add rtd for cstrs

docs/reference/reactors/rtd/_SUMMARY.md

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+* [cstr_cumulative](cstr_cumulative.md)
+* [cstr_differential](cstr_differential.md)
+* [tanks_series_cumulative](tanks_series_cumulative.md)
+* [tanks_series_differential](tanks_series_differential.md)

docs/reference/reactors/rtd/cstr_cumulative.md

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+# polykin.reactors.rtd
+
+::: polykin.reactors.rtd
+    options:
+        members:
+            - cstr_cumulative

docs/reference/reactors/rtd/cstr_differential.md

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+# polykin.reactors.rtd
+
+::: polykin.reactors.rtd
+    options:
+        members:
+            - cstr_differential

docs/reference/reactors/rtd/tanks_series_cumulative.md

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+# polykin.reactors.rtd
+
+::: polykin.reactors.rtd
+    options:
+        members:
+            - tanks_series_cumulative

docs/reference/reactors/rtd/tanks_series_differential.md

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+# polykin.reactors.rtd
+
+::: polykin.reactors.rtd
+    options:
+        members:
+            - tanks_series_differential

mkdocs.yml

@@ -170,6 +170,8 @@ nav:
           - Thermal Conductivity: reference/properties/thermal_conductivity/
           - Vaporization Enthalpy: reference/properties/vaporization_enthalpy/
           - Viscosity: reference/properties/viscosity/
+      - Reactors:
+          - Residence Time Distributions: reference/reactors/rtd/
       - Thermodynamics:
           #- reference/thermo/index.md
           - Activity Coeff. Models: reference/thermo/acm/

src/polykin/reactors/__init__.py

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+# PolyKin: A polymerization kinetics library for Python.
+#
+# Copyright Hugo Vale 2024
+
+from .rtd import *

src/polykin/reactors/rtd.py

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+# PolyKin: A polymerization kinetics library for Python.
+#
+# Copyright Hugo Vale 2024
+
+from math import gamma
+
+from numpy import exp
+
+__all__ = ['cstr_differential',
+           'cstr_cumulative',
+           'tanks_series_differential',
+           'tanks_series_cumulative',
+           ]
+
+
+def cstr_differential(t: float, tavg: float) -> float:
+    r"""Differential residence time distribution for a single CSTR.
+
+    $$ E(t) = \frac{1}{\bar{t}} e^{-t/\bar{t}} $$
+
+    **References**
+
+    * Levenspiel, O. "Chemical reaction engineering", John wiley & sons, 1998, 
+      p. 322.
+
+    Parameters
+    ----------
+    t : float
+        Time.
+    tavg : float
+        Average residence time, $\bar{t}$.
+
+    Returns
+    -------
+    float
+        Differential residence time distribution.
+    """
+    return (1/tavg)*exp(-t/tavg)
+
+
+def cstr_cumulative(t: float, tavg: float) -> float:
+    r"""Cumulative residence time distribution for a single CSTR.
+
+    $$ F(t) = 1 - e^{-t/\bar{t}} $$
+
+    **References**
+
+    * Levenspiel, O. "Chemical reaction engineering", John wiley & sons, 1998, 
+      p. 327.
+
+    Parameters
+    ----------
+    t : float
+        Time.
+    tavg : float
+        Average residence time, $\bar{t}$.
+
+    Returns
+    -------
+    float
+        Cumulative residence time distribution.
+    """
+    return 1 - exp(-t/tavg)
+
+
+def tanks_series_differential(t: float, tavg: float, N: int) -> float:
+    r"""Differential residence time distribution for a series of equal CSTRs.
+
+    $$ E(t) =  \frac{1}{\bar{t}} \left(\frac{t}{\bar{t}} \right)^{N-1} 
+               \frac{N^N}{(N-1)!} e^{-N t / \bar{t}} $$
+
+    **References**
+
+    * Levenspiel, O. "Chemical reaction engineering", John wiley & sons, 1998, 
+      p. 322.
+
+    Parameters
+    ----------
+    t : float
+        Time.
+    tavg : float
+        Total average residence time, $\bar{t}$.
+    N : int
+        Number of tanks in series.
+
+    Returns
+    -------
+    float
+        Differential residence time distribution.
+    """
+    q = t/tavg
+    return q**(N-1) * (N**N / gamma(N)) * exp(-N*q) / tavg
+
+
+def tanks_series_cumulative(t: float, tavg: float, N: int) -> float:
+    r"""Cumulative residence time distribution for a series of equal CSTRs.
+
+    $$ F(t) = 1 - e^{-N t / \bar{t}} \; 
+        \sum_{i=0}^{N-1} \frac{(N t / \bar{t})^i}{i!}  $$
+
+    **References**
+
+    * Levenspiel, O. "Chemical reaction engineering", John wiley & sons, 1998, 
+      p. 327.
+
+    Parameters
+    ----------
+    t : float
+        Time.
+    tavg : float
+        Total average residence time, $\bar{t}$.
+    N : int
+        Number of tanks in series.
+
+    Returns
+    -------
+    float
+        Cumulative residence time distribution.
+    """
+    q = t/tavg
+    S = sum((N*q)**i / gamma(i+1) for i in range(1, N))
+    return 1 - exp(-N*q) * (1 + S)

tests/reactors/test_rtd.py

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+from numpy import exp, isclose
+
+from polykin.reactors.rtd import *
+
+
+def test_cstr_differential():
+    assert isclose(cstr_differential(0, 1), 1)
+    assert isclose(cstr_differential(1e8, 1), 0)
+    assert isclose(cstr_differential(1, 1), exp(-1))
+
+
+def testcstr_cumulative():
+    assert isclose(cstr_cumulative(0, 1), 0)
+    assert isclose(cstr_cumulative(1e8, 1), 1)
+    assert isclose(cstr_cumulative(1, 1), 0.63, rtol=0.01)
+
+
+def test_tanks_series_differential():
+    # N = 1
+    N = 1
+    assert isclose(tanks_series_differential(0, 1, N), 1)
+    assert isclose(tanks_series_differential(1e8, 1, N), 0)
+    assert isclose(tanks_series_differential(1, 1, N), exp(-1))
+    # N > 1
+    for N in range(2, 10):
+        assert isclose(tanks_series_differential(0, 1, N), 0)
+        assert isclose(tanks_series_differential(1e8, 1, N), 0)
+    assert isclose(tanks_series_differential(1, 1, 20), 1.8, atol=0.1)
+
+
+def test_tanks_series_cumulative():
+    for N in range(1, 10):
+        assert isclose(tanks_series_cumulative(0, 1, N), 0)
+        assert isclose(tanks_series_cumulative(1e8, 1, N), 1)
+    assert isclose(tanks_series_cumulative(1, 1, N=1), 0.63, rtol=0.01)
+    assert isclose(tanks_series_cumulative(0.85, 1, N=2), 0.5, atol=0.01)
+    assert isclose(tanks_series_cumulative(1, 1, N=20), 0.52, atol=0.01)
+    assert isclose(tanks_series_cumulative(0.5, 1, N=20), 0.0, atol=0.01)
+    assert isclose(tanks_series_cumulative(1.6, 1, N=20), 1.0, atol=0.01)