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    Distillation CSTR Ravi

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    Movie 4U
    1. A continuous stirred tank reactor (CSTR) is a batch reactor equipped with an impeller to provide efficient mixing. 2. The mathematical model for a CSTR involves mass balances for total mass and component A, as well as an energy balance. 3. The state variables are volume (V), concentration of component A (CA), and temperature (T). The state equations describe how these variables change over time based on inlet and outlet flows, heat generation from reaction, and heat removal from cooling.

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    Distillation CSTR Ravi

    Uploaded by

    Movie 4U
    12 views6 pages
    1. A continuous stirred tank reactor (CSTR) is a batch reactor equipped with an impeller to provide efficient mixing. 2. The mathematical model for a CSTR involves mass balances for total mass and component A, as well as an energy balance. 3. The state variables are volume (V), concentration of component A (CA), and temperature (T). The state equations describe how these variables change over time based on inlet and outlet flows, heat generation from reaction, and heat removal from cooling.

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    tubular heat distillation

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    distillation CSTR Ravi

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    1. A continuous stirred tank reactor (CSTR) is a batch reactor equipped with an impeller to provide efficient mixing. 2. The mathematical model for a CSTR involves mass balances for total mass and component A, as well as an energy balance. 3. The state variables are volume (V), concentration of component A (CA), and temperature (T). The state equations describe how these variables change over time based on inlet and outlet flows, heat generation from reaction, and heat removal from cooling.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    12 views6 pages

    Distillation CSTR Ravi

    Uploaded by

    Movie 4U
    1. A continuous stirred tank reactor (CSTR) is a batch reactor equipped with an impeller to provide efficient mixing. 2. The mathematical model for a CSTR involves mass balances for total mass and component A, as well as an energy balance. 3. The state variables are volume (V), concentration of component A (CA), and temperature (T). The state equations describe how these variables change over time based on inlet and outlet flows, heat generation from reaction, and heat removal from cooling.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    of 6

    NAME-RAVI

    ROLL NO.-2017UIC3128

    Continuously Stirred
    Tank Reactor
    (CSTR)
    A continuous stirred tank reactor (CSTR) is a batch reactor equipped with an
    impeller or other mixing device to provide efficient mixing. In chemical
    engineering the name CSTR is often used to refer an idealised agitated tank
    reactor used to model operation variables required to attain a specified
    output.
    Reactant A is continuously supplied to the reactor with a volumetric flow
    rate Fi , a molar concentration(or composition) CAf and a temperature Tf.
    The contents of the reactor are mixed with a motorized agitator. An exit
    stream, which contains a mixture of both the reactant A and product B, is
    withdrawn from the reactor continuously with a volumetric flow rate Fo, a
    composition CA and a temperature T. To remove the exothermic heat that is
    generated due to the prescribed chemical reaction, a cooling jacket
    surrounds the reactor. A coolant stream with a volumetric flow rate Fj and an
    inlet temperature Tjin (< T) continuously takes out the heat to maintain the
    desired reaction temperature.
    Mathematical Modelling Of
    CSTR:

    1.Total Mass Balance:

    𝑎𝑐𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑖𝑛𝑝𝑢𝑡 𝑜𝑓 𝑡𝑜𝑡𝑎𝑙 𝑜𝑢𝑡𝑝𝑢𝑡 𝑜𝑓 𝑡𝑜𝑡𝑎𝑙


    ⇒ 𝑡𝑜𝑡𝑎𝑙 𝑚𝑎𝑠𝑠
    𝑡𝑖𝑚𝑒
    = 𝑚𝑎𝑠𝑠
    𝑡𝑖𝑚𝑒
    − 𝑚𝑎𝑠𝑠
    𝑡𝑖𝑚𝑒
    ±
    𝑡𝑜𝑡𝑎𝑙 𝑚𝑎𝑠𝑠 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝑑
    𝑜𝑟 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑑
    𝑡𝑖𝑚𝑒

    𝑑 (𝑝𝑉)
    ⇒ 𝑑𝑡
    = piFi −𝑝𝐹 ± 0

    ⇒ 𝐴𝑑 (ℎ)
    𝑑𝑡
    = 𝐹𝑖 − 𝐹 while (pi = p)

    pi ,p : densities
    of inlet and outlet
    streams.
    2.Mass Balance of Component A :

    ⇒𝐴𝑐𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛
    𝑡𝑖𝑚𝑒
    𝑜𝑓 𝐴
    =
    𝑖𝑛𝑝𝑢𝑡 𝑜𝑓 𝐴
    𝑡𝑖𝑚𝑒
    −
    𝑖𝑛𝑝𝑢𝑡 𝑜𝑓 𝐵
    𝑡𝑖𝑚𝑒
    −
    𝐷𝑖𝑠𝑎𝑝𝑝𝑒𝑎𝑟𝑎𝑛𝑐𝑒 𝑜𝑓 𝐴 𝑑𝑢𝑒 𝑡𝑜 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛
    𝑡𝑖𝑚𝑒

    ⇒ 𝑑(𝐶𝑑𝑡𝐴𝑉) = 𝐹𝑖 (𝐶𝐴𝑖 − 𝐶𝐴 ) − 𝑟𝑉

    ⇒ 𝑉 𝑑𝐶𝑑𝑡𝐴 + 𝐶𝐴𝑑𝑡𝑑𝑉 = 𝐹𝑖 𝐶𝐴𝑖 − 𝐹𝐶𝐴 − 𝑟𝑉


    ⇒ 𝑉𝑑𝐶
    𝑑𝑡
    𝐴
    + 𝐶𝐴 𝐹𝑖 − 𝐶𝐴 𝐹 = 𝐹𝑖 𝐶𝐴𝑖 − 𝐹𝐶𝐴 − 𝑟𝑉

    ⇒ 𝑉𝑑𝐶
    𝑑𝑡
    𝐴
    = 𝐹𝑖 𝐶𝐴𝑖 − 𝐶𝐴 𝐹𝑖 − 𝑟𝑉

    ⇒
    𝐸
    𝑑 (𝐶𝐴 ) 𝐹𝑖 −
    = (𝐶𝐴𝑖 − 𝐶𝐴 ) − 𝑘0 𝑒 𝑅𝑇 𝐶𝐴
    𝑑𝑡 𝑉
    𝐸
    (while r = 𝑘0 𝑒 −
    𝑅𝑇 𝐶𝐴 𝑉 )

    r : Rate of the
    reaction/unit volume.

    3.Total Energy Balance:


    𝑇𝑜𝑡𝑎𝑙 𝐸𝑛𝑒𝑟𝑔𝑦 𝑖𝑛𝑝𝑢𝑡 𝑜𝑓 𝑡𝑜𝑡𝑎𝑙 𝑜𝑢𝑡𝑝𝑢𝑡 𝑜𝑓 𝑡𝑜𝑡𝑎𝑙
    𝑎𝑐𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑒𝑛𝑒𝑟𝑔𝑦 𝑒𝑛𝑒𝑟𝑔𝑦
    = − −
    𝑡𝑖𝑚𝑒 𝑡𝑖𝑚𝑒 𝑡𝑖𝑚𝑒
    𝐸𝑛𝑒𝑟𝑔𝑦 𝑟𝑒𝑚𝑜𝑣𝑒𝑑 𝑏𝑦 𝐸𝑛𝑒𝑟𝑔𝑦 𝑎𝑑𝑑𝑒𝑑 𝑑𝑢𝑒 𝑡𝑜
    𝑡ℎ𝑒 𝑐𝑜𝑜𝑙𝑎𝑛𝑡
    + 𝑒𝑥𝑜𝑡ℎ𝑒𝑟𝑚𝑖𝑐 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛
    𝑡𝑖𝑚𝑒 𝑡𝑖𝑚𝑒

    ⇒
    𝑑(𝑉𝑝𝐶𝑝 𝑇)
    = 𝐹𝑖 𝑝𝐶𝑝 𝑇𝑖 − 𝐹𝑝𝐶𝑝 𝑇 − 𝑄 + (−∆𝐻)𝑟𝑉
    𝑑𝑡

    ⇒𝑉 𝑑𝑡 + 𝑇 𝑑𝑡 = 𝐹𝑖 𝑇𝑖 − 𝐹𝑇 − 𝑝𝐶
    𝑑𝑇 𝑑𝑉 𝑄
    +
    (−∆𝐻 )𝑟𝑉
    𝑝𝐶𝑝
    𝑝

    ⇒ 𝑉 𝑑𝑇
    𝑑𝑡
    + 𝑇(𝐹𝑖 − 𝐹) = 𝐹𝑖 𝑇𝑖 − 𝐹𝑇 −
    𝑄
    𝑝𝐶
    +
    (−∆𝐻 )𝑟𝑉
    𝑝𝐶𝑝
    𝑝

    ⇒ 𝑉 𝑑𝑇
    𝑑𝑡
    = 𝐹𝑖 (𝑇𝑖 − 𝑇) −
    𝑄
    𝑝𝐶
    +
    (−∆𝐻 )𝑟𝑉
    𝑝𝐶𝑝
    𝑝

    ⇒ 𝑑𝑇
    𝑑𝑡
    𝐹
    = 𝑖 (𝑇𝑖 − 𝑇) −
    𝑉
    𝑄
    𝑉𝑝𝐶
    +
    (−∆𝐻 )𝑟
    𝑝𝐶𝑝
    𝑝

    ⇒ 𝑑𝑡 = 𝑉 (𝑇𝑖 − 𝑇) + 𝐽𝑘0𝑒
    𝐸
    𝑑𝑇 𝐹𝑖 − 𝑄
    𝑅𝑇 𝐶𝐴 −
    𝑝𝐶𝑝 𝑉
    (−∆𝐻 ) 𝐸
    −
    where J= & r= 𝑘0 𝑒 𝑅𝑇 𝐶𝐴
    𝑝𝐶𝑝

    Summarising the steps in mathematical modelling of CSTR:


    1. State variables: V, CA , T.
    2. State Equations:
    𝐴𝑑 (ℎ)
    1. = 𝐹𝑖 − 𝐹
    𝑑𝑡
    𝐸
    𝑑 (𝐶𝐴 ) 𝐹𝑖
    2. 𝑑𝑡
    =
    𝑉
    (𝐶𝐴𝑖 − 𝐶𝐴 ) − 𝑘0 𝑒 −
    𝑅𝑇 𝐶𝐴
    𝐸
    𝑑𝑇 𝐹𝑖 𝑄
    3. 𝑑𝑡 = 𝑉
    (𝑇𝑖 − 𝑇) + 𝐽𝑘0 𝑒 −
    𝑅𝑇 𝐶𝐴 −
    𝑝𝐶𝑝 𝑉

    3. Output variables: V, CA , T
    4. Input variables:
     Disturbances: CAi , Fi , Ti
     Manipulated variables: Q, F

    5. Constant Parameters : p, Cp , (- ⃤ Hr), k0 , E(Activation energy), r

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