Question

A natural gas-fired furnace in a textile plant is used to provide steam at \(130^{\circ} \mathrm{C}\). At times of high demand, the furnace supplies heat to the steam at a rate of \(30 \mathrm{MJ} / \mathrm{s}\). The plant also uses up to \(6 \mathrm{MW}\) of electrical power purchased from the local power company. The plant management is considering converting the existing process plant into a cogeneration plant to meet both their process-heat and power requirements. Your job is to come up with some designs. Designs based on a gas turbine or a steam turbine are to be considered. First decide whether a system based on a gas turbine or a steam turbine will best serve the purpose, considering the cost and the complexity. Then propose your design for the cogeneration plant complete with pressures and temperatures and the mass flow rates. Show that the proposed design meets the power and process-heat requirements of the plant.

Short answer

In summary, a gas turbine-based cogeneration plant is chosen due to lower installation and maintenance costs, better efficiencies, low environmental impact, and quick start-up times. The proposed design includes a gas turbine, a heat recovery steam generator (HRSG), and a generator producing 6 MW of power. The mass flow rates and temperatures are calculated as follows: a natural gas mass flow rate of 0.312 kg/s, a steam mass flow rate of 55.2 kg/s, and a steam temperature of 130°C. These characteristics meet the specified power and process-heat requirements of the plant.

Step-by-step solution

Decide between gas turbine-based or steam turbine-based systems

After considering cost and complexity, we can determine that a gas turbine-based system will be better suited for this cogeneration plant. This is because gas turbines have relatively lower installation and maintenance costs compared to steam turbines, can provide better efficiencies, and also produce a lower environmental impact. Additionally, gas turbine systems have a quicker start-up time compared to steam turbine systems.

Propose a gas turbine-based cogeneration plant design

Since we decided on a gas turbine-based system, our design proposal will consist of the following components: 1. A gas turbine unit that provides mechanical power to generate electricity. 2. A heat recovery steam generator (HRSG) to supply steam at \(130^{\circ} \mathrm{C}\) to the process plant using the exhaust heat from the gas turbine. 3. A generator coupled to the gas turbine to produce electrical power. The proposed design involves injecting natural gas into the gas turbine's combustion chamber, where it is mixed with air and combusted. The high-temperature, high-pressure exhaust gases then drive the turbine, which is connected to the generator to produce \(6 \mathrm{MW}\) of electrical power. The hot exhaust gases from the gas turbine are channeled into the HRSG to produce steam at the required temperature of \(130^{\circ} \mathrm{C}\) for the process plant. The amount of heat extracted from the gas turbine exhaust will be adjusted to produce the \(30 \mathrm{MJ} / \mathrm{s}\) required heat for the steam.

Calculation of mass flow rates, pressures, and temperatures

To determine if the proposed design meets the power and process-heat requirements of the plant, we need to calculate the mass flow rates, pressures, and temperatures. We consider the following as given: 1. Power required: \(6 \mathrm{MW}\) 2. Process-heat rate: \(30 \mathrm{MJ} / \mathrm{s}\) First, let's calculate the gas mass flow rate through the gas turbine. To do this, let's consider an overall efficiency \(\eta\) of the gas turbine (including electrical conversion efficiency) to be around \(35\%\). Then, to produce \(6 \mathrm{MW}\) of power, the heat input required is: $$\frac{6 \mathrm{MW}}{\eta} = \frac{6 \times 10^6 \mathrm{W}}{0.35} = 17.14 \times 10^6 \mathrm{W}$$ Assuming that natural gas has a heating value of around \(55 \mathrm{MJ} / \mathrm{kg}\), the mass flow rate of natural gas needed would be: $$\frac{17.14 \times 10^6 \mathrm{W}}{55 \times 10^6 \mathrm{J} / \mathrm{kg}} = 0.312\;\mathrm{kg} / \mathrm{s}$$ Now, let's calculate the mass flow rate of steam required to supply the \(30 \mathrm{MJ} / \mathrm{s}\) demand: Assuming the heat capacity of water is approximately \(4.18 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}\), and the difference in temperature between the input and output of the HRSG (which is the process-heat requirement) is \(130^{\circ} \mathrm{C}\). Then, the mass flow rate of steam needed would be: $$\frac{30 \times 10^6 \mathrm{J} / \mathrm{s}}{4.18 \times 10^3 \mathrm{J} / \mathrm{kg} \cdot \mathrm{K} \times 130 \mathrm{K}} = \frac{30 \times 10^6 \mathrm{J} / \mathrm{s}}{543.4 \times 10^3 \mathrm{J} / \mathrm{kg}} = 55.2\;\mathrm{kg} / \mathrm{s}$$ As a result, our proposed gas turbine-based cogeneration plant design has the following mass flow rates and temperatures: 1. Natural gas mass flow rate: \(0.312\;\mathrm{kg} / \mathrm{s}\) 2. Steam mass flow rate: \(55.2\;\mathrm{kg} / \mathrm{s}\) 3. Steam temperature: \(130^{\circ} \mathrm{C}\) These calculations show that the proposed design meets the power and process-heat requirements of the plant, thereby serving as a suitable solution in this scenario.