# The Physics of CHP Cogeneration and Heat Engine Efficiency

## The Value of Combined Heat and Power Cogeneration

Credit: iStock/Martin Wahlborg

How does CHP work? To understand CHP you have to begin with the Carnot cycle, and how it describes the function and efficacy of any heat engine. The thermodynamic Carnot cycle (proposed by Nicolas Carnot in 1824) is a four-stage process that describes the reciprocal operations of a heat engine consisting of a piston in a cylinder, driven by a volume of confined gas that expands and contracts with temperature and applied heat. The piston is attached to a crankshaft that allows for cyclical motion. These four stages of the Carnot cycle are as follows:

• During the first stage, heat is applied to the confined gas, which causes it to expand greatly as it absorbs the heat—which, in turn, drives the piston outwards. This is an isothermal stage (involving heat addition and absorption at constant temperature). As the gas expands, it experiences a drop in pressure, and the movement of the cylinder turns the crankshaft and performs work. The entropy of the gas increases during this stage.
• The second stage is adiabatic, neither losing or gaining heat, as the gas volume continues to expand (performing more work), but its temperature drops. Since heat is neither gained nor lost, entropy of the gas stays constant (isentropic) during the second stage.
• The third stage sees the crankshaft continuing its turn, driving the piston back into the cylinder. Like the first stage, this stage is isothermal and involves rejection of waste heat from the drive cylinder to the exterior environment. As the volume reduces, internal pressure increases while the temperature stays constant. Since heat is lost, entropy falls during this part of the cycle.
• The fourth and last stage sees an increase in both pressure and temperature as the gas is further compressed by the cylinder (the system now does work on the gas instead of the other way around). Like the second stage, this stage is adiabatic and isentropic, with entropy staying constant. Completion of this stage brings the system back to the starting point of stage one and the cycle begins again.

So it is the third stage—when the piston compresses the gas, which reduces volume while temperature stays constant—that gives off waste heat to the environment. The cycle can be represented by comparing the cycle’s maximum and minimum temperatures, and its maximum and minimum levels of entropy:

Where:

TH = the system’s maximum temperature of the heat source during stage one;

TC = the system’s minimum temperature of the exterior environment (cold reservoir) that receives expelled waste heat during stage three;
SB = the system’s maximum entropy during stage two;
SA = the system’s minimum entropy during stage four;
QH = the amount of heat put into the system during stage one from the exterior heat source;
QC = the amount of heat expelled from the system to the exterior environment (cold reservoir) during stage three—represented by the red shaded area; and
W = the amount of work performed by the system, equal to the amount of heat put into the system (QH) less the amount of waste heat (QC)—represented by the white shaded area.

The efficiency of a heat engine represented by the above diagram is calculated as follows:

n =W / QH = (QH – QC) / QH
or
n = 1 – (TC / TH)

And, since TC can never be absolute zero, and there is always some loss of heat, no physical system can ever be 100% efficient. Therefore, waste heat is always produced by any mechanical or electrical system that performs work. And, it is this waste heat that is captured and put to work by CHP cogeneration systems.

Types of CHP Systems and How They Work
How is this heat captured and put to work? There are several types of CHP systems. Each is designed to generate electricity and heat energy in a single integrated system. CHP systems can be installed onto exiting electrical production systems by means of retrofitting. Instead of utilizing onsite equipment to provide heating and cooling, CHP clients can utilize heat recovered from the electrical production process.

What kinds of CHP systems are used to accomplish this? At the small scale of distributive energy—applications less than 5 kilowatts (kW)—there is micro CHP. Small-scale internal combustion engines and stand-alone internal combustion engines can utilize this application for power production. It has even found applications in solar energy systems, with both concentrated solar utilizing Stirling engines and photovoltaic cell (PVC) arrays, as well as advanced fuel cells. In terms of reducing green house gas emissions (with up to 14% reductions over standard energy production) in conjunction with Stirling engines and generating energy from gas turbines, this system is the most cost-effective energy production system on the market. Micro CHP systems produce both heat and electricity, thereby reducing the price of the first, and allowing the second to be sold back to the grid.

It’s latest applications combine micro CHP with PVC arrays as a power back up to residential and commercial rooftop solar energy systems. These types of systems have been shown to significantly reduce waste energy, and allow for economical expansion of PVC systems by reducing overall operational costs. The money saved by not having to separately produce heat energy can go to purchasing expanded PVC arrays. As part of trigeneration CHP applications, an absorption chiller is added to further reduce waste heat and allow for system cooling. Cooling PVC cells further increases their efficiency, making them more productive. Trigeneration CHP itself is a broader application that combines electrical generation, heat production, and cooling by the use of linked absorption chillers that can provide refrigeration.

CHP can also be applied to a larger scale by use of district heating. These are advanced applications of traditional steam pipe utilities. The largest district heating system in America provides steam from cogeneration systems for 2,000 buildings in New York City. Heat can be provided by standard power generation stations, geothermal power plant, solar energy systems, and large-scale heat pumps. New York has the largest, most extensive system of district heating in the world, with 105 miles of pressurized steam pipes running beneath the streets of the city. These pipes deliver steam heat to buildings throughout Manhattan. Also known as Heat Recovery Steam Generation (HRSG), this system significantly increases the efficiency of fuel usage and thereby reduces emissions and the city’s carbon footprint.

As described above, industrial CHP represents the most widespread application of this technology. The main difference between industrial CHP and utility CHP is that industrial cogeneration plans tend to operate at lower boiler pressures. So, there is some loss of power generation in exchange for improved emissions and achieving sustainability goals while utilizing waste heat. Other issues include maintaining the purity of the boiler feed water, and managing the load swings occurring with each production shift. Given the need for a constant heat supply these variations can represent a significant percentage of the overall energy load during production lows.

CHP, Microgrids, and The Energy Mix
micro grid CHP—not to be confused with Micro CHP—is defined as a small electrical power generation and distribution system that services only a few local buildings and businesses. They normally operate in conjunction with regional utilities. CHP linked to a local micro grid allows these few customers to share a heat energy supply system, without the need to build and operate individual CHP systems. This arrangement can greatly increase cost effectiveness through economies of scale. Such a locally centralized system can utilize its fuel source more efficiently than several small systems. It also allows for easy load leveling across its small customer base.

CHP systems augmenting microgrids must take into account infrastructure requirements, physical location of customers and their distance from the CHP unit, local building codes and land boundaries, and potential interference from pre-existing utility lines. And, the operators of these systems must coordinate budgets, contracts, and billing requirements with each customer who may have significantly different energy loads. However, once these hurdles have been overcome, the benefits of sharing a CHP system become apparent to all participants.

Return On Investment: the Economics of CHP
The economics of CHP systems are governed by a few basic capital costs, operational factors, and operational costs. First of these is the proposed CHP system’s generating capacity, measured in kW. This capacity drives both the upfront capital installation costs, the daily operating costs, and whether or not the system is worth installing in the first place. An overly large system compared to both the generator and the potential customer base is an unnecessary investment, while too small of capacity would not be useful for large utilities. The capacity will also determine the overall net installed costs.

Cost comparisons start with cost to purchase electricity to create the heat energy provided by the CHP system, along with the boiler fuel costs and CHP fuel costs. Add in incremental operations and maintenance costs and standby charges to determine annual operating costs. This value can then be compared to projected annual operating cost savings. Simple payback (measured in years) is determined by dividing the net installation costs by the annual operating cost savings.

Performance parameters to be examined during the decision to install a CHP system also start with the proposed system’s generating capacity. Using this information as a baseline, analyzing boiler efficiency and subsequent turbine efficiency are the next steps in the screening process. Sizing of the system will be determined largely by the HRSG steam pressure and the process steam pressure, along with both steam’s flow rates.