Hydrogen is considered to be a key element in the energy transition. This molecule is the most notable option for the decarbonisation of hard-to-abate sectors like transport, heavy industry, and the chemical industry. The storage, transport, and distribution of hydrogen requires equipment like compressors, piping, and pressure vessels. In many parts of the world, this equipment is currently in use for the storage, transportation, and distribution of natural gas.

However, changing a natural gas compression plant to hydrogen introduces a number of challenges that need to be accounted for. The implications of such changes have been investigated by A. Eijk in his EFRC conference paper *“Effect on Pulsation and Vibration Measures when Adjusting a Natural Gas System to Hydrogen Mixtures”*.

This article explores an equivalent case study for a typical gas compression station. Using BOSpulse, our in-house pulsation analysis software, we take a look at the expected difference for a compressor with a simple pulsation bottle when converting from natural gas to hydrogen.

The modifications required to make this system effective for hydrogen are due to the shift in resonant frequencies, caused by hydrogen’s lower density compared to natural gas. Because of the shifting of the resonance frequencies, a pulsation study is necessary to ensure the system is suited for the use of hydrogen.

## Pulsation Analysis In Compressors: Natural Gas vs. Hydrogen

To examine the challenges of converting a natural gas compression plant to hydrogen we focus on analysing the pulsations created by a reciprocating compressor when using both natural gas and hydrogen.

The main difference between natural gas and hydrogen is the difference in density. The density of a gas mixture scales linearly with the molar mass under the same pressure and temperature conditions. Based on **the ideal gas law**, the formula for density is given in Equation 1. At the same temperature and pressure, natural gas can be almost 10 times denser than hydrogen.

**Equation 1**

In which ρ is the density in kg/m^{3}, *M *is the molecular weight in kg/mol, *P *is the pressure in bar, *R *is the universal gas constant in J/mol/K, and *T* is the temperature in K. The speed of sound, which can be computed with Equation 2, is inversely proportional to the square root of the molar mass. The density of a gas therefore has a big influence on the speed of sound.

**Equation 2**

Here, *a *is the speed of sound in m/s, ρ is the density in kg/m^{3}, *P *is the pressure in bar, *R *is the universal gas constant in J/mol/K, γ is the isentropic constant, *Z* is the compressibility factor, *T* is the temperature in K and *M* is the molecular weight in kg/mol. Natural gas is primarily composed of methane, but it also contains a variety of other gases in smaller amounts. The difference in molar mass of the various molecules in the gas mixture allows for the speed of sound to vary about 10%, depending on the exact composition of the natural gas. **By introducing hydrogen to natural gas, the speed of sound can be changed by up to 300%.** The speed of sound as a function of hydrogen percentage in a Natural gas-hydrogen mixture is indicated in Figure 1 below.

**Figure 1 | The wave speed strongly depends on the composition of the gas.**

Pressure waves resulting from reciprocating compressors (or other reciprocating equipment) travel at the speed of sound and therefore will be significantly affected with a change in gas composition. The wavelength and frequency relationship of a pressure wave is given by Equation 3.

**Equation 3**

Where *λ* is the wavelength in m, *a* the speed of sound in m/s and *f* is the frequency in Hz. Acoustic resonance happens when a standing wave is present in a pipe segment. Standing waves can exist within a piping system when the length of a pipe segment matches with a ¼-wave or ½-wave, depending on whether the edges of the pipe segment should be considered as open or closed ends. The difference between ¼-waves or ½-waves is shown in Figure 2.

###### Open-Closed System

###### Open-Open System (or Closed-Closed)

**Figure 2 | Pressure pulsations in an open-closed system (left) and an open-open system (right).**

These waves are described by the following equations:

**Equation 4**

**Equation 5**

Where *f* is the resonant frequency in Hz, k is an integer indicating the harmonic sequence, *a* is the speed of sound in m/s and *L* is the length of pipe in m. Note that Equation 4 represents the resonant frequencies for an open-open system, while Equation 5 gives the resonant frequency for an open-closed system. Looking at the equation, it is clear that if the speed of sound triples, the resonant frequency of the system triples too for an element of the same length and for the same harmonic *k*.

## Pulsation Damper Design

The differences between a natural gas system and a hydrogen system will be demonstrated with some examples made in BOSPulse, a software package produced by Dynaflow Research Group (DRG) to analyse pressure pulsations. Beyond the analysed case, attention should be paid to the operating conditions of the piping after the compressor, as the temperature changes the speed of sound and thereby the pressure pulsation scenario of the model.

### Resonance Frequency

The most straightforward set-up consists of a simple bottle with a length of 1 m and a diameter of 700 mm, which connects a 120 mm diameter, 320 mm long pipe on one side, and a similar 2 m long pipe on the other side. The short pipe on the inlet of the bottle resembles the general recommendation to have the pulsation bottle as close to the compressor as possible. Equation 4 and 5 explain why: with a short length, the excitation frequency is as high as possible. Usually, the base frequency of a compressor is lower, which creates a large bandwidth that ensures safe operations. A harmonic flow boundary condition is applied at the start of the short pipe. The frequency is varied from 1 Hz to 1500Hz to capture the first few harmonics. The other end contains a non-reflecting boundary condition to prevent any reflections flowing back into the system from that side, which would model a long transport line.

The first pipe section up to the bottle is an **open-closed system**, which means the resonance frequencies are and shown on the left in Figure 2. For natural gas, with a wave speed of 395 m/s, the first harmonic is expected at 309 Hz and the second harmonic at 926 Hz. When the system is filled with pure hydrogen instead, the wave speed of the pressure pulsations is increased to 1322 m/s, which is 3.34x higher. The first two harmonics are then found at a frequency of 1033 Hz and 3098 Hz. The peaks can be clearly seen in the frequency spectrum in Figure 3.

Overall, the higher acoustic resonance frequencies are a positive effect of using hydrogen, because the acoustic resonance frequencies are more likely to be separated from the structural natural frequencies.

**Figure 3 | The resonance frequencies for the simple bottle system for natural gas or hydrogen.**

### Transmission Loss

The transmission loss *TL* over the bottle is used to check how much the pulsation is reduced by the system for each frequency. It is a measure for the amount of damping. A higher value of *TL* means a larger reduction of pulsations. *TL* is found using the equation below for each frequency, where P_{inc} is the incident pulsation, and P_{trans} is the transmitted pulsation after the bottle.

**Equation 6**

Figure 4 is obtained for the case of either pure hydrogen or pure natural gas. For most frequencies, the pulsations are effectively damped. At some frequencies, namely those corresponding with the ¼-wave between the boundary condition and the bottle inlet, and the ½-wave between the bottle ends, acoustic modes exist. At the frequencies of these modes, the pulsation bottle damping is reduced and, in some cases, the incoming pulsations are even amplified. During a pulsation study, the length and volume of a pulsation bottle will be sized to ensure effective damping at the relevant excitation frequencies.

When a compressor system is run with a different gas composition, this will have an effect on the frequencies for which the bottle is designed to dampen. **There is a high likelyhood that a bottle designed for natural gas would not function properly for hydrogen.**

**Figure 4 | The transmission loss over the pulsation bottle for natural gas and pure hydrogen.**

### Bottle Sizing According To API 618

Compressor systems are assessed according to the API 618 code. It prescribes equations for the preliminary sizing of pulsation bottles:

**Equation 7**

**Equation 8**

Where V_{s} is the minimum volume of the pulsation bottle on the suction side and V_{d} on the discharge side. k is the mean isentropic exponent, Ts is the suction temperature, *M* is the molar mass, *PD* is the displaced volume per revolution, and *r* is the stage pressure ratio at the cylinder flanges. These equations give an indication of the different required bottle size depending on the gas. The molar mass of hydrogen is approx. 9 times smaller than the molar mass of natural gas. The equations show that if the molar mass is 9 times smaller, the volume should be 1.7 times larger (∜9).

### Allowable pulsation level according to API 618

The API 618 code also prescribes the allowable pulsation levels for the pipe system at a certain frequency:

**Equation 9**

in which *P _{all} *is the allowable pulsation level, expressed as a percentage,

*P*is the mean static pressure in bar,

_{L}*D*is the inner pipe diameter in millimeters,

*f*is the pulsation frequency of the compressor in Hz and

*c*is the wave speed in m/s. If a natural gas system was converted to hydrogen, keeping the same compressor setup and running speed, this would lead to higher allowable pulsation levels due to the change in wave speed. This can be explained by the fact that gasses with higher wave speeds have a larger wave length, which will lead to lower unbalanced forces on the pipe segments. Due to the fact that the pressure nodes and antinodes are spaced further apart, the pressure changes will occur over larger distances, hence the local pressure differences and unbalanced forces are smaller compared to a gas with a low wave speed.

### Compressor Sizing And Structural Integrity

**Compressor sizing:**hydrogen systems will likely have different demands for flow rates and pressures. Different sized compressors, or compressors operating at different running speeds will require new pulsation studies to be performed.**Structural integrity:**hydrogen is known to cause embrittlement of materials, especially in metals. This effect becomes stronger when operating at higher pressures. Only some pipe materials are suitable for use with hydrogen.

## Conclusions

We have seen that it is not so straightforward to operate a compressor system with hydrogen while it was originally designed for natural gas. Generally, the switch to hydrogen will always require for some design changes to be made to the compressor set-up. To summarise, below are the most important implications of the change in gas we encountered during this case study.

**The resonance frequency of hydrogen is about three times as high compared to natural gas.** When the compressor system is largely reused, the structural natural frequencies will not change much, which is beneficial, as the distance between the structural natural frequencies and the resonance frequencies is larger, hence the risk of any interference is reduced.

**The higher resonance frequency is primarily caused by the higher wave speed of hydrogen**. This also drives the allowable pulsation level according to the API 618 design code. Given that the compressor runs at the same speed and the line pressure is the same, hydrogen will lead to a higher allowable pulsation level.

**Another point of attention is the design of the pulsation bottle.** It has been shown that the transmission loss over the bottle shows a totally different behavior. Operating an existing system with a different gas without conducting a new pulsation analysis can be a risky undertaking. Resonance might occur in the pulsation bottle, which causes it to do the exact opposite of what it is designed for: amplification of the pulsation signal. This could damage downstream equipment and must be prevented at all costs.

At Dynaflow we think there are many opportunities for using existing compressor facilities for hydrogen. Instead of starting from scratch and needing to develop an entirely new compressor, it is much easier to make small adaptations to an existing proven design. It is however of utmost importance to always conduct a new pulsation analysis to ensure the trustworthiness of your equipment.

*Authors: Thijs Krijger, Senior Engineer and Thijs van Lith, Engineer at Dynaflow Research Group*