exerpy.components¶

Component¶

class exerpy.components.component.Component(**kwargs)[source]¶

Bases: object

Base class for all ExerPy components.

This class serves as the parent class for all exergy analysis components. It provides the basic structure and methods for exergy analysis calculations including the calculation of exergetic efficiency and exergy balance.

Parameters:

**kwargs (dict) – Arbitrary keyword arguments that will be assigned as attributes to the component.

Variables:

E_F (float) – Exergy fuel of the component \(\dot{E}_\mathrm{F}\) in \(\mathrm{W}\).
E_P (float) – Exergy product of the component \(\dot{E}_\mathrm{P}\) in \(\mathrm{W}\).
E_D (float) – Exergy destruction of the component \(\dot{E}_\mathrm{D}\) in \(\mathrm{W}\).
epsilon (float) – Exergetic efficiency of the component \(\varepsilon\) in \(-\).

Notes

The exergetic efficiency is calculated as the ratio of exergy product to exergy fuel:

\[\varepsilon = \frac{\dot{E}_\mathrm{P}}{\dot{E}_\mathrm{F}}\]

The exergy balance for any component follows the principle:

\[\dot{E}_\mathrm{F} = \dot{E}_\mathrm{P} + \dot{E}_\mathrm{D}\]

CombustionChamber¶

class exerpy.components.combustion.base.CombustionChamber(**kwargs)[source]¶

Bases: Component

Class for exergy and exergoeconomic analysis of combustion chambers.

This class performs exergy and exergoeconomic analysis calculations for combustion chambers, considering both thermal and mechanical exergy flows, as well as chemical exergy flows. The combustion gas leaves at outlet 0, every further material outlet is ash or slag. With split physical exergy, the exergy product is the increase of the thermal exergy from all inlets to all outlets and the exergy fuel the decrease of the chemical and the mechanical exergy. Without the split, the product is the increase of the physical exergy and the fuel the decrease of the chemical exergy. The ash is heated with the gas, so the increase of its physical exergy is product, while its chemical exergy is subtracted from the fuel.

Variables:

E_F (float) – Exergy fuel of the component \(\dot{E}_\mathrm{F}\) in \(\mathrm{W}\).
E_P (float) – Exergy product of the component \(\dot{E}_\mathrm{P}\) in \(\mathrm{W}\).
E_D (float) – Exergy destruction of the component \(\dot{E}_\mathrm{D}\) in \(\mathrm{W}\).
epsilon (float) – Exergetic efficiency of the component \(\varepsilon\) in \(-\).
inl (dict) – Dictionary containing inlet stream data with mass flows and specific exergies.
outl (dict) – Dictionary containing outlet stream data with mass flows and specific exergies.
Z_costs (float) – Investment cost rate of the component in currency/h.
C_P (float) – Cost of product stream \(\dot{C}_P\) in currency/h.
C_F (float) – Cost of fuel stream \(\dot{C}_F\) in currency/h.
C_D (float) – Cost of exergy destruction \(\dot{C}_D\) in currency/h.
c_P (float) – Specific cost of product stream (currency per unit exergy).
c_F (float) – Specific cost of fuel stream (currency per unit exergy).
r (float) – Relative cost difference, \((c_P - c_F)/c_F\).
f (float) – Exergoeconomic factor, \(\dot{Z}/(\dot{Z} + \dot{C}_D)\).
Ex_C_col (dict) – Custom cost coefficients collection passed via kwargs.

Notes

This component requires the calculation of both physical and chemical exergy.

aux_eqs(A, b, counter, T0, equations, chemical_exergy_enabled, split_physical_exergy=True)[source]¶

Add auxiliary cost equations for the combustion chamber.

The hot gas leaving the chamber at outlet 0 is the product, so the cost of its thermal exergy is left to the cost balance. What the chamber does not raise is blended: the gas takes the mass-weighted mean of the specific costs of all inlets (F-principle).

With split physical exergy the rule is written for the mechanical exergy; without the split the stream carries a single cost variable for its physical exergy, that variable is the product, and no mechanical rule exists. The cost balance determines it:

\[\dot{C}^\mathrm{PH}_\mathrm{gas} + \dot{C}^\mathrm{CH}_\mathrm{gas} + \sum_\mathrm{A} \bigl(\dot{C}^\mathrm{PH}_\mathrm{A} + \dot{C}^\mathrm{CH}_\mathrm{A}\bigr) = \sum_{i} \bigl(\dot{C}^\mathrm{PH}_{\mathrm{in},i} + \dot{C}^\mathrm{CH}_{\mathrm{in},i}\bigr) + \dot{Z}\]

The chemical rule is written in either mode, and a combustion chamber needs the chemical exergy to be enabled at all, since the fuel enters as chemical exergy.

For \(x = \mathrm{M}\) (only with split physical exergy) and \(x = \mathrm{CH}\), the rule \(\dot m_\mathrm{gas}\,c^{x}_\mathrm{gas} = \sum_{i} \dot m_{i}\,c^{x}_{\mathrm{in},i}\) over all inlets \(i\) is written into the matrix as

\[-\frac{1}{\dot{E}^{x}_{\mathrm{gas}}}\,\dot{C}^{x}_{\mathrm{gas}} + \sum_{i} \frac{\dot m_{i}}{\sum_{j} \dot m_{j}} \frac{1}{\dot{E}^{x}_{\mathrm{in},i}}\,\dot{C}^{x}_{\mathrm{in},i} = 0\]

An inlet without exergy of the form \(x\) brings no cost of it and is left out of the sum. If the gas has no exergy of the form \(x\), the row sets its cost to zero, \(\dot{C}^{x}_{\mathrm{gas}} = 0\).

Every further outlet \(\mathrm{A}\), such as ash or slag, stems from the fuel stream \(\mathrm{f}\), the inlet with the largest chemical exergy flow, in the share \(k = \dot m_\mathrm{A} / \dot m_\mathrm{f}\) [33]. Its chemical exergy keeps the specific cost of the fuel (F-principle), and with split physical exergy its mechanical exergy mixes like that of the gas:

\[\frac{\dot{C}^{\mathrm{CH}}_{\mathrm{A}}}{\dot{E}^{\mathrm{CH}}_{\mathrm{A}}} = \frac{\dot{C}^{\mathrm{CH}}_{\mathrm{f}}}{\dot{E}^{\mathrm{CH}}_{\mathrm{f}}}\]

The increase of its physical exergy \(x\) (T with split physical exergy, PH without) is product and costs as much per unit as the increase of the gas (P-principle):

\[\frac{\dot{C}^{x}_{\mathrm{A}} - k\,\dot{C}^{x}_{\mathrm{f}}} {\dot{E}^{x}_{\mathrm{A}} - k\,\dot{E}^{x}_{\mathrm{f}}} = \frac{\dot{C}^{x}_{\mathrm{gas}} - \sum_{i} \dot{C}^{x}_{\mathrm{in},i} + \sum_\mathrm{A} k\,\dot{C}^{x}_{\mathrm{f}}} {\dot{E}^{x}_{\mathrm{gas}} - \sum_{i} \dot{E}^{x}_{\mathrm{in},i} + \sum_\mathrm{A} k\,\dot{E}^{x}_{\mathrm{f}}}\]

If the ash gains no physical exergy, it keeps the cost of its share of the fuel, \(\dot{C}^{x}_{\mathrm{A}} = k\,\dot{C}^{x}_{\mathrm{f}}\).

Parameters:

A (numpy.ndarray) – Current cost matrix.
b (numpy.ndarray) – Current RHS vector.
counter (int) – Starting row index.
T0 (float) – Ambient temperature.
equations (dict or list) – Structure for equation labels.
chemical_exergy_enabled (bool) – Must be True to include chemical exergy mixing.
split_physical_exergy (bool, optional) – If True, the physical exergy of a material stream is split into a thermal and a mechanical share, each with its own cost variable. If False, the stream carries a single cost variable for its physical exergy. Default is True.

Returns:

A (numpy.ndarray) – Updated cost matrix.
b (numpy.ndarray) – Updated RHS vector.
counter (int) – Updated row index.
equations (dict or list) – Updated labels.

Raises:

ValueError – If chemical_exergy_enabled is False.

calc_exergy_balance(T0: float, p0: float, split_physical_exergy) → None[source]¶

Compute the exergy balance of the combustion chamber.

The sums run over all inlets and over all outlets, the combustion gas at outlet 0 and any ash or slag at further outlets. With split physical exergy, the thermal exergy of the streams is raised (product) at the expense of their chemical and mechanical exergy (fuel):

\[\dot{E}_\mathrm{P} = \sum \dot{E}^{\mathrm{T}}_{\mathrm{out}} - \sum \dot{E}^{\mathrm{T}}_{\mathrm{in}}\]

\[\dot{E}_\mathrm{F} = \Bigl(\sum \dot{E}^{\mathrm{CH}}_{\mathrm{in}} - \sum \dot{E}^{\mathrm{CH}}_{\mathrm{out}}\Bigr) + \Bigl(\sum \dot{E}^{\mathrm{M}}_{\mathrm{in}} - \sum \dot{E}^{\mathrm{M}}_{\mathrm{out}}\Bigr)\]

Without the split:

\[\dot{E}_\mathrm{P} = \sum \dot{E}^{\mathrm{PH}}_{\mathrm{out}} - \sum \dot{E}^{\mathrm{PH}}_{\mathrm{in}}\]

\[\dot{E}_\mathrm{F} = \sum \dot{E}^{\mathrm{CH}}_{\mathrm{in}} - \sum \dot{E}^{\mathrm{CH}}_{\mathrm{out}}\]

An inlet below the ambient temperature brings thermal exergy that the chamber has to make up first, so it reduces the product.

The exergy destruction \(\dot{E}_\mathrm{D} = \dot{E}_\mathrm{F} - \dot{E}_\mathrm{P}\) is the same in both cases: the total exergy of all inlets less that of all outlets.

Parameters:

T0 (float) – Ambient temperature (K).
p0 (float) – Ambient pressure (Pa).
split_physical_exergy (bool) – Whether to split thermal and mechanical exergy.

Raises:

ValueError – If fewer than two inlets or no outlets are defined, if a stream is no material stream, if outlet 0 is missing or if a stream has no chemical exergy.

exergoeconomic_balance(T0, chemical_exergy_enabled=False, split_physical_exergy=True)[source]¶

Perform exergoeconomic cost balance for the combustion chamber.

\[\sum_{i} \bigl(\dot{C}^{\mathrm{PH}}_{\mathrm{in},i} + \dot{C}^{\mathrm{CH}}_{\mathrm{in},i}\bigr) - \dot{C}^{\mathrm{PH}}_{\mathrm{gas}} - \dot{C}^{\mathrm{CH}}_{\mathrm{gas}} - \sum_\mathrm{A} \bigl(\dot{C}^{\mathrm{PH}}_{\mathrm{A}} + \dot{C}^{\mathrm{CH}}_{\mathrm{A}}\bigr) + \dot{Z} = 0\]

This method computes cost coefficients and ratios. Fuel and product take the same exergy forms as in calc_exergy_balance(), all outlets (gas and ash) against all inlets, so that \(\dot{C}_\mathrm{P} = \dot{C}_\mathrm{F} + \dot{Z}\). With split physical exergy:

\[\dot{C}_\mathrm{P} = \sum \dot{C}^{\mathrm{T}}_{\mathrm{out}} - \sum \dot{C}^{\mathrm{T}}_{\mathrm{in}}\]

\[\dot{C}_\mathrm{F} = \Bigl(\sum \dot{C}^{\mathrm{CH}}_{\mathrm{in}} - \sum \dot{C}^{\mathrm{CH}}_{\mathrm{out}}\Bigr) + \Bigl(\sum \dot{C}^{\mathrm{M}}_{\mathrm{in}} - \sum \dot{C}^{\mathrm{M}}_{\mathrm{out}}\Bigr)\]

Without the split:

\[\dot{C}_\mathrm{P} = \sum \dot{C}^{\mathrm{PH}}_{\mathrm{out}} - \sum \dot{C}^{\mathrm{PH}}_{\mathrm{in}}\]

\[\dot{C}_\mathrm{F} = \sum \dot{C}^{\mathrm{CH}}_{\mathrm{in}} - \sum \dot{C}^{\mathrm{CH}}_{\mathrm{out}}\]

Parameters:

T0 (float) – Ambient temperature (K).
chemical_exergy_enabled (bool, optional) – If True, chemical exergy is considered in the calculations.
split_physical_exergy (bool, optional) – If True, the physical exergy of a material stream is split into a thermal and a mechanical share, each with its own cost variable. If False, the stream carries a single cost variable for its physical exergy. Default is True.

HeatExchanger¶

class exerpy.components.heat_exchanger.base.HeatExchanger(**kwargs)[source]¶

Bases: Component

Class for exergy and exergoeconomic analysis of heat exchangers.

This class performs exergy and exergoeconomic analysis calculations for heat exchanger components, accounting for two inlet and two outlet streams across various temperature regimes, including above and below ambient temperature, and optional dissipative behavior.

Variables:

E_F (float) – Exergy fuel of the component \(\dot{E}_\mathrm{F}\) in \(\mathrm{W}\).
E_P (float) – Exergy product of the component \(\dot{E}_\mathrm{P}\) in \(\mathrm{W}\).
E_D (float) – Exergy destruction of the component \(\dot{E}_\mathrm{D}\) in \(\mathrm{W}\).
epsilon (float) – Exergetic efficiency of the component \(\varepsilon\) in \(-\).
inl (dict) – Dictionary containing inlet stream data with mass flows and specific exergies.
outl (dict) – Dictionary containing outlet stream data with mass flows and specific exergies.
Z_costs (float) – Investment cost rate of the component in currency/h.
C_P (float) – Cost of product stream \(\dot{C}_P\) in currency/h.
C_F (float) – Cost of fuel stream \(\dot{C}_F\) in currency/h.
C_D (float) – Cost of exergy destruction \(\dot{C}_D\) in currency/h.
c_P (float) – Specific cost of product stream (currency per unit exergy).
c_F (float) – Specific cost of fuel stream (currency per unit exergy).
r (float) – Relative cost difference, \((c_P - c_F)/c_F\).
f (float) – Exergoeconomic factor, \(\dot{Z}/(\dot{Z} + \dot{C}_D)\).
Ex_C_col (dict) – Custom cost coefficients collection passed via kwargs.

Bases: Input

dissipative: bool | None | UnsetType¶

kA: float | None | UnsetType¶

parameters: dict[str, Any] | None | UnsetType¶

aux_eqs(A, b, counter, T0, equations, chemical_exergy_enabled, split_physical_exergy=True)[source]¶

Add auxiliary cost equations for the heat exchanger.

The hot stream gives up exergy and the cold stream takes it up, so which stream carries the product depends on where the two sit relative to the ambient temperature. The stream that is fuel follows the F-principle; the product is left to the cost balance.

Writing \(x\) for the cost variable of the physical exergy, the rules below hold in both split modes: \(x = \mathrm{T}\) with split physical exergy and \(x = \mathrm{PH}\) without it. What changes is only that the mechanical rule at the end exists only with the split.

Case 1, all streams above \(T_0\): the hot stream is the fuel.

\[\frac{\dot{C}^{x}_{\mathrm{in},1}}{\dot{E}^{x}_{\mathrm{in},1}} = \frac{\dot{C}^{x}_{\mathrm{out},1}}{\dot{E}^{x}_{\mathrm{out},1}}\]

Case 2, all streams at or below \(T_0\): the cold stream carries the cold exergy that is consumed, so it is the fuel.

\[\frac{\dot{C}^{x}_{\mathrm{in},2}}{\dot{E}^{x}_{\mathrm{in},2}} = \frac{\dot{C}^{x}_{\mathrm{out},2}}{\dot{E}^{x}_{\mathrm{out},2}}\]

Case 3, both streams crossing \(T_0\): both outlets are product, priced alike (P-principle).

\[\frac{\dot{C}^{x}_{\mathrm{out},1}}{\dot{E}^{x}_{\mathrm{out},1}} = \frac{\dot{C}^{x}_{\mathrm{out},2}}{\dot{E}^{x}_{\mathrm{out},2}}\]

Case 4, only the hot inlet above \(T_0\): the cold stream is the fuel.

\[\frac{\dot{C}^{x}_{\mathrm{in},2}}{\dot{E}^{x}_{\mathrm{in},2}} = \frac{\dot{C}^{x}_{\mathrm{out},2}}{\dot{E}^{x}_{\mathrm{out},2}}\]

Case 5, only the cold inlet below \(T_0\): the hot stream is the fuel.

\[\frac{\dot{C}^{x}_{\mathrm{in},1}}{\dot{E}^{x}_{\mathrm{in},1}} = \frac{\dot{C}^{x}_{\mathrm{out},1}}{\dot{E}^{x}_{\mathrm{out},1}}\]

Case 6, the hot stream always above and the cold stream always below \(T_0\): the unit has no product and is dissipative. It is handled by dis_eqs(), and nothing is written here.

On top of the rule for the case, the pressure and the composition pass through on both branches \(i\) at their own specific cost. The mechanical rule exists only with split physical exergy, since without it the stream has no mechanical cost variable; the chemical rule exists whenever chemical exergy is enabled:

\[\frac{\dot{C}^\mathrm{M}_{\mathrm{in},i}}{\dot{E}^\mathrm{M}_{\mathrm{in},i}} = \frac{\dot{C}^\mathrm{M}_{\mathrm{out},i}}{\dot{E}^\mathrm{M}_{\mathrm{out},i}} \qquad \frac{\dot{C}^\mathrm{CH}_{\mathrm{in},i}}{\dot{E}^\mathrm{CH}_{\mathrm{in},i}} = \frac{\dot{C}^\mathrm{CH}_{\mathrm{out},i}}{\dot{E}^\mathrm{CH}_{\mathrm{out},i}}\]

Parameters:

A (numpy.ndarray) – Current cost matrix.
b (numpy.ndarray) – Current RHS vector.
counter (int) – Starting row index for auxiliary equations.
T0 (float) – Ambient temperature (K).
equations (dict or list) – Structure for equation labels.
chemical_exergy_enabled (bool) – Must be True to include chemical exergy mixing.
split_physical_exergy (bool, optional) – If True, the physical exergy of a material stream is split into a thermal and a mechanical share, each with its own cost variable. If False, the stream carries a single cost variable for its physical exergy. Default is True.

Returns:

A (numpy.ndarray) – Updated cost matrix.
b (numpy.ndarray) – Updated RHS vector.
counter (int) – Updated row index after adding equations.
equations (dict or list) – Updated labels.

Raises:

ValueError – If required cost variable indices are missing.

calc_exergy_balance(T0: float, p0: float, split_physical_exergy) → None[source]¶

Compute the exergy balance of the heat exchanger.

Case 1: All streams above ambient temperature

If split_physical_exergy=True:

\[\dot{E}_{\mathrm{P}} = \dot{E}^{\mathrm{T}}_{\mathrm{out},2} - \dot{E}^{\mathrm{T}}_{\mathrm{in},2}\]

\[\dot{E}_{\mathrm{F}} = \dot{E}^{\mathrm{PH}}_{\mathrm{in},1} - \dot{E}^{\mathrm{PH}}_{\mathrm{out},1} + \bigl(\dot{E}^{\mathrm{M}}_{\mathrm{in},2} - \dot{E}^{\mathrm{M}}_{\mathrm{out},2}\bigr)\]

Else:

\[\dot{E}_{\mathrm{P}} = \dot{E}^{\mathrm{PH}}_{\mathrm{out},2} - \dot{E}^{\mathrm{PH}}_{\mathrm{in},2}\]

\[\dot{E}_{\mathrm{F}} = \dot{E}^{\mathrm{PH}}_{\mathrm{in},1} - \dot{E}^{\mathrm{PH}}_{\mathrm{out},1}\]

Case 2: All streams below or equal to ambient temperature

If split_physical_exergy=True:

\[\dot{E}_{\mathrm{P}} = \dot{E}^{\mathrm{T}}_{\mathrm{out},1} - \dot{E}^{\mathrm{T}}_{\mathrm{in},1}\]

\[\dot{E}_{\mathrm{F}} = \dot{E}^{\mathrm{PH}}_{\mathrm{in},2} - \dot{E}^{\mathrm{PH}}_{\mathrm{out},2} + \bigl(\dot{E}^{\mathrm{M}}_{\mathrm{in},1} - \dot{E}^{\mathrm{M}}_{\mathrm{out},1}\bigr)\]

Else

\[\dot{E}_{\mathrm{P}} = \dot{E}^{\mathrm{PH}}_{\mathrm{out},1} - \dot{E}^{\mathrm{PH}}_{\mathrm{in},1}\]

\[\dot{E}_{\mathrm{F}} = \dot{E}^{\mathrm{PH}}_{\mathrm{in},2} - \dot{E}^{\mathrm{PH}}_{\mathrm{out},2}\]

Case 3: Both stream crossing ambient temperature

If split_physical_exergy=True:

\[\dot{E}_{\mathrm{P}} = \dot{E}^{\mathrm{T}}_{\mathrm{out},1} + \dot{E}^{\mathrm{T}}_{\mathrm{out},2}\]

\[\dot{E}_{\mathrm{F}} = \dot{E}^{\mathrm{PH}}_{\mathrm{in},1} + \dot{E}^{\mathrm{PH}}_{\mathrm{in},2} - \bigl(\dot{E}^{\mathrm{M}}_{\mathrm{out},1} + \dot{E}^{\mathrm{M}}_{\mathrm{out},2}\bigr)\]

Else:

\[\dot{E}_{\mathrm{P}} = \dot{E}^{\mathrm{PH}}_{\mathrm{out},1} + \dot{E}^{\mathrm{PH}}_{\mathrm{out},2}\]

\[\dot{E}_{\mathrm{F}} = \dot{E}^{\mathrm{PH}}_{\mathrm{in},1} + \dot{E}^{\mathrm{PH}}_{\mathrm{in},2}\]

Case 4: Only the hot inlet above ambient temperature

If split_physical_exergy=True:

\[\dot{E}_{\mathrm{P}} = \dot{E}^{\mathrm{T}}_{\mathrm{out},1}\]

\[\dot{E}_{\mathrm{F}} = \bigl(\dot{E}^{\mathrm{PH}}_{\mathrm{in},1} + \dot{E}^{\mathrm{PH}}_{\mathrm{in},2}\bigr) - \bigl(\dot{E}^{\mathrm{PH}}_{\mathrm{out},2} + \dot{E}^{\mathrm{M}}_{\mathrm{out},1}\bigr)\]

Else:

\[\dot{E}_{\mathrm{P}} = \dot{E}^{\mathrm{PH}}_{\mathrm{out},1}\]

\[\dot{E}_{\mathrm{F}} = \bigl(\dot{E}^{\mathrm{PH}}_{\mathrm{in},1} + \dot{E}^{\mathrm{PH}}_{\mathrm{in},2}\bigr) - \dot{E}^{\mathrm{PH}}_{\mathrm{out},2}\]

Case 5: Only the cold inlet below ambient temperature

If split_physical_exergy=True:

\[\dot{E}_{\mathrm{P}} = \dot{E}^{\mathrm{T}}_{\mathrm{out},2}\]

\[\dot{E}_{\mathrm{F}} = \bigl(\dot{E}^{\mathrm{PH}}_{\mathrm{in},1} - \dot{E}^{\mathrm{PH}}_{\mathrm{out},1}\bigr) + \bigl(\dot{E}^{\mathrm{PH}}_{\mathrm{in},2} - \dot{E}^{\mathrm{M}}_{\mathrm{out},2}\bigr)\]

Else:

\[\dot{E}_{\mathrm{P}} = \dot{E}^{\mathrm{PH}}_{\mathrm{out},2}\]

\[\dot{E}_{\mathrm{F}} = \bigl(\dot{E}^{\mathrm{PH}}_{\mathrm{in},1} - \dot{E}^{\mathrm{PH}}_{\mathrm{out},1}\bigr) + \dot{E}^{\mathrm{PH}}_{\mathrm{in},2}\]

Case 6: Hot stream always above and cold stream always below ambient temperature (dissipative case):

\[\dot{E}_{\mathrm{P}} = \mathrm{NaN}\]

\[\dot{E}_{\mathrm{F}} = \bigl(\dot{E}^{\mathrm{PH}}_{\mathrm{in},1} - \dot{E}^{\mathrm{PH}}_{\mathrm{out},1}\bigr) - \dot{E}^{\mathrm{PH}}_{\mathrm{out},2} + \dot{E}^{\mathrm{PH}}_{\mathrm{in},2}\]

If dissipative is True, the component is treated as dissipative:

\[\dot{E}_{\mathrm{P}} = \mathrm{NaN}\]

\[\dot{E}_{\mathrm{F}} = \bigl(\dot{E}^{\mathrm{PH}}_{\mathrm{in},1} - \dot{E}^{\mathrm{PH}}_{\mathrm{out},1}\bigr) - \dot{E}^{\mathrm{PH}}_{\mathrm{out},2} + \dot{E}^{\mathrm{PH}}_{\mathrm{in},2}\]

Parameters:

T0 (float) – Ambient temperature (K).
p0 (float) – Ambient pressure (Pa).
split_physical_exergy (bool) – Whether to split thermal and mechanical exergy.

Raises:

ValueError – If required inlets or outlets are missing.

dis_eqs(A, b, counter, T0, equations, chemical_exergy_enabled=False, all_components=None, split_physical_exergy=True)[source]¶

Construct cost equations for a dissipative HeatExchanger.

Distributes the heat exchanger’s extra cost difference (C_diff) to all other productive components (non-dissipative and non-CycleCloser) in proportion to their exergy destruction (E_D) and adds an overall cost balance row that enforces:

\[(\dot C_{\mathrm{in},1} - \dot C_{\mathrm{out},1}) + (\dot C_{\mathrm{in},2} - \dot C_{\mathrm{out},2}) - \dot C_{\mathrm{diff}} = -\,\dot Z_{\mathrm{costs}}\]

A main working fluid keeps its specific cost between inlet and outlet for each exergy share \(x\) (thermal, mechanical, chemical). Where its inlet or outlet carries no exergy of a share, the outlet carries no cost of it, and the cost of the inlet stays in \(\dot C_\mathrm{diff}\):

\[\frac{\dot{C}^{x}_{\mathrm{in}}}{\dot{E}^{x}_{\mathrm{in}}} = \frac{\dot{C}^{x}_{\mathrm{out}}}{\dot{E}^{x}_{\mathrm{out}}} \qquad \text{or} \qquad \dot{C}^{x}_{\mathrm{out}} = 0 \quad \text{for} \quad \dot{E}^{x}_{\mathrm{in}} = 0 \ \text{or} \ \dot{E}^{x}_{\mathrm{out}} = 0\]

The auxiliary fluid, e.g. the cooling water of a condenser, brings its cost into the component and leaves without cost, \(\dot{C}^{x}_{\mathrm{aux,out}} = 0\), so its cost is part of \(\dot C_\mathrm{diff}\) [33]. It is the side that is discharged: the exergy analysis follows each outlet through splitters, mixers and dissipative components, and the side whose paths all end in a loss stream of E_L is the auxiliary fluid (attribute auxiliary_side). If neither side or both are discharged, a stream that gains exergy is taken as the auxiliary fluid, and if both lose exergy, both are main working fluids.

Parameters:

A (numpy.ndarray) – The current cost matrix.
b (numpy.ndarray) – The current right-hand-side vector.
counter (int) – The current row index in the cost matrix.
T0 (float) – Ambient temperature (K).
equations (dict) – Dictionary mapping row indices to equation labels.
chemical_exergy_enabled (bool, optional) – Flag indicating whether chemical exergy is considered.
all_components (list, optional) – Global list of all component objects; if not provided, defaults to [].
split_physical_exergy (bool, optional) – If True, the physical exergy of a material stream is split into a thermal and a mechanical share, each with its own cost variable. If False, the stream carries a single cost variable for its physical exergy. Default is True.

Returns:

tuple – Updated (A, b, counter, equations).

exergoeconomic_balance(T0, chemical_exergy_enabled=False, split_physical_exergy=True)[source]¶

Perform exergoeconomic cost balance for the heat exchanger.

\[\dot{C}^{\mathrm{T}}_{\mathrm{in},1} + \dot{C}^{\mathrm{M}}_{\mathrm{in},1} + \dot{C}^{\mathrm{T}}_{\mathrm{in},2} + \dot{C}^{\mathrm{M}}_{\mathrm{in},2} - \dot{C}^{\mathrm{T}}_{\mathrm{out},1} - \dot{C}^{\mathrm{M}}_{\mathrm{out},1} - \dot{C}^{\mathrm{T}}_{\mathrm{out},2} - \dot{C}^{\mathrm{M}}_{\mathrm{out},2} + \dot{Z} = 0\]

In case the chemical exergy of the streams is know:

\[\dot{C}^{\mathrm{CH}}_{\mathrm{in},1} = \dot{C}^{\mathrm{CH}}_{\mathrm{out},1}\]

\[\dot{C}^{\mathrm{CH}}_{\mathrm{in},2} = \dot{C}^{\mathrm{CH}}_{\mathrm{out},2}\]

This method computes cost coefficients and ratios:

Case 1: All streams above ambient temperature

\[\dot{C}_P = \dot{C}^{\mathrm{T}}_{\mathrm{out},2} - \dot{C}^{\mathrm{T}}_{\mathrm{in},2}\]

\[\dot{C}_F = \dot{C}^{\mathrm{PH}}_{\mathrm{in},1} - \dot{C}^{\mathrm{PH}}_{\mathrm{out},1} + \bigl(\dot{C}^{\mathrm{M}}_{\mathrm{in},2} - \dot{C}^{\mathrm{M}}_{\mathrm{out},2}\bigr)\]

Case 2: All streams below or equal to ambient temperature

\[\dot{C}_P = \dot{C}^{\mathrm{T}}_{\mathrm{out},1} - \dot{C}^{\mathrm{T}}_{\mathrm{in},1}\]

\[\dot{C}_F = \dot{C}^{\mathrm{PH}}_{\mathrm{in},2} - \dot{C}^{\mathrm{PH}}_{\mathrm{out},2} + \bigl(\dot{C}^{\mathrm{M}}_{\mathrm{in},1} - \dot{C}^{\mathrm{M}}_{\mathrm{out},1}\bigr)\]

Case 3: Both stream crossing ambient temperature

\[\dot{C}_P = \dot{C}^{\mathrm{T}}_{\mathrm{out},1} + \dot{C}^{\mathrm{T}}_{\mathrm{out},2}\]

\[\dot{C}_F = \dot{C}^{\mathrm{PH}}_{\mathrm{in},1} + \dot{C}^{\mathrm{PH}}_{\mathrm{in},2} - \bigl(\dot{C}^{\mathrm{M}}_{\mathrm{out},1} + \dot{C}^{\mathrm{M}}_{\mathrm{out},2}\bigr)\]

Case 4: Only the hot inlet above ambient temperature

\[\dot{C}_P = \dot{C}^{\mathrm{T}}_{\mathrm{out},1}\]

\[\dot{C}_F = \bigl(\dot{C}^{\mathrm{PH}}_{\mathrm{in},1} + \dot{C}^{\mathrm{PH}}_{\mathrm{in},2}\bigr) - \bigl(\dot{C}^{\mathrm{PH}}_{\mathrm{out},2} + \dot{C}^{\mathrm{M}}_{\mathrm{out},1}\bigr)\]

Case 5: Only the cold inlet below ambient temperature

\[\dot{C}_P = \dot{C}^{\mathrm{T}}_{\mathrm{out},2}\]

\[\dot{C}_F = \dot{C}^{\mathrm{PH}}_{\mathrm{in},1} - \dot{C}^{\mathrm{PH}}_{\mathrm{out},1} + \bigl(\dot{C}^{\mathrm{PH}}_{\mathrm{in},2} - \dot{C}^{\mathrm{M}}_{\mathrm{out},2}\bigr)\]

Case 6: Hot stream always above and cold stream always below ambient temperature (dissipative case):

\[\dot{C}_P = \mathrm{NaN}\]

\[\dot{C}_F = \bigl(\dot{C}^{\mathrm{PH}}_{\mathrm{in},1} - \dot{C}^{\mathrm{PH}}_{\mathrm{out},1}\bigr) - \dot{C}^{\mathrm{PH}}_{\mathrm{out},2} + \dot{C}^{\mathrm{PH}}_{\mathrm{in},2}\]

Parameters:

T0 (float) – Ambient temperature (K).
chemical_exergy_enabled (bool, optional) – If True, chemical exergy is considered in the calculations.
split_physical_exergy (bool, optional) – If True, the physical exergy of a material stream is split into a thermal and a mechanical share, each with its own cost variable. If False, the stream carries a single cost variable for its physical exergy. Default is True.

SimpleHeatExchanger¶

class exerpy.components.heat_exchanger.simple.SimpleHeatExchanger(**kwargs)[source]¶

Bases: Component

Class for exergy and exergoeconomic analysis of simple heat exchangers.

This class performs exergy and exergoeconomic analysis calculations for heat exchanger components, accounting for one inlet and one outlet stream across various temperature regimes, including above and below ambient temperature, and optional dissipative behavior.

Variables:

E_F (float) – Exergy fuel of the component \(\dot{E}_\mathrm{F}\) in \(\mathrm{W}\).
E_P (float) – Exergy product of the component \(\dot{E}_\mathrm{P}\) in \(\mathrm{W}\).
E_D (float) – Exergy destruction of the component \(\dot{E}_\mathrm{D}\) in \(\mathrm{W}\).
epsilon (float) – Exergetic efficiency of the component \(\varepsilon\) in \(-\).
inl (dict) – Dictionary containing inlet stream data with mass flows and specific exergies.
outl (dict) – Dictionary containing outlet stream data with mass flows and specific exergies.
Z_costs (float) – Investment cost rate of the component in currency/h.
C_P (float) – Cost of product stream \(\dot{C}_P\) in currency/h.
C_F (float) – Cost of fuel stream \(\dot{C}_F\) in currency/h.
C_D (float) – Cost of exergy destruction \(\dot{C}_D\) in currency/h.
c_P (float) – Specific cost of product stream (currency per unit exergy).
c_F (float) – Specific cost of fuel stream (currency per unit exergy).
r (float) – Relative cost difference, \((c_P - c_F)/c_F\).
f (float) – Exergoeconomic factor, \(\dot{Z}/(\dot{Z} + \dot{C}_D)\).
Ex_C_col (dict) – Custom cost coefficients collection passed via kwargs.
T_hot (float, optional) – Temperature of the heat source in K, for a stream that takes in heat above the ambient temperature. Given, the fuel is the exergy of the heat at that temperature, \(\dot{E}_\mathrm{F} = \dot{Q}\,(1 - T_0/T_\mathrm{hot})\), so the loss of the heat transfer from the source counts as exergy destruction of the component.
T_cold (float, optional) – Temperature of the heat consumer in K, for a stream that releases heat above the ambient temperature. Given, the product is the exergy of the heat at that temperature, \(\dot{E}_\mathrm{P} = |\dot{Q}|\,(1 - T_0/T_\mathrm{cold})\).
the (Without them, the heat is valued at the exergy change of the stream itself, and the loss of)
component. (heat transfer to or from the outside lies outside the)

class Input(*, name: Annotated[str, msgspec.Meta(min_length=1)], dissipative: bool | None | UnsetType = UNSET, T_hot: Annotated[float, msgspec.Meta(description='Absolute temperature, in K unless a unit is given'), Limit(gt=0, ge=None, le=None)] | None | UnsetType = UNSET, T_cold: Annotated[float, msgspec.Meta(description='Absolute temperature, in K unless a unit is given'), Limit(gt=0, ge=None, le=None)] | None | UnsetType = UNSET)[source]¶

Bases: Input

T_cold: Annotated[float, msgspec.Meta(description='Absolute temperature, in K unless a unit is given'), Limit(gt=0, ge=None, le=None)] | None | UnsetType¶

T_hot: Annotated[float, msgspec.Meta(description='Absolute temperature, in K unless a unit is given'), Limit(gt=0, ge=None, le=None)] | None | UnsetType¶

dissipative: bool | None | UnsetType¶

aux_eqs(A, b, counter, T0, equations, chemical_exergy_enabled, split_physical_exergy=True)[source]¶

Auxiliary equations for the simple heat exchanger.

Writing \(x\) for the cost variable of the physical exergy, the rules hold in both split modes with \(x = \mathrm{T}\) for split physical exergy and \(x = \mathrm{PH}\) without it.

The cost of the heat follows the direction of its exergy, which below the ambient temperature is against the heat (see heat_exergy_reversed()).

Heat as product, when its exergy leaves: heat released above or taken in below the ambient temperature. The stream gives up the fuel, so it follows the F-principle:

\[\frac{\dot{C}^{x}_\mathrm{in}}{\dot{E}^{x}_\mathrm{in}} = \frac{\dot{C}^{x}_\mathrm{out}}{\dot{E}^{x}_\mathrm{out}}\]

Heat as fuel, when its exergy enters: the cost balance alone prices the outlet, so no rule is written:

\[\dot{C}^{x}_\mathrm{out} = \dot{C}^{x}_\mathrm{in} + \dot{C}^\mathrm{TOT}_\mathrm{heat} + \dot{Z}\]

The pressure and the composition pass through at their own specific cost in either case. The mechanical rule exists only with split physical exergy, since without it the stream has no mechanical cost variable; the chemical rule exists whenever chemical exergy is enabled:

\[\frac{\dot{C}^\mathrm{M}_\mathrm{in}}{\dot{E}^\mathrm{M}_\mathrm{in}} = \frac{\dot{C}^\mathrm{M}_\mathrm{out}}{\dot{E}^\mathrm{M}_\mathrm{out}} \qquad \frac{\dot{C}^\mathrm{CH}_\mathrm{in}}{\dot{E}^\mathrm{CH}_\mathrm{in}} = \frac{\dot{C}^\mathrm{CH}_\mathrm{out}}{\dot{E}^\mathrm{CH}_\mathrm{out}}\]

Without a heat connection there is no cost variable for the heat, so no rule is written for the physical exergy and the cost balance alone prices the outlet. The heat then has no cost, and the component warns.

Parameters:

A (numpy.ndarray) – Coefficient matrix of the cost equation system.
b (numpy.ndarray) – Right-hand side vector of the cost equation system.
counter (int) – Index of the next free row.
T0 (float) – Ambient temperature in \(\mathrm{K}\).
equations (dict) – Dictionary documenting the equations.
chemical_exergy_enabled (bool) – Whether chemical exergy is part of the analysis.
split_physical_exergy (bool, optional) – If True, the physical exergy of a material stream is split into a thermal and a mechanical share, each with its own cost variable. If False, the stream carries a single cost variable for its physical exergy. Default is True.

Returns:

tuple – The updated matrix, vector, row index and equation dictionary.

calc_exergy_balance(T0: float, p0: float, split_physical_exergy) → None[source]¶

Compute the exergy balance of the simple heat exchanger.

Heat release :math:dot{Q}<0

Case 1: Both streams above ambient temperature. With split physical exergy the heat is valued at the change of thermal exergy, so the friction of the stream is exergy destruction. Without the split \(\mathrm{PH}\) takes the place of \(\mathrm{T}\): the pressure drop is then part of the exergy of the heat, and the component warns.

\[\dot{E}_{\mathrm{P}} = \dot{E}^{\mathrm{T}}_{\mathrm{in}} - \dot{E}^{\mathrm{T}}_{\mathrm{out}}\]

\[\dot{E}_{\mathrm{F}} = \dot{E}^{\mathrm{PH}}_{\mathrm{in}} - \dot{E}^{\mathrm{PH}}_{\mathrm{out}}\]

Case 2: Inlet above and outlet below ambient temperature. The product is the thermal exergy the stream gains below the ambient temperature. The heat released above it serves no purpose, since heat transfer across the ambient temperature has no meaningful product [2], so the thermal exergy of the inlet is destroyed. Without the split the warm and the cold exergy cannot be told apart: the heat carries the net change of physical exergy, \(\dot{E}_{\mathrm{P}} = \dot{E}_{\mathrm{F}} = |\dot{E}^{\mathrm{PH}}_{\mathrm{out}} - \dot{E}^{\mathrm{PH}}_{\mathrm{in}}|\), nothing is destroyed, and the component warns.

\[\dot{E}_{\mathrm{P}} = \dot{E}^{\mathrm{T}}_{\mathrm{out}}\]

\[\dot{E}_{\mathrm{F}} = \dot{E}^{\mathrm{T}}_{\mathrm{in}} + \dot{E}^{\mathrm{T}}_{\mathrm{out}} + \bigl(\dot{E}^{\mathrm{M}}_{\mathrm{in}} - \dot{E}^{\mathrm{M}}_{\mathrm{out}}\bigr)\]

Case 3: Both streams below ambient temperature

If split_physical_exergy=True:

\[\dot{E}_{\mathrm{P}} = \dot{E}^{\mathrm{T}}_{\mathrm{out}} - \dot{E}^{\mathrm{T}}_{\mathrm{in}}\]

\[\dot{E}_{\mathrm{F}} = \bigl(\dot{E}^{\mathrm{T}}_{\mathrm{out}} - \dot{E}^{\mathrm{T}}_{\mathrm{in}}\bigr) + \bigl(\dot{E}^{\mathrm{M}}_{\mathrm{in}} - \dot{E}^{\mathrm{M}}_{\mathrm{out}}\bigr)\]

Else:

\[\dot{E}_{\mathrm{P}} = \dot{E}^{\mathrm{PH}}_{\mathrm{out}} - \dot{E}^{\mathrm{PH}}_{\mathrm{in}}\]

\[\dot{E}_{\mathrm{F}} = \dot{E}^{\mathrm{PH}}_{\mathrm{out}} - \dot{E}^{\mathrm{PH}}_{\mathrm{in}}\]

Heat injection :math:dot{Q}>0

Case 1: Both streams above ambient temperature. As for the heat release, the heat is the change of thermal exergy with split physical exergy and of physical exergy without.

\[\dot{E}_{\mathrm{P}} = \dot{E}^{\mathrm{PH}}_{\mathrm{out}} - \dot{E}^{\mathrm{PH}}_{\mathrm{in}}\]

\[\dot{E}_{\mathrm{F}} = \dot{E}^{\mathrm{T}}_{\mathrm{out}} - \dot{E}^{\mathrm{T}}_{\mathrm{in}}\]

Case 2: Inlet below and outlet above ambient temperature. The product is the thermal exergy of the outlet. The cold exergy of the inlet is used up while the heat warms the stream to the ambient temperature, which has no meaningful product [2], so it is destroyed, as when a stream is cooled across the ambient temperature. Without the split, as there, \(\dot{E}_{\mathrm{P}} = \dot{E}_{\mathrm{F}} = |\dot{E}^{\mathrm{PH}}_{\mathrm{out}} - \dot{E}^{\mathrm{PH}}_{\mathrm{in}}|\) and the component warns.

\[\dot{E}_{\mathrm{P}} = \dot{E}^{\mathrm{T}}_{\mathrm{out}}\]

\[\dot{E}_{\mathrm{F}} = \dot{E}^{\mathrm{T}}_{\mathrm{in}} + \dot{E}^{\mathrm{T}}_{\mathrm{out}} + \bigl(\dot{E}^{\mathrm{M}}_{\mathrm{in}} - \dot{E}^{\mathrm{M}}_{\mathrm{out}}\bigr)\]

Case 3: Both streams below ambient temperature. The cold exergy the stream gives up leaves with the heat and is the product; the pressure drop is fuel and destroyed [2].

If split_physical_exergy=True:

\[\dot{E}_{\mathrm{P}} = \dot{E}^{\mathrm{T}}_{\mathrm{in}} - \dot{E}^{\mathrm{T}}_{\mathrm{out}}\]

\[\dot{E}_{\mathrm{F}} = \dot{E}^{\mathrm{T}}_{\mathrm{in}} - \dot{E}^{\mathrm{T}}_{\mathrm{out}} + \bigl(\dot{E}^{\mathrm{M}}_{\mathrm{in}} - \dot{E}^{\mathrm{M}}_{\mathrm{out}}\bigr)\]

Else:

\[\dot{E}_{\mathrm{P}} = \dot{E}^{\mathrm{PH}}_{\mathrm{in}} - \dot{E}^{\mathrm{PH}}_{\mathrm{out}}\]

\[\dot{E}_{\mathrm{F}} = \dot{E}^{\mathrm{PH}}_{\mathrm{in}} - \dot{E}^{\mathrm{PH}}_{\mathrm{out}}\]

Fully dissipative or :math:dot{Q}=0

\[\dot{E}_{\mathrm{P}} = \mathrm{NaN}\]

\[\dot{E}_{\mathrm{F}} = \dot{E}^{\mathrm{PH}}_{\mathrm{in}} - \dot{E}^{\mathrm{PH}}_{\mathrm{out}}\]

Parameters:

T0 (float) – Ambient temperature (K).
p0 (float) – Ambient pressure (Pa).
split_physical_exergy (bool) – Whether to split thermal and mechanical exergy.

Raises:

ValueError – If required inlet or outlet are missing.

exergoeconomic_balance(T0, chemical_exergy_enabled=False, split_physical_exergy=True)[source]¶

Perform exergoeconomic cost balance for the simple heat exchanger.

Fuel and product costs follow the exergy definitions of calc_exergy_balance(). The heat is the product or a fuel by the direction of its exergy (see heat_exergy_reversed()), with \(\dot{C}_\mathrm{Q}\) the cost of the heat connection, zero without one, and \(\dot{Z}\) including the share of dissipative costs.

Heat as product (heat released above or taken in below the ambient temperature). The stream gives up the fuel at the specific costs it enters with, \(x \in \{\mathrm{T}, \mathrm{M}\}\) with split physical exergy and \(x = \mathrm{PH}\) without:

\[\dot{C}_\mathrm{F} = \sum_x c^{x}_\mathrm{in} \bigl(\dot{E}^{x}_\mathrm{in} - \dot{E}^{x}_\mathrm{out}\bigr), \qquad \dot{C}_\mathrm{P} = \dot{C}_\mathrm{Q}\]

Without a heat connection \(\dot{C}_\mathrm{P} = \dot{C}_\mathrm{F} + \dot{Z}\).

Heat as fuel, both streams above the ambient temperature, or without split:

\[\dot{C}_\mathrm{F} = \dot{C}_\mathrm{Q}, \qquad \dot{C}_\mathrm{P} = \dot{C}^{x}_\mathrm{out} - \dot{C}^{x}_\mathrm{in} \quad (x = \mathrm{PH})\]

Both streams below the ambient temperature, with split:

\[\dot{C}_\mathrm{F} = \dot{C}_\mathrm{Q} + \dot{C}^{\mathrm{M}}_\mathrm{in} - \dot{C}^{\mathrm{M}}_\mathrm{out}, \qquad \dot{C}_\mathrm{P} = \dot{C}^{\mathrm{T}}_\mathrm{out} - \dot{C}^{\mathrm{T}}_\mathrm{in}\]

The stream crossing the ambient temperature, with split:

\[\dot{C}_\mathrm{F} = \dot{C}^{\mathrm{T}}_\mathrm{in} + \dot{C}_\mathrm{Q} + \dot{C}^{\mathrm{M}}_\mathrm{in} - \dot{C}^{\mathrm{M}}_\mathrm{out}, \qquad \dot{C}_\mathrm{P} = \dot{C}^{\mathrm{T}}_\mathrm{out}\]

Without a product (dissipative), \(\dot{C}_\mathrm{P}\) is NaN; for \(\dot{Q} = 0\), \(\dot{C}_\mathrm{F} = \dot{C}^{\mathrm{PH}}_\mathrm{in} - \dot{C}^{\mathrm{PH}}_\mathrm{out}\).

Parameters:

T0 (float) – Ambient temperature (K).
chemical_exergy_enabled (bool, optional) – If True, chemical exergy is considered in the calculations. Default is False.
split_physical_exergy (bool, optional) – If True, the physical exergy of a material stream is split into a thermal and a mechanical share, each with its own cost variable. If False, the stream carries a single cost variable for its physical exergy. Default is True.
Attributes Set
————–
C_P (float) – Cost rate of product (currency/time).
C_F (float) – Cost rate of fuel (currency/time).
c_P (float) – Specific cost of product (currency/energy).
c_F (float) – Specific cost of fuel (currency/energy).
C_D (float) – Cost rate of exergy destruction (currency/time).
r (float) – Relative cost difference (dimensionless).
f (float) – Exergoeconomic factor (dimensionless).

heat_exergy_reversed(T0, split_physical_exergy=True)[source]¶: True if the exergy of the heat flows against the heat, as it does below the ambient temperature.

SteamGenerator¶

class exerpy.components.heat_exchanger.steam_generator.SteamGenerator(**kwargs)[source]¶

Bases: Component

Class for exergy and exergoeconomic analysis of heat exchangers.

Variables:

E_F (float) – Exergy fuel of the component \(\dot{E}_\mathrm{F}\) in \(\mathrm{W}\).
E_P (float) – Exergy product of the component \(\dot{E}_\mathrm{P}\) in \(\mathrm{W}\).
E_D (float) – Exergy destruction of the component \(\dot{E}_\mathrm{D}\) in \(\mathrm{W}\).
epsilon (float) – Exergetic efficiency of the component \(\varepsilon\) in \(-\).
inl (dict) – Dictionary containing inlet stream data with mass flows and specific exergies.
outl (dict) – Dictionary containing outlet stream data with mass flows and specific exergies.
Z_costs (float) – Investment cost rate of the component in currency/h.
C_P (float) – Cost of product stream \(\dot{C}_P\) in currency/h.
C_F (float) – Cost of fuel stream \(\dot{C}_F\) in currency/h.
C_D (float) – Cost of exergy destruction \(\dot{C}_D\) in currency/h.
c_P (float) – Specific cost of product stream (currency per unit exergy).
c_F (float) – Specific cost of fuel stream (currency per unit exergy).
r (float) – Relative cost difference, \((c_P - c_F)/c_F\).
f (float) – Exergoeconomic factor, \(\dot{Z}/(\dot{Z} + \dot{C}_D)\).
Ex_C_col (dict) – Custom cost coefficients collection passed via kwargs.
T_hot (float) – Temperature of the heat source \(T_\mathrm{hot}\) in \(\mathrm{K}\).

Notes

The component has several input and output streams as follows.

Inlet streams:

inl[0]: Feed water inlet (high pressure)
inl[1]: Steam inlet (intermediate pressure)
inl[2]: Heat inlet (providing the heat input Q)
inl[3]: Water injection (high pressure)
inl[4]: Water injection (intermediate pressure)

Outlet streams:

outl[0]: Superheated steam outlet (high pressure)
outl[1]: Superheated steam outlet (intermediate pressure)
outl[2]: Drain / Blow down outlet

The heat is picked by its kind rather than by its index, among inlets and outlets, so it may sit on any connector (the EBSILON parser maps it to an outlet). Every material inlet that is neither the feed water nor the steam inlet is a water injection, and the drain is the material outlet that is neither of the two steam outlets, on whatever connector, and may be missing. The heat source of a steam generator is usually outside of the model, so its temperature is not known from the streams and has to be given as T_hot.

class Input(*, name: Annotated[str, msgspec.Meta(min_length=1)], T_hot: Annotated[float, msgspec.Meta(description='Absolute temperature, in K unless a unit is given'), Limit(gt=0, ge=None, le=None)] | None | UnsetType = UNSET)[source]¶

Bases: Input

T_hot: Annotated[float, msgspec.Meta(description='Absolute temperature, in K unless a unit is given'), Limit(gt=0, ge=None, le=None)] | None | UnsetType¶

aux_eqs(A, b, counter, T0, equations, chemical_exergy_enabled, split_physical_exergy=True)[source]¶

Auxiliary equations for the steam generator.

The heat carries the cost into the component and the steam carries it out. Writing \(x\) for a cost variable of a stream, the rules are the same in every split mode and only the set of \(x\) changes: \(\{\mathrm{T}, \mathrm{M}\}\) with split physical exergy, \(\{\mathrm{PH}\}\) without, and \(\mathrm{CH}\) in addition when chemical exergy is enabled.

The drain leaves at the state of the boiler water, so it is priced like the high pressure steam, for every cost variable it carries (P-principle):

\[\frac{\dot{C}^{x}_\mathrm{steam,HP}}{\dot{E}^{x}_\mathrm{steam,HP}} = \frac{\dot{C}^{x}_\mathrm{drain}}{\dot{E}^{x}_\mathrm{drain}}\]

What the component does not raise passes through at its own specific cost (F-principle). That is the mechanical exergy with the split, and the chemical exergy when it is enabled; the product variable, \(\mathrm{T}\) with the split and \(\mathrm{PH}\) without, is left to the cost balance:

\[\frac{\dot{C}^{x}_\mathrm{feed}}{\dot{E}^{x}_\mathrm{feed}} = \frac{\dot{C}^{x}_\mathrm{steam,HP}}{\dot{E}^{x}_\mathrm{steam,HP}} \qquad \frac{\dot{C}^{x}_\mathrm{in,IP}}{\dot{E}^{x}_\mathrm{in,IP}} = \frac{\dot{C}^{x}_\mathrm{steam,IP}}{\dot{E}^{x}_\mathrm{steam,IP}}\]

Both steam outlets come from the same heat, so they are produced at the same specific cost (P-principle):

\[\frac{\dot{C}^\mathrm{T}_\mathrm{steam,HP}}{\dot{E}^\mathrm{T}_\mathrm{steam,HP}} = \frac{\dot{C}^\mathrm{T}_\mathrm{steam,IP}}{\dot{E}^\mathrm{T}_\mathrm{steam,IP}} \qquad \text{or, without the split,} \qquad \frac{\dot{C}^\mathrm{PH}_\mathrm{steam,HP}}{\dot{E}^\mathrm{PH}_\mathrm{steam,HP}} = \frac{\dot{C}^\mathrm{PH}_\mathrm{steam,IP}}{\dot{E}^\mathrm{PH}_\mathrm{steam,IP}}\]

Parameters:

A (numpy.ndarray) – Coefficient matrix of the cost equation system.
b (numpy.ndarray) – Right-hand side vector of the cost equation system.
counter (int) – Index of the next free row.
T0 (float) – Ambient temperature in \(\mathrm{K}\).
equations (dict) – Dictionary documenting the equations.
chemical_exergy_enabled (bool) – Whether chemical exergy is part of the analysis.
split_physical_exergy (bool, optional) – If True, the physical exergy of a material stream is split into a thermal and a mechanical share, each with its own cost variable. If False, the stream carries a single cost variable for its physical exergy. Default is True.

Returns:

tuple – The updated matrix, vector, row index and equation dictionary.

calc_exergy_balance(T0: float, p0: float, split_physical_exergy) → None[source]¶

Compute the exergy balance of the steam generator.

The fuel is the exergy of the heat entering the component,

\[\dot{E}_{\mathrm{F}} = \dot{Q} \cdot \left(1 - \frac{T_0}{T_\mathrm{hot}}\right)\]

with \(T_\mathrm{hot}\) the temperature of the heat source, which the component takes from its T_hot attribute. The heat source of a steam generator is usually outside of the model, so that temperature is not known from the streams and has to be given.

The product is the physical exergy the water and steam streams gain,

\[\dot{E}_\mathrm{P} = \Bigl[ \dot E^{\mathrm{PH}}_{\mathrm{out,HP}} - \dot E^{\mathrm{PH}}_{\mathrm{in,HP}} \Bigr] + \Bigl[ \dot E^{\mathrm{PH}}_{\mathrm{out,IP}} - \dot E^{\mathrm{PH}}_{\mathrm{in,IP}} \Bigr] - \sum \dot E^{\mathrm{PH}}_{\mathrm{w}}\]

where the subscripts HP and IP denote the high and the intermediate pressure streams and w the water injections. The drain is not part of the product, so its exergy is counted as destruction, together with the losses of the component.

Parameters:

T0 (float) – Ambient temperature (K).
p0 (float) – Ambient pressure (Pa).
split_physical_exergy (bool) – Whether to split thermal and mechanical exergy. The fuel and the product of this component are the same either way.

Raises:

ValueError – If required inlets or outlets are missing.

Notes

Without T_hot the fuel cannot be evaluated from the heat, and the thermal exergy the water and steam streams gain is used instead. That makes the fuel of the component an approximation of itself: with split physical exergy it exceeds the product by the mechanical exergy alone, and without the split the two are equal and the exergy destruction is zero. The component warns in that case.

exergoeconomic_balance(T0, chemical_exergy_enabled=False, split_physical_exergy=True)[source]¶

Perform the exergoeconomic cost balance of the steam generator.

Fuel and product follow calc_exergy_balance(): the fuel is the heat entering the component and the product is the cost the water and steam streams gain. The drain is not part of the product, so the cost leaving with it raises the cost of the exergy destruction.

Parameters:

T0 (float) – Ambient temperature in \(\mathrm{K}\).
chemical_exergy_enabled (bool, optional) – If True, chemical exergy is considered in the calculations.
split_physical_exergy (bool, optional) – If True, the physical exergy of a material stream is split into a thermal and a mechanical share, each with its own cost variable. If False, the stream carries a single cost variable for its physical exergy. Default is True.

Turbine¶

class exerpy.components.turbomachinery.turbine.Turbine(**kwargs)[source]¶

Bases: Component

Class for exergy analysis of turbines.

This class performs exergy analysis calculations for turbines, with definitions of exergy product and fuel varying based on the temperature relationships between inlet stream, outlet stream, and ambient conditions.

Parameters:

**kwargs (dict) – Arbitrary keyword arguments passed to parent class.

Variables:

E_F (float) – Exergy fuel of the component \(\dot{E}_\mathrm{F}\) in \(\mathrm{W}\).
E_P (float) – Exergy product of the component \(\dot{E}_\mathrm{P}\) in \(\mathrm{W}\).
E_D (float) – Exergy destruction of the component \(\dot{E}_\mathrm{D}\) in \(\mathrm{W}\).
epsilon (float) – Exergetic efficiency of the component \(\varepsilon\) in \(-\).
P (float) – Power output of the turbine in \(\mathrm{W}\).
inl (dict) – Dictionary containing inlet stream data with temperature, mass flows, enthalpies, and specific exergies. Must have at least one inlet.
outl (dict) – Dictionary containing outlet streams data with temperature, mass flows, enthalpies, and specific exergies. Can have multiple outlets, their properties will be summed up in the calculations.

Notes

The exergy analysis considers three cases based on temperature relationships:

\[ \begin{align}\begin{aligned}\begin{split}\dot{E}_\mathrm{P} = \begin{cases} -P & T_\mathrm{in}, T_\mathrm{out} \geq T_0\\ -P + \dot{E}_\mathrm{out}^\mathrm{T} & T_\mathrm{in} > T_0 \geq T_\mathrm{out}\\ -P + \dot{E}_\mathrm{out}^\mathrm{T} - \dot{E}_\mathrm{in}^\mathrm{T} & T_0 \geq T_\mathrm{in}, T_\mathrm{out} \end{cases}\end{split}\\\begin{split}\dot{E}_\mathrm{F} = \begin{cases} \dot{E}_\mathrm{in}^\mathrm{PH} - \dot{E}_\mathrm{out}^\mathrm{PH} & T_\mathrm{in}, T_\mathrm{out} \geq T_0\\ \dot{E}_\mathrm{in}^\mathrm{T} + \dot{E}_\mathrm{in}^\mathrm{M} - \dot{E}_\mathrm{out}^\mathrm{M} & T_\mathrm{in} > T_0 \geq T_\mathrm{out}\\ \dot{E}_\mathrm{in}^\mathrm{M} - \dot{E}_\mathrm{out}^\mathrm{M} & T_0 \geq T_\mathrm{in}, T_\mathrm{out} \end{cases}\end{split}\end{aligned}\end{align} \]

aux_eqs(A, b, counter, T0, equations, chemical_exergy_enabled, split_physical_exergy=True)[source]¶

Auxiliary equations for the turbine.

The power is the product of the turbine and the expanding stream is its fuel, so every cost variable the stream carries follows the F-principle: it leaves the component at the specific cost at which it entered.

With split physical exergy, for every material outlet:

\[\frac{\dot{C}^\mathrm{T}_\mathrm{in}}{\dot{E}^\mathrm{T}_\mathrm{in}} = \frac{\dot{C}^\mathrm{T}_\mathrm{out}}{\dot{E}^\mathrm{T}_\mathrm{out}} \qquad \frac{\dot{C}^\mathrm{M}_\mathrm{in}}{\dot{E}^\mathrm{M}_\mathrm{in}} = \frac{\dot{C}^\mathrm{M}_\mathrm{out}}{\dot{E}^\mathrm{M}_\mathrm{out}}\]

Without the split the stream carries a single cost variable for its physical exergy, and the two rules above collapse into one:

\[\frac{\dot{C}^\mathrm{PH}_\mathrm{in}}{\dot{E}^\mathrm{PH}_\mathrm{in}} = \frac{\dot{C}^\mathrm{PH}_\mathrm{out}}{\dot{E}^\mathrm{PH}_\mathrm{out}}\]

With chemical exergy enabled, either way:

\[\frac{\dot{C}^\mathrm{CH}_\mathrm{in}}{\dot{E}^\mathrm{CH}_\mathrm{in}} = \frac{\dot{C}^\mathrm{CH}_\mathrm{out}}{\dot{E}^\mathrm{CH}_\mathrm{out}}\]

The power leaving the turbine is one single product, so all of its outlets are priced alike (P-principle), against the first of them that carries power:

\[\frac{\dot{C}^\mathrm{TOT}_\mathrm{ref}}{\dot{E}^\mathrm{TOT}_\mathrm{ref}} = \frac{\dot{C}^\mathrm{TOT}_\mathrm{out}}{\dot{E}^\mathrm{TOT}_\mathrm{out}}\]

Expanding below the ambient temperature is only resolved with the split. Without it the component warns and charges the outlet with the specific cost of the physical exergy of the inlet; with it, the case is not implemented and no equation is written.

Parameters:

A (numpy.ndarray) – The current cost matrix.
b (numpy.ndarray) – The current right-hand-side vector.
counter (int) – The current row index in the matrix.
T0 (float) – Ambient temperature.
equations (list or dict) – Data structure for storing equation labels.
chemical_exergy_enabled (bool) – Flag indicating whether chemical exergy auxiliary equations should be added.
split_physical_exergy (bool, optional) – If True, the physical exergy of a material stream is split into a thermal and a mechanical share, each with its own cost variable. If False, the stream carries a single cost variable for its physical exergy. Default is True.

Returns:

A (numpy.ndarray) – The updated cost matrix.
b (numpy.ndarray) – The updated right-hand-side vector.
counter (int) – The updated row index after adding all auxiliary equations.
equations (list or dict) – Updated structure with equation labels.

calc_exergy_balance(T0: float, p0: float, split_physical_exergy) → None[source]¶

Calculate the exergy balance of the turbine.

Performs exergy balance calculations considering the temperature relationships between inlet stream, outlet stream, and ambient conditions.

Parameters:

T0 (float) – Ambient temperature in \(\mathrm{K}\).
p0 (float) – Ambient pressure in \(\mathrm{Pa}\).
split_physical_exergy (bool) – Flag indicating whether physical exergy is split into thermal and mechanical components.

Notes

Below the ambient temperature the expansion produces cold exergy along with the power. Crediting it to the product requires the thermal part of the physical exergy, so with split_physical_exergy=False the balance falls back to

\[\dot{E}_\mathrm{P} = |P| \qquad \dot{E}_\mathrm{F} = \dot{E}^\mathrm{PH}_\mathrm{in} - \sum \dot{E}^\mathrm{PH}_\mathrm{out}\]

which leaves the cold exergy in the outlet stream instead of counting it as product. The exergy destruction is the same either way, the exergetic efficiency is not.

exergoeconomic_balance(T0, chemical_exergy_enabled=False, split_physical_exergy=True)[source]¶

Perform exergoeconomic cost balance for the turbine.

The general exergoeconomic balance equation is:

\[\dot{C}^{\mathrm{T}}_{\mathrm{in}} + \dot{C}^{\mathrm{M}}_{\mathrm{in}} - \dot{C}^{\mathrm{T}}_{\mathrm{out}} - \dot{C}^{\mathrm{M}}_{\mathrm{out}} + \dot{Z} = 0\]

In case the chemical exergy of the streams is known:

\[\dot{C}^{\mathrm{CH}}_{\mathrm{in}} = \dot{C}^{\mathrm{CH}}_{\mathrm{out}}\]

This method computes cost rates for product and fuel, and derives exergoeconomic indicators. The turbine may have multiple power outputs and multiple material outlets. The product cost includes the total cost of all power streams, while material outlet costs are summed accordingly.

Case 1: Inlet and outlet above ambient temperature

Both inlet and first material outlet satisfy \(T \geq T_0\):

\[\dot{C}_{\mathrm{P}} = \sum \dot{C}^{\mathrm{TOT}}_{\mathrm{power,out}}\]

\[\dot{C}_{\mathrm{F}} = \dot{C}^{\mathrm{PH}}_{\mathrm{in}} - \sum \dot{C}^{\mathrm{PH}}_{\mathrm{material,out}}\]

Case 2: Inlet above and outlet at or below ambient temperature

Inlet satisfies \(T > T_0\) and first material outlet \(T \leq T_0\):

\[\dot{C}_{\mathrm{P}} = \sum \dot{C}^{\mathrm{TOT}}_{\mathrm{power,out}} + \sum \dot{C}^{\mathrm{T}}_{\mathrm{material,out}}\]

\[\dot{C}_{\mathrm{F}} = \dot{C}^{\mathrm{T}}_{\mathrm{in}} + \bigl(\dot{C}^{\mathrm{M}}_{\mathrm{in}} - \sum \dot{C}^{\mathrm{M}}_{\mathrm{material,out}}\bigr)\]

Case 3: Both inlet and outlet at or below ambient temperature

Both inlet and first material outlet satisfy \(T \leq T_0\):

\[\dot{C}_{\mathrm{P}} = \sum \dot{C}^{\mathrm{TOT}}_{\mathrm{power,out}} + \bigl(\sum \dot{C}^{\mathrm{T}}_{\mathrm{material,out}} - \dot{C}^{\mathrm{T}}_{\mathrm{in}}\bigr)\]

\[\dot{C}_{\mathrm{F}} = \dot{C}^{\mathrm{M}}_{\mathrm{in}} - \sum \dot{C}^{\mathrm{M}}_{\mathrm{material,out}}\]

Parameters:

T0 (float) – Ambient temperature (K).
chemical_exergy_enabled (bool, optional) – If True, chemical exergy is considered in the calculations. Default is False.
split_physical_exergy (bool, optional) – If True, the physical exergy of a material stream is split into a thermal and a mechanical share, each with its own cost variable. If False, the stream carries a single cost variable for its physical exergy. Default is True.
Attributes Set
————–
C_P (float) – Cost rate of product (currency/time).
C_F (float) – Cost rate of fuel (currency/time).
c_P (float) – Specific cost of product (currency/energy).
c_F (float) – Specific cost of fuel (currency/energy).
C_D (float) – Cost rate of exergy destruction (currency/time).
r (float) – Relative cost difference (dimensionless).
f (float) – Exergoeconomic factor (dimensionless).

Compressor¶

class exerpy.components.turbomachinery.compressor.Compressor(**kwargs)[source]¶

Bases: Component

Class for exergy and exergoeconomic analysis of compressors.

This class performs exergy and exergoeconomic analysis calculations for compressors, considering thermal, mechanical, and physical exergy flows. The exergy product and fuel are calculated based on temperature relationships between inlet, outlet, and ambient conditions.

Parameters:

**kwargs (dict) – Arbitrary keyword arguments passed to parent class. Optional parameter ‘Z_costs’ (float): Investment cost rate of the component in currency/h.

Variables:

E_F (float) – Exergy fuel of the component \(\dot{E}_\mathrm{F}\) in \(\mathrm{W}\).
E_P (float) – Exergy product of the component \(\dot{E}_\mathrm{P}\) in \(\mathrm{W}\).
E_D (float) – Exergy destruction of the component \(\dot{E}_\mathrm{D}\) in \(\mathrm{W}\).
epsilon (float) – Exergetic efficiency of the component \(\varepsilon\) in \(-\).
P (float) – Power input to the compressor in \(\mathrm{W}\).
inl (dict) – Dictionary containing inlet stream data with temperature, mass flows, enthalpies, and specific exergies.
outl (dict) – Dictionary containing outlet stream data with temperature, mass flows, enthalpies, and specific exergies.
Z_costs (float) – Investment cost rate of the component in currency/h.

Notes

The exergy analysis considers three cases based on temperature relationships:

Case 1 - Both temperatures at or above ambient (\(T_\mathrm{in}, T_\mathrm{out} \geq T_0\)):

\[\begin{split}\dot{E}_\mathrm{P} &= \dot{m} \cdot (e_\mathrm{out}^\mathrm{PH} - e_\mathrm{in}^\mathrm{PH})\\ \dot{E}_\mathrm{F} &= |\dot{W}|\end{split}\]

Case 2 - Inlet below, outlet above ambient (\(T_\mathrm{in} < T_0 < T_\mathrm{out}\)):

\[\begin{split}\dot{E}_\mathrm{P} &= \dot{m} \cdot e_\mathrm{out}^\mathrm{T} + \dot{m} \cdot (e_\mathrm{out}^\mathrm{M} - e_\mathrm{in}^\mathrm{M})\\ \dot{E}_\mathrm{F} &= |\dot{W}| + \dot{m} \cdot e_\mathrm{in}^\mathrm{T}\end{split}\]

Case 3 - Both temperatures below ambient (\(T_\mathrm{in}, T_\mathrm{out} \leq T_0\)):

\[\begin{split}\dot{E}_\mathrm{P} &= \dot{m} \cdot (e_\mathrm{out}^\mathrm{M} - e_\mathrm{in}^\mathrm{M})\\ \dot{E}_\mathrm{F} &= |\dot{W}| + \dot{m} \cdot (e_\mathrm{in}^\mathrm{T} - e_\mathrm{out}^\mathrm{T})\end{split}\]

For all valid cases, the exergy destruction is:

\[\dot{E}_\mathrm{D} = \dot{E}_\mathrm{F} - \dot{E}_\mathrm{P}\]

where:

\(\dot{W}\): Power input
\(e^\mathrm{T}\): Thermal exergy
\(e^\mathrm{M}\): Mechanical exergy
\(e^\mathrm{PH}\): Physical exergy

aux_eqs(A, b, counter, T0, equations, chemical_exergy_enabled, split_physical_exergy=True)[source]¶

Auxiliary equations for the compressor.

The power driving the compressor is its fuel and what the stream gains is its product. With chemical exergy enabled the composition does not change, so its specific cost passes through unchanged (F-principle), whether or not the physical exergy is split:

\[\frac{\dot{C}^\mathrm{CH}_\mathrm{in}}{\dot{E}^\mathrm{CH}_\mathrm{in}} = \frac{\dot{C}^\mathrm{CH}_\mathrm{out}}{\dot{E}^\mathrm{CH}_\mathrm{out}}\]

Without split physical exergy no further equation is written. The stream carries a single cost variable for its physical exergy, that variable is the only one the component produces, and the cost balance alone determines it:

\[\dot{C}^\mathrm{PH}_\mathrm{out} = \dot{C}^\mathrm{PH}_\mathrm{in} + \dot{C}^\mathrm{TOT}_\mathrm{power} + \dot{Z}\]

With split physical exergy the outlet carries two cost variables, so one equation is needed, and which one depends on where the stream sits relative to the ambient temperature.

Both streams above \(T_0\): the thermal and the mechanical exergy are both gained, so both are part of the product and are priced alike (P-principle):

\[\frac{\dot{C}^\mathrm{T}_\mathrm{out} - \dot{C}^\mathrm{T}_\mathrm{in}} {\dot{E}^\mathrm{T}_\mathrm{out} - \dot{E}^\mathrm{T}_\mathrm{in}} = \frac{\dot{C}^\mathrm{M}_\mathrm{out} - \dot{C}^\mathrm{M}_\mathrm{in}} {\dot{E}^\mathrm{M}_\mathrm{out} - \dot{E}^\mathrm{M}_\mathrm{in}}\]

Inlet at or below and outlet above \(T_0\): the outlet carries thermal exergy that the inlet did not have, so the whole of it is product:

\[\frac{\dot{C}^\mathrm{T}_\mathrm{out}}{\dot{E}^\mathrm{T}_\mathrm{out}} = \frac{\dot{C}^\mathrm{M}_\mathrm{out} - \dot{C}^\mathrm{M}_\mathrm{in}} {\dot{E}^\mathrm{M}_\mathrm{out} - \dot{E}^\mathrm{M}_\mathrm{in}}\]

Both streams at or below \(T_0\): the cold exergy of the stream is consumed, so it is fuel and follows the F-principle:

\[\frac{\dot{C}^\mathrm{T}_\mathrm{in}}{\dot{E}^\mathrm{T}_\mathrm{in}} = \frac{\dot{C}^\mathrm{T}_\mathrm{out}}{\dot{E}^\mathrm{T}_\mathrm{out}}\]

A share the stream does not gain passes through at its own specific cost instead, and a share the outlet does not carry has no cost, \(\dot{C}^{x}_\mathrm{out} = 0\).

Below the ambient temperature the split is what separates the cold exergy from the pressure rise, so running without it there makes the component warn.

Parameters:

A (numpy.ndarray) – The current cost matrix.
b (numpy.ndarray) – The current right-hand-side vector.
counter (int) – The current row index in the matrix.
T0 (float) – Ambient temperature.
equations (list or dict) – Data structure for storing equation labels.
chemical_exergy_enabled (bool) – Flag indicating whether chemical exergy auxiliary equations should be added.
split_physical_exergy (bool, optional) – If True, the physical exergy of a material stream is split into a thermal and a mechanical share, each with its own cost variable. If False, the stream carries a single cost variable for its physical exergy. Default is True.

Returns:

A (numpy.ndarray) – The updated cost matrix.
b (numpy.ndarray) – The updated right-hand-side vector.
counter (int) – The updated row index (increased by 2 if chemical exergy is enabled, or by 1 otherwise).
equations (list or dict) – Updated structure with equation labels.

calc_exergy_balance(T0: float, p0: float, split_physical_exergy) → None[source]¶

Calculate the exergy balance of the compressor.

Performs exergy balance calculations considering the temperature relationships between inlet stream, outlet stream, and ambient conditions.

Parameters:

T0 (float) – Ambient temperature in \(\mathrm{K}\).
p0 (float) – Ambient pressure in \(\mathrm{Pa}\).
split_physical_exergy (bool) – Flag indicating whether physical exergy is split into thermal and mechanical components.

exergoeconomic_balance(T0, chemical_exergy_enabled=False, split_physical_exergy=True)[source]¶

Perform exergoeconomic cost balance for the compressor.

The general exergoeconomic balance equation is:

\[\dot{C}^{\mathrm{T}}_{\mathrm{in}} + \dot{C}^{\mathrm{M}}_{\mathrm{in}} - \dot{C}^{\mathrm{T}}_{\mathrm{out}} - \dot{C}^{\mathrm{M}}_{\mathrm{out}} + \dot{Z} = 0\]

In case the chemical exergy of the streams is known:

\[\dot{C}^{\mathrm{CH}}_{\mathrm{in}} = \dot{C}^{\mathrm{CH}}_{\mathrm{out}}\]

This method computes cost rates for product and fuel, and derives exergoeconomic indicators. The compressor consumes power (fuel) to increase the exergy of the working fluid (product).

Case 1: Both inlet and outlet above ambient temperature

Both inlet and outlet satisfy \(T \geq T_0\):

\[\dot{C}_{\mathrm{P}} = \dot{C}^{\mathrm{PH}}_{\mathrm{out}} - \dot{C}^{\mathrm{PH}}_{\mathrm{in}}\]

\[\dot{C}_{\mathrm{F}} = \dot{C}^{\mathrm{TOT}}_{\mathrm{power,in}}\]

Case 2: Inlet at or below and outlet above ambient temperature

Inlet satisfies \(T \leq T_0\) and outlet \(T > T_0\):

\[\dot{C}_{\mathrm{P}} = \dot{C}^{\mathrm{T}}_{\mathrm{out}} + \bigl(\dot{C}^{\mathrm{M}}_{\mathrm{out}} - \dot{C}^{\mathrm{M}}_{\mathrm{in}}\bigr)\]

\[\dot{C}_{\mathrm{F}} = \dot{C}^{\mathrm{TOT}}_{\mathrm{power,in}} + \dot{C}^{\mathrm{T}}_{\mathrm{in}}\]

Case 3: Both inlet and outlet at or below ambient temperature

Both inlet and outlet satisfy \(T \leq T_0\):

\[\dot{C}_{\mathrm{P}} = \dot{C}^{\mathrm{M}}_{\mathrm{out}} - \dot{C}^{\mathrm{M}}_{\mathrm{in}}\]

\[\dot{C}_{\mathrm{F}} = \dot{C}^{\mathrm{TOT}}_{\mathrm{power,in}} + \bigl(\dot{C}^{\mathrm{T}}_{\mathrm{in}} - \dot{C}^{\mathrm{T}}_{\mathrm{out}}\bigr)\]

Parameters:

T0 (float) – Ambient temperature (K).
chemical_exergy_enabled (bool, optional) – If True, chemical exergy is considered in the calculations. Default is False.
split_physical_exergy (bool, optional) – If True, the physical exergy of a material stream is split into a thermal and a mechanical share, each with its own cost variable. If False, the stream carries a single cost variable for its physical exergy. Default is True.
Attributes Set
————–
C_P (float) – Cost rate of product (currency/time).
C_F (float) – Cost rate of fuel (currency/time).
c_P (float) – Specific cost of product (currency/energy).
c_F (float) – Specific cost of fuel (currency/energy).
C_D (float) – Cost rate of exergy destruction (currency/time).
r (float) – Relative cost difference (dimensionless).
f (float) – Exergoeconomic factor (dimensionless).

Raises:

ValueError – If no inlet power stream is found.

Pump¶

class exerpy.components.turbomachinery.pump.Pump(**kwargs)[source]¶

Bases: Component

Class for exergy analysis of pumps.

This class performs exergy analysis calculations for pumps, with definitions of exergy product and fuel varying based on the temperature relationships between inlet stream, outlet stream, and ambient conditions.

Parameters:

**kwargs (dict) – Arbitrary keyword arguments passed to parent class.

Variables:

E_F (float) – Exergy fuel of the component \(\dot{E}_\mathrm{F}\) in \(\mathrm{W}\).
E_P (float) – Exergy product of the component \(\dot{E}_\mathrm{P}\) in \(\mathrm{W}\).
E_D (float) – Exergy destruction of the component \(\dot{E}_\mathrm{D}\) in \(\mathrm{W}\).
epsilon (float) – Exergetic efficiency of the component \(\varepsilon\) in \(-\).
P (float) – Power input to the pump in \(\mathrm{W}\).
inl (dict) – Dictionary containing inlet stream data with temperature, mass flows, enthalpies, and specific exergies.
outl (dict) – Dictionary containing outlet stream data with temperature, mass flows, enthalpies, and specific exergies.

Notes

The exergy analysis considers three cases based on temperature relationships:

Case 1 - Both temperatures at or above ambient (\(T_\mathrm{in}, T_\mathrm{out} \geq T_0\)):

\[\begin{split}\dot{E}_\mathrm{P} &= \dot{m} \cdot (e_\mathrm{out}^\mathrm{PH} - e_\mathrm{in}^\mathrm{PH})\\ \dot{E}_\mathrm{F} &= |\dot{W}|\end{split}\]

Case 2 - Inlet below, outlet above ambient (\(T_\mathrm{in} < T_0 < T_\mathrm{out}\)), with split physical exergy:

\[\begin{split}\dot{E}_\mathrm{P} &= \dot{m} \cdot \bigl(e_\mathrm{out}^\mathrm{T} + e_\mathrm{out}^\mathrm{M} - e_\mathrm{in}^\mathrm{M}\bigr)\\ \dot{E}_\mathrm{F} &= |\dot{W}| + \dot{m} \cdot e_\mathrm{in}^\mathrm{T}\end{split}\]

Case 3 - Both temperatures below ambient (\(T_\mathrm{in}, T_\mathrm{out} \leq T_0\)), with split physical exergy:

Without the split, cases 2 and 3 fall back to case 1 and the pump warns.

For all valid cases, the exergy destruction is:

\[\dot{E}_\mathrm{D} = \dot{E}_\mathrm{F} - \dot{E}_\mathrm{P}\]

If the outlet is colder than the inlet, fuel and product are not defined and the exergy destruction is the exergy balance, \(|\dot{W}| + \dot{m}\,(e_\mathrm{in}^\mathrm{PH} - e_\mathrm{out}^\mathrm{PH})\).

where:

\(\dot{W}\): Power input
\(e^\mathrm{PH}\): Physical exergy
\(e^\mathrm{M}\): Mechanical exergy

aux_eqs(A, b, counter, T0, equations, chemical_exergy_enabled, split_physical_exergy=True)[source]¶

Auxiliary equations for the pump.

The power driving the pump is its fuel and what the stream gains is its product. With chemical exergy enabled the composition does not change, so its specific cost passes through unchanged (F-principle), whether or not the physical exergy is split: