連續攪拌槽反應器

連續攪拌槽反應器（英語：Continuous Stirred-Tank Reactor，簡稱CSTR），也可以稱作全混流反应器，vat-reactor或是backmix reactor，是化學工程中一個常見的化學反應器模型。CSTR通常是指在使用continuous agitated-tank reactor要達到指定出料條件時用來估計關鍵操作變數的模型^{[notes 1]} 。該數學模型適用於所有流体：液體、氣體和漿體。

CSTR的行為通常會以連續理想攪拌槽反應器（Continuous Ideally Stirred-Tank Reactor，CISTR）建模，所有由CISTR進行的計算皆已假設其為完美攪拌（英语：perfect mixing）。在一個完美攪拌的反應器中，出料的組成會與反應器內的組成一致，而組成與滯留時間及反應速率有關。以工程方面來說，一般會假設滯留時間是攪拌時間的5－10倍。CISTR模型通常用於簡化工程計算並可用於描述及研究反應器。然而實際上，反應只能接近而無法達到完美狀態，特別是在具工業規模的反應器中。

反應模型

假設反應為理想情況（完美攪拌），則在體積為 $V$ 的反應器內物料 $i$ （莫耳數為 $N_{i}$ ）的總質量平衡可表示成：

$[{\text{accumulation}}]=[{\text{in}}]-[{\text{out}}]+[{\text{generation}}]$ （累積量＝進料－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 $i$ 的進料莫爾流率， $F_{i}$ 是出料莫爾流率， $\nu _{i}$ 為化学计量数。反應速率 $r$ ，通常與反應物濃度以及速率常数（ $k$ ）有關。速率常數一般可以由阿伦尼乌斯方程求得。一般來說，溫度升高時，反應速率也會隨之提升。滯留時間（英语：Residence time） $\tau$ 是指試劑在槽內所耗費的平均時間。
假設：
- 固定密度（適用於大部分液體、莫耳數不會產生淨變化或是沒有劇烈溫度變化的氣體）
- 等温过程（ $k$ 為常數）
- 穩態（英语：steady-state (chemical engineering)）（ $G_{A}=r_{A}V$ ）
- 基元反應、不可逆化学反应（ $v_{a}=-1$ ）
- 速率方程（ $r=kC_{A}$ )
$A\rightarrow product$

$N_{A}=C_{A}V$ （ $C_{A}$ 為物料 $A$ 的濃度， $V$ 為反應器體積， $N_{A}$ 為物料 $A$ 的莫爾數）
$C_{A}={\frac {C_{Ao}}{1+k\tau }}$ ^[1]
上式中的變數、出口濃度和停留時間的值是主要的設計準則。

如果要建立一個非等溫或是單一反應的系統時，則必須要考慮額外的控制變數。如果系統被認為處於不穩定狀態，那麼就必須求解微分方程或是耦合微分方程組。

CSTR是一類具有多重穩態、極限循環和混沌等複雜行為的系統。

應用

CSTR通常應用於廢水處理過程中。CSTR可以促進稀釋速率，使它們能抵抗鹼性或酸性的揮發性脂肪酸廢棄物。與其他類型的反應器相比，CSTR的效率較低，因為它們需要更大的反應器體積以達到與其他反應器模型（如塞流反應器（英语：Plug_flow_reactor_model））相同的反應速率。

參見

層流反應器（英语：Laminar flow reactor）
微反應器（英语：Microreactor）
連續振動阻隔反應器（英语：Oscillatory baffled reactor）
塞流反應器（英语：Plug flow reactor model）

備註

^ 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).

參考資料

^ ^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]