Unformatted Attachment Preview
Vinyl chloride monomer (VCM) is the precursor in the production of poly vinyl chloride (PVC),
one of the most important and widely-used polymers in the world. There is significant variety
in the finished forms that PVC can be produced in, ranging from crystal clear and rigid
polymers, to very soft and flexible polymers. This wide range of finishes enables PVC to be
used in a wide variety of end uses. Rigid PVC is used in the manufacture of pipes, doors,
windows, bottles and bank cards, while softer more flexible PVC can be used in plumbing,
electrical cable insulation and can be mixed with cotton or linen for the production of canvas.
In 1902, VCM was obtained from the thermal cracking of 1,2-dichloroethane (EDC), although
since polymer science was not very developed at this time the discovery did not lead to any
industrial or commercial consequence. Ten years later a method to obtain VCM from the
catalytic hydrochlorination of acetylene was developed. This was the first industrially used
approach for the production of VCM and was used almost exclusively for 30 years. However,
due to the high energy demands in acetylene production a cheaper alternative approach was
sought. As availability of ethylene increased by the mid-20th century, production of VCM from
both hydrochlorination of acetylene and thermal cracking of EDC obtain from direct chlorination
of ethylene were developed. In 1958, the first large-scale production of VCM solely from
ethylene, known as the balanced process, was introduced.
A simplified block flow diagram (BFD) of the balanced process illustrating the main process
streams of the current VCM production process used by Ramsay Limited, is shown in Figure
1. Firstly the intermediate 1,2-dichloroethane, commonly referred to as EDC, is made from
ethylene by two different routes; direct chlorination and oxychlorination. In direct chlorination,
the ethylene reacts with chlorine to form EDC (reaction 1) which is produced at a sufficient
purity so that it can be fed directly to the next stage of the process, namely EDC cracking. The
direct chlorination reaction is exothermic and takes place in an innovative boiling reactor.
In oxychlorination, ethylene reacts with hydrogen chloride and oxygen in a highly exothermic
reaction to form the intermediate EDC (reaction 2). The oxychlorination reaction in the current
process is of fluidised bed design with steam generation to remove the heat generated by the
process. The EDC produced via oxychlorination must past through EDC distillation to increase
the purity of the EDC before it is fed to the EDC cracker.
In the cracking furnace, EDC is heated to high temperatures in the region of 480°C and cracked
down to form VCM and HCl (reaction 3). Due to the incomplete nature of the endothermic
cracking reaction, a number of hydrocarbon by-products are formed as well as coke. The
product stream from the EDC cracker, consisting of VCM, unconverted EDC, hydrocarbon byproducts and hydrogen chloride, passes through to VCM distillation. In this purification block,
hydrogen chloride is recovered and recycled back to the oxychlorination reactor. Since the
recovered HCl is re-used in this way, all the chlorine entering the process is completely
converted (combination of reactions 1-3 to give reaction 4). The unconverted EDC, and lowboiling compounds which are converted by chlorination to high-boiling compounds, are
recycled back to EDC distillation for purification before the unconverted EDC is returned to the
EDC cracker. Finally, polymer-grade VCM is obtained from VCM distillation and can be used
in the production of PVC.
C2H4 + Cl2 C2H4Cl2
C2H4 + 2HCl + 1/2O2 C2H4Cl2 + H2O
2C2H4Cl2 2C2H3Cl + 2HCl
2C2H4 + Cl2 + 1/2O2 2C2H3Cl + H2O
Figure 1. Simplified Block Flow Diagram (BFD) of the existing
balanced process for VCM production.
Focus 2: CENG0019 – due 19 May at 3pm
Pressure drops in pipe flows
Your report should consider the following:
Significant pressure drops have been observed in cooling water pipes supplying cooling
utilities to the EDC distillation units. Ramsay Limited would like this to be investigated further.
To do this, consider a vertical cylindrical pipe of length 𝐿 and diameter 𝐷 = 2𝑅. Assume that
when the fluid enters the pipe its velocity is uniform (i.e., it has the same value over the entire
cross-section of the pipe) and equal to 𝑈0 in the axial direction. In the radial and angular
directions, the velocity is zero. So, if we use cylindrical spatial coordinates, we can write:
𝑧 = 0 ∶ 𝒗(𝑟, 𝜃, 𝑧) = 𝑈0 𝒆𝑧
Here 𝒗 is the fluid velocity and 𝒆𝑧 is a vector of unit magnitude parallel to the coordinate axis
𝑧; furthermore, we have assumed that the pipe inlet is located at 𝑧 = 0.
Near the pipe entrance, the velocity profile changes in the axial direction. But after a certain
entrance length, the profile becomes fully developed, no longer changing with 𝑧.
1. Pressure Drop and Friction Factor
To calculate (unrecoverable) pressure drops in steady, fully developed pipe flows of the cooling
water circuit, engineers employ relations written in terms of a friction factor defined as follows:
𝑓 ≡ (𝜋𝑅𝐿) 𝑧(𝜌𝑈 2 )
where 𝐹𝑧 is the axial component of the force exerted by the fluid on the wall of the pipe, while
𝜌 and 𝑈 are the fluid density and mean velocity, respectively. The fluid is incompressible.
a) Prove that, in a pipe of constant diameter and for an incompressible fluid, the mean
velocity 𝑈 is equal to the inlet velocity 𝑈0 . Is this true only for Newtonian fluids?
b) Explain why in vertical pipes pressure changes are not fully unrecoverable. What is the
cause of recoverable pressure changes and what is the mathematical expression of such
c) Balancing the linear momentum over an appropriate control volume, prove that, in a
steady, fully developed flow, the unrecoverable pressure drop ∆𝑃 over the length 𝐿
(where 𝑃 is the dynamic pressure of the fluid) is related to 𝐹𝑧 as follows:
𝐹𝑧 = 𝜋𝑅2 ∆𝑃
Explain why i) unrecoverable pressure drops are expressed in terms of dynamic pressure
of the fluid and ii) Eq. 2.2 is invalid for developing flows.
2. Empirical Relations for the Friction Factor
By combining Eqs. 2.1 and 2.2, one obtains an equation relating the friction factor to the
unrecoverable drop in pressure over a pipe of length 𝐿. This equation gives ∆𝑃, provided 𝑓 is
known. In the literature, there are various relations that allow calculating 𝑓. Most of them are
empirical, derived by researchers who used dimensional analysis to guide their experimental
campaigns. You are asked to use this method to identify the dimensionless numbers on which
𝑓 depends for the cooling water pipes supplying cooling utilities to the EDC distillation units.
The starting point is Eq. 2.1, which defines 𝑓 and relates it to the frictional force 𝐹𝑧 . For
Newtonian fluids with viscosity 𝜇, this is given by:
𝐹𝑧 = ∫0 [ − 𝜇 (
] 𝜋𝐷 𝑑𝑧
To solve the integral above, one must solve the mass and linear momentum balance equations
for the fluid with appropriate boundary conditions (the flow is steady).
a) Explain how Eq. 3.1 is derived.
b) Report the steady-state mass and linear momentum balance equations in vector form
(i.e., without using spatial coordinates) and the boundary conditions.
c) Nondimensionalize the mathematical problem using the following dimensionless
variables (note that 𝜃 is already dimensionless):
∙,∙ 𝑧̅ ≡
∙,∙ 𝑃̅ ≡
and show that:
𝑓 = 𝑓(𝐿/𝐷, Re) with Re ≡
d) Prove that for fully developed flows 𝑓 depends on Re only. In light of this, what does a
dependence of 𝑓 on 𝐿/𝐷 reveal, and what does it account for?
e) Figure 2 reports the friction factor 𝑓 as a function of the Reynolds number Re for fully
developed pipe flows. For laminar flows 𝑓 depends on Re only, as expected, but for
turbulent flows it depends also on 𝑘/𝐷, where 𝑘 is a length characterizing the roughness
of the pipe wall. Moreover, this dependence is more pronounced at large values of Re.
How would you justify this experimental finding?
f) Using the laminar velocity profile, show that in the laminar flow regime 𝑓 = 16/Re.
3. Entrance Effects
Pressure drop calculations based on relations such as those shown in Figure 2 are valid only
for fully developed flows. However, entrance effects are always present. As mentioned, near
the entrance of any pipe there exist a region where the velocity profile evolves from its inlet
shape (assumed to be uniform) to its fully developed shape; refer to Figure 3. To judge whether
entrance effects are negligible, one must know the entrance length 𝐿𝑒 . This is the objective of
this part of the investigation.
We will restrict the analysis to laminar flows in which Re ≫ 1.
a) Using scaling arguments and the mass balance equation (in cylindrical coordinates),
identify the length and velocity scales in the wall layer.
b) Using scaling arguments and the equation governing the evolution of the velocity
component 𝑣𝑧 , identify the pressure scale and estimate the order of magnitude of 𝐿𝑒 .
Use linear momentum penetration theory to interpret the estimate found for 𝐿𝑒 .
c) Using scaling arguments, prove that 𝑃 is approximately a function of 𝑧 only.
d) Suggest a criterion for judging whether entrance effects can be neglected. For a pipe
with 𝑅 = 10 cm and 𝐿 = 100 m, if Re = 1500, can entrance effects be neglected? Explain
your answer briefly.
e) The estimate found for 𝐿𝑒 is valid for laminar flows. For turbulent flows, do you expect 𝐿𝑒
to be much larger, much shorter or about the same as for the laminar case? That is, for
turbulent flows, do you expect the condition for neglecting entrance effects to be more
demanding, less demanding or equally demanding when compared with the condition
holding for the laminar case? Justify your answer.
Figure 2. Friction factor for steady, fully developed pipe flows [taken from L. F. Moody,
Trans. ASME, 66, 671-684 (1944), as presented in W. L. McCabe and J. C. Smith, Unit
Operations of Chemical Engineering, McGraw-Hill, New York (1954)].
Figure 3. Evolution of the velocity profile in the pipe entrance region. Le is
the entrance length, while δ(z) is the thickness of the “wall layer,”
the region where ∂r v z ≠ 0.
END OF CENG0019