Mathematical Formulation of Static Control Model of Oxygen ...
Assignment number 2:
Development of static control model of BOF steelmaking process:
Hot metal of C 4.5%, Mn 0.2%, Si 1.0% at 1300 C is charged in BOF steelmaking vessel.
Calculate the weights of scrap, lime, iron ore to be charged and oxygen to be blown such that the cost of production is minimum (or profit be maximum).
Assume that final composition of liquid steel be 0.03%C; 0.05% Mn and rest Fe.
The detailed calculation procedure is given in subsequent section.
The additional constraint data are provided in subsequent section.
A worked out example is also shown in excel sheet using solver. You are required to build your own program.
Heat data are also provided in another excel sheet.
Mathematical Formulation of Static Control Model of Oxygen Steelmaking Process : An Attempt to Develop the solution using Solver package of MS-EXCEL.
This problem is an example to demonstrate the application of Linear Programming in Industrial Processes. The Steelmaking Process can be mathematically defined as a set of linear equations consisting of various heat and mass balances and constraints. The Objective is to determine various Parameters in such a manner that our Profit is maximum.
Lets have a look upon the Process:
[pic]
Liquid Hot Metal (Temperature 1250-1400 C) ,consisting of impurities dissolved in elemental form (C,Mn,P,Si) and solid scrap is charged into Basic Oxygen Furnace. Oxygen is blown from top lance to oxidize the impurities. Carbon is removed in the gaseous form producing CO/CO2 gas. Rest impurities are removed in the form of oxides and forming Slag. Fluxes like Lime is added to neutralize the acidic component of these oxides going to the slag phase. Heat is evolved due to the oxidation of impurities . Surplus Heat is balanced by adding iron ore .
[pic]
Material Flow of the Oxygen Steelmaking Process
Hence objective of the process is to produce liquid Steel with a targeted Weight , composition and Temperature with maximum profit.
List of Symbols:
WT_HM : Weight of Hot Metal
WT_SCR: Weight of Scrap
WT_LIME: Weight of Lime
WT_ORE : Weight of Iron Ore
WT_STEEL: Weight of Steel
WT_OXY : Weight of Oxygen ** All weights in Kgs.
WT_GAS: Weight of waste gas
C_HM : Carbon % of Hot Metal
Mn_HM : Mn % of Hot Metal
P_HM : P% of Hot Metal
Fe_HM : Fe% of Hot Metal
C_ST: Carbon % of Steel
Mn_ST: Mn % of Steel
P_ST : P% of Steel
Fe_ST : Fe% of Steel
T_ST : Steel Temperature
T_HM : Hot Metal Temperature
CaO_LIME : CaO % of Lime,
PCO, PCO2: CO and CO2 % of waste gas
HDISS_X : Heat of dissolution per kg of X
CP_X : Specific Heat per Kg K of X
HRX_X : Heat of Reaction per Kg of X.
HDECOMP_ORE: Heat of decomposition of ore per Kg
P_X : Price per Kg of X.
[pic]
Flow Chart for Developing the Static model using MS-Excel-Solver
Elemental Balances:
Mass Balance of Iron:
[pic]
Mass Balance of Silicon:
[pic]
Mass Balance of Carbon:
[pic]
Mass Balance of Oxygen:
[pic]
Mass Balance of CaO:
[pic]
Heat Balance :
Heat Balance may be written as following:
Heat Input + Heat generated due to Chemical Reactions = Heat Output + Heat Losses
For estimating Heat Inputs and Outputs , Reference is taken at 298 K.
Heat Input:
Heat Input consists of Sensible heat of liquid hot metal and Scrap.
[pic]
Heat Output:
Heat Output term consists of Sensible heats of Steel , Slag and Waste Gases.
[pic]
Heat generated due to Chemical Reactions:
For estimating heat of reactions , we are starting with Fe,C and Si dissolved in Hot metal at a given Temperature (1250 to 1400 C) .
Following Steps are involved in calculation of heat of reaction:
1. Take out the heat of solution of the element, from dissolved state to pure state.
2. Cool the material to room temperature from actual temperature, sensible heat, Say at T_HM to at 298 K.
3. React the material at room temperature., heat of reaction
4. Heat the product to the final temperature, sensible heat; the final temperature could be T_ST K.
[pic]
[pic]
Heat Losses :
Heat Loss = Losses due to (Radiation+Conduction) + Heat required for decomposition of
Iron-Ore
Heat required for decomposition of Iron-Ore = WT_ORE*HDECOMP_ORE
Above balances are required to be solved along with following additional constraints:
1. [pic]
2. [pic]
3. [pic]
4.[pic]
5.[pic]
6.[pic]
The Objective function is defind as profit which is to be maximized:
[pic]
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