Estimation of Metal Recovery Using Exponential Distribution

Transcription

1 Inrnaional rd Journal o Sinii sarh in Enginring (IJSE).irjsr.om Volum 1 Issu 1 ǁ D. 216 ǁ PP Esimaion o Mal ovry Using Exponnial Disribuion Hüsyin Ankara Dparmn o Mining Enginring, Eskishir Osmangazi Univrsiy, Eskishir, Turky. -mail: hankara@ogu.du.r ABSTACT : Th mal rovry is idly usd or h assssmn o plan prorman. I has bn ormulizd as a uniorm union in h orm o a raio o oupu o inpu. In his sudy, mal rovry ormula in an xponnial orm as dvlopd basd on xponnial disribuion. Th mal rovry in h xponnial orm as shon ih h sablishmn o probabiliy dnsiy unions, basd on ighs o valuabl mal (or minral) in onnra and ailing (or slag) dpnding on igh o valuabl mal in d. Th los igh o valuabl mal in d as drmind using h daa ovr a 1-monh priod a Elazığ rrohrom plan in Turky. Amongs daa, only h los igh and apaiy r r-analyzd ovr a 6-monh priod. suls o his sudy india ha mal rovry basd on h xponnial disribuion an b usd ivly o sima h los igh o valuabl mal in d. Kyords: Mal rovry, rrohrom, minral prossing, mallurgial pross I. INTODUCTION Prorman assssmn in a minral or mallurgial pross plan and h onrol o opraion using h valuad rsuls ar qui imporan. In his sudy o mal rovry ormula ar usd o valua h plan prorman. Th irs quaion has bn rormulad using assays aording o an xponnial disribuion [1]. Th plan prorman an b assssd by alulaing h igh o a valuabl mal rom h ighs o d (F), onnra (C) and ailing (T) and hir orrsponding assays, and, rspivly. Plan rovry is ormulad as [2]: C 1% (1) F sin inpu is qual o oupu; F C T (2) Plan rovry an b rrin as; C 1 % (3) C T Mal rovris obaind rom Eqs. (1) and (3) ar disr, i.. hy only giv rsuls rlad o dini im ram o opraion and hn i is no possibl o mak any simaion or h plan. Thror, i hy ar rormulad ih h us o valuabl mal ighs, plan prorman ould b ivly simad. II. FOMULIZATION OF THE METAL ECOVEY USING EXPONENTIAL DISTIBUTION laionships bn omponns o o-dimnsional oninuous random variabl ar pariularly imporan in probabiliy and saisial analysis. Th shadd porion o h random variabl (Fig. 1) shos h inrrn ara [3], hih is indiaiv o h igh probabiliy o a valuabl mal in d ( F ). As shon in Eq. (2), shadd porion rprsns a o-dimnsional oninuous random variabl ih ighs o a valuabl mal in ailing and onnra omponns. In his as, h probabiliy o man igh o valuabl mal in ailing, T, bing lss han h igh o valuabl mal in d is givn by; P( T ) ( ) d (4) hr, () is h probabiliy dnsiy union o igh o valuabl mal in ailing. Probabiliy o man igh o valuabl mal in onnra, mal in d is givn by.irjsr.om C, bing grar han h igh o valuabl 7 Pag

2 Probabiliy Dnsiy Esimaion o Mal ovry Using Exponnial Disribuion P C ) ( ) d ( (5) hr, () is h probabiliy dnsiy union o igh o valuabl mal in onnra. () () Inrrn ara () Fig. 1. Th inrrn diagram or h inrrn ara. Sin igh o valuabl mal in onnra and igh o valuabl mal in ailing ar assumd o b indpndn random variabls, h probabiliis o o indpndn variabls ar muliplid [4]. Hn, h mal rovry,, or h possibl valus o igh o valuabl mal in d is dind as: ( ) P( T ) P( C ) (6) Probabiliy dnsiy unions ar rplad ino q. (7). ( ) ( ) ( ) dd Inpu and oupu variabls (suh as d, onnra and ailing) in plan rovry ormulaion ar xprssd ih only on paramr. In his as, i omplis ih h xponnial disribuion hih has only on-paramr C and T, man ighs o valuabl mal in onnra and ailing, probabiliy dnsiy union. Firs hn valuabl mal ras in onnra λ and ailing μ pr uni igh ar alulad: 1 C (8) 1 T (9) I probabiliy dnsiy unions drivd rom xponnial disribuion ar rin as igh o valuabl mal in d: ) ( (1) ( ) (11) Sin h ighs o valuabl mal in onnra and ailing should b probabiliy dnsiy unions o onnra and ailing ar ingrad as in Eq. (7). dd ( ).ijrs.org Connra,Tailing (7) C and T, (12) (13) 8 Pag

3 Esimaion o Mal ovry Using Exponnial Disribuion Whn h ighs o valuabl mal ar rplad ino Eq. (14): C C T C T C CT ( ) CT (14) III. CASE STUDY: ESTIMATION OF METAL ECOVEY OF A FEOCHOME PLANT In his sudy, Elazığ rrohrom plan-a in Turky is invsigad. This plan as sablishd in 1977 ih a high arbon rrohrom produion apaiy o 5, ons pr yar. Thr ar o ar urnas ih a por o 17 MWA ah [5]. Th mallurgial balan or his plan ovr a 1-monh priod as abulad (Tabl 1). Th man ighs o valuabl mal in rrohrom and slag, obaind rom h rrohrom plan ovr a 1- monh priod, r plad ino Eqs. (8), (9) and (13) C T ( ) (15) Tabl 1. Th man valus o obsrvaion ovr a 1-monh priod. Ims Man Assays Man Mal Cr Man ighs Cr (%) Wighs (ons) (ons) Frrohrom Slag (or Tailing) Eq. 16 is plod or h possibl valus o ighs o valuabl mal in h d (Fig. 2). I an b sn ha h plan rovry in on-monh priod dos no hang or ds onaining 27 ons and highr malli hrom. Hovr, h plan rovry drass rapidly or ds onaining lss han 13 ons o malli hrom. In ordr o run his plan a a alulad rovry, a las 39.1 ons or highr daily rrohrom produion apaiy pr day should b ahivd. Tabl 2. Valus o minimum produion apaiy ovr a 6-monh priod. Days Frrohrom Produion Slag Wighs () Assays (%) Wighs () Assays (%) ijrs.org 9 Pag

4 ovry (%) Esimaion o Mal ovry Using Exponnial Disribuion monh 6-monh Wigh (on) Fig. 2. Curvs o rovry vrsus igh o valuabl mal in d. In ordr o invsiga h siuaion mniond abov, h los rrohrom produion amouns r olld ovr a 6-monh priod (Tabl 2). Th los daily rrohrom produions r obsrvd a 45 and 85 ons. Th mallurgial balan or h los produions as abulad ovr a 6-monh priod (Tabl 3). Th man ighs o valuabl mal in rrohrom and slag, obaind rom h rrohrom plan ovr a 6-monh priod, r plad ino Eqs. (8), (9) and (13) C T ( ) (16) Im Tabl 3. Th man valus o obsrvaion ovr a 6-monh priod. Man Assays Man Mal Cr Man ighs Cr (%) Wighs (ons) (ons) Frrohrom Slag (or Tailing) Th graph o possibl valus o valuabl mal ighs in h d is shon in Fig.2. Alhough daily rrohrom produion o plan drass by 3.53 ons (Tabl 3), h rovry dos no sho a onsidrabl hang (Fig. 2). Boh alulaions prormd using h suggsd rovry ormula do no also india a signiian dirn. As a rsul, plan prorman ould b br assssd applying h suggsd rovry ormula. IV. CONCLUSION In his sudy h plan rovry basd on diniions and quaions o h xponnial disribuion as dvlopd or improving is us in an asily appliabl mannr o h minral and mallurgial prossing plans. I as ound ha h improvd plan rovry ould b usd in drminaion o minimum produion apaiy o h plan a a rquird rovry. I is also possibl o sima h apd rovry a any igh o valuabl mal in h d..ijrs.org 1 Pag

5 Esimaion o Mal ovry Using Exponnial Disribuion A as sudy or h implmnaion o rovry ormula as sd using h hisorial daa rom h Elazığ Frrohrom Plan olld ovr a 1-monh priod. Th minimum daily rrohrom produion apaiy o h plan as ound o b highr han 39 ons rrohrom pr day a a rquird rovry. I as drmind ha h rovry obaind a h los apaiy ovr h 6-monh priod is vry los o h rovry simad ih h suggsd rovry ormula i h plan is oprad undr onrol. In onlusion, i is suggsd ha improvd rovry ormula ould b usd as an iin ool or h assssmn o plan prorman. EFEENCES [1]. Ankara, H., 21, A Suggsd Improvmn o Th Plan ovry Formula: A Cas Sudy or Elazig Frrohrom Plan. Asian Journal o Chmisry, 22(3), [2]. Wills, B. A. and Napir-Munn, T. J., 26, Wills Minral Prossing Thnology, Unid Kingdom: Elsvir Sin & Thnology Books. [3]. Kapur, K. C. and Lambrson, L.., 1977, liabiliy in Enginring Dsign, USA, Jhon Wily & Sons In. [4]. Kara, I., 2, Olasılık, 4 h d., Turky, Bilim Tknik Yayınvi (in Turkish) [5]. Ayn, E., 21, Drminaion o Los Coss in Produion Priod by Using Sysm liabiliy in Elazığ Frrohrom Plan, M.S. Thsis, Osmangazi Univrsiy, Eskişhir, Turky (in Turkish, unpublishd)..ijrs.org 11 Pag