Process Simulation Introduction

Model, what for? A good model of the apparatus is needed for: Process simulation optimisation design apparatus design can be done with pen and piece of paper but even quite simple optimization problem needs to involve the computer

The model It is a representation of real object (apparatus or part of the apparatus) It let us foresee behavior of physical objects without experiments in the real world. However, usually the basis of the models are experiments Approximation of constants/coefficients in model equations Physical parameters of chemicals, etc.

Classification of the models Physical – mathematical Physical – one physical quantity replaced with another (easier to measure) or use of scaled down objects (cars, planes in wind tunnels) Mathematical - representation by the use of equations.

Classification of the models Black box – white box Black box – know nothing about process in apparatus, only dependences between inputs and outputs are established. Practical realisation of Black box is the neural network White box – process mechanism is well known and described by system of equations

Classification of the models Deterministic – Stochastic Deterministic – for one given set of inputs only one set of outputs are found with probability equal 1. Stochastic – random phenomenon affects on process course (e.g. weather), output set is given as distribution of random variables

Classification of the models Microscopic- macroscopic Microscopic – includes part of process or apparatus Macroscopic – includes whole process or apparatus

Elements of the model 1. Balance dependences Based upon basic nature laws of conservation of mass of conservation of energy of conservation of electric charge, etc. Balance equation: Input – Output = Accumulation

Elements of the model 2. Constitutive equations – apply to unconvectional streams Newton eq. – for viscous friction Fourier eq. – for heat conduction Fick eq. – for mass diffusion

Elements of the model 3. Phase equilibrium equations – important for mass transfer 4. Physical properties equations – for calculation parameters as functions of temperature, pressure and concentrations. 5. Geometrical dependences – involve influence of apparatus geometry on transfer coefficients – convectional streams.

Structure of the simulation model Structure depends on: Type of object work: Continuous, steady running Periodic, unsteady running Distribution of parameters in space Equal in every point of apparatus – aggregated parameters (butch reactor with ideal mixing) Parameters vary with space – displaced parameters

Structure of the model Steady stateUnsteady state Aggregated parameters Algebraic eq.Ordinary differential eq. Displaced parameters Differential eq. 1. Ordinary for 1- dimensional case 2. Partial for 2&3- dimensional case (without time derivative, usually elliptic) Partial differential eq. (with time derivative, usually parabolic)

Process simulation the act of representing some aspects of the industry process (in the real world) by numbers or symbols (in the virtual world) which may be manipulated to facilitate their study.

Process simulation (steady state) Flowsheeting problem Design (specification) problem Optimization problem Synthesis problem by Rafiqul Gani

Flowsheeting problem Given: All input information All operating condition All equipment parameters To calculate: All outputs FLOWSHEET SCHEME INPUT OPERATING CONDITIONS EQUIPMENT PARAMETERS PRODUCTS

R.Gani

Specyfication problem Given: Some input&output information Some operating condition Some equipment parameters To calculate: Rest of inputs&outputs Rest of operating condition Rest of equipment parameters FLOWSHEET SCHEME INPUT OPERATING CONDITIONS EQUIPMENT PARAMETERS PRODUCTS

Specyfication problem NOTE: degree of freedom is the same as in flowsheeting problem.

To gues: D, Q r Solve the flowsheeting problem STOP Is target product composition satisfied ? Adjust D, Q r Given: feed composition and flowrates, target product composition Find: product flowrates, heating duties

Process optimisation the act of finding the best solution (minimize capital costs, energy... maximize yield) to manage the process (by changing some parameters, not apparatus)

To gues: D, Q r Solve the flowsheeting problem STOP Is target product composition satisfied AND  =min. Adjust D, Q r Given: feed composition and flowrates, target product composition Find: product flowrate, heating dutie

Process synthesis/design problem the act of creation of a new process. Given: inputs (some feeding streams can be added/changed) Outputs (some byproducts may be unknown) To find: flowsheet equipment parameters operations conditions

Process synthesis/design problem flowsheet undefined INPUTOUTPUT

To gues: D, Q r Solve the flowsheeting problem STOP Is target product composition satisfied AND  =min. Adjust D, Q r As well as N, N F, R/D etc. Given: feed composition and flowrates, target product composition Find: product flowrate, heating dutie

Process synthesis/design problem Separation method & equipment methanol water methanol water Methods: distillation, membrane separation, flash, extraction Equipment: how many apparatus are needed what is apparatus design and conditions

Process simulation - why? COSTS Material – easy to measure Time – could be estimated Risc – hard to measure and estimate

Modelling objects in chemical and process engineering 1. Unit operation 2. Process build-up on a few unit operations

Software for process simulation Universal software: Worksheets – Excel, Calc (Open Office) Mathematical software – MathCAD, Matlab Specialized software – flowsheeting programs. Equipped with: Data base of apparatus models Data base of components properties Solver engine User friendly interface

Software process simulators (flawsheeting programs) Started in early 70’ At the beginning dedicated to special processes Progress toward universality Some actual process simulators: 1. ASPEN One 2. HYSIM 3. ChemCAD 4. PRO/II 5. ProMax

Chemical plant system The apparatus set connected with material and energy streams. Most contemporary systems are complex, i.e. consists of many apparatus and streams. Simulations can be use during: Investigation works – new technology Project step – new plants (technology exists), Runtime problem identification/solving – existing systems (technology and plant exists)

Chemical plant system characteristic parameters can be specified for every system according to separately: 1. Material streams 2. Apparatus

Apparatus-streams separation Why separate? It’s make calculations easier Assumption: All processes (chemical reaction, heat exchange etc.) taking places in the apparatus and streams are in the chemical and thermodynamical equilibrium state.

Streams parameters Flow rate (mass, volume, mol per time unit) Composition (mass, volume, molar fraction) Temperature Pressure Vapor fraction Enthalpy

Streams degrees of freedom DF s =NC+2 e.g.: NC=2 -> DF s =4 Assumed: F1, F2, T, P Calculated: enthalpy vapor fraction

Apparatus parameters Characteristics for each apparatus type. E.g. heat exchanger : Heat exchange area, A [m 2 ] Overall heat-transfer coefficient, U (k) [Wm -2 K -1 ] Log Mean Temperature Difference, LMTD [K] degrees of freedom are unique to equipment type

Types of flowsheeting calculation According to the system Static calculation Dynamic calculation According to calculation target: Simulation Design Identifying

Calculation subject Number of equations of mass and energy balance for entire system Can be solved in two ways:

Types of balance calculation Overall balance (without apparatus mathematical model use) Detailed balance on the base of apparatus model

Overall balance Apparatus is treated as a black box Needs more stream data User could not be informed about if the process is physically possible to realize.

Overall balance – Example Countercurrent, tube-shell heat exchanger Given three streams data: 1, 2, 3 hence parameters of stream 4 can be easily calculated from the balance equation There is possibility that calculated temp. of stream 4 can be higher then inlet temp. of heating medium (stream 1). DF=5

Overall balance – Example Given: 1.m A =10kg/s 2.m B =20kg/s 3.t 1 = 70°C 4.t 2 =40°C 5.t 3 =20°C c pA =c pB =f(t) 1, m B 2 4 3, m A

Apparatus model involved Process is being described with use of modeling equations (differential, dimensionless etc.) Only physically possible processes taking place Less stream data required (smaller DF number) Heat exchange example: given data for two streams, the others can be calculated from a balance and heat exchange model equations

Loops and cut streams Loops occur when: some products are returned and mixed with input streams when output stream heating (cooling) inputs some input (also internal) data are undefined To solve: one stream inside the loop has to be cut initial parameters of cut stream has to be defined Calculations has to be repeated until cut streams parameters are converted.

Loops and cut streams

Simulation of system with heat exchanger using Excel

I.Problem definition Simulate system consists of: Shell-tube heat exchanger, four pipes and two valves on output pipes. Parameters of input streams are given as well as pipes, heat exchanger geometry and valves resistance coefficients. Component 1 and 2 are water. Pipe flow is adiabatic. Find such a valves resistance to satisfy condition: both streams output pressures equal 1bar.

II. Flawsheet s6 s s2s3s4s5 s7 s8 s9 s10

Stream s1 P s1 =200kPa, t s1 = 85°C, f1 s1 = 1000kg/h Stream s6 P s6 =200kPa, t s6 = 20°C, f2 s6 = 1000kg/h Numerical data:

Equipment parameters: 1. L 1 =7m d 1 =0,025m 2. L 2 =5m d 2 =0,16m, s=0,0016m, n= L 3 =6m, d 3 =0,025m   4 =50 5. L 5 =7m d 5 =0,025m 6. L 6 =10m, d 6 =0,025m   7 =40

III.Stream summary table Uknown:T s2, T s3, T s4, T s5, T s7, T s8, T s9, T s10, P s2, P s3, P s4, P s7, P s8, P s9, f1 s2, f1 s3, f1 s4, f1 s5, f2 s7, f2 s8, f2 s9, f2 s10 number of unknown variables: 24 WE NEED 24 INDEPENDENT EQUATIONS.

f1 s2 = f1 s1 f1 s7 = f1 s6 f1 s3 = f1 s2 f1 s8 = f1 s7 f1 s4 = f1 s3 f1 s9 = f1 s8 f1 s5 = f1 s4 f1 s10 = f1 s9 Equations from equipment information 14 equations. Still do define =10 equations

Heat balance equations New variable: Q Still to define: =9 equations

Heat exchange equations New variables: k,  T m : number of equations to find 9+2-2=9

Heat exchange equations Two new variables:  T and  S number of equations to find: 9+2-1=10

Heat exchange equations Three new variables: Nu T, Nu S, d eq, number of equations to find: =10

Heat exchange equations

Two new variables Re T and Re S, number of equations to find: =8

Pressure drop

Two new variables Re 1 and 1, number of equations to find: 8+2-3=7

Pressure drop Two new variables Re 2t and 2T, number of equations to find: 7+2-3=6

Pressure drop Two new variables Re 3 and 3, number of equations to find: 6+2-3=5

Pressure drop Number of equations to find: 5-1=4

Pressure drop Two new variables Re 5 and 5, number of equations to find: 4+2-3=3

Pressure drop Two new variables Re 2S and 2S, number of equations to find: 3+2-3=2

Pressure drop Two new variables Re 6 and 6, number of equations to find: 2+2-3=1

Pressure drop Number of equations to find: 1-1=0 !!!!!!!!!!!!!!

Agents parameters Temperatures are not constant Liquid properties are functions of temperature Specyfic heat c p Viscosity  Density  Thermal conductivity Prandtl number Pr

Agents parameters Data are usually published in the tables

Data in tables are difficult to use Solution: Approximate discrete data by the continuous functions. Agents parameters

Approximation Approximating function Polynomial Approximation target: find optimal parameters of approximating function Approximation type Mean-square – sum of square of differences between discrete (from tables) and calculated values is minimum.

Polynomial approximation

The end as of yet.