s1 2015 flowsheeting
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Department of Mining Engineering and Metallurgical Engineering WESTERN AUSTRALIAN SCHOOL OF MINES
Process Engineering 451/661 – S1 2015
PROCESS ENGINEERING PRRE4001/6003
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MODULE 1: “Do-it-Yourself Flowsheets”
Why would you do it yourself?
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Kidd Creek Copper and Zinc Mine (Canada), www.mining-technology.com
Flowsheet
Metallurgical flowsheets - Visual and quantitative; static or dynamic - Process design and plant operation
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1. Mixing – 2 or more input streams are combined to form a single output stream
2. Splitting – an input stream is divided into 2 or more output streams of identical composition (or size distribution, for solids)
3. Separation – an input stream is divided into 2 or more output streams of different composition (or size distribution for solids)
4. Reaction – refers to alteration of minerals and other materials by chemical reaction
5. Material transfer – mostly involves the movement of liquids, gases and slurries through pipes, etc.
6. Energy transfer – heating, cooling, heat recovery and recycling
Unit Processes
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Flowsheet Features
IMPORTANT TERMS: ■ Input stream ■ Feed stream ■ Product and waste streams – tailings, concentrate ■ Recycle and bypass streams
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6 A process flowsheet summarising the steps taken in the treatment of bauxite ore to
produce aluminium metal (Hayes, P. , 1993, pp 9)
Flowsheet
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Numbering Unit Processes
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First: Choose the “ Main Flow”
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Second: Identify Branches
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Third: Number Unit Processes to Follow Main Flow
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Fourth: Number Streams to Follow Unit Processes
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Fourth: Number Streams to Follow Unit Processes
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Tutorials – First: Choose the “Main Flow”
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Second: Identify Branches
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Tutorials – Second: Identify Branches
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Third: Number Unit Processes to Follow Main Flow
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Tutorials – Third: Number Unit Processes to Follow Main Flow
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Tutorials – Third: Number Unit Processes to Follow Main Flow
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Fourth: Number Streams to Follow Unit Processes
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Tutorials – Fourth: Number Streams to Follow Unit Processes
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Tutorials – Fourth: Number Streams to Follow Unit Processes
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Numbered Flowsheet
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Stream Characteristics
Species – uniquely distinguishable material entity within a stream Examples: ● Furnace gas: SO2, O2, CO, CO2, N2 ● Slurry: water, solids ● Matte: Cu2S, FeS
Stream Information:
Note: Stream unknowns; Assignment of stream unknowns (pp 11-12)
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MASS BALANCE: Unknown Stream Flows
Streams 1 and 3 – contain relationships between total flow and species flow Stream 4 – contains similar relationship as 1 and 3; modified Stream 2 – no useful equation; contains trivial information
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MASS BALANCE: Stream Equations
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Stream Equations: Gas Volume to Mass Conversion
Units: ● Standard Cubic Metre, Nm3 – a cubic metre of ideal gas at STP (O0C and 1 atmosphere pressure) ● 1 mole (STP) 22.4 x 10-3 Nm3 (22.4 L) ● vol % = mol% for ideal gases
Moles of SO2 = 0.065 (Total Moles in Gas)
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MASS BALANCE EQUATIONS
Total Mass Balance: ΣMass Flow for Input Streams = ΣMass Flow for Output Streams
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MOLE BALANCE: Unknown Stream Flows
Mole balance: more convenient to use when stoichiometry of species within streams is well defined or when a number of gas streams are involved
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MOLE BALANCE: Stream Equations
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MOLE BALANCE EQUATION
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Solve Linear Equations using Matrix Inversion
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Heat Balance Equation
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Heat Balance Equation Terms
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Sensible Heat
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Heat of Reaction
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Sensible Heat
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Sensible Heat Data – FREED Database
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Sensible Heat Data – FREED Database
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LABELS for SENSIBLE HEAT Data
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Thermodynamic Data – FREED Database
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Heat Balance Data in Excel from FREED
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Simple Maths for Flowsheets
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Set up unknowns Find all independent equations between them through examining: o Stream Characteristics o Mass and Mole Balances o Heat Balances o Unit Process Characteristics Analyse each unit process separately
Need Systematic Approach to:
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Important Definitions
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o Process Components o Common Stream Variables o Active Components
Analysis of Unit Processes
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Process Components
Note: A determination of the number of components for a unit process is fundamentally important knowledge for a material balance since one independent material balance can be written for each component within the unit process.
Stream species – represent all of the physically distinguishable elements, compounds or materials which collectively constitute a given stream. Process components – represent the minimum number of independently distinguishable physical entities present amongst the species of a unit process, from which all input and output species can be assembled, taking into account all intrinsic relationships which exist amongst the species, such as stoichiometric linkages and chemical reactions.
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Species and Components
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Use one material balance equation for each common stream variable assigned to the
process.
What is a common stream variable?
Common Stream Variables
Note: When the flow of a species in two different streams can be represented by the same unknown, the unknown is called a common variable.
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Common Stream Variables in a Mixer
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The number of components for which a material balance equation can still be written after the assignment of flow unknowns is the number of “active components”
Active Components
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Mixers
Splitters
Separators
Reactors
Characteristic Equations for Unit Processes
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Unit Process Analysis
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No reactions Number of components C is equal to the number of neutral species S
C = S
Write one material balance for each Active Component
MIXER
Example: Mixer material balance, pp 28
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Operating Parameter: Split Fraction
ΣSFj = 1, SF = OS-1
Write SE = Cactive(OS-1) splitter equations
SPLITTER
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Splitter Equations
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Splitter Equations
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C = S
Write one material balance for each Active Component
(OS-1) independent split fractions
Create an unknown for each undefined split fraction
Write SE splitter equations where:
Splitter Analysis
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Operating Parameter: Separation Coefficient
Total Independent SC’s = S(OS-1)
SEPARATOR
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Independent SC’s = S(OS-1) = 3(2-1)=3
SCA2 = 1 SCB2 = 0 SCC2 =0.15
Independent Separation Coefficients
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Write SCE independent separator equations: Example: Cactive = 1 Equation: mC(2) = 0.15mC(1)
Independent Separator Equations
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C = S Write one material balance for each Active Component
Total Independent Separation Coefficients SC = S(OS-1)
Use Common Variable for each SC = 1
Write SCE independent separator equations, where:
Separator Analysis
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Key Parameter: R = Number of independent reactions
C = (SR –R) + S
Write one material balance for each component
C < S
REACTOR
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Number of Independent Reactions
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Finding the Independent Reactions
See Appendix 4 for details
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Finding the Independent Reactions
Combine the reactions to eliminate elements not in the set: Eliminate C (1) – (3) CO + 2H2 CH4 + O (1A) Unchanged: H2 + O H2O (2) Eliminate O (1A) + (2) CO + 3H2 CH4 + H2O (1B) (2) + (3A) CO2 + H2 CO + H2O (2B) Or (4)-(1)-2x(2) CO2 + 4H2 CH4 + 2H2O for 1B
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Identifying Reaction Components
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Identifying Reaction Components
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Other Reaction Equations
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Example: Component Balance Method for a Reactor
Neutral Species: N2 (S = 1) Reaction Species: H2, O2, H2O (SR = 3) Independent Reactions: H2 + 0.5O2 H2O (R = 1) Neutral Components: N2 (1) Reaction Element Components: C = (SR – R) = (3-1) = 2
Example: pp 38
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So far …
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Main Steps for Unit Process Analysis
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Method for Unit Process Analysis 1. Choose a mole or mass balance 2. Summarise the input/output – diagram 3. Annotate the input/output diagram – identify and name
streams, show known species, stream flow rates, temperatures (if relevant pressures)
4. Analyse the unit process – determine the number of unknowns, active components, restrictions, DOF
5. Write out the equation set for the unit process – component balance equations, restriction equations, any heat balance equation
6. Solve the equation set – Matrix Inversion for linear; Solver for non-linear
7. Summarise the final stream data 8. Verify the balances – total mass balance, individual element
and neutral species balances for a mole balance within reactor
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Summarise Analysis Using Table
Example: pp 44
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Unit Process Analysis Examples
Linear Equations: Example 1, pp 45 – Gas Mixer Example 2, pp 49 – Reactor (Refine) Example 3, pp 51- Reactor (Burner) Non-Linear Equations: Example 4, pp 60 – Reactor (Equilibrium) Example 5, pp 64 – Reactor (Burner FT) Heat Balance: Example 7 – Reactor (Burner FT) Example 8 – Reactor (Heat Loss) Tutorials 7,8,9
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Example 1 – Gas Mixer
See Copy of EJG Flowsheeting Worksheet (Blackboard) for details
Natural gas containing 90.0% methane, 6.0% ethane and 4.0% nitrogen by mass is mixed with normal air (79.0% N2, 21.0% O2 by volume) such that the availability of oxygen is 15% in excess of that required to produce CO2 and H2O upon subsequent combustion. Complete a material balance to determine (1) the appropriate flow of air to mix with 100 kg/h of natural gas and (2) the flow rate and composition of the mixed gas.
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Example 2 – Reactor (Refine)
See Copy of EJG Flowsheeting Worksheet (Blackboard) for details
100 tonnes of “hard” lead (97.5 wt% Pb, 2.5 wt% Sb) are melted in a steel kettle and treated with 5.0 tonnes of lead oxide in an attempt to reduce the antimony in lead. The PbO reacts with the Sb to produce a slag consisting of PbO and Sb2O3, assaying 23.0 wt% Sb, plus a Pb-Sb alloy with negligible oxygen. Perform a material balance to calculate the final wt% Sb in the alloy.
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Example 3 – Reactor (Burner)
See Copy of EJG Flowsheeting Worksheet (Blackboard) for details
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Method for Solving Coupled Linear and Non-Linear Equations
1. Guess initial values for an appropriate number of unknowns within the linear set to give a DOF = 0;
2. Also guess initial values for any flow unknowns present in the non-linear equation set, which are not present in the linear equation set;
3. Use matrix inversion to provide a placeholder solution for the linear set; 4. Create placeholder solutions for each of the non-linear equations by writing
each into a separate cell from the matrix inversion calculation; 5. Initiate the solution, by selecting a cell containing a non-linear equation
placeholder solution as the Set Objective cell within Solver, with the objective value set to the correct equation solution; others as Constraints within Solver;
6. Finally, select all cells containing initial guesses for unknowns in the By Changing Cells box within Solver, and use Solver to vary their values until the Objective and all Constraints achieve their required values.
Study Example 4, pp 60 – Reactor (Equilibrium)
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Example 7 – Reactor (Burner FT)
See Copy of EJG Flowsheeting Worksheet (Blackboard) for details Do Example 8, pp 66
Solution of Equation Set (from Example 3) nN2 – 0.79NAir = 0.143 (R1) nCO2 = 6.010 (R2) 2nH2O = 23.641 (R3) 0.20NOffgas + 2nCO2 + nH2O – 0.42NAir = 0 (R4) 0.90NOffgas – nN2 – nCO2 – nH2O = 0 (R5)
Soln Nair 113.869
NOffGas 119.922 nN2 90.100
nCO2 6.010
nH2O 11.821
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Flowsheet Analysis
Method for Flowsheet Analysis: 1. Sketch and annotate an input/output diagram for
the flowsheet 2. Analyse each unit process separately within the
flowsheet, using the established method 3. Summarise the number of unknowns, active
components, restrictions, DOF, and other operating parameters
4. Solve the total flowsheet 5. Finally, verify the flowsheet balance (total mass
balance, element and neutral species balances)
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Hematite Reduction Linear Equations
Simple Flowsheet Analysis Example
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Simple Flowsheet Analysis Example
A Direct Iron Reduction (DRI) plant employs hydrogen to reduce 2000 kg/h of Fe2O3 through the reaction Fe2O3(s) + 3H2(g) 3H2O(g) + 2Fe(s). The reduction gas is obtained by mixing recycle gas with fresh gas containing 99.0% H2 and 1.0%N2 by volume. Upon leaving the furnace, the exit gas is passed through a condenser to remove all water vapour. A portion is then bled to control N2 build up before being mixed with fresh furnace reduction gas and recycled to the reactor. Analyse and complete a material balance for the total flowsheet to determine the %N2 entering the reactor when 8% of the gas exits the bleed. Also determine the recycle/feed ratio necessary to maintain a H2O/H2 ratio of 0.26 in the reactor off-gas, which is required to ensure complete reduction of iron oxide.
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Simple Flowsheet Analysis Example
Hematite Reduction Non-Linear Equations
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Solve Non-Linear Equations Using Solver
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Solve Non-Linear Equations Using Solver
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Solve Non-Linear Equations Using Solver
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Solve Linear Equations Separately
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Write non-linear equations in separate cells
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Run Solver with Matrix Inversion to Solve
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Sensitivity Analysis
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NiO Reduction mole and heat balance
Simple Flowsheet Analysis Example
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NiO Reduction with Hydrogen Mole and Heat Balance
Basis 1 kg mol NiO
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Flowsheet Annotation Solve mole and heat balances
to find T, T4 and all flows. Basis 1 kg mol NiO
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5 linear equations, 3 non-linear heat balances
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Solve Linear Equations with Matrix Inversion
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Thermodynamic Table
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Heat Balance Fluid Bed Reactor
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1 Equation 4 Unknowns
nH2, nH2(5), T, T4
Heat Balance Fluid Bed Reactor
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Placeholder Heat Balance Solution
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