lecture note 8 bme for Biomedical engineering

Metallurgical engineering

1. Magnetic Separation Processes for Lejja Iron Ore for Metallurgical Processes: A Study on Enhancing Iron Recovery and Quality Ocheri C & C.N. Mbah Department. of Metallurgical and Materials Engineering, Enugu State University of Science & Technology ( ESUT) , Agbani Enugu Nigeria.
Corresponding Author: Ocheri C.
Email: [email protected] Phone no: [phone]

2. Lesson 3: Life Tables 3.0 Overview  The goal of this lesson is to review elements of ordinary life tables that are essential to understanding multiple-decrement life tables. The focus of the first section (3.1) is on understanding what the columns of an ordinary life table reveal. The second section (3.2) shows how to construct a life table. For more extensive coverage of ordinary life tables, see  Population Analysis for Planners , another free, online course developed as part of the DAPR project.

3. 3.1 An Ordinary Life Table An ordinary life table is a statistical tool that summarizes the mortality experience of a population and yields information about longevity and life expectation. Although it is generally used for studying mortality, the life table format can be used to summarize any duration variable, such as duration of marriage, duration of contraceptive use, etc. An Example of a Life Table A typical life table contains several columns, each with a unique interpretation. We will learn about these columns and their interpretations by examining an illustrative life table. First, an introduction to the notation:

4. Table 3.1.1: Life Table Column Notation Column Notation Definition 1 (x, x+ n) Age interval or period of life between two exact ages stated in years 2 n q x Proportion of persons alive at the beginning of the age interval who die during the age interval 3 l x Of the starting number of newborns in the life table (called the radix of the life table, usually set at 100,000) the number living at the beginning of the age interval (or the number surviving to the beginning of the age interval) 4 n d x The number of persons in the cohort who die in the age interval  (x, x+ n) 5 n L x Number of years of life lived by the cohort within the indicated age interval  (x, x+ n)  (or person-years of life in the age interval) 6 T x Total person-years of life contributed by the cohort after attaining age x 7 e x Average number of years of life remaining for a person alive at the beginning of age interval x

5. The table below (Table 3.1.2) gives an ordinary life table of the 1997 United States population (adapted from NCHS;  National Vital Statistics Reports  Vol. 47, No. 19, June 30, 1999). T able 3.1.2: Abridged Life Table for the Total United States Population, 1997 (1) Age Interval (x, x + n) (2) n q x (3) l x (4) n d x (5) n L x (6) T x (7) e x < 1 0.00723 100000 723 99371 7650789 76.5 1-4 .00144 99277 143 396774 7551418 76.1 5-9 .00092 99135 91 495432 7154644 72.2 10-14 .00116 99043 115 494997 6659212 67.2 15-19 .00374 98929 370 493801 6164215 62.3 20-24 .00492 98558 485 491596 5670414 57.5 25-29 .00509 98073 499 489137 5178818 52.8 30-34 .00630 97574 615 486397 4689680 48.1 35-39 .00840 96959 814 482862 4203284 43.4 40-44 .01196 96145 1149 478017 3720422 38.7 45-49 .01757 94996 1669 471055 3242404 34.1 50-54 .02618 93327 2443 460915 2771349 29.7 55-59 .04123 90884 3747 445708 2310434 25.4 60-64 .06457 87136 5627 422450 1864727 21.4 65-69 .09512 81510 7753 389159 1442277 17.7 70-74 .14365 73757 10595 343402 1053118 14.3 75-79 .20797 63162 13135 284018 709716 11.2 80-84 .31593 50026 15805 211466 425698 8.5 85-89 .46155 34221 15795 130736 214232 6.3 90-94 .62682 18427 11550 60800 83496 4.5 95-99 .77325 6876 5317 18825 22696 3.3 100+ 1.0000 1559 1559 3871 3871 2.5

6. Interpretation of and Relationships among the Columns The  n q x  column has a probabilistic interpretation: n q x  ~ Probability that a person of age x will die in the           age interval (x, x + n) Also note that  Or with reference to the columns, Column 2  = 

7. Example in Table 3.1.2:             

8. A graph of  n q x  across the life span is given in Figure 3.1.1. A graph of age-specific death rates would have a similar shape. Figure 3.1.1:  n q x  across the Life Span for US 1997

9. The l x  column also has a probabilistic interpretation: ~ Proportion of the newborns surviving to that age (In Table 3.1.2, divide Column 3 by 100,000.) These proportions are called survival probabilities. A plot of the survival probabilities across the life span is given in Figure 3.1.2. Figure 3.1.2: l x  across the Life Span for US 1997

10. There are simple relationships between the  n d x  column and the l x  and the  n q x  columns in the life table: (a)    (In Table 3.1.2 multiply Column 3 by Column 2.) b) Because everybody eventually dies, the sum of the number of deaths in all the age intervals will be equal to the radix of the life table, i.e.:

11. Example In Table 3.1.2: The sum of the  n d x  column is equal to 100,000 =  l (c) The relationships in (b) can be extended as follows: Because everybody who survives to age x will eventually die, the sum of deaths from that age to the end of the table will be equal to the number surviving to that age, i.e.:

12. (d) Number of persons dying before a specified age x is the sum of deaths from the beginning of the table to that specified age: Number dying before age x =  Example In Table 3.1.2, the number of persons dying before age 10: (e)  From (d) above, the proportion (probability) that a newborn will die before reaching age x is calculated as: Example In Table 3.1.2, the probability of dying before reaching age 10:  (f) Although not shown in the life table, one useful quantity to calculate from the table is the proportion surviving each age interval. This proportion is denoted as  n p x.  Note that:   Therefore,   Also note that one can write:   Or the l x  column is related to the  n p x  column by the relation:

13. Thus, one can compute the cumulative survival function as the product of survival probabilities of each interval: Example In Table 3.1.2: Exercise 6  Question 1 The radix of the life table is usually 100,000 but may be a different number. Where in an ordinary life table can you always look to find out what the radix is? In the first row of Column 7 In the first row of Column 3 In the last row of Column 7 In the last row of Column 1 Question 2 According to Column 7 of Table 3.1.2, a newborn in the US in 1997 may expect to reach age 76.5. Once that child gets to age 50, what age would he/she expect to reach? No change -- 76.5 29.7 79.7 63.8 Question 3 According to Table 3.1.2, of those born in the US in 1997 who make it to age 70, what percentage are expected to die before they reach age 75? 14% 20% 6% 9% Question 4 According to Table 3.1.2, what is the probability of a newborn in the US in 1997 surviving to age 20? .992 .950 .986 .917 Find answers in the Answer Key below.

14. Thus, one can compute the cumulative survival function as the product of survival probabilities of each interval: Example In Table 3.1.2: 3.2 Construction of an Ordinary Life Table Knowledge of ordinary life table construction is essential in the construction of a multiple-decrement life table. There are a number of methods available to construct an ordinary life table using data on age-specific death rates. The most common methods are those of Reed Merrell, Greville, Keyfitz, Frauenthal, and Chiang (for a discussion of these methods see Namboodiri and Suchindran, 1987). In this section we construct an ordinary life table with data on age-specific death rates based on a simple method suggested by Fergany (1971. "On the Human Survivorship Function and Life Table Construction,"  Demography 8(3):331-334). In this method the age-specific death rate ( n m x ) will be converted into the proportion dying in the age interval ( n q x  ) using a simple formula: Formula (1) where e is the symbol for the base number of a natural log (a constant equal to 2.71828182...) and n is the length of the age interval. (Note: do not confuse the symbol e here with the e x  used in "expected life" notation.) Once  n q x  is calculated with age-specific death rates, the remaining columns of the life table are easily calculated using the following relationships:

15. Thus, one can compute the cumulative survival function as the product of survival probabilities of each interval: Example In Table 3.1.2:   (As in Table 3.1.2, multiply Column 3 by Column 2.) (As in Table 3.1.2, subtract Column 4 from Column 3.) (Divide Column 4 in Table 3.1.2 by the corresponding age-specific death rate. Note: Table 3.1.2 did not use the Fergany method.) (Obtain cumulative sums of Column 5 in Table 3.1.2.) (In Table 3.1.2, divide Column 6 by Column 3.)

16. Thus, one can compute the cumulative survival function as the product of survival probabilities of each interval: Example In Table 3.1.2: Example Converting the Age-Specific Death Rate into the Proportion Dying in the Age Interval Table 2.5.2 of Lesson 2.5 shows that the age-specific death rate for age group 1-4 ( 4 m 1 ) for Costa Rican males in 1960 is .00701 per person. (Keep in mind that tables presenting age-specific death rates will usually present the rate as "number of deaths per 1000 people," but in the calculations used in constructing an ordinary life table, the age-specific death rate is "number of deaths per person.") Using formula  (1)  from above, 4 q 1  = 1 - e  - 4*0.00701  = 1 - 0.97235 = 0.02765 Fergany Method, Step by Step In this example we use the age-specific death rates from Table 2.5.2 of Lesson 2.5 to complete the construction of a life table for 1960 Costa Rican males. We will follow the Fergany Method. Step 1 Obtain age-specific death rates. Note that age-specific death rates are per person (Column 2 of Table 2.5.2). Step 2 Convert age-specific death rates (nMx) to the proportion dying in the age interval ( n q x ) values using the following formula (formula  (1)  from above): , where  n  is the length of the age interval

17. Thus, one can compute the cumulative survival function as the product of survival probabilities of each interval: Example In Table 3.1.2: Table 3.2.1: Life Table Construction: 1960 Costa Rican Males

18. Figure : 1 Blast Furnace 99% Completed STATEMENT OF PROBLEM Ajaokuta Steel Plant has capacity to produce 1.3 million tonnes of steel per annum There fore about 2.135 million tonnes of iron concentrate will be genetaed from Itakpe iron project This is conservatively estimated to last for about 25 years which is negligible for a life of a nation. The discovery and processing of the Lejja iron ore will increase the capacity & requirement of the Blast Furnace need. FACS Blast Furnace 99% Completed

19. Significance of the Study Industrial and Technological Transformation Lejja is a rural community which does not have so basic social amenities for the growth and development of her people Technology: key to unlock the potential of the Ezeagu community and its environs ,

20. SINTER PLANT COAL YARD COKE OVEN BLAST FURNACE RAW MATERIAL: IRON ORE, LIMESTONE, DOLOMITE ETC. COKE SINTER POWER PLANT NATURAL GAS POWER FOR SALE POWER FOR INTERNAL USE STEAM TURBO BLOWER BLAST AIR PIG IRON PIG CASTER PIG IRON FOR SALE OXYGEN PLANT LIME OXYGEN HOT METAL STEEL MAKING SHOP LIQUID STEEL CONTNUOUS CASTER BLOOMS MEDIUM SECTION STRL MILL BILLETS WIRE ROD MILL LIGHT SECTION MILL BILLETS WIRE RODS, COILS etc ROUNDS, SQUARES HEXAGONS, ANGLES BEAMS, CHANNELs BILLET MILL Alumino -Silicate Refractory Plant Engineering Shops Complex Tar Bonded Dolomite Refractory Plant Value Chain Activities in Iron and Steel Producing Industries Slabs LIME Plant

21. MATERIALS The iron ores were sourced at Dunoka , Amankwo & Umuakpo - Lejja Figure : 2 At the Lejja Iron ore Figure : 3 Sa,ples of iron ore collected at Lejja

22. Comminution Jaw crusher – Gyratory crusher – Hammer crusher Edge mill – Ball or rod mill – Method : Mineral Processing OUTBOUND INBOUND

23. Method : Mineral Processing Mineral Ore Charged into Magnetic separator Product Ore Concentrate Tailings OUTBOUND INBOUND

24. Methods The ore sample was processes at the National Metallurgical Development Centre Jos, Plateau State, Nigeria Five kilograms of the ground ore from each of the three samples were loaded into the machine's storage tank via the hopper and fed into the machine at a rate of 30 kilograms per hour. The machine was operated at a current of 25 amps and a disc height of one inch. This process yielded two products: the concentrate (Fet) collected at the disc arms and the tailing or gangue collected over the belt. Figure 4 shows the Magnetic Separator as was used to perform the experiments on the three iron ore samples. 1 Lejja Iron Ore   i. Iron ore Concentrate (Magnetite Fe 3 O 4 ) = 13.4g ii. Iron Ore Concentrate (Hematite Fe 2 O 3 ) = 129.3g iii. Gangue (Non-Magnetic)                      = 27.2g Figure : 4 Magnetic Separator

25. X-Ray Diffraction (XRD )

26. Scanning Electron Micrscopy (SEM) Before Beneficiation Process After the Beneficiation Process Figure : 5 Before Beneficiation Figure : 6 Beneficted iorn Ore

27. Elemental Analysis - XRD & XRF Crude Iron ore Magnetic Separation Elements Wt(%) Elements Wt(%) O 20.2 O 10.25 C 2.01 Fe 70.80 Fe 68.30 Si 0.45 Ti 4.10 C 4.40 Mn 2.20 Na 2.09 Si 2.00 Al 0.15 Al 1.10 Zn 7.46     Cl 1.22     Mg 3.90           Crude Iron ore Magnetic Separation Lejja Ore S/NO Compounds % % 1 SiO 2 29.55 3.90 2 Al 2 O 3 2.10 1.88 3 Fe 2 O 3 60.80 81.70 4 TiO 2 0.19 0.32 5 CaO 0.11 0.10 6 P 2 O 5 0.22 0.34 7 K 2 O 0.03 0.02 8 MnO 0.70 0.06 9 MgO 0.20 0.74 10 Na 2 O 0.32 0.29 11 Cu 0.05 0.04 12 Zn Nd Nd 13 Rb 0.07 Nd 14 Zr Nd Nd 15 Br 0.07 0.16 16 Cr 0.10 0.11 17 LOI 5.44 10.32 18 Total 100 100

28. Energy Dispersive Spectroscopy (EDX) Before Beneficiation After Beneficiation

29. Fourier Transform Infrared Spectroscopy (FTIR) of Lejja Iron Ore The three main peaks at 800.9cm -1 , 551.06 cm -1 , and 460.7 cm -1 in the haematite FTIR spectrum are useful for comparison. These peaks, which are unique to hematite and other iron oxides, are indicative of the Fe-O bond. These peaks can be used to identify whether an impurity is present in a hematite sample by comparing its FTIR spectra to one known to be present. The peaks located at 1,050 cm -1 , 2,950 cm -1 , and 2,340cm -1 are additional peaks that can be utilised for comparison. An analysis of a hematite sample's crystallinity was conducted using FTIR. The degree to which the crystals in the sample are organised was determined using the crystallinity metric.

30. Thermogravimetric Analysis ( TGA) / Differential Thermogravity Analysis (DTA) The DTA/TGA results indicate: 1. Dehydration of iron hydroxides (e.g., goethite) below 397°C. 2. Decomposition of iron oxides (e.g., hematite) at higher temperatures. 3. Possible transformation of iron oxides to more stable forms. These findings have implications for: 1. Iron ore processing: Thermal treatment can enhance ore quality. 2. Steel production: Understanding thermal transformations informs optimal processing conditions. 3. Material properties: Thermal stability and decomposition temperatures guide material selection. Figure :  DTA (TGA) of Lejja iron ore

31. Hot Metal Pig iron Slag Blast furnace gases RAW MATERIAL: IRON ORE, LIMESTONE, DOLOMITE ETC SINTER PLANT COKE BLAST AIR OUTBOUND INBOUND Lejja Iron Ore …… Production iron Ore

32. Figure 7 : Wire Rods produced from Wire Rod Mill Wire Rod mill and Light section Mill & Foundry Figure 6 : Wire Rod Mill in Operations Figure 9 : High Chromium Grinding Media Figure 8 : Light Section Mill in Operations