timer Asked: Apr 30th, 2020

Question Description

Hey guys, I have some reports upcoming and would appreciate some help! Everything is well-guided with questions to answer but please only take part if you are very good at chemical engineering - if I like your work I will give you more work!

Word limit: 8 pages MAX, 11pt Arial, double line spacing and 2cm margin.

The report should be numbered, a cover page unnecessary and references to be included appropriately.

This report will be covering module: Transport Phenomena

Official Task (Questions detailed in pdf): Pressure drops in pipe flows

As is typical for medium to large scale chemical plants, the VCM plant contains a separate cooling water circuit which distributes cooling water, available at a supply pressure of 10 barg and temperature of 25°C, to the different process units throughout the VCM process where cooling water is required. The used cooling water is then returned to the cooling water circuit at a minimum pressure of 3 barg and temperature of 35°C. A number of safety incidents have occurred due to higher than expected pressure drops being observed in the cooling water circuit of the VCM plant. The focus of this investigation will be on understanding the pressure drops in the pipe flows of the cooling water circuit.

DESIGN BRIEF (context)

Ramsay Limited is a company that produces vinyl chloride monomer (VCM), one of the world’s most important commodity chemicals, which is used as a precursor in the production of poly vinyl chloride (PVC). Following the development of a new technology route by one of their leading competitors, which has led to a decrease in the price of VCM, Ramsay Limited is looking to evaluate the efficiency of their existing technology. They are also developing their own new technology for the Oxychlorination reactor which could potentially be ready for commercialisation in the next 6 months, following completion of pilot plant testing. In addition to this they are analysing known aspects of the new oxychlorination technology developed by their competitors. Furthermore, in the last year there has been an increase in the number of minor safety incidents and near misses reported at Ramsay Limited’s older plants and at the PVC facilities of important neighbouring clients. To ensure that these incidents do not escalate into more serious safety incidents, a review of the control, dynamics, transport and safety of these plants is required. With these issues in mind, Ramsay Limited has requested your company to carry out this evaluation of their existing and new technology options with the aim to ensure the safety of their existing process is maintained and to improve their commercial advantage over their leading competitors.

Please check the official pdf I have uploaded - but all the reports are in response to the above briefing!

Unformatted Attachment Preview

THE PRODUCTS 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. BACKGROUND 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. PROCESS DESCRIPTION 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 (reaction 1) C2H4 + 2HCl + 1/2O2  C2H4Cl2 + H2O (reaction 2) 2C2H4Cl2  2C2H3Cl + 2HCl (reaction 3) 2C2H4 + Cl2 + 1/2O2  2C2H3Cl + H2O (reaction 4) CENG0017/18/19/20 6 Figure 1. Simplified Block Flow Diagram (BFD) of the existing balanced process for VCM production. CENG0017/18/19/20 7 Focus 2: CENG0019 – due 19 May at 3pm Transport Phenomena Pressure drops in pipe flows Deliverables Your report should consider the following: Introduction 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 𝑓 ≡ (𝜋𝑅𝐿) 𝑧(𝜌𝑈 2 ) (2.1) 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? [3] 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 changes? [2] 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: CENG0017/18/19/20 12 𝐹𝑧 = 𝜋𝑅2 ∆𝑃 (2.2) 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. [10] 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: 𝐿 𝜕𝑣𝑧 𝐹𝑧 = ∫0 [ − 𝜇 ( 𝜕𝑟 )| 𝑟=𝑅 ] 𝜋𝐷 𝑑𝑧 (3.1) 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. [5] b) Report the steady-state mass and linear momentum balance equations in vector form (i.e., without using spatial coordinates) and the boundary conditions. [2] c) Nondimensionalize the mathematical problem using the following dimensionless variables (note that 𝜃 is already dimensionless): 𝑟̅ ≡ 𝑟 𝐷 ∙,∙ 𝑧̅ ≡ 𝑧 𝐷 ̅≡ ∙,∙ 𝒗 𝒗 𝑈 ∙,∙ 𝑃̅ ≡ 𝑃 𝜌𝑈 2 (3.2) and show that: 𝑓 = 𝑓(𝐿/𝐷, Re) with Re ≡ 𝜌𝑈𝐷 𝜇 (3.3) [10] 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? [10] 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 CENG0017/18/19/20 13 of the pipe wall. Moreover, this dependence is more pronounced at large values of Re. How would you justify this experimental finding? [5] f) Using the laminar velocity profile, show that in the laminar flow regime 𝑓 = 16/Re. [6] 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. [10] 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 . [15] c) Using scaling arguments, prove that 𝑃 is approximately a function of 𝑧 only. [12] 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. [5] 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. [5] CENG0017/18/19/20 14 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)]. Inlet Velocity Profile Developing Velocity Profile Fully Developed Velocity Profile 𝑟 𝑈0 𝑧 (𝑧) 𝐿𝑒 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 CENG0017/18/19/20 15 ...
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