Problem 7.2

Integrated Energy Grids

Problem 7.2

Note: This problem is similar to 7.1 but now it assumes that the mass flow in the district heating network is variable.

A district heating system is used to transport heat generated using a heat pump to two distant buildings. The pipeline diameter is 0.5 m, the supply temperature is \(T^S\)=80\(^{\circ}\)C and the return temperature is \(T^R\)=40\(^{\circ}\)C. Assume the mass flow to be constant and that the heat losses in the pipelines due to dissipation to the ambient can be neglected.

The heat transfer coefficient of building A is \(U_A\) = 2 MW/k, the heat transfer coefficient of building B is \(U_B\) = 3 MW/k, the ambient temperature is 5\(^{\circ}\)C and the interior comfort temperature of the buildings must be 20\(^{\circ}\)C.

Calculate the mass flow needed at the heat exchanger that serves every building, assuming that the input and output temperature correspond to \(T^S\) and \(T^R\).

Note

If you have not yet set up Python on your computer, you can execute this tutorial in your browser via Google Colab. Click on the rocket in the top right corner and launch “Colab”. If that doesn’t work download the .ipynb file and import it in Google Colab.

import numpy as np

We can calculate the rate of heat extracted in every building as

\(q_{A,B}=U_{A,B}(T_{indoor}-T_{ambient})\)

T_ind = 20 #C
T_amb = 5 #C
U_A = 2 # MW/K
U_B = 3 # MW/K

q_A = U_A*(T_ind-T_amb)
q_B = U_B*(T_ind-T_amb)
print(str(q_A) + " MW are extracted in building A.")
print(str(q_B) + " MW are extracted in building B.")

30 MW are extracted in building A.
45 MW are extracted in building B.

If we apply the energy nodal balance to the two buildings

\(q_{buildingA}=c_pm_A(T^S-T^R)\)

\(q_{buildingB}=c_pm_B(T^S-T^R)\)

The mass flow can be estimated as

c_p = 4186 #J/kgK
T_S = 80 #C
T_R = 40 #C

m_A=q_A*1000000/(c_p*(T_S-T_R))  # MW -> W
m_B=q_B*1000000/(c_p*(T_S-T_R))  # MW -> W

print("Required mass flow in heat exchanger in building A: " + str(round(m_A,1)) + "kg/s")
print("Required mass flow in heat exchanger in building B: " + str(round(m_B,1)) + "kg/s")

Required mass flow in heat exchanger in building A: 179.2kg/s
Required mass flow in heat exchanger in building B: 268.8kg/s