Problem 6.2

Problem 6.2#

Integrated Energy Grids

Problem 6.2

Let us assume that the countries in Problem 6.1 are considering repurposing their methane gas network into a hydrogen network. In order to run the existing pipelines with hydrogen, the pressure needs to be reduced to \(P\)=40 bar, and the average flow velocity can be increased to \(u\) = 30 m/s. Calculate the capacity of every pipeline (in MW), and relative to their initial design when they transported methane gas.

The energy content of \(H_2\) is 120 GJ/tonne. To calculate the speed of sound in hydrogen \(c\), assume the universal gas constant \(R\)=8.314 J/molK, the molar mass of hydrogen \(M\)=2 g/mol, compression factor \(Z\)=1.03, and temperature T=25\(^{\circ}\)C.

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.

Then install the following packages by executing the following command in a Jupyter cell at the top of the notebook.

!pip install numpy

import numpy as np

For methane, the cross-sectional area \(A\) and the speed of sound in gas \(c\) can be calculated as

D = 0.6 # m
u = 15 # m/s
P = 50*100000 #Pa
Z = 1.31
R = 8.314 # J/molK
M = 0.016 # Kg/mol
T = 273+25 # K
e = 50 # GJ/t or MJ/kg

A = np.pi*(D/2)**2
c=np.sqrt(Z*R*T/M)
c

np.float64(450.3900615022494)

The density can be calculated as

rho = P / c**2
rho

np.float64(24.648608512719843)

The capacity of every pipeline can be calculated as \(Q = \rho A u e\)

capacity_CH4 = rho*A*u*e
capacity_CH4

np.float64(5226.922401172076)

So, we obtain that the capacity is aproximately 5.2 GW

For hydrogen, the speed of sound in gas \(c\) can be calculated as

D = 0.6 # m
u_H2 = 30 # m/s
P_H2 = 40*100000 #Pa
Z = 1.03
R = 8.314 # J/molK
M = 0.002 # Kg/mol
T = 273+25 # K
e_H2 = 120 # GJ/t or MJ/kg

c_H2=np.sqrt(Z*R*T/M)
c_H2

np.float64(1129.5793818939862)

The density can be calculated as

rho_H2 = P_H2 / c_H2**2
rho_H2

np.float64(3.1349201118119416)

The new capacity of every pipeline can be calculated as \(Q = \rho A u e\)

capacity_H2 = rho_H2*A*u_H2*e_H2
capacity_H2

np.float64(3190.9600056864097)

capacity_H2/capacity_CH4

np.float64(0.610485436893204)

Even though the volumetric energy density for hydrogen is three times lower than that of methane, since the velocity in the pipelines is higher, the transport capacity for hydrogen is only reduced to 60% of that of methane.

(rho_H2*e_H2)/(rho*e)

np.float64(0.30524271844660195)