第三章 管式反应器
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Fig5.6 on page 103
By comparing the batch expressions with these plug flow expressions we find: • For systems of constant density (constantvolume batch and constant-density plug flow ) the performance equations are identical, τfor plug flow is equivalent to t for the batch reactor, and the equations can be used interchangeable. • For systems of changing density there is no direct correspondence between the batch and plug flow equations and the correct equation must be used for each particular situation. In this case the performance equations cannot be used interchangeable.
• Solution For this stoichiometry and with inerts,
3 1 A 2 1 y A0 0.5 A A y A0 2 0.5 1
In which case the plug flow performance equation becomes
Introducing these three terms in the material balance equation we obtain
Fig 5.5 on page101Lev
FA=(FA+dFA) + (-rA)dV Noting that
dFA=d[FA0(1-xA)]=-FA0dxA We obtain on replacement FA0dxA=(-rA)dV This , then, is the equation which accounts for A in the differential section of reactor of volume dV. For the reactor as a whole the expression must be integrated. Now FA0, the feed rate, is constant, but (-rA) is certainly dependent on the concentration or conversion of materials. Grouping the terms accordingly, we obtain
Graphical Integration. First evaluate the function to integrated at selected values (see table ) and plot this function (see Fig ).
• Counting squares or estimating by eye we 1 2 find 0.8 1 x
=0
input = output + disappearance by reaction + accumulation
m olesA reacting volum eof tim evolum eof fluid elem ent
A Area 1 x dxA 1.70 0.8 1.36 0 A
Numeห้องสมุดไป่ตู้ical Integration. Using Simpson’s rule, applicable to an even number of uniformly spaced intervals on the xA axis, we find
FA0
C A0
x Ai
(rA )
• For the special case of constant-density systems xA=1-CA/CA0 or dxA=-dCA/CA0 In which case the performance equation can be expressed in terms of concentrations, or
C A0
x Af
0
x Af dxA C A0 0 rA
dxA 1 xA 2 kC A0 1 A xA
1 1 2
2 C A0 k
1
0.8
0
1 xA 1 x dxA A
• The integral can be evaluated in any one of three ways: graphically, numerically, or analytically. Let us illustrate these methods
x Af dx V 1 C Af dCA A 0 FA0 C A0 (rA ) C A0 C A 0 (rA )
A 0
These performance equations can be written either in terms of concentration or conversion. Whatever its form, the performance equations interrelate the rate of reaction, the extent of reaction, the reactor volume, and the feed rate, and if any one of these quantities is unknown it can be found from the other three.
Referring to Fig left, we see for volume dV that: Input of A, moles/time = FA Output of A, moles/time = FA+dFA Disappearance of A by reaction, moles/time = (rA)dV
x A xA0 I ( x A )dxA 3 I 0 4I1 I 3 I 5 2I 2 I 4 I n
第三章 管式反应器
3. 1平推流反应器 the Plug Flow Reactor
• 平推流反应器（PFR）：反应器中的流动状态 是人们设想的一种理想流动，即在反应器内具 有严格均匀的速度分布，且轴向没有任何混合。 • PFR is characterized by the fact that the flow of fluid through the reactor is orderly with no element of fluid overtaking or mixing with any other element ahead or behind. Actually, there may be lateral mixing of fluid in a PFR; however, there must be no mixing or diffusion along the flow path. The necessary and sufficient condition for plug flow is for the residence time in the reactor to be the same for all elements of fluid.
Example3.2-2 Plug Flow Reactor performance • A homogenous gas reaction A3P has a reported rate at 215℃, (-rA) = 0.01CA1/2 , (mol/liter· sec). Find the space-time needed for 80% conversion of a 50%A-50% inert feed to a plug flow reactor operating at 215 ℃ and 5 atm (CA0=0.0625 mol/liter).
Steady-state Plug Flow Reactor
• In a plug flow reactor the composition of the fluid varies from point to point along flow path; consequently, the material balance for a reaction component must be made for a differential element of volume dV. Thus for reactant A, the material balance becomes
平推流反应器特点：
（1）在正常情况下，它是连续定态操作，故在 反应器的各个截面上，过程参数（浓度、温度 等）不随时间而变化； （2）反应器内浓度、温度等参数随轴向位置变 化，故反应速率随轴向位置变化。 （3）由于径向具有严格均匀的速度分布，也就 是在径向不存在浓度分布。
PFR的基础设计方程 对PFR建立物料衡算式，就可以得到PFR的基 础设计方程式。在PFR中进行平推流动时，物 料衡算式有如下特点： （1）由于流动处于稳定状态，各点浓度、温度 和反应速度均不随时间而变化，故单元时间上t 可任取； （2） 由于沿流动方向浓度、温度和（－rA）都 在改变，故应取单元体积△V＝dV； （3）稳定状态下，单元时间、单元体积内反应 物的积累量为零。
• Fig. Below displays these performance equations and shows that the space-time needed for any particular duty can always be found by numerical or graphical integration. However, for certain simple kinetic forms analytic integration is possible– and convenient. Some of the simpler integrated forms for plug flow are as table 3.2-1.
• Equation 3.2-5 allows the determination of reactor size for a given feed rate and required conversion. • As a more general expression for plug reactors. If the feed on which conversion is based, subscript 0, enters the partially converted, subscript i, and leaves at a conversion designated by subscript f, we x Af dx V have A
By comparing the batch expressions with these plug flow expressions we find: • For systems of constant density (constantvolume batch and constant-density plug flow ) the performance equations are identical, τfor plug flow is equivalent to t for the batch reactor, and the equations can be used interchangeable. • For systems of changing density there is no direct correspondence between the batch and plug flow equations and the correct equation must be used for each particular situation. In this case the performance equations cannot be used interchangeable.
• Solution For this stoichiometry and with inerts,
3 1 A 2 1 y A0 0.5 A A y A0 2 0.5 1
In which case the plug flow performance equation becomes
Introducing these three terms in the material balance equation we obtain
Fig 5.5 on page101Lev
FA=(FA+dFA) + (-rA)dV Noting that
dFA=d[FA0(1-xA)]=-FA0dxA We obtain on replacement FA0dxA=(-rA)dV This , then, is the equation which accounts for A in the differential section of reactor of volume dV. For the reactor as a whole the expression must be integrated. Now FA0, the feed rate, is constant, but (-rA) is certainly dependent on the concentration or conversion of materials. Grouping the terms accordingly, we obtain
Graphical Integration. First evaluate the function to integrated at selected values (see table ) and plot this function (see Fig ).
• Counting squares or estimating by eye we 1 2 find 0.8 1 x
=0
input = output + disappearance by reaction + accumulation
m olesA reacting volum eof tim evolum eof fluid elem ent
A Area 1 x dxA 1.70 0.8 1.36 0 A
Numeห้องสมุดไป่ตู้ical Integration. Using Simpson’s rule, applicable to an even number of uniformly spaced intervals on the xA axis, we find
FA0
C A0
x Ai
(rA )
• For the special case of constant-density systems xA=1-CA/CA0 or dxA=-dCA/CA0 In which case the performance equation can be expressed in terms of concentrations, or
C A0
x Af
0
x Af dxA C A0 0 rA
dxA 1 xA 2 kC A0 1 A xA
1 1 2
2 C A0 k
1
0.8
0
1 xA 1 x dxA A
• The integral can be evaluated in any one of three ways: graphically, numerically, or analytically. Let us illustrate these methods
x Af dx V 1 C Af dCA A 0 FA0 C A0 (rA ) C A0 C A 0 (rA )
A 0
These performance equations can be written either in terms of concentration or conversion. Whatever its form, the performance equations interrelate the rate of reaction, the extent of reaction, the reactor volume, and the feed rate, and if any one of these quantities is unknown it can be found from the other three.
Referring to Fig left, we see for volume dV that: Input of A, moles/time = FA Output of A, moles/time = FA+dFA Disappearance of A by reaction, moles/time = (rA)dV
x A xA0 I ( x A )dxA 3 I 0 4I1 I 3 I 5 2I 2 I 4 I n
第三章 管式反应器
3. 1平推流反应器 the Plug Flow Reactor
• 平推流反应器（PFR）：反应器中的流动状态 是人们设想的一种理想流动，即在反应器内具 有严格均匀的速度分布，且轴向没有任何混合。 • PFR is characterized by the fact that the flow of fluid through the reactor is orderly with no element of fluid overtaking or mixing with any other element ahead or behind. Actually, there may be lateral mixing of fluid in a PFR; however, there must be no mixing or diffusion along the flow path. The necessary and sufficient condition for plug flow is for the residence time in the reactor to be the same for all elements of fluid.
Example3.2-2 Plug Flow Reactor performance • A homogenous gas reaction A3P has a reported rate at 215℃, (-rA) = 0.01CA1/2 , (mol/liter· sec). Find the space-time needed for 80% conversion of a 50%A-50% inert feed to a plug flow reactor operating at 215 ℃ and 5 atm (CA0=0.0625 mol/liter).
Steady-state Plug Flow Reactor
• In a plug flow reactor the composition of the fluid varies from point to point along flow path; consequently, the material balance for a reaction component must be made for a differential element of volume dV. Thus for reactant A, the material balance becomes
平推流反应器特点：
（1）在正常情况下，它是连续定态操作，故在 反应器的各个截面上，过程参数（浓度、温度 等）不随时间而变化； （2）反应器内浓度、温度等参数随轴向位置变 化，故反应速率随轴向位置变化。 （3）由于径向具有严格均匀的速度分布，也就 是在径向不存在浓度分布。
PFR的基础设计方程 对PFR建立物料衡算式，就可以得到PFR的基 础设计方程式。在PFR中进行平推流动时，物 料衡算式有如下特点： （1）由于流动处于稳定状态，各点浓度、温度 和反应速度均不随时间而变化，故单元时间上t 可任取； （2） 由于沿流动方向浓度、温度和（－rA）都 在改变，故应取单元体积△V＝dV； （3）稳定状态下，单元时间、单元体积内反应 物的积累量为零。
• Fig. Below displays these performance equations and shows that the space-time needed for any particular duty can always be found by numerical or graphical integration. However, for certain simple kinetic forms analytic integration is possible– and convenient. Some of the simpler integrated forms for plug flow are as table 3.2-1.
• Equation 3.2-5 allows the determination of reactor size for a given feed rate and required conversion. • As a more general expression for plug reactors. If the feed on which conversion is based, subscript 0, enters the partially converted, subscript i, and leaves at a conversion designated by subscript f, we x Af dx V have A