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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8"/>
<title>
Separation Processes 1
</title>
<meta content="Separation processes 1 notes" name="description"/>
<meta content="Marcus Bannerman <[email protected]" name="author"/>
<meta content="yes" name="apple-mobile-web-app-capable"/>
<meta content="black-translucent" name="apple-mobile-web-app-status-bar-style"/>
<meta content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no, minimal-ui" name="viewport"/>
<script src="header.js"></script>
</head>
<body>
<div class="reveal">
<div class="slides">
<section>
<section>
<h2>
Partial Column Designs and Batch Columns
</h2>
<div class="center">
</div>
</section>
</section>
<section>
<section data-menu-title="Partial distillation column designs">
<div style="display:flex;align-items:center;">
<div style="flex: 1 1 calc(100% * 0.551);">
<ul>
<li>
We have studied standard distillation columns where
the feed tray is located within the middle of the column.
</li>
<li class="fragment" data-fragment-index="1">
The feed tray may instead be located at the very top
or bottom of the column to create either an
<b>enrichment/rectification</b>
column or a
<b>stripping</b>
column.
</li>
<li class="fragment" data-fragment-index="2">
These configurations can be extremely useful if the
feed-conditions or operating-modes are favourable.
</li>
</ul>
</div>
<div style="flex: 1 1 calc(100% * 0.41);">
<figure>
<div class="center">
<img src="img/fractionation_column_01.svg"/>
<figcaption>
A typical multistage distillation column.
</figcaption>
</div>
</figure>
</div>
</div>
</section>
<section data-menu-title="Enrichment columns">
<div style="display:flex;align-items:center;">
<div style="flex: 1 1 calc(100% * 0.551);">
<ul>
<li>
<b>Enrichment columns</b>
have the feed tray located at
the bottom of the column.
</li>
<li class="fragment" data-fragment-index="1">
This allows a low-concentration volatile component to
be extracted at high purity from the feed stream.
</li>
<li class="fragment" data-fragment-index="2">
This design is also key to the understanding of
<b>multi-stage batch distillation</b>, as the large reboiler/still
volume allows it to be approximated as an enrichment column
with a slowly-varying bottoms concentration.
</li>
</ul>
</div>
<div style="flex: 1 1 calc(100% * 0.41);">
<figure>
<div class="center">
<img src="img/enrichment_column_wboiler.svg"/>
<figcaption>
A enrichment distillation column with reboiler.
</figcaption>
</div>
</figure>
</div>
</div>
</section>
<section>
<div style="display:flex;align-items:center;">
<div style="flex: 1 1 calc(100% * 0.551);">
<ul>
<li>
<b>Enrichment columns</b>
may also be designed without
a reboiler if the feed stream partially/fully vapourises on
entry to the column.
</li>
<li class="fragment" data-fragment-index="1">
This is an efficient (but rare) configuration if the
feed stream is to be condensed anyway as part of the overall
plant design.
</li>
<li class="fragment" data-fragment-index="2">
However, the reflux ratio is no-longer an adjustable
parameter but is set by the ratio of the two product
flow-rates, $R=W/D.$
</li>
<li class="fragment" data-fragment-index="3">
The design of enrichment columns is relatively
straightforward, requiring only the enrichment
<span style="color:teal">
operating line equation</span>.
\begin{align*}
y_n &= x_{n+1}\frac{R}{R+1} + \frac{x_D}{R+1}
\end{align*}
</li>
</ul>
</div>
<div style="flex: 1 1 calc(100% * 0.41);">
<figure>
<div class="center">
<img src="img/enrichment_column_woboiler.svg"/>
<figcaption>
A enrichment distillation column without re-boiler.
</figcaption>
</div>
</figure>
</div>
</div>
</section>
<section data-menu-title="Enrichment column design">
<figure>
<div class="center">
<img src="img/enrichment_column_design.svg" style="width:50%;"/>
<figcaption>
The design of an enrichment column with no reboiler
(vapour feed at
$y_F$
entering at the bottom).
</figcaption>
</div>
</figure>
</section>
<section data-menu-title="Stripping column">
<div style="display:flex;align-items:center;">
<div style="flex: 1 1 calc(100% * 0.551);">
<ul>
<li>
<b>Stripping columns</b>
are handled similarly to
enrichment column design and may be designed without a
condenser if the feed stream is liquid.
</li>
<li class="fragment" data-fragment-index="1">
This condenser-less design is useful when separating
highly-volatile compounds which would otherwise require a
cryogenic condenser (e.g., separation of air or natural gas as
propane boils at -42${}^\circ$
C, ethane at -89
${}^\circ$
C).
</li>
<li class="fragment" data-fragment-index="2">
Its design only requires the use of the stripping
section equation, which we can rewrite:
\begin{align*}
y_{m} &= x_{m+1}\frac{L_m}{V_m} - x_{W}\frac{W}{V_m} \\
&=x_{m+1}\frac{F}{F-W} - x_{W}\frac{W}{F-W}
\end{align*}
</li>
</ul>
</div>
<div style="flex: 1 1 calc(100% * 0.41);">
<figure>
<div class="center">
<img src="img/stripping_column_wocondenser.svg"/>
<figcaption>
A stripping distillation column without condenser.
</figcaption>
</div>
</figure>
</div>
</div>
</section>
<section>
<figure>
<div class="center">
<img src="img/stripping_column_design.svg" style="width:50%;"/>
<figcaption>
The design of a stripping column without a condenser
(liquid feed
$x_F$
entering at the top).
</figcaption>
</div>
</figure>
</section>
<section>
<div style="display:flex;align-items:center;">
<div style="flex: 1 1 calc(100% * 0.551);">
<ul>
<li>
One important example of this design is in the
<b>SAGE gas terminal</b>.
</li>
<li class="fragment" data-fragment-index="1">
High-pressure gas passes through an expansion turbine
(turbo-expander), which causes it to cool and condense (
<b>Joule-Thomson effect</b>).
</li>
<li class="fragment" data-fragment-index="2">
This liquid is fed to a
<b>stripping column</b>
which
is used to separate off a variable fraction of NGLs, allowing
the plant to control its gas composition (and recover NGLs
which are sold on).
</li>
<li class="fragment" data-fragment-index="3">
The product vapour/gas is then re-compressed using a
compressor which is partially powered by the expansion turbine
(turbo-expander) for efficiency.
</li>
<li class="fragment" data-fragment-index="4">
At no point is a condenser required to liquefy the
light fractions of the gas (methane, ethane, propane, …).
</li>
</ul>
</div>
<div style="flex: 1 1 calc(100% * 0.41);">
<figure>
<div class="center">
<img src="img/stripping_column_wocondenser.svg"/>
<figcaption>
A stripping distillation column without condenser.
</figcaption>
</div>
</figure>
</div>
</div>
</section>
</section>
<section>
<section data-menu-title="Batch multi-stage distillation">
<div style="display:flex;align-items:center;">
<div style="flex: 1 1 calc(100% * 0.551);">
<ul>
<li>
<b>Batch distillation</b>
is a technique to carry out
small scale or controlled separations on a fixed volume.
</li>
<li class="fragment" data-fragment-index="1">
The design of
<b>single-stage</b>
batch distillation
systems follows Rayleigh's equation:
\begin{align*}
\ln\left(\frac{L_{final}}{L_{initial}}\right) =
\int_{x_{initial}}^{x_{final}} \frac{{\rm d}x}{y-x}
\end{align*}
</li>
<li class="fragment" data-fragment-index="2">
This single-stage approach is limited to either low
recovery or highly volatile systems.
</li>
<li class="fragment" data-fragment-index="3">
<b>Multi-stage</b>
batch distillation, such as the
column on the right, enables high purities to collected while
still running in batch operation.
</li>
<li class="fragment" data-fragment-index="4">
Most batch stills are in-fact multi-stage
systems…
</li>
</ul>
</div>
<div style="flex: 1 1 calc(100% * 0.41);">
<figure>
<div class="center">
<img src="img/batch_multistage.svg" style="width:70%;"/>
<figcaption>
A multi-stage batch distillation column.
</figcaption>
</div>
</figure>
</div>
</div>
</section>
<section>
<div style="display:flex;align-items:center;">
<div style="flex: 1 1 calc(100% * 0.551);">
<ul>
<li>
The copper stills used in the whisky industry contain
more than one stage of distillation.
</li>
<li class="fragment" data-fragment-index="1">
No insulation is deliberately used to allow
condensation to form inside the still causing a small reflux
stream to form.
</li>
<li class="fragment" data-fragment-index="2">
This counter-current flow of liquid and vapour results
in more than one stage of distillation overall.
</li>
<li class="fragment" data-fragment-index="3">
But how can we design multi-stage distillation columns
like this one?
</li>
</ul>
</div>
<div style="flex: 1 1 calc(100% * 0.41);">
<figure>
<div class="center">
<img src="img/multistage_copper_still.svg" style="width:70%;"/>
<figcaption>
A multi-stage batch distillation column.
</figcaption>
</div>
</figure>
</div>
</div>
</section>
<section>
<div style="display:flex;align-items:center;">
<div style="flex: 1 1 calc(100% * 0.551);">
<ul>
<li>
The first step is to realise that Rayleigh's equation
still holds for this system:
\begin{align*}
\ln\left(\frac{L_{final}}{L_{initial}}\right) =
\int_{x_{initial}}^{x_{final}} \frac{{\rm d}x}{y-x}
\end{align*}
</li>
<li class="fragment" data-fragment-index="1">
$y$
is the “produced” concentration given a liquid
concentration of
$x$
in the still.
</li>
<li class="fragment" data-fragment-index="2">
If we can calculate the top product concentration
$x_D$
which will be produced from a multi-stage still given
the still concentration
$x$, we can write
\begin{align*}
\ln\left(\frac{L_{final}}{L_{initial}}\right) =
\int_{x_{initial}}^{x_{final}} \frac{{\rm d}x}{x_D-x}
\end{align*}
</li>
<li class="fragment" data-fragment-index="3">
All we need is some relationship between $x_D$
and
$x$
for the column, then we can integrate it.
</li>
</ul>
</div>
<div style="flex: 1 1 calc(100% * 0.41);">
<figure>
<div class="center">
<img src="img/pot_still_03.svg" style="width:60%;"/>
<figcaption>
A simplified diagram of a pot still.
</figcaption>
</div>
</figure>
</div>
</div>
</section>
<section data-menu-title="Fixed reflux ratio">
<div style="display:flex;align-items:center;">
<div style="flex: 1 1 calc(100% * 0.551);">
<ul>
<li>
If we can
<b>assume that we have a fixed reflux
ratio</b>, then multi-stage batch distillation columns can be
assumed to be an enrichment distillation column with a slowly
varying bottoms product concentration.
</li>
<li class="fragment" data-fragment-index="1">
The bottoms product varies slowly as there is a large
volume of liquid in the reboiler, acting as “feed” to the
column.
</li>
<li class="fragment" data-fragment-index="2">
We can then find the relationship $x_D-x$
by
performing repeated distillation column designs for the range
$x\in\left[x_{initial},x_{final}\right]$
…
</li>
</ul>
</div>
<div style="flex: 1 1 calc(100% * 0.41);">
<figure>
<div class="center">
<img src="img/batch_multistage.svg" style="width:70%;"/>
<figcaption>
A multi-stage batch distillation column.
</figcaption>
</div>
</figure>
</div>
</div>
</section>
<section>
<figure>
<div class="center">
<img src="img/multistage_batch_column_design_fixedR.svg" style="width:50%;"/>
<figcaption>
As the bottoms product concentration drops over time,
so does the top product concentration. The slope of the
operating line remains constant as the reflux ratio doesn't
change.
</figcaption>
</div>
</figure>
</section>
<section>
<figure>
<div class="center">
<img src="img/multistage_batch_column_design_fixedR_int.svg" style="width:65%;"/>
<figcaption>
Plotting these differences, we can perform the
integration using the trapezium rule (note that this integral
is negative as we're integrating backwards). The area of a
trapezium is
$(Y_1+Y_2) * (X_2-X_1)/2$.
</figcaption>
</div>
</figure>
</section>
<section data-menu-title="Fixed top-product composition">
<ul>
<li>
An alternative batch distillation operating mode to fixed
reflux-ratio is
<b>fixed top-product concentration</b>.
</li>
<li class="fragment" data-fragment-index="1">
This assumes that the reflux ratio of the batch column is
varied to keep the top-product concentration fixed.
</li>
<li class="fragment" data-fragment-index="2">
This piece of process control can be done by altering the
reflux ratio depending on the temperature at the top of the column
(temperature is concentration at fixed pressure).
</li>
<li class="fragment" data-fragment-index="3">
As the distillation continues, the reflux ratio must
increase exponentially to maintain the top product concentration.
</li>
<li class="fragment" data-fragment-index="4">
In this case, $x_D$
is constant and we have
\begin{align*}
\ln\left(\frac{L_{final}}{L_{initial}}\right) &=
\int_{x_{initial}}^{x_{final}} \frac{{\rm d}x}{x_D-x}\\
&=\left[-\ln(x_D-x)\right]_{x_{initial}}^{x_{final}} \\
x_D(L_{initial}-L_{final})&=x_{initial} L_{initial}-x_{final} L_{final}
\end{align*}
</li>
<li class="fragment" data-fragment-index="5">
This can be obtained directly from a mass balance.
</li>
<li class="fragment" data-fragment-index="6">
Fixed reflux ratio and fixed top-product concentration
methods can both achieve identical separations; however, fixed
reflux ratio is the simplest to perform operationally.
</li>
</ul>
</section>
</section>
</div>
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