# Residue Cost Formation of a High Bypass Turbofan Engine
## 6 Operational Diagnosis of the Fuel Impact  
### Fuel Impact in Terms of Malfunctions and Dysfunctions  
A thermoeconomic diagnosis is based on a comparison of two operating conditions of a process: the actual and reference conditions denoted by the states \(\mathbf{\mathsf{x}}\) and \(\mathbf{\mathsf{x}}_{0}\), respectively. The reference condition is commonly the design condition, the state of the plant after an overhaul, or the state after an acceptance test [36]. However, the reference condition can also be associated with a change in the environmental conditions, a change in fuel quality, operation at partial load, or intervention from the control system. The objective of the diagnosis is to identify and quantify the additional resource consumption (\(\Delta\dot{F}_{T}=\dot{F}(\mathbf{\mathsf{x}})-\dot{F}(\mathbf{\mathsf{x}}_{0})\)) caused by the increases in component irreversibilities (\(\Delta I_{T}\)) [19; 37]. The fuel impact is the sum of the variations in the exergy destroyed by each component(internal irreversibility \(\Delta\mathbf{I}\)), exergy delivered to the environment (external irreversibility \(\Delta\mathbf{R}\)), and total production (\(\Delta\mathbf{P}_{s}\)). \[\Delta F_{T}=\mathbf{u}^{t}\left(\Delta\mathbf{I}+\Delta\mathbf{R}+\Delta \mathbf{P}_{s}\right) \tag{22}\]  
The variation in internal and external irreversibilities (\(\Delta\mathbf{I}+\Delta\mathbf{R}\)) on the right side of Equation (22) is known as the exergy technical savings and represents the irreversibility attributed to improper operation of the components that can be avoided. The fuel impact defined by Equation (22) can be expressed in terms of malfunctions and dysfunctions. \[\Delta\dot{F}_{T}=\mathbf{u}^{t}\left(\mathbf{MF}_{e}^{t}+\mathbf{MF}^{t}+ \mathbf{MR}^{t}+\mathbf{DF}_{K}+\mathbf{DF}_{\Delta\mathbf{P}_{s}}\right) \tag{23}\]  
Malfunctions are the endogenous irreversibility variations and can be divided into internal and external malfunctions. The internal malfunction of a component is an irreversibility variation in such a component due to the variation of the exergy unit consumption of resources coming from the environment (\(\mathbf{MF}_{e}^{t}=\left(\Delta\mathbf{K}_{D}-\Delta(\mathbf{K}\mathbf{P}) \right)\mathbf{P}(x_{0})\)) or from other productive components of the energy system (\(\mathbf{MF}^{t}=\Delta(\mathbf{K}\mathbf{P})\mathbf{P}(x_{0})\)) [38]. External malfunction is due to the yielding variations of residues in each component (\(\mathbf{MR}^{t}=\Delta(\mathbf{K}\mathbf{R})\mathbf{P}(x_{0})\)). Dysfunctions are exogenous irreversibility variations in a component. They are induced by the malfunctions of other components, which force the component to consume more or less resources in order to satisfy its local production (\(\mathbf{DF}_{K}=\left[\mathbf{I}\right](x)+\left|\mathbf{R}\right)(x) \left(\mathbf{MF}^{t}+\mathbf{MR}^{t}\right)\)) and the total production of the energy system (\(\mathbf{DF}_{\Delta\mathbf{P}_{s}}=\left[\mathbf{U}_{D}+\left|\mathbf{I}\right) (x)+\left|\mathbf{R}\right)(x)\right]\Delta\mathbf{P}_{s}\)). The dysfunction of a component depends on its position in the system and can be reduced only if the malfunction is reduced. The fuel impact can also be conceived of as the sum of the cost of the total malfunctions; see Equation (24). The malfunction cost of a component is the sum of the malfunction and the dysfunctions that it induces: \(\mathbf{MF}_{e}^{*t}=\mathbf{MF}_{e}^{t}\), \(\mathbf{MF}^{*t}=\mathbf{MF}^{t}+\left|\mathbf{I}\right)(x)\left(\mathbf{MF}^ {t}+\mathbf{MR}^{t}\right)\), \(\mathbf{MR}^{*t}=\mathbf{MR}^{t}+\left|\mathbf{R}\right)(x)\left(\mathbf{MF}^ {t}+\mathbf{MR}^{t}\right)\). \[\Delta\dot{F}_{T}=\mathbf{u}^{t}\left(\mathbf{MF}_{e}^{*t}+\mathbf{MF}^{*t}+ \mathbf{MR}^{*t}+\mathbf{DF}_{\Delta\mathbf{P}_{s}}\right) \tag{24}\]  
The fuel impact can also be conceived of as the sum of the cost of the total malfunctions.