连续搅拌槽反应器

连续搅拌槽反应器（英语：Continuous Stirred-Tank Reactor，简称CSTR），也可以称作vat-reactor或是backmix reactor，是化学工程中一个常见的化学反应器模型。CSTR通常是指在使用continuous agitated-tank reactor要达到指定出料条件时用来估计关键操作变数的模型^{[notes 1]} 。该数学模型适用于所有流体：液体、气体和浆体。

CSTR的行为通常会以连续理想搅拌槽反应器（Continuous Ideally Stirred-Tank Reactor，CISTR）建模，所有由CISTR进行的计算皆已假设其为完美搅拌（英语：perfect mixing）。在一个完美搅拌的反应器中，出料的组成会与反应器内的组成一致，而组成与滞留时间及反应速率有关。以工程方面来说，一般会假设滞留时间是搅拌时间的5－10倍。CISTR模型通常用于简化工程计算并可用于描述及研究反应器。然而实际上，反应只能接近而无法达到完美状态，特别是在具工业规模的反应器中。

反应模型[编辑]

假设反应为理想情况（完美搅拌），则在体积为 $V$ 的反应器内物料 $i$ （莫耳数为 $N_{i}$ ）的总质量平衡可表示成：

$[{\text{accumulation}}]=[{\text{in}}]-[{\text{out}}]+[{\text{generation}}]$ （累积量＝进料－出料＋生成）

${\frac {dN_{i}}{dt}}=F_{io}-F_{i}+V\nu _{i}r_{i}$ ${\frac {dN_{i}}{dt}}=F_{io}-F_{i}+V\nu _{i}r_{i}$ ^[1]
其中， $F_{io}$ 是物料 $i$ 的进料莫尔流率， $F_{i}$ 是出料莫尔流率， $\nu _{i}$ 为化学计量数。反应速率 $r$ ，通常与反应物浓度以及速率常数（ $k$ ）有关。速率常数一般可以由阿伦尼乌斯方程求得。一般来说，温度升高时，反应速率也会随之提升。滞留时间（英语：Residence time） $\tau$ 是指试剂在槽内所耗费的平均时间。
假设：
- 固定密度（适用于大部分液体、莫耳数不会产生净变化或是没有剧烈温度变化的气体）
- 等温过程（ $k$ 为常数）
- 稳态（英语：steady-state (chemical engineering)）（ $G_{A}=r_{A}V$ ）
- 基元反应、不可逆化学反应（ $v_{a}=-1$ ）
- 速率方程（ $r=kC_{A}$ )
$A\rightarrow product$

$N_{A}=C_{A}V$ （ $C_{A}$ 为物料 $A$ 的浓度， $V$ 为反应器体积， $N_{A}$ 为物料 $A$ 的莫尔数）
$C_{A}={\frac {C_{Ao}}{1+k\tau }}$ ^[1]
上式中的变数、出口浓度和停留时间的值是主要的设计准则。

如果要建立一个非等温或是单一反应的系统时，则必须要考虑额外的控制变数。如果系统被认为处于不稳定状态，那么就必须求解微分方程或是耦合微分方程组。

CSTR是一类具有多重稳态、极限循环和混沌等复杂行为的系统。

应用[编辑]

CSTR通常应用于废水处理过程中。CSTR可以促进稀释速率，使它们能抵抗碱性或酸性的挥发性脂肪酸废弃物。与其他类型的反应器相比，CSTR的效率较低，因为它们需要更大的反应器体积以达到与其他反应器模型（如塞流反应器（英语：Plug_flow_reactor_model））相同的反应速率。

参见[编辑]

层流反应器（英语：Laminar flow reactor）
微反应器（英语：Microreactor）
连续振动阻隔反应器（英语：Oscillatory baffled reactor）
塞流反应器（英语：Plug flow reactor model）

备注[编辑]

^ Chemical reactors often have significant heat effects, so it is important to be able to add or remove heat from them. In a CSTR (continuous stirred tank reactor) the heat is added or removed by virtue of the temperature difference between a jacket fluid and the reactor fluid. Often, the heat transfer fluid is pumped through agitation nozzle that circulates the fluid through the jacket at a high velocity. The reactant conversion in a chemical reactor is a function of a residence time or its inverse, the space velocity. For a CSTR, the product concentration can be controlled by manipulating the feed flow rate, which changes the residence time for a constant chemical reactor. Occasionally the term "continuous" is misinterpreted as a modifier for "stirred", as in 'continuously stirred'. This misinterpretation is especially prevalent in the civil engineering literature. As explained in the article,"continuous" means 'continuous-flow' — and hence these devices are sometimes called, in full, continuous-flow stirred-tank reactors (CFSTR's).

参考资料[编辑]

^ ^1.0 ^1.1 Schmidt, Lanny D. The Engineering of Chemical Reactions. New York: Oxford University Press. 1998. ISBN 0-19-510588-5.

[1] Chemical reactors often have significant heat effects, so it is important to be able to add or remove heat from them. In a CSTR (continuous stirred tank reactor) the heat is added or removed by virtue of the temperature difference between a jacket fluid and the reactor fluid. Often, the heat transfer fluid is pumped through agitation nozzle that circulates the fluid through the jacket at a high velocity. The reactant conversion in a chemical reactor is a function of a residence time or its inverse, the space velocity. For a CSTR, the product concentration can be controlled by manipulating the feed flow rate, which changes the residence time for a constant chemical reactor. Occasionally the term "continuous" is misinterpreted as a modifier for "stirred", as in 'continuously stirred'. This misinterpretation is especially prevalent in the civil engineering literature. As explained in the article,"continuous" means 'continuous-flow' — and hence these devices are sometimes called, in full, continuous-flow stirred-tank reactors (CFSTR's).

[Schmidt-2] 1.0 ^1.1 Schmidt, Lanny D. The Engineering of Chemical Reactions. New York: Oxford University Press. 1998. ISBN 0-19-510588-5.

[notes 1]

[1]