UNIVERSITY COLLEGE LONDON EXAMINATION FOR INTERNAL STUDENTS MODULE Code: CENG0006 COMPUTATIONAL MODELLING AND ANALYSIS LEVEL: Undergraduate and Undergraduate Masters This paper is suitable for candidates who attended classes for these modules in the following academic year(s): Year 2020/21 Suitable for all candidates Assignment Title Coursework (40% of the module) Submission Deadline As stated in the Assessment tab of the Chemical Engineering Student Intranet. Word limit / page limit Note to students: Any over-length pieces of work will be penalised by a 10% deduction in mark, but will not take the student’s mark below the Pass Mark overall for the module, and the over- length part of the work will not be marked. • The report should be maximum 10 pages (but can be less) excluding appendices, be typed with minimum 11pt Arial font (or equivalent font and size), minimum single line spacing, and with minimum 2 cm margin. • The pages should be numbered. • A cover page should not be included, and appendices are permitted. Marking Criteria Included in the assignment instructions Submission Link Assessment section in Moodle under the heading Submission links (See further instructions in the submission link) All work should be completed strictly individually, but all available notes, books and internet sources can be used. UCL’s policy for Academic Misconduct applies, including for collusion and plagiarism: https://www.ucl.ac.uk/academic-manual/chapters/chapter-6-student-casework- framework/section-9-student-academic-misconduct-procedure   1. Uploading your submission • Unless specifically instructed otherwise in the assessment document, please upload your work as a single .pdf file via the submission link on Moodle and by the given deadline. • Wherever possible you should type your answers and follow guidelines in the assessment document on the preferred format (font, line spacing and so on). • If you do have to include any elements that are not typed/computer generated (e.g. figures, diagrams, equations etc.), or you are unable to type your answers for any reason, please follow the advice for submitting handwritten answers for any submission that requires scanning documents (the webpage refers to 24-hour timed exams but is applicable to all online submissions). • If for any reason you are not able to use the app recommended by ISD at the link above, you can consult the following resources for advice about preparing your submission: • Submitting handwritten assignments to Moodle using mobile or tablet Devices - Device Camera • Submitting handwritten assignments to Moodle using mobile or tablet devices - MS One Drive App • If handwritten work is not readable then it would not be possible to allocate marks to the work. • Please DOUBLE CHECK that the file you are uploading is the correct one and is complete (with all pages visible) before the deadline. You will not be allowed to re-submit the file after the deadline. 2. Technical Problems If you encounter difficulties downloading or submitting your assessment via Moodle, then please immediately notify (by email) the Teaching & Learning Team (chemeng.teaching.admin@ucl.ac.uk). Please note that the final submission must be via Moodle. Work submitted via email will not be accepted and will not be marked. 3. Advice and other support • Advice about Extenuating Circumstances • UCL Engineering EC App • Student Support and Wellbeing CENG0006: Coursework-2 Linear Programming using GAMS and Differential Equations Modelling using gPROMS Prepare a report (pdf) and submit via TurnItIn including a copy of the GAMS code (.gms and output .lst) for Question 1 and a copy of the gPROMS code (.gpj) file(s) for Part A of Question 2 in the appendix of the report. In addition to the TurnItIn submission, GAMS code (.gms) and output (.lst) files for Question 1 and gPROMS code (.gpj) file(s) for Part A of Question 2 must be submitted as a single zipped/compressed file folder via Moodle. Each question carries marks distributed as shown below [ ]. Question – 1: Process Flowsheet Optimisation by using GAMS Consider the following flowsheet of a gas phase reaction for the production of methanol: Fig. 1. Process flowsheet The component mole fractions of the feed stream are given by: CO2 0.1 CH4 0.05 CO 0.184 H2 0.59 H2O 0.008 CH3OH 0 N2 0.068 The following equations should be used. Reactor Mixer Separator-2 Separator-1 Reactor Feed 1 2 3 4 5 7 6 Purge Product For each component i −= j ijjFlowin(i)Flowout(i) where σij = stoichiometric coefficient for component i in reaction j νj = extent of reaction for reaction j CO + 2H2 → CH3OH ν1 = 1280 kmol/hr CO2 + H2 → CO + H2O ν2 = 360 kmol/hr Separator 1 Assume all CO2, CH4, CO, H2 and N2 go into stream 5. 99% of H2O and 96% of CH3OH go into the product stream. Separator 2 10% of stream 5 is purged in stream 7. The product value is given by £1000 per kmol of stream 4 and the feed cost is given by £1.5 per kmol of stream 1. The processing costs of mixer, reactor, separator-1 and separator-2 are given by £0.1, £0.2, £0.15 and £0.15 per kmol of the inlet flowrates to these equipments respectively. The objective is to maximize profit where profit is given by product (stream 4) value minus feed (stream 1) cost and processing costs of the four equipments. Due to environmental regulations a maximum of 200 kmols/hr of CO2 and 5.5 kmols/hr of CH3OH can be purged in stream 7. Set this problem as a Linear Programming problem and provide the formulation in 1-2 pages in the report. [25] Solve it by using GAMS. Use ‘SETS’, ‘PARAMETERS’ and ‘TABLE’ features wherever possible in the GAMS input file. The input file must also contain adequate comment statements for ease of understanding. In the report, provide values of the profit (in £/hr), feed (stream 1) component flowrates (in kmols/hr), product (stream 4) component flowrates (in kmols/hr), and CO2 and CH3OH flowrates in the purge (stream 7). [25] Question – 2: Dynamic Modelling of Transmission of Infectious Diseases Computational modelling can be used to predict the transmission of infectious diseases (such as, pandemic influenza, Ebola transmission, Zika transmission) and guide the public health policy. Consider Fig. 2 and the following compartmental model (Roosa and Chowell, 2019) of the 1918 influenza pandemic in San Francisco, California, given by the system of simultaneous Ordinary Differential Equations (ODEs): = −. . = . . − . = . − . = . = . where N is the total population size. The population can be considered to consist of 4 classes, S, E, I and R, denoting the numbers of susceptible, exposed, infectious and recovered individuals, respectively, and N = S + E + I + R. The constant parameters in the model are denoted by , and , where the nominal values of the parameters are: = 0.56 = 1 1.9 = 1 4.1 Part A: Simulation: Assume that N = 500000. Simulate the ODE model using gPROMS for S(0) = I(0) = N/2, E(0) = R(0) = C(0) = 0 and t = [0, 17], and plot the state and auxiliary variables, i.e., S, E, I, R and C, as a function of t. [25] Part B: There is an uncertainty of ±10% from the reported nominal values of the constant parameters, , and . Simulate the ODE model in Part A for some variations (to be selected by you) in the values of the constant parameters from their nominal values and report the effect of these variations on the state and auxiliary variables. Plot the state and auxiliary variables as a function of t for some selected values of the constant parameters. [25] From: Assessing parameter identifiability in compartmental dynamic models using a computational approach: application to infectious disease transmission models Fig. 2. Simple SEIR – Population is divided into 4 classes: susceptible (S), exposed (E), infectious (I), and recovered/removed (R). Class C represents the auxiliary variable C(t) and tracks the cumulative number of infectious individuals from the start of the outbreak. This is presented as a dashed line, as it is not a state of the system of equations, but simply a class to track the cumulative incidence cases; meaning, individuals from the population are not moving to class C. Parameter(s) above arrows denote the rate individuals move between classes. Reference: Roosa, K., Chowell, G. Assessing parameter identifiability in compartmental dynamic models using a computational approach: application to infectious disease transmission models. Theor Biol Med Model 16, 1 (2019). https://doi.org/10.1186/s12976-018-0097-6 Hint1: The variables that may not have a physical meaning or the units, can be declared as NoType without any unit, but still take care regarding the upper/lower bounds and the default values. Hint2: If you are expecting a curve when you are plotting the results but you got a straight line then check the reporting interval value and choose an appropriate value for the interval.




























































































































































































































































































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