## 3 Modeling Methods and Results
In [17], the results of experimental investigations on the operating conditions of a rolling piston expander applied in the ORC system were presented together with expanders' geometrical dimensions. Basing on data reported in [17] the authors decided to carry out additional computations for R245 fa as a working fluid and the same boundary conditions, and the expanders' geometrical dimensions. For the purpose of the comparison, the shaft rotational speed was  
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). simulated in the range of \(n=300\)-700 rpm, similar to the experiment. The polytropic exponent was assumed as \(m=1.2\) which corresponds to the average conditions during the experiment. Figure 10 shows the comparison of the experimental results reported in [17] with data obtained from the above described model. As plenty of experimental results were presented in [17] the authors decided to select and plot in Figure 10 a set of dotted regression lines which formed the expanders' working area, and represented the mean values of the experimental characteristics under different experimental conditions (i.e., variable shaft load and mass flow through the expander). Using the model, the authors calculated the output power characteristic (visualized via red solid line in Figure 10) for the mean values of the experimental parameters. As can be seen in Figure 10, the obtained via model line fit within the mean range of experimental results, and the order of magnitudes of output power, and the slope of both modeled and experimental characteristics were in good agreement. For this reason it can be stated that the model is a good tool for estimating the power output in rolling piston expanders. Moreover, in relation to the variation of the working chamber volume, gas pressure, and temperature, the obtained modeling results showed good agreement with experimental and numerical modeling results presented in many publications [23; 24; 25; 26; 27]. In Figures 11-13, an influence of eccentricity, cylinder length and expansion ratio, for different polytropic exponents, is presented correspondingly. Dependence of power on eccentricity and cylinder length was almost linear. Power increased both with an increasing polytropic exponent, and increasing the geometrical characteristic values (eccentricity, cylinder length) of the expander. From Figure 13, it was observed that for very low polytropic exponents (\(m<1.5\)) power hardly depended on expansion ratio \(\sigma\). A visible increase in power with increasing \(\sigma\) was observed for \(m>1.7\). For the fixed geometrical dimensions presented, power in the range of 0.1-1.0 MW can be obtained using the rolling piston expander. 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). As was stated above, in order to decrease gas pressure, throttling valves in pressure reduction stations are used. However, before a gas is throttled, it has to be heated up to prevent hydrate formation [2]. Figure 14 shows this processes in the T-s chart. First, gas at the temperature and pressure at Point 1 is isobarically heated up to the temperature at Point 1\({}^{\prime}\).