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Subsections


THEORETICAL ANALYSIS

System Parameters

In order to determine the economic benefits associated with each type of cogeneration system, a generic system representing each cycle was developed and analyzed using some fundamental thermodynamic principles. Each system was chosen to match an assumed set of facility load requirements. The requirements chosen were:
  1. Constant steam load requirement of 100,000# per hour.
  2. Steam pressure of 30 psia.
  3. All electricity generated would offset electricity being purchased from the local utility.
For the purpose of determining the key operational characteristics of each system, the above assumptions greatly simplify calculation and at the same time return results which accurately represent a given systems' characteristics.

System Description

A total of five systems were analyzed, two of which are non-cogenerating systems, and the remaining three which are cogenerating systems. They are:
  1. A gas fired boiler satisfying the steam load while purchasing electricity from the local utility.
  2. An electric boiler satisfying the steam load while purchasing electricity from the local utility.
  3. A Rankine cycle system using a gas fired boiler to produce steam at 150 psia, a backpressure steam turbine to expand steam to 30 psia while generating electricity.
  4. A Brayton cycle system using a gas turbine generator to produce electricity and a heat recovery steam generator to produce steam at 30 psia.
  5. An Otto cycle system using a reciprocating engine generator to produce electricity and a heat recovery steam generator to produce steam at 30 psia.
Each system was modeled in Engineering Equation Solver (EES) software, using equations and assumptions to establish the state points at each location in the cycle. EES was then able to simultaneously solve all the equations, and return information concerning the power (electrical) output and the overall efficiency of each cycle. The EES code for each system is available in Appendix A.

Next, the information gained from EES was input into a spreadsheet to establish trends of how each system performed given differing energy costs. The results were non-dimensionalized so that only the ratio of fuel cost to electrical costs need be known to determine the cost characteristics of a given system. The thermal load was assumed to be 100,000 pounds per hour as stated above, but the results would be similar if this load were changed. It is only important that the same load characteristics be applied to each system. A more detailed discussion of each system follows.

System 1 - Natural Gas Boiler System

The most common method used to satisfy both a thermal and electrical load is operating a steam boiler to satisfy the thermal load and purchasing electricity from a utility. This system is the control system, and was used as a basis of comparison for the other systems. Some operational parameters have been assumed to allow analysis.
  1. Fuel-to-steam efficiency of 80%.
  2. Electricity-to-water pump efficiency of 90%.

System 2 - Electrical Boiler System

In certain circumstances, electrical utilities are suggesting that it may be possible or desirable to satisfy all the given operational parameters with an electric boiler as a substitute for the gas fired boiler listed above in System 1. Therefore, System 2 considers the economic effects of such a system. It must satisfy all the heat related operational parameters (i.e. be a complete substitute for the gas fired boiler) assumed in System 1.

System 3 - Steam Turbine System

System 3 consists of a gas fired boiler providing steam to satisfy the heat load as well as drive a steam turbine generator. The operational characteristics of the cogeneration system have been altered to allow for the production of electricity, but the steam turbine exhaust must still be at the same state as in the two previous systems. Specifically, the boiler steam pressure was increased to 150 psia, allowing the steam to be expanded in the turbine and still meet the exit requirements for the assumed steam load. Some facilities actually generate steam at similar pressures and throttle the steam to 30 psia without using a steam turbine to generate electricity. This method of steam production is less efficient and undesirable.*

To model the steam turbine system in EES, isentropic steam turbine and isentropic pump efficiency of 90% were assumed.12 These system operating parameters are common to systems operating today, specifically at Georgia Tech and the Westin Peachtree Plaza hotel.

System 4 - Natural Gas Turbine System

System 4 consists of a gas turbine as the prime mover driving an electric generator. The waste heat in the form of exhaust is routed to a HRSG, where it is used as the heat source to produce steam. The steam characteristics must be identical to that in System 1. The gas turbine produces a considerable amount of electricity. It is assumed that this electricity can be consumed on site, thereby offsetting an identical amount of electricity purchased from the electric utility.

In order to analyze the gas turbine, several operational additional parameters were assumed.

  1. Full load operation.
  2. Isentropic turbine efficiency of 90%
  3. Isentropic compressor efficiency of 82%
  4. HRSG efficiency of 70%.
The isentropic efficiencies taken for the turbine and compressor both represent the range of efficiencies attainable for gas turbine equipment.13 Although heat recovery boilers cannot match fuel fired boilers in term of fuel-to-steam efficiencies, due to the lower temperature of the fire side, gas turbine exhaust still has a relatively high temperature, therefore fuel-to-steam efficiencies do not suffer greatly.

System 5 - Spark Ignition Reciprocating Engine System

System 4 is similar to System 5, except the instead of a gas turbine as the prime mover, a natural gas fired Otto cycle reciprocating engine is used. The reciprocating engine generally operates at a higher efficiency, but in doing so provides less thermal energy to the waste heat boilers, reducing the amount of steam generated without supplementary firing.

To account for the effects of energy lost in the operation of the reciprocating engine, a mean frictional pressure of 35 psia was assumed. The frictional mean effective pressure corrects the calculated mean effective pressure in the cylinder determined when a perfect, frictionless engine is assumed.

Analysis

A thermodynamic analysis was performed on all the systems. Using Engineering Equation Solver to simultaneously solve the equations derived from this analysis, all the state points from each system could be specified, and in so doing, the amounts of heat and/or power available from each system could be determined. The results were applied to a spreadsheet, where differing energy costs could be assumed, and the resulting data could be plotted to show data trends.

System Performance Characteristics

EES simultaneously solves all the equations to fix the thermodynamic state at each point in the cycle. The assumptions mentioned in the System Description section above were used to help fix the state of each point in the cycles analyzed.

The natural gas boiler system and the electric boiler system were both non-electrical generating systems, so there was no economic benefit derived from the production of electricity. Any electricity consumed would have to be purchased from an electric utility.

The other three systems produced some amount of electricity. The steam turbine system produced the least electricity given a fixed input of thermal energy. This follows with the earlier discussion concerning the fuel-to-electrical efficiency of steam turbine cogeneration systems. The actual fuel-to-electrical efficiency of the steam turbine cogeneration system was 0.116 BTU electricity per BTU fuel. Since the overall pressure differential of steam turbine cogeneration systems falls far below that of Rankine cycle power plants, the fuel-to-electrical efficiency of a Rankine cogeneration system is lower than a Rankine cycle power plant. It is important to realize this when considering a cogeneration cycle.

The steam turbine system produced the least amount of electricity in terms of total kW. The actual electricity produced was a direct function of the 100,000 pound required steam load assumed in the system description section. The steam turbine system produced approximately 3700 kW. Once again, this was lower than if a pure Rankine power cycle was used, simply because the Rankine power cycle is geared solely to produce electricity and leave as little recoverable heat as possible.

The gas turbine fuel-to-electrical efficiency was almost double that of the steam turbine system. The gas turbine system returned a fuel-to-electrical efficiency of 0.303 BTU of electricity per BTU fuel. This number accurately represents the efficiencies attainable with current simple system gas turbine cogeneration systems. A 0.303 fuel-to-electrical efficiency translates roughly to a heat rate of 11,250 BTU fuel per kWh electricity, which is in the middle of the range of heat rates common in gas turbine systems (recall Figure 2 in Chapter IV).

The gas turbine produced approximately 18 MW when satisfying the assumed steam load of 100,000 pounds per hour. This is considerably more than the steam turbine system, due to the nature of the cycle. Recall that the gas turbine cycle is a topping cycle, which requires an increased amount of fuel energy input in the beginning of the cycle in order to meet the thermal load leaving the end of the cycle (where the thermal energy is recovered). Since more of this increased amount of fuel energy is converted to electricity in a topping cycle, the amount of electricity is not just double that of a steam turbine system as the efficiencies might initially lead one to think.

The reciprocating engine system returned the largest fuel-to-electrical efficiency of 0.341 BTU electricity per BTU of fuel. Once again, this number falls well within the range of reasonable values for a reciprocating engine system. As mentioned earlier, a frictional mean effective pressure of 35 psi was taken to account for the effects of friction that are normally not considered when analyzing the ideal Otto cycle. The energy lost to friction can theoretically be reclaimed if the thermal energy normally discarded in the coolant system were passed through a thermal recovery heat exchanger. Generally speaking, the thermal quality of the coolant is low and recovery of this energy is often not worth the cost of the additional equipment. In larger applications, however, this can be economically attractive and should be considered.

Because much of the discarded thermal energy coming from a reciprocating engine is in the coolant system, requiring additional heat input in the beginning of the cycle , and the fuel-to-electrical efficiency is so high, the reciprocating engine system produces the largest amount of electricity when operating to meet the required thermal load. The actual amount of electricity generated is approximately 32 MW. Since this is a theoretical study, we will assume that a single reciprocating engine generator is used to meet this demand. In practice however, it is rare that a single reciprocating engine would be used to meet such a large load.

Results

Figure 5 shows a plot of the hourly cost of operation for each of the systems relative to the electrical-to-fuel cost ratio. The plot has been scaled to the cost of operating the base system, System 1. By scaling the cost of all the systems with the base system, the value of the base system becomes 1 for all cases and the remaining systems show the operating cost relative to the base system. For example, at an electrical to gas cost ratio of 5, the natural gas boiler system has a cost of 1 by definition, where the steam turbine cogeneration system has a cost of 0.6, meaning that for every dollar spent on System 1, 0.6 dollars must be spent on System 3 to provide the same amount of energy.

The lower end of the plot shows that as the cost of electrical energy approaches the cost of fuel energy, all the systems operate at nearly the same cost. However, this instance is very rare. As electrical energy becomes more expensive relative to gas, a cogeneration system's net operating cost decreases. In fact, it quickly becomes apparent that System 2, the electric boiler system, is economically unattractive under any circumstances.

Figure 5- Relative Hourly Cost of Operation for 5 Systems.

System 3, the steam turbine cogeneration system, shows a savings under all circumstances. Even using the conservative assumptions taken for analysis, the operating cost savings are considerable. Also, the relative ease of installation and low first cost of equipment make System 3 an attractive retrofit application. In some cases steam is generated at a higher than required pressure, then throttled before distribution. Throttling the steam wastes the energy required to generate it at a higher pressure. By substituting a steam turbine for the throttling valve, "free" electrical energy can be recovered.

System 4, the gas turbine, drops below zero very quickly on the plot. This means that the money saved by the sale or use of the electricity generated by the turbine exceeds the money spent for fuel to fire the turbine. Basically, the gas turbine becomes an income generating device. The more expensive the electricity in a given area relative to fuel, the greater the income generated.

The reciprocating system represented as System 5 has many of the same beneficial characteristics as System 4. Reciprocating engines may be operated at a higher electrical efficiency than a gas turbine, producing more electricity per unit fuel input. The plot shows that the reciprocating engine outpaces even the gas turbine in terms of monetary return. But the higher electrical efficiency reduces the amount of heat rejected to the waste heat boiler, possibly requiring some supplemental firing in the boiler. Also, reciprocating engines have a shorter life span and higher maintenance costs, decreasing their economic attractiveness.

It should be noted that under most electric and gas rates, operation of these systems would move both right and left along the electrical-to-fuel cost ratio axis hour-by-hour, day-by-day, and month-by-month. Therefore, a detailed analysis of the hourly energy load (both thermal and electrical energy) and the electrical rate structure must be carried out.
 
 



* The Georgia Tech power plant and Westin Peachtree Plaza Hotel both generate steam at higher
than required pressure (~150 psia) then throttle the steam to a lower pressure (~30 psia) before
sending out to meet required load.