**4. Methodology, analysis, and results**

Application of the steady-state energy balance, mass balance, and other thermodynamic relationships over the ORC pump (stream 1–2), turbine (stream 3–4), evaporator (stream 2–3), electric generator (EG), and the geothermal resource (stream a-b), yields the following set of model equations (**Tables 1** and **2**):

$$
\dot{W}\_{pump} = \dot{m}\_R (h\_2 - h\_1) \tag{1}
$$

$$w\_{pump} = h\_2 - h\_1 \tag{2}$$

$$h\_2 - h\_1 = v\_1(p\_2 - p\_1) \tag{3}$$

$$
\dot{Q}\_{Enap, ORC} = \dot{m}\_R (h\_3 - h\_2) \tag{4}
$$

$$
\dot{W}\_{Turb} = \dot{m}\_R (h\_3 - h\_4) \tag{5}
$$

$$
\dot{\mathcal{W}}\_{EG} = \eta\_{EG} \dot{\mathcal{W}}\_T \tag{6}
$$

$$
\dot{\mathcal{W}}\_{net,ORC} = \dot{\mathcal{W}}\_{EG} - \dot{\mathcal{W}}\_{pump} \tag{7}
$$

$$
\eta\_{th,ORC} = \frac{\dot{W}\_{net,ORC}}{\dot{Q}\_{Enap,ORC}} \tag{8}
$$

$$
\dot{Q}\_{Geo} = \dot{m}\_{Geo} q\_{Geo} \tag{9}
$$

$$
\dot{m}\_{\text{Geo}} = \frac{\dot{Q}\_{\text{Geo}}}{q\_{\text{Geo}}} \tag{10}
$$

$$
\dot{V}\_{\text{Geo}} = \frac{\dot{m}\_{\text{Geo}}}{\rho\_{\text{Geo}}} \tag{11}
$$

$$
\dot{Q}\_{Geo} = \dot{m}\_{Geo} (h\_a - h\_b) \tag{12}
$$

$$q\_{Geo} = c\_{p,Geo}(T\_a - T\_b) \tag{13}$$

$$
\dot{Q}\_{Geo} = \frac{\dot{Q}\_{Enap, ORC}}{\varepsilon\_{Enap, ORC}} \tag{14}
$$

$$
\eta\_{Geo} = \frac{\dot{W}\_{net,ORS}}{\dot{Q}\_{Geo}} \tag{15}
$$


#### **Table 1.**

*Thermodynamic properties of R-134a at the given conditions.*

*Introductory Chapter: ORC Power Generation Technology Using Low-Temperature Geothermal… DOI: http://dx.doi.org/10.5772/intechopen.101577*


#### **Table 2.**

*Summary of the ORC-LTGE performance results.*
