optimazing capacity desing in coal mines

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LI, Z. and TOPUZ . E. Optimizing design capacit y l nd field dimensions of underground coal mines. APCOM87. Proceedings of the Twentieth In tern at ional Symposium o n the Application of Computer and Mathematicsin the Mineral Indmnries. Vo lume I: Mining Johannesbu rg. SAlMM. 1987. pp. 115 - 122.

Optimizing Design Capacity and Field Dimensions ofUnderground Coal MinesZ. LI and E. TOPUZ

Department o Mining and Minerals Engineering Virginia Polytechnic institute and State U iver-sity Blacksburg Virginia USA

h paper presents a quantitative approach to the problem of determiningdesign capacity and field dimensions of undergroun d coa l mines using roomand-pillar mining systems. [n eva luating these design variables, relalionshipsamong mining costs, number of production sections in mines, location of central shafts mine field dimensions, section production, mine output, and cost

o p r o u o n l o s s due to underground man-traveHng are analyzed. Therebythe unit cost o f coal is ex pressed as a function of the design var iables as wellas in put parameters such as seam ang le, seam thick ness, seam depth,undergrou nd traveling speed of men, mine reco very and plant recovery. Theproblem is then formulated as a nonlinear optimization model in terms ofminimizing the un it cost of coal subject to a set of constraints and solvedanalytically for flat seams and numerically for inclined seams. Sensitivitya nalysis of the variables is also included in the paper.

IntroductionThe de tormina t i on of mic e des ign capa c i ty

and min e f ie ld dimensions unde r variousl a t ed to the problem of de te rm ining mine

mi ning condi t ion s i of primllry importanc eto the economi cs of develop in g an d subse -quen tl y opera t i ng on u nd e r gro u nd cOel l mi ne.Fo < example n over ra t ed desi gn capac i ty ofthe mine cll n i mmob i l ize l l a r ge amount ofca p i t a i j ove rs iz ed dime ns ions of t h e min ef i e l d can lead to decreased ava i l ab i l i t y ofworki ng t i me a t f aces a nd inc rease d co s t sfor mine v en t i l a t ion underground ma te r i -a l s handl in g and roadway ma in te na nce . Un_ders i zed mine f i e l d d imens i ons on the o th e rhand , br in g ab o u t f requent new mine develo pments wh ic h ore of course co s t ly esp ecia l l ycOlls i de r i ng t h a t min llble coa l seams be comedeeper and deepe r as the resource deple tes.An i mproper se l e c t i on of loc a t ion for th ep r odllc t i on sh a f t can r e su l t in i ncrease dcap i t a l and opora t in g cos t s . Dec i s ions re -

sh a f t loca t io n min e f i e ld dimensions andmin e de s ign capac i t y h ave a lon g- te rm c f f ec to n t he overa l l economics o f underg round co o lmine o p ~ r t i o and a wel l -p la nned ap prollehto the prOb lem can y ie l d subs tan t i a l mone-t ary savings .

This pa per p resen t s a q u an t i t a t i ve IIP pr oach to the p roblem of determin in g minedes ign ca paci ty and mi ne f i e ld dime n s i ons.

ormulafion of the problemCost-size relationship

In order t o formulate th e p ro blem th e re la t i onsh ip be t wee n mi n ing cos t and mine s iz eneed s to be quant i f i e d.Data

To der ive th e quant i t a t i ve r e l a ti onshipbetween mi n i n g cos t Ilnd mine s i ze use was

OPTIMIZINO DESIGN CAPACITY OF UNDERGROUND COAL MINES I


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made of the cos t es t imates for hypothe t ica ld r i f t mines with the number of sec t ions in amine ranging from 2 to 24, ex t rac t ing seamsof 1 83 meters , l y ing 229 meters below thesu r face as nccounted in the l i te r a tu r e. I , 2Through a s t a t i s t i c a l a n a l y s i s of t he da ta ,cap i t a l cos t (lie) nnd opera t ing cos t Ba) in1977 U.S . d o l l a r s fo r the base-case d r i f tmines are expressed as func t ions of the number of product ion se c t i ons i n mines (S):

[ la]aod

2628200 SI .0 . [ b]I t i s noted t h a t the da ta , though qui te

o ld , does serve the purpo:;;e of analyzing theproblem. For a more accu ra t e modeling, however , t he da ta mlly need to be ad ju s t ed tocur r en t pr ice l eve l s us ing h i s t o r i ca l i n f l a t i o n da ta o r p r e f e ~ b l y cur r en t da ta need tobe used .Effect of seam thickness on mining costs

Seam th ickness inf luences mining cos t s . Ina t h i n seam, more ex tens ive workings have tobe develeped nnd a g r e a t e r area o f groundhas t o be mined in order to ach ieve the samemine ou tpu t .as t h a t from 11 t h i c k e r seam . Asa r e s u l t , those cos t s r e l a t e d to t he exten tof e x t r a c t i o n are increased . For example ,cos t s fo r conveyor b e l t s , r a i l t r ack , waterand power l ines , haulage of coal , rocks , andsuppl ies , v en t i l a t i o n , en t ry cons t ruc t ion ,road way main tenance, sp i l l a g e cleaning androck du s t i ng b e c ome gre a t e r i n th i nn e r coa lseams. To take the e f f ec t of seam th icknessi n to account , a d j u s t i n g Cap i t a l cos t (Tc)and opera t ing cos t ( 1 0) are est imated as

Tc - 19685000(1.83 - m) [2a)ood

To - 574000(1.83 - m)where m i s seam th ickness . 2

[2b]These a d j u s t -

ments wi l l be added to the base-case cos t s .

Effect of seam depthThe e f f e c t of seam dep th on mining cos t s

116

r e s u l t s pr imar i ly from the v a r i a t i o n in thelcngtb of access open ings . For deeper coa lscams, the cap i t a l cos t for sh a f t sin1(ingand h o i s t f a c i l i t i e s becomes grea te r . 10a d d i t i o n , coa l hoi s t ing , men and suppl iest r an s p o r t i n g , 8nd mine v en t i l a t i o n becomomore expens ive . Deep seams may a l so requi r ehcavie r , t hus more cos t ly suppor ts than doshal low seams.

Thc cos t fo r sb a f t s ink ing var i e s depending on geologica l cond i t ions and geotechnic a l p r o p e r t i e s of the s t rn t a through whichthe s h a f t i s sunk, s ink ing methods used,l i n ing requi rements , l eng th of sb a f t , andsec t iona l area of the sha f t . Because thesec t iona l area of sh a f t i s dependent on themine capac i ty , so a l so is the sh a f t s ink ingcos t .

Tlw s h a f t sin1(ing cos t (Se) i s est imatedto be

Se - -5650000 + 49213(h + b tana) , [3aJwhere h is tho dep th of seam a t the sha l l ow e r boundary of th e proper ty , b i s the hor i zont8 l d i s t a n c e of the product ion s h a f t fromthe shal lower boundary of mine f i e l d alon gt he dip d i r e c t i on, and 0; is the i n c l i n a t i o nof seam (shown In Figure 1) .

The opera t in g cos t for coa l h o i s t i ng isformula ted as

[3b]where Cc i s the cos t for h o i s t i n g 8 u n i t ofcoa l along a u n i t l eng th of sh a f t and A i sthe annual mine output .

osts for cleaning and loading facilitiesCoal c lean ing cos t s depend on t he de g ree

of c lean ing and the tonnage of raw coa lfeed . Kate l l 2 has sugg es t ed a eas t to s i z ef a c t o r of 0.96 for t he cap i t a l cos t (Pc) and0.85 fo r

and

t he opera t ingK AO 96cK AO 85

o

cos t (Po ) t h a t i s ,[48]

[ b ]where Kc and Ko are cons tan ts for 8 s p e c i f ied degree of c l ean ing .

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h

S ll Ol(11) Cross section a -a

1 - .--- r- ---,Rectilinear

b - ~ ~ ' ' i(U,v ) I

o L ~ ~ ~, ,(b) Plane view of the mine rre tdFIGURE I. General layout of the mine

I n a d di t ion nccord in g to Katel1 2 , load i ngf n c i l i t i e s add 2% to the cap i ta l cos t and 1to the operat ing cos t .

Cost size relatiol/shipIn su mmllry , the cos t - s i z e r e la t ionsh ips

arc d er ived t hr ough a s t a t i s t i c a l analysisof the U. S. llureau o f Mines ond the EnergyInfo r mat ion Adm i n i s t r a t i on cos t es t imatesfor hypothet ica l d r i f t mines. Cost adj u s t -men t a are mode fo r s ha f t mines e ){t r ac tingseams with var ious th i cknesses and dep t hsand having s u r face lo adin g and clean in gf a c i l i t i es. The cos t - s ize r e la t ions h i p f ort he cap i t a l ost (Cc > Is

Cc - ( 1 + O.0 2){Bc + Tc + Sc + Pc) [5a )and t h a t for the opera t ing cos t (Co) i s

Co ( 1 + O.Ol)(BoAs s um ing a mi ne l i f e

+ To + So + Po ) 15b]o f T years and an in -

t e r e s t r a t e of i and sumrnine up the annualc a pi ta l and operat ing costs , one obtains theann ua l cos t for the ex t r ac t i o n and process-

ing of coal asCt - i TC e + Co [ 6 )

wbere iT i s the c q u o p R ~ o e n t cap i t a lr ec overy fac t or .

Locating a production shartrhe p roble m oC loca t i ng t he cen t ra l sha f t s

and surfllcl3 within the mi ne f ie ldse rv es fiS the ba s i s upon ~ h i c h the problemof dotormining t he mine f i e l d d imensions anddesign capac i ty Is approache d.

Ma n y fa c to r s may a f f ec t t he l oca t ion ofproduc t ion shaf t and cen t r a l surfa ce fac111 -t i e s . Among the m are cos t s fo r undergroundhaulage ot coa l and rocks , t r anspor ta t ion ofmen and suppl ie s , vent i l a t ion , and r oadwaymaint e nance . Other fac t o r s inc lude inc l ina-t io n of t he s e am, d i s t r i bu tion of coal overthe scorn, geol og y and hydrology of the su r -rou ndin g s t r a t a , su r f ac e to pography, andclosen ess of ro adl: aD d water and powe r sup-pl i e s .

In th e a na l ys i s , it i s assumed tha t theth ickness of seam and the a n gle o f inc l ina t i en are cons ta nt the geolog y and hydrologyo f overlyin g s t rn t a are uniform over themIne f i e l d an d the inf luence o f distanccsto access ib le r a i l and roads and water andp ower suppl i e s is ne g l ig ib l e.

I t s a l so assume d t ha t the shape of min ef ie l d is rectangUlar the boundar ie s of mi nef i e l d a r e pllra l l e l o r perpendic u l a r to thes t r i k e o r d ip d i r e c t i on o f the se am, a nd a l lu nder ground ha u la ge roa dwa ys are d evelopede i th e r a long o r across t he s t r ike . ] n o t he rword s , coal me n, a nd suppl i e s a rc t r ans -po r t ed ol o ng o r t h ogo na l se t s of open ings andthe t r ansp or t a t ion dis ta n ces arc re c t i l i n -car .

Under these condi t io ns, th e l oca t ion ofproduct ion s h nf t and cen t ra l s urface f a c i l i t ie s can be determi n ed by anal yzing cos t sfo r t r anspor ta t ion of coa l men, and sup-pl ies . As a r esu l t t h e opt ima l shaf t loca -

OPTIMIZING DESIGN CA PA CITY OF UNDERGROUND COAL MINES 117


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t iOD in t e rms of minimizing the cost forunderground t r an sp o r t a t i o n can be found tobe a t

a x/2 [7a]and

[ 7b]where x i s t he mine f i e l d dimension alongthe s t r ikc , y i s t h a t across i t , and a l anda 2 are cons tan t s . 3

t may be i n fe r red t h a t the inc lusion ofcos t s for mine ven t i l a t ion and roadway maintenance would change the opt imal l oca t ion ofsh a f t as determined above. However, the dev ia t i o n i s usua l ly ins ign i f i can t becausethese costs are r e l a t i v e l y small compared tothe cos t for t r anspor ta t ion . This i s t rueesp ec i a l l y when the inc l ina t ion of seam i ssmal l and the product ion shaf t i s locatedapproximately a t the cen te r of the minef i e l d because it can be shown t h a t for f l a tseams, a cen t r a l l y - lo ca t ed sh a f t i s the mostfavorable in terms of minimizing the cos t sfor mine v en t i l a t i o n and roadway maintenance. 3

umber o production sections in minesLet the product ion r a t e p) be defined as

the product ion per uni t of product ive t ime.Then the sec t ion product ion per s h i f t can beeva lua ted as

[8where p i s an e f f i c i en cy fac tor and Tp i sthe prodUctive s h i f t t ime which equals theto t a l sh i f t t i me Ts) le s s t he l unc h bre akt ime TL , the t ime spent on t r avel ing toand from the face (Tt) , and the t o t a l s h i f tdelay t ime Td ).

t i s important to note t h a t Tt i s a funct i o n of mine f i e ld dimensions. The t rave l -ing t ime can be evaluated as

[9where v t i s the t rave l l ing speed of men, wis the wai t ing t ime during t r anspor t ing menin to or out o f the mine, and D is the ton-llS

nage-weighted average of di s t ances from thepor ta l to faces throughout the l i f e of mine.This average di s t ance can be evaluated as

D = [x /2 Aly A2/x A3 / (x 2y) ] /2 [10]where Ai for i from 1 to 3 is a cons tan t in dependent o f x and y.3

Now, the number of product ion sec t ionsneeded to a t t a in i l cer ta in level of mineoutput A) can be determined as

S .. A/ dsnP s ) [ ]where d i s the number of days worked in ayear, s i s the number of s h i f t s per day, andn i s a f ac to r which t akes i n to account thee f f ec t of de lays occurr ing in the outbyt r anspor ta t ion systems on the mine output .Note t h a t in der iv ing the number of pro-duct ion sec t ions , it has been assumed tha tthe mine output is proport ional to the num-ber of product ion sec t ions in mines. Natu-r a l l y , the number of product ion sec t ions inmines increases with the output of mines.But the increase in the number of sec t ionsmay not be proport ional to the mine output .Genera l ly , the number of sec t ions in minescxponent ia l ly increases with the output ofmines a t an increasing r a t e of change. Thereason fo r the nonl inea r i ty i s t h a t as thenumber of product ion sec t ions inc reases , themanaging of the coal mining system becomesl ess ef fec t ive , the l o g i s t i c s of undergroundcoal mining becomes more compl icated, anddelays out by the sec t ions are expected tooccur more of ten . For s impl ic i ty , however,a l i n ea r r l ~ t i o n s h i p between the number ofsec t ions and the output of mines has beenassumed as often the case .

Cost of production lossesIn a previous sec t ion , mining cos t s were

d ea l t with . To be sp ec i f i c , the t ang ib lecos ts , t h a t i s , equipment investment, laborc o s t , and suppl ies and power cos t s werees t imated. For a more deta i led ana lys i s ,however, it i s necessary to inc lude i n t ang i -

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ble cos t s as wcl l . The most importan t compo nent o t i n ta ng i b le cos t s resu l t s trom pr o -d ue t i o n l osses due to t he time wa s ted on me ntr ave l l i n g unde r gro und. One may i nc rcaseunderg r ou nd ma n- tr ans po r t i ng speed s o r l imi t mi ne f ie ld d ime ns io ns t o ach i eve t h e mi ni mum loss o f a VAi la bl e fa ce t imc and wasteof cos t ly Inbo r . The cos t of product ionl osses r e su l t i n g from r educed ava i lab le f ac etime due to overs ized mine f i e l d d i mens i on smay be eva lua ted as fol lows .

Le t CL boa t he uni t cos t of product ionl oss , thl l t i s , t be d i f ference between thep r i ce of sa lab le coal and the c o s t fo r ext r a c t inB and processing the coa l . Th e n t hecos t due t o product ion l osses in a sh i f t i s

CsL .... T t mdu p rp CL ' ( 12whe rc rp i s the plan t r ecovery and mdu i st he sys tem av a i l ab i l i t y . The re fore the cos tof product ion l osses for each uni t o f coal

( 13 ]and the annua l cos t o f produc t i on los s es i s

CL - A rp Tt mdu p r p cL/ (P s r p ) ' [ 14 )Formulation of Ihe problem

Adding t he cos t of pro du c t ion los ses tot h e cos t for oqu ipment, l abor , and power andsuppl ies r e s u l t s in the to ta l a nn ua l c os t

[ 15 )Divid ing the a nn u a l sa lab l e coa l , which i seq u a l to r A , into t he to t a l an nual cos t( CT ) , t he t o ta l cos t ('or a u n i t o f sa l ablecoa l (Cu ) c a n be e xpr essed as a func t ion ofx, y, and A, d e noted a s

Cu - f{x , y,A). [ 16 )The prob l em o f de t e r mining t be f i e ld d i

mensions a nd des ig n capac i ty of a min e i sthen fo rmula ted In torms o f find i ng x , y,and A such .th a t tho cos t for a u n i t of sa l ab l e coa l i s minim ize d under t h e condi t iont ha t t h e a n nua l mine ou t pu t e qu a ls the ton-na ge of recoverable coa l in tbe proper tyd i v i ded by t h e l i fo of mine . Ma th ema t i ca l l y ,

thc prob l em ismi n. Cu - f x , y,A)s t . A r mYxym/(Tcosa)and x,y > O.

Solution or the problemAnalylical solution for a special case

[ 1 7a I[ l b ][ l7d

The problem can be so lved ana ly t ic a l l y un-der the condi t ion t h a t the i nc l ina ti on angleof coal seam i s zero . An ana l y t i ca l s o l u-t i on of t h i s spocia l case i s i mpor tan t i nt h a t it d emons t ra t e s ho w t be objec t ive func-t ion behaves , provides guid ance in s e l ec t i nga method for solving t h o gonera l pr oblem i nwh ich t he dip angle of seam i s no t z e r o, andse rves a s a t e s t problem f o r the pr ogrammedalgor i thm which i s used t o so l ve t he gene r a lpro b l em.

The fo l lowin g inp u t va lues are usc d inso l v ing t he prob l em:

mh,Ted,i

- L e3 m,. 229 m.. SO.OOlOeS / t / myr220 dAys/y-r.. 2 Shi f tS /day.. 10%' L r ,P m3 . 31/ t85%50

a 0y 1 . 345 t m3p .. 0 . 90n .. 0 . 90T _ 270 sVw 1 .732 ml sTt .. 28800 sTS .. 3600 sT 1800 sTd .. 6600 s

I t can be ana l y t i ca l l y f ound t h a t w ith aprocess ing plan t , t he o p t ima l mine f i e lddimensions , mine d es i g n capac i ty, a n d uni tcos t o f sa lab l e coal , r espec t i ve l y, a r e

x _ y _ 6 , OS3 m,A .. 2,253,834 t / y r ,

. odCu 22.75/t;

a nd wi thou t a proceSSing pl a n t ,x .. y .. 4,432 rn,A .. 1,208 ,350 t l yr ,

andCu 14 50 / t

Numerical solullon r Ihe problemTo so lve tho general prob lem in which t h e

i n c l i n a t i o n a ngle of seam does not e qua lOPTlMIZING DESIGN CA PA CITY OF UNDERGROUND COAL MINES 119


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zero, numeri cal methods must be used andthree ad d i t i ona l p i eces of informati on arerequ i red, namely, the un i t cos t s (S/ t /m) fort ranspor t ing a long ho r i z onta l ha u l a ge ways,upward and d ownward along i nc l i ned haul ageways, denot ed by Ch' c u ' and Cd' resp ect ive l y.

The prob l am was solved on an IB M personalcomp ut e r us l ns the Ne'iolton method and thenovidon - Fl c t che r - Powe ll mult id ime nsion a lse arch a lgor i thm . Given t ha t Cl' 50 , Ch0.001 085, Cu 0.00 1121, and Cd .. 0.001049 ,it was f ound t ha t with a process ins p l antthe op t imo l min e f ie l d d imens ions a l ong t hestri ke and t he d i p, mine des ign ca.pac i t yand uni t cos t of coal , respo c t i v e l y, wer e

xA

7 6 54 m nnd y 4 6 78 rn2 202 523 t /y r ,

Cu = S23 .58 / t ;and without 0. process ing p la nt

x - 5 896 m a nd y = 3,052 rnA 1,10 6,925 t / y r

and Cu .. 15.19/ t .

Discussion of resultsAnalysis of seusltlvlty

To s t u dy t be e f f ec t s o f i npu t para me t e r so n mI ne f i e l d d imens i ons , mine des ign capac i ty , and un i t cos t of coal an ana l ys i s ofse n s i t i v i t y was co nducted by so l ving thep roblem under various reining cond i t ions .This was mad o poss i b l e by r epe a t ing the exe cu t i on of th e p roblem on an ISH pe r sonalcomputer with o ne parameter var icd in arange of poss ib lo valu es and th e o t hers keptf i xed a t a val ue commonly found in prac t ice .Thos e f i xed v a lues a rc the sa me as thoseused in t he spec ia l case except tha t insteadof 229 m a valuo of 457 m i s used as thede pth of seam in the s e n s i t i v i t y anal y s i s .

The in put paramete rs t ha t were i nd ividua l ly analyzcd inc l ude seam ans i e , seam depth ,120

se am th i c kn e ss , un de rground t rave l spe e d ofmen, mine recovery , and p lan t re cove ry . Theresu l ts from ona l y z ing t h e e f fec t s of the sein pu t pa r a me te rs on t h e op t im a l mi ne f ie l ddimensions, mine des ign c apacity , and un i tcost of coal arc given in Table 1 t o 6.Discussion of results

Some obse rva t ion s can be made on t h e indl -v id ua l e f fe c t s of the in pu t parame t e r s onmine f ie l d dime nsion s des i gn c ap acit .y, anduni t cost of coal .

eam angleThe inc l i na t i o n an gle of seam a f fec t s th e

op t im.ll s hape o f t he mi ne f ie ld . Whe n t heseam i s f l n t a square shape i s mo s t favorn-b l e. As t he in c l i na t ion anele i s incre asedfrom 0 to 6 degrees , the r a t io of the opt i -ma l f i eld d i mension along t he s t r ike t o tha tac ross it changes from 1 to 1 .6 and t he min -imum un it cos t incre ases from 23. 62/ t to24 .5 9/ t .

TABLE 1.Ef f ec t s o f sea m ang l e a) on the op t ima

o246

x m)7,1567,94 L8,4908,862

y m)7,1566 5 085,9905 , 553

A ( t / y )3 , 14 9,32 53, 1 78,6043, 129,0003 026 352

23.6224.0124.3324.59

eam tfli knessAs the t h ic kness of seam i s from

1.22 to 2.44m, the opt imal mine f i e ld dimens ion s de crease from 8 0 19 to 5,745m Ilt noi nc re aa i n t; r a te of ehanee an d t he minimumcos t decreases from 30.30 t to $ i 8 . 5 8 / t a ta decreas ine ra tc of change .

TABL E 2.Ef fe c t s o f seam t hickne ss m) on t h e opt i mam m)1. 221. 521. 832.132.44

x_y (m)8,0197 ,6217 , 1566,5775,745

A ( t / y )2,6 36 ,9062 , 976,89 13, 149,3253, 103,6372, 707,00 0

33. :3027. 5223 . 6220 . 7818. 58

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Seam depthAs he depth of seam is increased f r om 229

to 838m, the optimal mine f i e ld dimensions,mine desien capaci ty , and the minimum costof coal increase from 6,053 to 8, 269m, from2.25 to 4.21 m il l ion t / y r , and from S22.75/ tto 24.83/ t a t a decreasing ra te of change,respec t ive ly .

TABLE 3.Ef fec t s of seam depth (b) on tbe optima

h m)229381533686838

x ..y m)6,0536,8517,4247,8828,269

Traveling speed

A ( t / y )2,253,8342,886,5963,389,5713,821,1754,205,589

22.7523.3523.8824.3724.83

As the undereround t r ave l ine speed of meni s increascd from 1.5240 to 1. 9034m/ s , theoptimal mine f ie ld dimensions and designcapac ty increase from 6,639 to 7,632 m andfrom 2.71 to 3.58 mil l ion t / y r a t an approx-imate ly cons t an t r te of change, respec t ive-ly, but the minimum cost of co l decreasesfrom 24.11/ t to 23.23/ t .

TABLE 4.Effects of t ravel speed (v t ) on the optima

v t (m/s)1. 5 2401.62561.72721. 82881. 9304

ine recovery

(m)6,6396,8947,1447,3907,632

A ( t /y )2,710,930

2 ~ 2 2 9 0 63,138,8593,358,8113,582,778

24.1123.8623.6323.4223.23

As the recovery of coal i s increased from507. to 90 , the optimal mine f i e ld dimen-s ions and the minimum cos t of coal decreasefrom 7,156 to 6,367m and from 23.62/ t to

22.60/ t a t a decreasing ra te of change, re -spec t ive ly , but the optimal design capac i tyincreases from 3.15 to 4.49 mil l ion t / y r a tan approx ima t e l y constant ra te of change.

TABLE 5.Effects of mine recovery ( r m) on the opt ima

5060708090

x y m)7, 1566,8966,6876,5146,367

lant recovery

A ( t /y )3,149,3253,509,5553,850,2134,175,4074,487,978

23.6223.2923.0222. 7922.60

As the recovery of plant i s increased f ro m80 to 100 , the optimal f i e ld dimensions,mine design capaci ty , and uni t cos t of coaldecrease from 7,990 to 5,902 m, from 3.93 to2.14 mil l ion t / y r , and f r om 28.96/ t to

15.56/ t a t a decreas ing ra te of change,re spec t ive ly .

TABLE 6.Effects of plant rec overy ( r p ) on the opt ima

808595100

x_y (m)7,9907,1566,3225,902

A ( t /y )3,926,1553,149,3252,458,3492,142,715

onclusions

Cu (S/ t )28.9623.6218.0515.56

The s tudy ind ica tes t ha t the optimal minef i e l d dimensions increase with seam depthand t rave l i n g speed of men and decrease wi thseam thickness , mine recovery, and plantrecovery; the minimum un i t cos t of coalincreases with seam depth ond scorn angle anddecreases with seam th ic kness, t r ave l ingspeed, mine recovery, and plant recovery;and the opt imal mine de s ign c a p a c i t yincreases with seam depth, t r ave l ing speed,and mine recovery -and decreases with plantrecovery.

When the seam is f l a t , a square shape ofmine f i e ld i s most favorable and as the seamangle increases the r a t i o of the optimalf i e l d d i mension along the s t r ik e to t ha tacross t becomes la rge r . I t is i n t e r e s t ingto not ice t ha t the optimal des i gn capac i ty

OPTlMIZING DESIGN CAPACITY OF UNDERGROUND COAL MINES 121


8/8

does not vary monotonica l ly but concavelywith seam th ickness or seam ang10.

Also, i t appea r s t h a t the plan t recoveryand the seam th ickness have a s ig n i f i can te f f ec t on the minimum uni t cos t of sa lab lecoal even though the uni t cos t of coal i si n scn s i t i v e to the f i e ld dimensions anddcsign capaci ty .

F ina l ly by bui ld ing such a qu an t i t a t i v emodel, the optimal mine l i f e can be d e te r -mined and the e f f ec t s of other input paramet e r s such as the r a t e of i n t e r e s t on themine design capac i ty mine f i e l d dimensions,mine se rv ice l i f e and the uni t cos t of coalcan be analyzed.

t should be mentioned t h a t the optimalso lu t ion from the quant i ta t ive ana lys i s i snot in tended to be the terminal decis i onbecause somc q u a l i t a t i v e fac tors a f f ec t i ngthe eva lua t ion of mine f i e ld dimensions anddesign capac i ty were not incorporated intothe an a ly t i ca l formula t ion . I nstead theq u an t i t a t i v e so l u t i o n i s expected to se rveas a usefu l a id in reaching the r igh t dec i -s ion concerning the des ign of undergroundcoal mines. The methodology present )d ht:lrecan be an important s t ep toward increasedappl i ca t ions of q u an t i t a t i v e methods in des igning underground coal mines.

122

References

1 KATELL S . HEMINGWAY, E. L and BERK-SHIRE, L H Basic es t imated cap i t a linves tment and opera t ing cos t s for under ground bituminous coal mines: mines withannual product ion of 1.06 to 4.99 mil . l iontons from a 72-inch coalbed. U.S. Bureauof Mines, IC-8682, 1975.

2. KATELL S . Economic ana lys i s of coalmining cos t s for underground and s t r i pmining opera t ions prepared for the n e r ~gy Informat ion Adminis tra t ion U.S.par tment of Energy, 1978.

D

3. Li, Z. Determining the s ize and l i f e ofunderground coa l mines. Ph.D. Disse r t a -t ion V:i:rg in i a Polytechnic Ins ti t u t e andSta te Univer s i ty Blacksburg, Va , U.S.A. ,1987.

MINING MINE PLANNING THEORY

optimazing capacity desing in coal mines

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