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A liquefied natural gas (LNG) regasification facility utilizes a vertical heat exchanger or vaporizer that consists of a shell with a single-pass tube bundle used to convert the fuel to its vapor form for subsequent delivery through a land-based pipeline. Pressurized LNG is off-loaded from an oceangoing tanker to the bottom of the vaporizer at \(T_{c, i}=-155^{\circ} \mathrm{C}\) and \(\dot{m}_{\mathrm{LNG}}=150 \mathrm{~kg} / \mathrm{s}\) and flows through the shell. The pressurized LNG has a vaporization temperature of \(T_{f}=-75^{\circ} \mathrm{C}\) and specific heat \(c_{p l}=4200 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\). The specific heat of the vaporized natural gas is \(c_{p, v}=2210 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\) while the gas has a latent heat of vaporization of \(h_{f g}=575 \mathrm{~kJ} / \mathrm{kg}\). The LNG is heated with seawater flowing through the tubes, also introduced at the bottom of the vaporizer, that is available at \(T_{h, i}=20^{\circ} \mathrm{C}\) with a specific heat of \(c_{\mu \mathrm{Sw}}=3985 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\). If the gas is to leave the vaporizer at \(T_{c o}=8^{\circ} \mathrm{C}\) and the seawater is to exit the device at \(T_{\text {hot }}=10^{\circ} \mathrm{C}\), determine the required vaporizer heat transfer area. Hint: Divide the vaporizer into three sections, as shown in the schematic, with \(U_{\mathrm{A}}=150 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), \(U_{\mathrm{B}}=260 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), and \(U_{\mathrm{C}}=40 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\).

Step by step solution

01

Calculate the heat required for each section of the vaporizer

To find the required heat transfer area, we need to determine the amount of heat that would be transferred in each section of the vaporizer. We can calculate this by using the mass flow rate, specific heat values, and the temperature differences. Section A: Heating the LNG from -155°C to -75°C \(Q_A = \dot{m}_{LNG} \cdot c_{pl} \cdot (T_f - T_{c,i})\) Section B: Vaporizing the LNG \(Q_B = \dot{m}_{LNG} \cdot h_{fg}\) Section C: Heating the vaporized gas to the desired exit temperature \(Q_C = \dot{m}_{LNG} \cdot c_{pv} \cdot (T_{co} - T_f)\)

02

Calculate the heat capacity rate for the seawater

Now, we have to find the heat capacity rate of the seawater, which is the product of the mass flow rate of seawater and its specific heat. \(\dot{C}_{Sw} = \dot{m}_{Sw} \cdot c_{pSw}\)

03

Calculate the mass flow rate of seawater

Since the seawater is the heating medium, the heat transferred to the LNG and vapor must equal the heat absorbed by the seawater. We can use this fact to determine the mass flow rate of seawater. \(Q_A + Q_B + Q_C = \dot{C}_{Sw} \cdot (T_{hot} - T_{h,i})\) Solve for \(\dot{m}_{Sw}\)

04

Calculate the logarithmic mean temperature difference (LMTD) for each section

LMTD is used to characterize the average temperature difference between the hot and cold fluids in the heat exchanger for each section. LMTD for Section A: \(T_{h,i-A} = T_{h,i}\) \(T_{c,i-A} = T_{c,i}\) \(T_{h,o-A} = T_{h,i} - Q_A/\dot{C}_{Sw}\) \(T_{c,o-A} = T_f\) \( \Delta T_{lm-A} = \frac{(T_{h,i-A} - T_{c,o-A}) - (T_{h,o-A} - T_{c,i-A})}{\ln[(T_{h,i-A} - T_{c,o-A})/(T_{h,o-A} - T_{c,i-A})]}\) LMTD for Section B: \(T_{h,i-B} = T_{h,o-A}\) \(T_{c,i-B} = T_f\) \(T_{h,o-B} = T_{h,i-B} - Q_B/\dot{C}_{Sw}\) \(T_{c,o-B} = T_f\) \( \Delta T_{lm-B} = \frac{(T_{h,i-B} - T_{c,o-B}) - (T_{h,o-B} - T_{c,i-B})}{\ln[(T_{h,i-B} - T_{c,o-B})/(T_{h,o-B} - T_{c,i-B})]}\) LMTD for Section C: \(T_{h,i-C} = T_{h,o-B}\) \(T_{c,i-C} = T_f\) \(T_{h,o-C} = T_{hot}\) \(T_{c,o-C} = T_{co}\) \( \Delta T_{lm-C} = \frac{(T_{h,i-C} - T_{c,o-C}) - (T_{h,o-C} - T_{c,i-C})}{\ln[(T_{h,i-C} - T_{c,o-C})/(T_{h,o-C} - T_{c,i-C})]}\)

05

Calculate the required heat transfer area for each section

With the overall heat transfer coefficients (U) and LMTD calculated in previous steps, we can calculate the required heat transfer area for each section of the vaporizer using the equation: \(A = \frac{Q}{U \cdot \Delta T_{lm}}\) \(A_A = \frac{Q_A}{U_A \cdot \Delta T_{lm-A}}\) \(A_B = \frac{Q_B}{U_B \cdot \Delta T_{lm-B}}\) \(A_C = \frac{Q_C}{U_C \cdot \Delta T_{lm-C}}\)

06

Calculate the total heat transfer area

Finally, sum up the heat transfer areas of the three sections to find the total heat transfer area required for the vaporizer. \(A_{total} = A_A + A_B + A_C\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

LNG Regasification

Liquefied natural gas (LNG) regasification is the process of converting LNG back into its gaseous state for use or transportation. During this process, LNG is typically warmed and vaporized in a device called a vaporizer or heat exchanger. This involves transferring heat from a warmer fluid, often seawater in coastal facilities, to the cold LNG.

This heat exchange is crucial because LNG is stored at extremely low temperatures, around -160°C, to keep it in liquid form and minimize volume for transport. By regasifying LNG, it becomes feasible to transport natural gas through pipelines to reach users who need it for residential, industrial, or commercial energy consumption.

Understanding LNG regasification is key for the wider distribution of natural gas, a cleaner-burning fossil fuel relative to coal and oil.

Heat Transfer Area

The heat transfer area is one of the most important aspects of designing a heat exchanger, such as the one used in LNG regasification. It determines the surface over which heat exchange occurs between two fluids at different temperatures. For LNG vaporizers, this is where the colder LNG receives heat from the warmer seawater to transform from liquid to gas.

Calculating the heat transfer area involves understanding how much heat needs to be transferred. This is calculated based on the mass flow rate of the LNG, its specific heat capacities, and the temperature difference it must overcome.

A larger heat transfer area can handle larger quantities of heat transfer, which is crucial in efficiently regasifying LNG at high flow rates.

Hence, optimizing the heat transfer area is vital for ensuring that the LNG can be efficiently converted while ensuring the vaporizer operates well within its design parameters.

Logarithmic Mean Temperature Difference (LMTD)

The Logarithmic Mean Temperature Difference (LMTD) is a key calculation in designing efficient heat exchangers. It serves as a simplified method to estimate the thermal driving force needed for heat exchange processes.

LMTD considers both the inlet and outlet temperatures of the hot and cold fluids and provides a mean temperature difference that fuels the heat exchange. It's important because the temperature differences aren't always linear, especially in counterflow or cross-flow heat exchangers.

By using LMTD, engineers can design heat exchangers, like those used in LNG regasification, more effectively. The heat exchanger's size and efficiency are directly influenced by this value, making it pivotal in determining how much heat can be effectively transferred.

An accurate LMTD ensures optimized regasification rates, aligning with operational needs while minimizing energy wastage.

Overall Heat Transfer Coefficient

The overall heat transfer coefficient (U) is another essential parameter in the design and operation of heat exchangers. It represents the heat transfer ability of the materials and configurations used in the exchanger, accounting for all forms of resistance to heat flow.

This coefficient includes the conductance of the heat exchanger materials, the resistance offered by the boundary layers of the fluids, and any fouling factors that might reduce heat transfer efficiency.

In an LNG regasification context, U values can vary for different sections of the vaporizer, reflecting changes in structure or material optimal for either phase of LNG. For example, U might be higher in areas where vaporization requires more intense heat exchange conditions.

Optimizing the overall heat transfer coefficient enhances the performance and energy efficiency of the heat exchanger, ensuring maximum conversion with minimal energy input.