Question

A steam boiler drum produces steam at a mass flow rate of \(64 \mathrm{~kg} \cdot \mathrm{s}^{-1}\) at 60 bar. This stream still contains \(2 \mathrm{wt} \%\) moisture. The feedwater from the economizer (a heat exchanger) is fed to the drum at a mass flow rate of \(62 \mathrm{~kg} \cdot \mathrm{s}^{-1}\). It contains \(3 \mathrm{ppm}_{\mathrm{w}}\) solids. Makeup water, containing \(50 \mathrm{ppm}_{\mathrm{w}}\) solids, is also fed into the drum at a mass flow rate of \(2 \mathrm{~kg} \cdot \mathrm{s}^{-1}\). Steam production is such that the solid content of the moisture leaving with the steam is \(5 \mathrm{ppm}_{\mathrm{w}}\). Blowdown, which is the release of hot liquid from the bottom of the drum, must keep the concentration of solids in the drum to \(1000 \mathrm{ppm}_{\mathrm{w}}\) - a. Calculate the blowdown requirement in \(\mathrm{kg} \cdot \mathrm{s}^{-1}\). b. Calculate the heat loss associated with blowdown in \(\mathrm{kW}\).

Short answer

In this problem, we analyzed the mass flow rates and the balance of solids in a steam boiler drum. We determined that the blowdown requirement to maintain the proper concentration of solids (1000 ppm) is 182 kg/s. However, we don't have enough information to calculate the exact heat loss associated with blowdown, because the specific enthalpy of the inlet feedwater is not given. The heat loss can be approximated based on the enthalpy difference between the drum and the inlet feedwater if the specific enthalpy of the inlet feedwater was provided.

Step-by-step solution

Mass balance equation

Let's set up mass balance equations for water mass and solid mass. Let \(B\) be the blowdown mass flow rate in \(\mathrm{kg} \cdot \mathrm{s}^{-1}\). The total mass flow into the drum is the sum of feedwater and makeup water, while the mass flow out of the drum is the sum of steam and blowdown: $$ (62+B) \mathrm{~kg} \cdot \mathrm{s}^{-1} = 64 \mathrm{~kg} \cdot \mathrm{s}^{-1} + B $$ Solving this equation for \(B\), we obtain: $$ B = 64 - 62 \Longrightarrow B = 2 \mathrm{~kg} \cdot \mathrm{s}^{-1} $$

Analyze solids balance

Next, analyze the balance of solids in the system to maintain the concentration at 1000 ppm. The solid in the drum is fed by feedwater and makeup water, and leaves through blowdown. Let's set up these equations: $$ (62 \times 3 \times 10^{-6}) + (2 \times 50 \times 10^{-6}) = 2 \times (1000 \times 10^{-6}) + B \times (5 \times 10^{-6}) $$ Now, we know \(B = 2 \mathrm{~kg} \cdot \mathrm{s}^{-1}\), so we can simplify and solve the equation: $$ 0.000186 = 0.002 + 10^{-5}B $$

Calculate blowdown requirement

By rearranging the equation above and solving for \(B\), we find the blowdown requirement: $$ B = \frac{0.000186 - 0.002}{10^{-5}} = 182 \mathrm{~kg} \cdot \mathrm{s}^{-1} $$ Therefore, the blowdown requirement is \(182 \mathrm{~kg} \cdot \mathrm{s}^{-1}\).

Calculate heat loss associated with blowdown

The heat loss associated with the blowdown is given by its mass flow rate multiplied by the specific enthalpy difference between the inlet and outlet. With the conditions given in the problem, we can calculate the specific enthalpy of the blowdown water at 60 bar and assuming the enthalpy of the incoming feedwater is the same as that of the remaining liquid in the drum: $$ Q_{loss} = m_{B} \cdot (h_{out} - h_{in}) $$ Assuming saturated liquid conditions at the outlet, the enthalpy is approximately \(758.4 \mathrm{~kJ} \cdot \mathrm{kg}^{-1}\). Since the specific enthalpy of the inlet feedwater is not given, we can assume that it is much lower than the one at the outlet due to the temperature difference. The heat loss can now be calculated: $$ Q_{loss} = 182 \times (758.4 - h_{in})\mathrm{~kW} $$ We don't have enough information to find the exact heat loss in \(\mathrm{kW}\), but it can be approximated based on the enthalpy difference between the drum and the inlet feedwater if it were given.

Key concepts

Mass Flow Rate in Steam Boilers

Understanding the mass flow rate is crucial for controlling the operation of a steam boiler. The mass flow rate is a measure of the amount of mass moving past a certain point per unit of time, generally expressed in kg/s (kilograms per second). In the context of a steam boiler drum, it's important to balance the mass of steam being produced with the mass of feedwater being supplied.

For a steam boiler, it's essential to maintain this balance to ensure the boiler operates safely and efficiently. If the mass flow rate of steam is higher than the feedwater supply, the boiler may run dry, causing damage. Conversely, if the steam produced is less than the feedwater supply, it can lead to inefficiencies and safety concerns. By using mass balance equations we can find the proper flow rates for different parts of the system, including the makeup water and blowdown, to keep the system running smoothly and avoid these issues.

Blowdown Requirement for Maintaining Water Quality

The blowdown requirement refers to the process of removing a portion of the water from the boiler to manage the concentration of solids or impurities and thus maintain water quality within the drum. A high concentration of solids can lead to issues such as scaling and corrosion, which can affect the efficiency and lifespan of the boiler.

In our exercise, the blowdown is needed to keep the concentration of solids at 1000 ppm, which is an important operational parameter for ensuring the long-term health of the boiler. The calculation requires setting up a solids balance equation and solving for the blowdown rate. This balance takes into account the solids coming in with the feedwater and makeup water, as well as those leaving with the steam and the blowdown itself. Through these calculations, plant operators ensure that the boiler works efficiently without allowing the buildup of impurities that could lead to equipment failure or inefficiency.

Heat Loss Calculation During Blowdown

When discussing heat loss calculation in steam boilers, it involves understanding the energy that is lost during the blowdown process. Blowdown is essentially a double-edged sword; it's necessary for controlling the solid content in the drum, but it also results in a loss of heat energy.

Heat loss occurs because the hot water discharged during blowdown has a high thermal energy compared to cooler feedwater. Calculating this loss involves determining the specific enthalpy (energy per mass) of the blowdown and the feedwater, and then using the mass flow rate of the blowdown. The larger the mass flow rate and the enthalpy difference, the higher the heat loss. Calculations like these are crucial for plant operators as they seek to optimize their processes to minimize energy waste, thereby reducing operating costs and improving environmental outcomes.