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Process Integration for Environmental Control in Engineering Curricula (PIECE)

Program for North American Mobility in Higher Education (NAMP). Process Integration for Environmental Control in Engineering Curricula (PIECE). Module. 2. Steady State Process Simulation. Propose. This module has been developed to help the students:.

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Process Integration for Environmental Control in Engineering Curricula (PIECE)

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  1. Program for North American Mobility in Higher Education (NAMP) Process Integration for Environmental Control in Engineering Curricula (PIECE)

  2. Module 2 Steady State Process Simulation

  3. Propose This module has been developed to help the students: • Understand and simulate processes in steady state. • Solve technical and economic problems more quickly, efficiently and successfully.

  4. Statement of intent The student will. • Review basic concepts used in steady – state simulation. • Understand the purpose of steady – state simulation. • Develop models of a processes in steady state. • Simulate processes with help of computer simulators.

  5. Contents This module is divided in 3 tiers Tier 1. Introduction to simulation tool. Tier 2. How to use computer tool. Tier 3. How to apply in real world.

  6. Tier 1 Introduction to Steady State, Process Simulation tool

  7. Contents Tier 1 is divided in 3 sections • Basic concepts. • Steady – state simulation in a process integration context. • Steady – state simulation in a broader context.

  8. 1Basic Concepts

  9. Statement of intent Basic concepts • Show the basic concepts of steady – state simulation. • Improve process simulation skills. • Create your own simulation flowsheets. • Recognize why simulation is useful in the process industries.

  10. Contents Basic Concepts • Steady – state. • Models and simulation. • Creating models. • Unit efficiencies. • Stream components. • Units. • Performing a steady – state simulation study.

  11. Steady – state Steady – State By steady state we mean, in most systems, the conditions when nothing is changing with time. Mathematically this corresponds to having all time derivatives equal to zero, or to allowing time to become very large (go to infinity).

  12. Steady – state Steady – State The design of process systems requires both: • Steady – state model. • Dynamic models. One use for the steady – state models is in determining the possible region of steady – state operation for a process that can be limited by constraints such as safety, product quality, and equipment performance.

  13. Models & simulation Model A model is an abstraction of a process operation used to build, change, improve or control a process. Uses of a model: • Equipment design, sizing and selection. • Comparison of possible configurations. • Evaluation of process performance against limits (e.g. Concentrations, effluent discharge rates). • De-bottlenecking and optimization. • Control strategy development and evaluation.

  14. Models & simulation Model The model is an abstraction of the real word • Models vary by: • Phenomena represented (energy, classifications phase change). • Level of detail and granularity • Assumptions (perfect mixing, zero heat loss). • Kind of input required • Functions performed (constraint satisfaction, optimization). • Nature of output generated

  15. Models & simulation Models vary by purpose and category Purpose • Operator training simulator. • Control strategy evaluation. • Investment justification(e.g. new equipment purchase). • Other… • Category • Physical (e.g. mimic panel) vs. Mathematical. • Qualitative vs. Quantitative. • Empirical vs. First principle based. • Steady state vs. Dynamic state.

  16. Models & simulation Physical Model From a balance: Mathematical Model

  17. Models & simulation Quantitative Qualitative Using non – numeric descriptors. • Fuzzy, logic. • Expert system. • Turn an alarm on. Using numbers, and quantifying the magnitude of the response.

  18. Models & simulation Empirical First – principle based • Derived from observation. • Often simple. • May or may not have theoretical foundation. • Valid only within range of observation. • Derived from fundamental physical laws. • Most reliable, but we often don’t have them.

  19. Models & simulation Steady – State Dynamic

  20. Models & simulation Requirements of a good model • Accuracy: close enough to the target. It is required in quantitative and qualitative models. • Validity: we must consider the range of the model. The model must have a solid foundation or justification. • Right level of complexity: models can be simple, usually macroscopic, or detailed, usually microscopic. The detail level of phenomena should be considered. Easy to understand. • Computational efficiency: the models should be calculable using reasonable amounts of time and computing resources.

  21. Models & simulation Simulation Predicts the behavior of a plant by solving the mathematical relationships that describe the behavior of the plant’s constituent components. Involves performing a series of experiments with a process model.

  22. Models & simulation Importance of steady – state simulation • Better understanding of the process. • Consistent set of typical mill data. • Objective comparative evaluation of options for return on investment etc. • Identification of bottlenecks, instabilities, etc. • Ability to perform many experiments cheaply once model built. • Avoidance of ineffective solutions.

  23. d ò ò ò = - × + b dV F n dS B dV V dt V S V Models & simulation Constructing a model When we try to represent a phenomena, to predict future conditions, or to know how the process will behave in certain situation, it is common to use mathematical expressions.

  24. Creating models Constitutive relations Relate the diffusive flux of a certain quantity with the local properties of the material and with the transport driving force. Express the movement of a certain quantity in the decreasing gradient direction of the quantity.

  25. Creating models Constitutive relations • Fick’s first law: Mass diffusion • Fourier’s law: Thermal diffusion • Newton’s law: Kinematic viscosity

  26. Creating models Variation EquationsConservation Equations or Equations of change Those relate the accumulation of a quantity with the rate of entrance or formation of the same quantity in a specific volume. Those are based in fundamental principles and have universal description.

  27. Creating models Conservation of mass It is common practice to express the balance in a differential element, and convert the equation to a differential form. In a differential element:

  28. Creating models Conservation of mass Note: steady – state no change in the time. For a pure component: Conservation of chemical species:

  29. Creating models Conservation of energy Where HV is rate of heat generated by external source (electricity, compression, chemical reactions, etc.). Note: steady – state no change in the time.

  30. Unit efficiencies Unit efficiencies An engineer may define energy efficiency in a very restrictive equipment sense. Energy efficiency has been used to describe what actually may be conservation. Energy efficiency in a more subjective sense may refer to the relative economy with which energy inputs are used to provide services.

  31. Unit efficiencies Typical Efficiencies Values • Compressors e = 0.8 • Motor e = 0.9 • Pump e = 0.5 • Turbine e = 0.8

  32. Stream components Stream Components Overall stream flows and components are calculated based on physical and chemical properties such as: • Ideal gas law and equations of state. • Solubility relations (solid in liquid and gas in liquid). • Reaction stoichiometry and equilibrium. • Simple vapor/liquid relationships such as Raout’s law.

  33. A C B B A A B Stream components Conversion of stream components • Mechanical work. • Via chemical reaction. • Heat.

  34. Units Engineering Units The official international system of units is the SI . But older systems, particularly the centimeter – gram – second (cgs) and foot – pound – second (fps), are still in use. • It was originated in France, in 1790 by the French Academy of Science. • The units should be based on unvarying quantities in nature. • Multiples of units should be decimal. • The base units should be used to derive other units.

  35. Units Engineering Units

  36. Performing a SS simulation study Performing a Steady – State simulation Study • Steady state model derivation. • Calculation order. • Recycle streams. • Convergence and iteration. • Recycle convergence methods. • Granularity model.

  37. Performing a SS simulation study Steady state model derivation 1.- Define Goals. a)      Specific design decisions. b)      Numerical values. c)      Functional relationships. d)      Required accuracy. 2.- Prepare information. a)      Sketch process and identify system. b)      Identify variables of interest. c)      State assumptions and data.

  38. Performing a SS simulation study Steady state model derivation 3.- Formulate model. a)      Conservation balances. b)      Constitutive equations. c)      Rationalize (combine equations and collect terms). d)      Check degrees of freedom. e)      Dimensionless groups (Pr, Nu, Re, etc.). 4.- Determine solution. a)      Analytical. b)      Numerical.

  39. Performing a SS simulation study Steady state model derivation • 5.- Analyze results • a) Check results for correctness • Limiting and approximate answers • Accuracy of numerical method • b) Interpret results • Plot solution • Relate results to data and assumptions • Evaluate sensitivity • Answer “what if questions”

  40. Performing a SS simulation study Steady state model derivation 6.- Validate model. a)      Select key values for validation. b)      Compare with experimental results.

  41. Performing a SS simulation study Calculation Order In most process simulators, the units are computed (simulated) one at a time. The calculation order is automatically computed to be consistent with the flow of information in the simulation flowsheet, where the information flow depends on the specifications for the chemical process. 1 2 3 4

  42. Performing a SS simulation study Recycle Flows A simulation flowsheet usually contains information recycle loops. That is, cycles for which too few streams variables are known to permit the equation for each unit to be solved independently. 1 2 3 4 For these processes, a solution technique is needed to solve the equations for all the units in the recycle loop.

  43. New values from The calculation Initial guessing values Calculation Performing a SS simulation study Solution technique Consist in guessing a value for the recycle stream. This value is generally not going to equal the calculated value, this represent another problem which is solved by “iteration”.

  44. Performing a SS simulation study Iteration Convergence units use convergence subroutines to compare the newly computed variables (in the feed stream to the convergence unit) with guessed values (in the product stream from the convergence unit) and to compute new guess values when the two streams are not identical to within convergence tolerances. This procedure is call iteration. It involves re – calculating the flowsheet.

  45. Performing a SS simulation study Convergence Is the process to compare the guessed value with the computed value, until find a value within the tolerance range. Guess value No Yes Guess value – calculated value < Tolerance Convergence When the criteria is achieve, the solution is found, and is time to stop the iteration.

  46. Start Convergence? Stop Performing a SS simulation study Convergence t = 0, k=0Guess torn streams Initialize each unit no Xijyij k = k + 1 no

  47. Performing a SS simulation study Recycle convergence methods Where is the vector of guesses for n recycle (tear) variables and is the vector of the recycle variable computed from the guesses after one pass through the simulation units in the recycle loop. Clearly, the objective of the convergence unit is to adjust so as to drive toward zero.

  48. Locus of Iterates f(x*) x0* x1* Performing a SS simulation study Successive substitution as the basic and obvious method Also call direct iteration. In this method the new guess for x is simply made equal to f(x*). When the slope of the locus of iterates (f(x),x) is close to unity, a large number of iterations may be required before convergence occurs

  49. Performing a SS simulation study Other convergence methods When the method of successive substitutions requires a large number of iterations, another methods are used to accelerate convergence: • Wegstein’s method. • Newton – Raphson method. • Broyden’s quasi – Newton method. • The dominant – eigenvalue method.

  50. Performing a SS simulation study Wegstein’s method In this method, the two previous iterates of f(x*) and x* are extrapolated linearly to obtain the next value of x as the point of intersection. Locus of Iterates f(x*) x0* x1*

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