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polykin.reactors.rtd¤

F_laminar_flow ¤

F_laminar_flow(t: float, tavg: float) -> float

Cumulative residence time distribution for a tubular reactor with laminar flow.

\[ F(t) = \begin{cases} 0 , & t \le \bar{t}/2 \\ 1 - \frac{1}{4} (t/\bar{t})^{-2} , & \text{else} \end{cases} \]

References

  • Levenspiel, O. "Chemical reaction engineering", 3rd ed., John Wiley & Sons, 1999, p. 344.
PARAMETER DESCRIPTION
t

Residence time.

TYPE: float

tavg

Average residence time, \(\bar{t}\).

TYPE: float

RETURNS DESCRIPTION
float

Cumulative residence time distribution.
See also
  • E_laminar_flow: related method to determine the differential distribution.
Source code in src/polykin/reactors/rtd.py 
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def F_laminar_flow(t: float, tavg: float) -> float:
    r"""Cumulative residence time distribution for a tubular reactor with
    laminar flow.

    $$ F(t) =
    \begin{cases}
        0 , & t \le \bar{t}/2 \\
        1 - \frac{1}{4} (t/\bar{t})^{-2} , & \text{else}
    \end{cases} $$

    **References**

    * Levenspiel, O. "Chemical reaction engineering", 3rd ed., John Wiley &
      Sons, 1999, p. 344.

    Parameters
    ----------
    t : float
        Residence time.
    tavg : float
        Average residence time, $\bar{t}$.

    Returns
    -------
    float
        Cumulative residence time distribution.

    See also
    --------
    * [`E_laminar_flow`](E_laminar_flow.md): related method to determine the
      differential distribution.
    """
    q = t/tavg
    if q <= 1/2:
        return 0
    else:
        return 1 - 1/(4*q**2)