# Use of Rolling Piston Expanders for Energy Regeneration in Natural Gas Pressure Reduction Stations—Selected Thermodynamic Issues

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## Abstract

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## 1. Introduction

- Very high pressure (1.6 MPa and more),
- High pressure (0.5–1.6 MPa),
- Medium pressure (0.01–0.5 MPa),
- Low pressure (lower than 0.01 MPa).

- Pressure reduction stations, used for reduction and stabilization of gas pressure,
- Pressure reduction and measuring stations, used for reduction and stabilization of gas pressure and measuring of gas properties,
- Measuring stations, used for measuring the gas flow rate or its calorific value,
- Distribution and measuring stations, used for separating the gas stream to at least two output streams and measuring its parameters.

- First stage (high pressure reduction stations), applied in high pressure transmission pipelines, providing the reduction of the gas pressure to ca. 500 kPa,
- Second stage (medium pressure reduction stations) applied in distribution pipelines, providing the reduction of the gas pressure to ca. 10 kPa.

- Low cycle frequency,
- Low specific speed,
- High pressure drops in one stage,
- Low rotational speed (approx. 3000 rev/min),
- Ease of hermetic sealing.

- Internal friction, reducing the efficiency and reliability of the machine,
- Need for lubrication and frequent replacement of wearing parts,
- Large weight in relation to power and efficiency,
- Internal and external leakages reducing expander efficiency.

## 2. The Assembly and Mathematical Description of a Rolling Piston Expander

_{1}, α

_{2}, α

_{3}and α

_{4}(see Figure 2 for details). α

_{1}and α

_{2}are the angles which define the inlet port edges. α

_{3}(also referred as the filling angle [21]), and α

_{4}(also referred as the evacuation angle [21]) are the angles which define the outlet port edges. The proper arrangement of the “steering edges” has a significant influence on the expander operation. This issue is comprehensively described in [21].

_{1}angle (in Figure 2 it is represented by Point B), the volume of the working chamber slightly increases, the inlet valve opens, and the working fluid flows into the working chamber through the radial gap (y) formed between the surfaces of the cylinder and the piston. The rate of pressure increase depends on the width of the radial gap y, the machine rotational speed, and the working fluid thermal properties, namely the pressure (p

_{s}) and temperature (T

_{s}) at the expander inlet. When piston reaches the position defined by the α

_{2}angle (in Figure 2 it is represented with Point G) the inlet port is fully opened to the working chamber. During further counter-clockwise piston movement, the filling of the working chamber continues. The filling of the working chamber ends when the inlet valve closes (typically when the piston reaches the position defined by the angle ϕ = π/3 [20,21]). In Figure 4 it is represented by Point 2. At this stage a portion of the working fluid is still enclosed within the working chamber. During further counter-clockwise piston movement, the working chamber increases its volume, and the gas is expanded. The expansion ends when the piston reaches the position defined by the α

_{3}angle (in Figure 2 it is represented with Point D, and in Figure 4 with Point 3). The working cycle proceeds, and when the piston reaches the position defined by the angle ϕ = 2π + α

_{1}, the inlet valve opens again. The second working chamber is filled with working fluid flowing through the inlet port. When the piston reaches the position defined by the angle ϕ = 2π + α

_{2}, the outlet valve opens and the evacuation of the gas enclosed in the first working chamber starts (in Figure 4 it is represented by Point 4). The evacuation proceeds simultaneously with the expansion of the working fluid in the second working chamber, and ends when the piston reaches the position defined by the angle ϕ = 4π − α

_{4}(in Figure 4 it is represented by Point 5). The outlet valve closes at this point. During further counter-clockwise piston movement, the residual working fluid (remained in the first working chamber after the evacuation) is compressed (see process 5–1 in Figure 4). The expansion of the working fluid in the second working chamber ends when the piston reaches the position defined by the angle ϕ = 4π (i.e., after two full revolutions). The expander working cycle is completed at this point.

_{w}and the variable piston radius-vector ρ

_{w}. While ψ is the angle between ρ

_{w}and the vane vertical axis. The length of ρ

_{w}changes with the changing piston position and can be described by the equation:

_{ABC}(ϕ) is a cross sectional area of the working chamber. The cross sectional area can be determined using the calculation procedure valid for multi-vane expanders. This procedure is comprehensively described in [14,21].

_{k}(ϕ

_{u}) is a function dependent only on construction parameters and the chamber position:

_{ABC}(ϕ) (see Figure 5a) the cross section area can be described by the equation:

_{ABD}(ϕ) cross sectional area can be calculated similarly to A

_{ABC}(ϕ) if ϕ < π (see Figure 5b). The position of the working chamber is described by the angle ϕ

_{u}= π, the angle of vane inclination to the piston radius is ψ

_{u}, and the angle between point B and point C is λ

_{u}(see Figure 5b). The additional parameters can be described by Equations (10)–(12):

## 3. Modeling Methods and Results

- Eccentricity e,
- Length of the cylinder L,
- Expansion ratio σ = p
_{s}/p_{d}, - Polytropic exponent m.

_{CH4}= 518.33 J/(kg K)). Additionally, it was assumed that clearance volume is equal to zero and pressure fluctuations at the inlet and outlet, caused by valves inertness, are negligible and can be omitted. In each case, the pressure at the outlet was held constant and set to p

_{d}= 500 kPa, while rotational speed was equal to n = 3000 rpm.

_{max}twice in a one cycle. The volume increases with increasing rotor rotation angle according to an S-shaped curve. With increasing eccentricity, the volume greatly increases, and in the middle range of the half-cycle, linear growth is observed.

_{s}to a minimal temperature T

_{min}after expansion. It can be seen that in Figure 9, T

_{s}was very high and increased with increasing m. This temperature resulted from heat input that had to be provided to the working fluid before the expansion started. Heating was necessary in order to heat up the working fluid to the temperature T

_{s}for which the temperature of the working fluid after expansion would be higher than the limiting temperature T

_{min}. This was done in order to prevent hydrate formation in the gas [2]. During all calculations, T

_{min}was set to 274 K. In T-chart heat is the area under the T-curve, and it was observed that with increasing m, the heat necessary for heating the working fluid increased as well.

_{min}at Point 3. This process is represented by successive points 1–2–3 in Figure 14. The area under the curve from Point 1 to 2 represents heat q that has to be provided to the gas during isobaric heating, when a rolling piston is used.

_{t}

_{2–3}to heat input, and is expressed as follows

_{d}, with increasing inlet pressure p

_{s}, PRF decreases. This means, that for higher inlet pressures, temperature at Point 2 strongly increases, and thus heat input is higher. For very high pressures (σ ≥ 8), usage of the rolling piston is justified only for m ≤ 1.4. For processes close to adiabatic conditions (m → k) PRF increases. One can see that for low expansion ratios (σ = 2) and a small polytropic exponent (m < 1.4), almost 60% of work can be recovered.

## 4. Summary and Conclusions

- Rolling pistons expanders feature important advantages, i.e., a very simple design, suitability for wet gas conditions, negligible clearance volume and ease of gas-tight sealing, making them especially promising for natural gas pressure reduction processes.
- The results of first experiments on a small power ORC system adopting the rolling piston expander [17] proved that it is possible to feed the rolling piston expander using low-boiling working fluid instead of air.
- The modeling results showed that for very low polytropic exponents, the power of the rolling piston expander fed by natural gas hardly depended on the expansion ratio and increased with increasing expansion ratio and polytropic exponents.
- For the range of parameters studied, the modeled power output of the rolling piston expander (having a cylinder radius of 0.15 m) varied in the range of 0.1–1.0 MW.
- The results of the analysis performed using the novel PRF coefficient have shown that the use of a rolling piston expander for energy regeneration in natural gas pressure reduction stations is economically viable only when the expander operates under moderate expansion ratio, and the low value of the polytropic exponent. Almost 60% of work can be recovered for an expansion ratio of 2, and a polytropic exponent lower than 1.4.
- The data obtained from the presented analysis may be used as guidelines for the design of the rolling piston expanders for further experimental research.
- The potential use of a rolling piston expander for energy regeneration in natural gas pressure reduction stations can significantly reduce the electricity consumption of the gas transport process and thereby indirectly contribute to lowering the amount of pollutants (dusts and gases) released into the environment during the combustion processes in power plants.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Comparison of isenthalpic throttling and polytropic expansion of natural gas depicted in a Mollier diagram, (gas pressure before reduction: 6 MPa, gas pressure after reduction: 2.5 MPa), 0–1–2: isobaric heating, 1–3: isenthalpic throttling, 2–4: polytropic expansion.

**Figure 3.**The process of gas expansion in the rolling piston expander. (

**a**) Beginning of the working cycle; (

**b**) end of the working chamber filling; (

**c**) end of expansion; (

**d**) the moment of the inlet valve re-opening; (

**e**) the moment of the outlet valve opening (beginning of the evacuation); (

**f**) end of the evacuation; (

**g**) end of the working cycle.

**Figure 5.**The scheme used for determination of the working chamber volume. (

**a**) π > ϕ > 0; (

**b**) 2π > ϕ > π.

**Figure 8.**Pressure in a working chamber versus rotor rotation angle for different polytropic exponents (m), m = 1.333 (blue line), m = 1.4973 (red line), m = 1.6615 (orange line), m = 1.8258 (violet line), m = 1.99 (green line).

**Figure 9.**Temperature in a working chamber versus rotor rotation angle for different polytropic exponents (m), m = 1.333 (blue line), m = 1.4973 (red line), m = 1.6615 (orange line), m = 1.8258 (violet line), m = 1.99 (green line).

**Figure 10.**Calculated power of the expander vs. rotor speed compared to experimental data reported in [17].

**Figure 11.**Electric power versus e/R ratio for different polytropic exponents (m), m = 1.333 (blue line), m = 1.4973 (red line), m = 1.6615 (orange line), m = 1.8258 (violet line), m = 1.99 (green line).

**Figure 12.**Electric power versus L/R ratio for different polytropic exponents (m), m = 1.333 (blue line), m = 1.4973 (red line), m = 1.6615 (orange line), m = 1.8258 (violet line), m = 1.99 (green line).

**Figure 13.**Electric power versus σ = p

_{s}/p

_{d}for different polytropic exponents (m), m = 1.333 (blue line), m = 1.4973 (red line), m = 1.6615 (orange line), m = 1.8258 (violet line), m = 1.99 (green line).

**Figure 14.**Isobaric heating, isenthalpic throttling and polytropic expansion of natural gas depicted in the T-s diagram.

**Figure 15.**Power recovery factor (PRF) versus the polytropic exponent (m), for different expansion ratios σ, σ = 2.0 (blue line), σ = 3.5 (red line), σ = 5.0 (orange line), σ = 6.5 (violet line), σ = 8.0 (green line).

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**MDPI and ACS Style**

Kolasiński, P.; Pomorski, M.; Błasiak, P.; Rak, J. Use of Rolling Piston Expanders for Energy Regeneration in Natural Gas Pressure Reduction Stations—Selected Thermodynamic Issues. *Appl. Sci.* **2017**, *7*, 535.
https://doi.org/10.3390/app7060535

**AMA Style**

Kolasiński P, Pomorski M, Błasiak P, Rak J. Use of Rolling Piston Expanders for Energy Regeneration in Natural Gas Pressure Reduction Stations—Selected Thermodynamic Issues. *Applied Sciences*. 2017; 7(6):535.
https://doi.org/10.3390/app7060535

**Chicago/Turabian Style**

Kolasiński, Piotr, Michał Pomorski, Przemysław Błasiak, and Józef Rak. 2017. "Use of Rolling Piston Expanders for Energy Regeneration in Natural Gas Pressure Reduction Stations—Selected Thermodynamic Issues" *Applied Sciences* 7, no. 6: 535.
https://doi.org/10.3390/app7060535