Problem 7.1

Problem 7.1#

Integrated Energy Grids

Problem 7.1

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 water velocity is 2 m/s, the supply temperature \(T^S\) is variable through the network 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.

a) Calculate the rate of heat extracted in every building.

b) Calculate the input and output temperature at the heat xxchanger that serves every building.

c) Calculate the supply temperature required for the water flow supplied by the heat pump.

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.

b) Calculate the input and output temperature at the Heat Exchanger that serves every building.

If we apply the energy nodal balance to every node in the network

\(q_{heatpump}=c_pm(T^S-T^{R})\)

\(q_{buildingA}=c_pm(T^S-T^{2})\)

\(q_{buildingB}=c_pm(T^{2}-T^{R})\)

The mass flow can be estimated as

\(m=\rho u A\)

rho = 1000 # kg/m3
velocity = 2 # m/s
d = 0.5 # m
c_p = 4186 #J/kgK
u = 2 #m/s
T_R= 40 #C

A =np.pi*(d/2)**2
m = rho*u*A
m

392.6990816987241

T_2=T_R + q_B*1000000/(c_p*m)
T_S=T_2 + q_A*1000000/(c_p*m)
print("Building B: input temperature: " + str(round(T_2,1)) + "C, output temperature : " +str(T_R) + "C")
print("Building A: input temperature: " + str(round(T_S,1)) + "C, output temperature : " +str(round(T_2,1)) + "C")

Building B: input temperature: 67.4C, output temperature : 40C
Building A: input temperature: 85.6C, output temperature : 67.4C

c) Calculate the supply temperature required for the water flow supplied by the heat pump.

Assuming that the heat losses through dissipation in the pipes can be neglected, the heatpump must supply the mass flow at the input temperature of building A.

d) Assuming that the electricity demand required for pumping the water is proportional to the cubic mass flow with a proportionality constant of 0.006 Ws\(^3\)kg\(^{-3}\), calculate its relative size compared to the thermal power supplied by the district heating system

c = 0.006 # Ws^3kg^-3
electricity_demand = c*m**3
relative=electricity_demand/(1000000*(q_A+q_B))

print("Electricity demand represents : " + str(round(relative*100,1)) + " % of thermal energy supply.")

Electricity demand represents : 0.5 % of thermal energy supply.