Question

13.6D A factory requires \(3750 \mathrm{~kW}\) of electric power and highquality steam at \(107^{\circ} \mathrm{C}\) with a mass flow rate of \(2.2 \mathrm{~kg} / \mathrm{s}\). Two options are under consideration: Option 1: A single boiler generates steam at \(2.0 \mathrm{MPa}, 320^{\circ} \mathrm{C}\), supplying a turbine that exhausts to a condenser at \(0.007\) MPa. Steam is extracted from the turbine at \(107^{\circ} \mathrm{C}\), returning as a liquid to the boiler after use. Option 2: A boiler generates steam at \(2.0 \mathrm{MPa}, 320^{\circ} \mathrm{C}\), supplying a turbine that exhausts to a condenser at \(0.007 \mathrm{MPa}\). A separate process steam boiler generates the required steam at \(107^{\circ} \mathrm{C}\), which is returned as a liquid to the boiler after use. The boilers are fired with natural gas and \(20 \%\) excess air. For \(7200 \mathrm{~h}\) of operation annually, evaluate the two options on the basis of cost.

Short answer

Compare the total annual costs for Option 1 and Option 2 considering energy consumption and operational expenses.

Step-by-step solution

- Determine steam and power requirements

Identify the electric power and mass flow rate of the steam required by the factory. Electric Power Required: 3750 kW Mass Flow Rate of Steam: 2.2 kg/s at 107°C

- Calculate the steam properties for both options

Note the steam conditions for both options:* For Option 1: Steam at 2.0 MPa, 320°C* For Option 2: Steam at 2.0 MPa, 320°C for turbine and a separate steam boiler generates steam at 107°C.

- Analyze Option 1: Single Boiler System

1. The boiler generates steam at 2.0 MPa, 320°C.2. Steam expands in the turbine and some are extracted to meet the steam requirement of 107°C.3. Remaining steam exhausts to a condenser at 0.007 MPa.4. Determine the enthalpy for each state using steam tables and apply the mass and energy balance equations to find the boiler fuel requirement considering 20% excess air.

- Analyze Option 2: Separate Process Steam Boiler

1. A boiler generates steam at 2.0 MPa, 320°C and sends it to the turbine.2. The turbine exhausts to a condenser at 0.007 MPa.3. A separate steam boiler generates the required steam at 107°C.4. Calculate total fuel consumption for both boilers again using energy balance and excess air considerations.

- Determine the cost for both options

1. Calculate the total annual energy consumption for both options (kWh).2. Convert energy consumption to cost using the cost of natural gas ($/kWh).3. Factor in operational costs to maintain the equipment.

- Compare costs and determine the better option

Compare the total costs from Step 5 for both options. The option with the lower cost will be the preferable choice for the factory.

Key concepts

Boiler Systems

Boiler systems are central components in steam power systems. They generate steam by applying heat energy to water, usually through the combustion of a fuel, such as natural gas.
This steam is used to both generate electricity and supply thermal energy for various processes. In our two options:

• Option 1: A single boiler is used to create high-pressure, high-temperature steam at 2.0 MPa and 320°C, which is then used in a turbine and to meet additional steam requirements.
• Option 2: Two boilers are used. One generates the same high-pressure steam for the turbine, and another separate boiler generates lower pressure steam at 107°C.

This segregation can impact efficiency, fuel consumption, and overall system costs, which will be elaborated on in further sections.

Steam Turbine

The steam turbine is a device that converts thermal energy of steam into mechanical energy, which is then used to generate electricity. In our context:
The high-pressure steam generated by the boiler expands through the turbine, performing work and producing electricity. In Option 1:

• Steam at 2.0 MPa and 320°C enters the turbine, expands, and performs work.
• A portion of this steam is extracted at 107°C to meet additional factory needs.
• The remaining steam continues to expand until it exits to a condenser at 0.007 MPa.

In Option 2:

• Steam at 2.0 MPa and 320°C enters the turbine, expands fully and exits to the condenser.
• A separate process boiler generates steam at 107°C to meet the factory's additional needs.

This setup affects efficiency and resource allocation, dependent largely on the turbine and boiler performance together.

Energy Balance

Energy balance is essential for evaluating steam power systems. It ensures that the energy input (fuel) matches the energy output (electricity and steam). In our exercise:
We apply energy balance equations to analyze the performance of the system. For Option 1:

• Calculate the enthalpy change of the steam as it moves through different states within the turbine.
• Apply mass and energy balance equations to determine fuel consumption.

For Option 2:

• Perform similar calculations for the turbine.
• Additionally, calculate energy requirements and fuel consumption for the separate process steam boiler.

Overall, energy balance helps us quantify and optimize the use of fuel and other resources within the system.

Enthalpy Calculations

Enthalpy calculations involve determining the energy content of steam at various states and are fundamental for energy balance. In our analysis:
We utilize steam tables to find the enthalpy values. For option 1, we find:

• Enthalpy at 2.0 MPa, 320°C (initial state).
• Enthalpy at 0.007 MPa (final state).

We also determine the enthalpy at the extraction point (107°C). For option 2:

• Similarly, calculate the enthalpy for steam at 2.0 MPa, 320°C for the turbine.
• Additionally, find the enthalpy for steam generated by the separate process boiler at 107°C.

These enthalpy values allow us to apply the energy balance equations effectively and determine the performance and efficiency of the system.

Fuel Consumption Analysis

Fuel consumption analysis is crucial for evaluating the cost and efficiency of steam power systems. The analysis involves determining the amount of fuel required to generate the necessary steam and electricity. In our two options:
We consider a 20% excess air for combustion, ensuring complete combustion of natural gas. For Option 1:

• Calculate the fuel required based on the energy needed to produce steam at 2.0 MPa and 320°C and to meet additional steam requirements.

For Option 2:

• Separate calculations are performed for the high-pressure steam boiler (for the turbine) and the process steam boiler (at 107°C).

We then determine the total annual energy consumption, convert it to cost using the cost of natural gas, and consider operational costs. The option with lower fuel consumption and operational costs is more economically viable.