## 4 Summary and Conclusions  
In this article the authors analyzed the suitability of rolling piston expanders for energy regeneration in natural gas pressure reduction stations. Since such analysis has not been conducted so far, a method that allowed calculations of a rolling piston expander was required. The authors proposed a novel mathematical model of the rolling piston expander useful for calculating the operating parameters of an expander fed by natural gas. The detailed mathematical description of the working chamber and formulas for calculating the output power of the expander are included in the model. The mathematical model was implemented into in-house code, and power performance of a rolling piston expander was studied for an ideal gas case. We examined the influence of the following quantities: eccentricity, cylinder length, expansion ratio, and the polytropic exponent, on the operating conditions and power output of the expander. Moreover, we defined a novel assessment parameter, the Power Recovery Factor (PRF), which can be used for assessing the efficiency of energy regeneration in a rolling piston expander fed by natural gas. We used the PRF to assess the various construction solutions of the rolling piston expander. The results of the presented survey give the following final conclusions:  
Figure 15: Power recovery factor (\(PRF\)) versus the polytropic exponent (\(m\)), for different expansion ratios \(\sigma\), \(\sigma=2.0\) (blue line), \(\sigma=3.5\) (red line), \(\sigma=5.0\) (orange line), \(\sigma=6.5\) (violet line), \(\sigma=8.0\) (green line). * 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. Encouraged by the results of the analytical modeling, the authors decided to continue research on this topic and design a lab-prototype of a rolling piston expander utilizing natural gas as a working fluid. The authors would like to thank [PERSON] for fruitful discussions during works on this paper. Calculations have been carried out using resources provided by Wroclaw Centre for Networking and Supercomputing ([[http://wcss.pl](http://wcss.pl)]([http://wcss.pl](http://wcss.pl))).