RTDs of ideal and real reactors Residence time distribution

1 rtds of ideal , real reactors

1.1 plug flow reactors
1.2 continuous stirred-tank reactors
1.3 oceanographic
1.4 biochemical

rtds of ideal , real reactors

the residence time distribution of reactor can used compare behaviour of 2 ideal reactor models: plug-flow reactor , continuous stirred-tank reactor (cstr), or mixed-flow reactor. characteristic important in order calculate performance of reaction known kinetics.

plug flow reactors

in ideal plug-flow reactor there no axial mixing , fluid elements leave in same order arrived. therefore, fluid entering reactor @ time



t


{\displaystyle t}

exit reactor @ time



t
+
τ


{\displaystyle t+\tau }

,



τ


{\displaystyle \tau }

residence time of reactor. residence time distribution function therefore dirac delta function @



τ


{\displaystyle \tau }

.

e
(
t
)
=
δ
(
t
−
τ
)



{\displaystyle e(t)=\delta (t-\tau )\,}

the variance of ideal plug-flow reactor zero.

the rtd of real reactor deviate of ideal reactor, depending on hydrodynamics within vessel. non-zero variance indicates there dispersion along path of fluid, may attributed turbulence, non-uniform velocity profile, or diffusion. if mean of



e
(
t
)


{\displaystyle e(t)}

curve arrives earlier expected time



τ


{\displaystyle \tau }

indicates there stagnant fluid within vessel. if rtd curve shows more 1 main peak may indicate channeling, parallel paths exit, or strong internal circulation.

continuous stirred-tank reactors

an ideal continuous stirred-tank reactor based on assumption flow @ inlet , instantly mixed bulk of reactor. reactor , outlet fluid have identical, homogeneous compositions @ times. ideal cstr has exponential residence time distribution:

e
(
t
)
=


1
τ



e

−
t

/

τ





{\displaystyle e(t)={\frac {1}{\tau }}e^{-t/\tau }\,}

in reality, impossible obtain such rapid mixing, on industrial scales reactor vessels may range between 1 , thousands of cubic meters, , hence rtd of real reactor deviate ideal exponential decay. example, there finite delay before



e
(
t
)


{\displaystyle e(t)}

reaches maximum value , length of delay reflect rate of mass transfer within reactor. noted plug-flow reactor, mean indicate stagnant fluid within vessel, while presence of multiple peaks indicate channeling, parallel paths exit, or strong internal circulation. short-circuiting fluid within reactor appear in rtd curve small pulse of concentrated tracer reaches outlet shortly after injection.

oceanographic

in chemical oceanography, residence time (t) of element defined amount of element in ocean @ steady state divided rate @ element added ocean:

t
=
(

mean concentration in ocean

)
×
(

ocean volume

)

/

(

input per year

)


{\displaystyle t=({\text{mean concentration in ocean}})\times ({\text{ocean volume}})/({\text{input per year}})}

where ocean volume (1.37×10 l). input sums inputs ocean. many elements, major input rivers , input per year mean river concentration times continental runoff rate. if concentration of element not changing, input , output of element must equal (steady state). residence time can calculated using estimated output, if known.

biochemical

residence time used when studying bacteria, in context given symbol Г. inverse of eigenvalue derived mass balance method.