafe or uneconomic operation.

7. Sankey Diagrams

A Sankey diagram represents energy flows using arrows whose widths are proportional to flow magnitude. It is especially useful for communicating an energy balance to technical and managerial audiences. The diagram should identify the period, energy basis, system boundary, and units. Every major input and output should be included, and the flow widths should be scaled consistently.

Figure: Illustrative Sankey representation of a 1000 GJ heating-process input and its outputs.

The illustrative flows sum to 1000 GJ. The corresponding first-law efficiency is 700/1000 = 70%. A Sankey diagram does not by itself show exergy destruction; a high-temperature exhaust stream may carry more recoverable value than its energy width alone suggests.

8. Worked Examples

Example 1: Boiler energy balance

A boiler receives 10,000 kg/h of fuel with an LHV of 40 MJ/kg. It produces 12,000 kg/h of steam. The enthalpy rise from feedwater to steam is 2,800 kJ/kg. Determine the useful heat output and energy efficiency, neglecting auxiliary electricity.

Fuel input:

10,000 × 40 = 400,000 MJ/h

Useful steam output:

12,000 × 2,800 kJ/kg = 33,600,000 kJ/h = 33,600 MJ/h

Therefore:

η = 33,600/400,000 = 0.084 = 8.4%

The result is unusually low for a boiler and should trigger investigation. Possible causes include an inconsistent steam enthalpy, a fuel-flow unit error, incomplete system boundary, or substantial unaccounted losses. The arithmetic is correct, but engineering interpretation requires data validation.

Example 2: Specific energy consumption

A production line consumes 18,000 kWh in a month and produces 240 tonnes of acceptable product. Its SEC is:

SEC = 18,000/240 = 75 kWh/t

If 20 tonnes are rejected and total throughput is used instead, the apparent value becomes 69.2 kWh/t. Reporting the lower value would conceal the energy associated with scrap; therefore, the selected denominator should be stated explicitly.

9. Applied Case: Illustrative Compressed-Air System

Background

An illustrative manufacturing plant operates three compressors supplying a common header. Production is intermittent, but compressors remain loaded during breaks. A monthly electricity review shows rising consumption without a proportional increase in output.

Problem and analysis

Measurements show 96,000 kWh/month for 1,200 tonnes of acceptable product, giving an SEC of 80 kWh/t. A night survey finds pressure decay and audible leaks. The compressors also operate at a pressure higher than required by the production equipment. The energy account separates compressor electricity, useful air delivered, unloaded running, leakage, and pressure-control losses.

Approach and solution

The plant repairs leaks, lowers header pressure after confirming that all users remain within specification, installs automatic shutoff valves for idle areas, and sequences compressors according to demand. A submeter records compressor power and a flow meter records delivered air. Operators are trained to report abnormal sound and pressure behavior. Safety controls prevent unauthorized pressure changes and ensure that stored compressed air is isolated before maintenance.

Outcome

After stabilization, monthly electricity falls to 72,000 kWh while acceptable production remains 1,200 tonnes. The new SEC is 60 kWh/t, a 25% reduction:

(80 − 60)/80 × 100 = 25%

The improvement should not be credited solely to leak repair until production mix, operating hours, pressure, and measurement accuracy have been checked. The case demonstrates the importance of a defined boundary, interval measurements, normalization, and verification.

Learning points

1. Idle operation can dominate energy use in intermittently loaded systems.
2. Pressure reduction is an energy measure only when process requirements remain satisfied.
3. Submetering converts a plant-wide symptom into actionable equipment information.
4. Savings claims require a baseline and an agreed measurement-and-verification method.
5. Safety procedures must accompany efficiency interventions.

10. Implementation, Governance and Contemporary Practice

Effective energy accounting depends on calibrated meters, documented data ownership, consistent time stamps, and reconciliation procedures. Electricity meters, fuel meters, flow meters, temperature sensors, and weighing systems should have suitable accuracy and calibration intervals. Missing data should be flagged rather than silently replaced. Estimates may be used, but their method and uncertainty must be recorded.

Energy management systems commonly follow a plan–do–check–act cycle: establish an energy review and baseline, implement operational controls and projects, check performance against EnPIs, and revise actions. Investment decisions should consider life-cycle cost, maintenance, reliability, safety, emissions, and production quality—not only simple payback.

Digital meters and industrial data platforms enable high-frequency load profiles, anomaly detection, and equipment-level dashboards. Machine-learning models can identify unusual consumption, but they require representative data, transparent validation, cybersecurity controls, and human review. Automated recommendations must not bypass interlocks or alter safety-critical operating limits. Data governance should address access rights, retention, privacy where personnel data are involved, and protection against manipulation.

Energy improvement must never compromise occupational safety. Insulation, pressure reduction, heat recovery, and control modifications require hazard assessment. Applicable electrical, pressure-vessel, combustion, environmental, and occupational-safety regulations take precedence over an energy target. Engineers should also consider rebound effects, in which lower operating cost increases usage, and burden shifting, in which a local improvement increases energy or emissions elsewhere in the system.

Challenges and Limitations

Energy balances are affected by meter bias, asynchronous readings, changing fuel quality, transient operation, unmeasured storage, and inconsistent production records. A balance closure error does not automatically indicate physical loss; it may indicate measurement uncertainty. EnPIs can be distorted by product mix or quality changes. External benchmarks may be inappropriate when technologies or climates differ. First-law efficiency can hide the destruction of high-quality energy, while exergy analysis requires a defensible reference environment and more detailed property data. Sankey diagrams communicate magnitude well but can oversimplify temporal variation and irreversibility.

Best practice is therefore to combine: (1) a transparent boundary; (2) calibrated measurement; (3) mass and energy reconciliation; (4) normalized indicators; (5) first- and second-law analysis; (6) safety and quality checks; and (7) documented verification of savings.

Chapter Summary

Energy accounting applies conservation of mass and energy to a defined industrial boundary. The first law quantifies energy transfers, while the second law identifies directionality and irreversibility through entropy generation. Efficiency measures useful energy relative to input, whereas exergy efficiency recognizes the quality and work potential of energy. Conduction, convection, and radiation explain important industrial heat losses. Load profiles reveal demand patterns and peak behavior; SEC and EnPIs normalize performance for comparison and control. Benchmarking is meaningful only when boundaries and operating conditions are comparable. Sankey diagrams communicate proportional energy flows, but they should be supported by measurement and thermodynamic analysis. Reliable implementation requires calibrated instruments, data governance, safety assessment, normalization, and verification.

Key Terms

Energy accounting: Quantified record of energy inputs, outputs, storage, and losses.

Control volume: Defined region through which mass and energy may cross.

Mass balance: Conservation relationship between mass entering, leaving, and accumulating.

First law: Principle of energy conservation.

Second law: Principle governing entropy generation and process direction.

Enthalpy: Property equal to internal energy plus flow-work term, h = u + pv.

Entropy: Thermodynamic property associated with energy dispersal and irreversibility.

Exergy: Maximum theoretical useful work relative to an environment.

Exergy destruction: Loss of work potential caused by irreversibility.

Energy efficiency: Useful energy output divided by energy input.

Heat transfer: Transfer of thermal energy by conduction, convection, or radiation.

Load profile: Variation of demand with time.

Load factor: Average demand divided by maximum demand.

Specific energy consumption: Energy used per unit of defined output.

Energy performance indicator: Measurable quantity used to monitor energy performance.

Benchmarking: Comparison of performance with a reference unit or period.

Sankey diagram: Flow diagram whose arrow widths represent quantities.

Normalization: Adjustment of performance data for relevant operating variables.

Measurement and verification: Process of determining and confirming savings.

Review Questions

Short Answer Questions

1. Why must a system boundary be stated before preparing an energy balance?
2. Distinguish heat and work from thermodynamic properties.
3. What does entropy generation indicate about a real process?
4. Define specific energy consumption and give one suitable industrial denominator.
5. What information is conveyed by the width of a Sankey arrow?

Long Answer Questions

1. Explain the steady-flow energy balance and discuss when kinetic and potential terms may be neglected.
2. Compare first-law efficiency and exergy efficiency using an industrial furnace as an example.
3. Describe the mechanisms of conduction, convection, and radiation and relate each to industrial heat loss.
4. Explain how load profiles, load factor, and demand charges influence electrical energy management.
5. Discuss the requirements for a fair internal or external energy benchmark.

Analytical / Application Questions

1. A process consumes 50,000 kWh and produces 600 tonnes of acceptable product. Calculate SEC. If 50 tonnes are rejected, explain why using total throughput would change the management interpretation.
2. An energy balance shows 1,000 GJ input, 650 GJ useful output, 250 GJ flue loss, and 150 GJ surface loss. Identify the inconsistency, propose likely causes, and state what measurements should be checked.
3. A plant reduces compressed-air pressure and electricity use but experiences several production interruptions. Evaluate whether the project should be considered successful and specify the technical, safety, and performance evidence required.

Multiple Choice Questions with Answers

Question 1

Which principle requires that the total energy input to a steady industrial process equal useful outputs plus losses?

A. Conservation of mass only

B. First law of thermodynamics

C. Second law of thermodynamics

D. Carnot principle

Correct Answer: B. First law of thermodynamics

Question 2

In the steady-flow energy balance, which property conveniently includes flow work?

A. Entropy

B. Internal energy

C. Enthalpy

D. Exergy

Correct Answer: C. Enthalpy

Question 3

Entropy generation in a real process is

A. always negative

B. zero in every steady process

C. always non-negative

D. equal to the energy input

Correct Answer: C. always non-negative

Question 4

A machine consumes 12,000 kWh and produces 200 t of acceptable product. Its SEC is

A. 6 kWh/t

B. 60 kWh/t

C. 600 kWh/t

D. 2,400 kWh/t

Correct Answer: B. 60 kWh/t

Question 5

The load factor is defined as

A. maximum demand divided by energy use

B. average demand divided by maximum demand

C. energy use divided by production

D. peak demand divided by average demand

Correct Answer: B. average demand divided by maximum demand

Question 6

Which temperature scale must be used in the Carnot efficiency equation?

A. Celsius

B. Fahrenheit

C. Kelvin

D. Any scale with equal intervals

Correct Answer: C. Kelvin

Question 7

What does exergy destruction primarily represent?

A. Conservation of energy

B. Loss of useful work potential due to irreversibility

C. Increase in product mass

D. Electrical meter resolution

Correct Answer: B. Loss of useful work potential due to irreversibility

Question 8

A Sankey diagram normally represents flow magnitude through

A. arrow color only

B. arrow width

C. text length

D. system pressure

Correct Answer: B. arrow width

Question 9

For a plane wall with steady one-dimensional conduction, heat transfer increases when

A. wall area decreases

B. thermal conductivity decreases

C. temperature difference increases

D. wall thickness increases

Correct Answer: C. temperature difference increases

Question 10

Why should acceptable product often be used as the SEC denominator instead of total throughput?

A. It hides rejected material

B. It accounts for product that meets quality requirements

C. It eliminates the need for meters

D. It always produces a lower SEC

Correct Answer: B. It accounts for product that meets quality requirements