Well Test Continuous Assessment Final

SCHOOL OF ENGINEERING Well Test Analysis and Design (EG551Q)

Continuous Assessment 1 Instructor: Dr. Panteha Ghahri Mai! "han Pasha

I.D:

#1$$%&%'

1.

Intro!uctio Intro!uction n an! O(ecti)es:. O(ecti)es:...... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... ............ ................. ...........1 .1 1.1

Intro!uctio Intro!uction.... n......... .......... .......... .......... .......... .......... .......... .......... ......... ......... .......... .......... .......... .......... .......... .......... ........... ............... ................... ...............1 .....1

1.&

*e++ *e ++ ,est ,est ,-es... ,-es........ .......... .......... .......... .......... .......... .......... .......... .......... .......... ......... ......... .......... .......... .......... .......... .......... .......... .......... .......... ...........& ......&

1./

Instrument Instrument Gau0es:.... Gau0es:......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... ............ ........& .&

1.

Pressure Pressure 2ui+! u ,est:.... ,est:......... .......... .......... .......... .......... .......... ......... ......... .......... .......... .......... .......... .......... .......... .......... ............. ................../ ........../

1.#

Pressure Pressure Dra34!o3n Dra34!o3n ,est:... ,est:........ .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... ......... ......... .......... .......... .......... ............../ ........./

1.$

,echnica ,echnica++ rearation rearation 5or the the 3e++ 3e++ testin0:. testin0:..... ......... .......... .......... .......... .......... .......... .......... ........... ............... ................... .........../ ./

1.6

O(ecti)es:. O(ecti)es:...... .......... ......... ......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... ......... ......... .......... .......... ........... ............... ........../ ./

&.

Metho!o+o0Metho!o+o0-..... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .............. ................... .............. ....

/.

Resu+ts:.... Resu+ts:......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... ......... ......... .......... .......... .......... .......... .......... .......... .......... ............. .............. ......

.

7ncertaint7ncertaint- Ana+-sis. Ana+-sis...... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... ......... ......... .......... .......... ............. ................. .............$ ....$

#.

Conc+usion Conc+usion:.... :......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... ......... ......... .......... ........... ................ ................... ................6 .......6

2i(+io0rah-.................................... 2i(+io0rah-........................................................... .............................................. .............................................. ..............................................i .......................i E8uations use!:........................................... use!:.................................................................. .............................................. ........................................................ ................................. ii Aen!i9 A................................. A........................................................ .............................................. .............................................. ................................................ii .........................ii i Aen!i9 2........................................ 2............................................................... ............................................... ................................................................ ........................................ .) Aen!i9 C........................................ C............................................................... ............................................... ..............................................................)iii ......................................)iii

Table of Figures and Tabl Fi0ure 1: *e++ test o(ecti)es...................... o(ecti)es............................................. .............................................. ........................................................ ................................. 1 Fi0ure &: Pressure (ui+!4u an! !ra3!o3n cur)es............................................. cur)es.................................................................... ....................... / Fi0ure /: *e++ test ressure )s time +ot........................................ +ot............................................................... .......................................... .....................# ..# Fi0ure : Pro!uction rate )s time 5or the 3e++ test.....................................................................# Fi0ure #: Sensiti)it- ana+-sis 0rahs 5or 3e++(ore stora0e ermea(i+it- an! s;in 5actor resecti)e+- <5rom +e5t to ri0ht=........................................ ri0ht=................................................................ ..........................................................$ ..................................$ Fi0ure $: Grah +otte! 5or A0ar3a+>s metho! 5or the 5irst 5ir st (ui+!u.........................................iii (ui+!u.........................................iii Fi0ure 6: MDH semi4+o0 ana+-sis 5or !ra3!o3n......................................................................) Fi0ure ': Chan0e in ressure )s teste! time 5or 3e++(ore stora0e.............................................) Fi0ure ?: ,-e cur)e match usin0 2our!et>s metho!........................................................ metho!........................................................ .......)i ....... )i Fi0ure 1%: Lo0 4+o0 +ot 5or 5ina+ (ui+!u in e9ce+ an! so5t3are...........................................)iii @,a(+e ,a(+e 1: List o5 3e++ test o(ecti)es1 ,a(+e ,a(+e &: *e *e++ ++ test !ata.............................................. !ata..................................................................... .................................................................. ...........................................  ,a(+e ,a(+e /: F+o3rate sche!u+e............................................ sche!u+e................................................................... .............................................. ...................................... ............... ,a(+e ,a(+e : Resu+ts o5 3e++ test ana+-sis.............................................. ana+-sis..................................................................................... ....................................... ....# ,a(+e ,a(+e #: Sensiti)it- ana+-sis arameter............................ arameter................................................... .............................................. ................................... ............$ $

1. Introduction and b!ecti"es# 1.1 Introduction ,he main o(ecti)e o5 the 3e++ testin0 is to 5i0ure out the caa(i+it- o5 a 5ormation to -ie+! h-!rocar(ons. In a!!ition it is si0ni5icant to 5in! out the 5un!amenta+ e9+anation 5or a 3e++s e55icienc-. Accurate+- mo!e++e! er5orme! an! re)ie3e! 3e++ test most+- can 0i)e ;no3+e!0e a(out Permea(i+it- reser)oir ressure !e0ree o5 3e++ (ore !ama0e
Well Test objectives 1. Reservoir Evaluation 2. Reservoir escription #. Reservoir $anagement%$onitoring

Test includes to evaluate Flow capacity, productivity, initial reservoir pressure, fuid sampling or PVT analysis Reservoir anisotropy, !eterogeneity, drainage geometry, "oundary conditions. &u"divided in to t!ree areas 1. Future $onitoring includes systematic test design, operations, analysis, and interpretation at appraisal p!ase. 2. E'tended well testing or long term pressure drawdown and "uild up data rom down(!ole gauge. #. Time lapsed well testing perormed during )eld development p!ase *+!eng, 2-

Fi0ure 1: *e++ test o(ecti)es

1.$ Well Test Ty%es Fo++o3in0 are the t-es o5 3e++ tests consi!ere! 5or !eterminin0 the sai! roerties are: 1. T&e dra'do'n test recor!s !ecreasin0 (ottom4ho+e ressure at constant 5+o3 rate. &.  T&e buildu% test  is carrie! out (- shuttin0 in the 3e++ a5ter a erio! o5 ro!uction an! recor! the increasin0 ressure. /. Flo' Test use! 5or the 3e++ !esi0ne! to e9+ain the 5+o3 o5 the mo)ea(+e 5+ui!s to the sur5ace an! ro)i!e the 5easi(i+it- o5 the reser)oir.one o5 the 5+o3 tests +i;e !ri++ stem tests
1./ Instru,ent Gauges# ,here are main+- t3o t-es o5 2HP 0au0es i.e Mechanica+ an! E+ectrica+ t-e 0au0es. 7sa0e o5 each 0au0e !een!s on the accurac- o5 !ata nee!e! an! cost. Mechanica+ 0au0es are not )er- ou+ar amon0 the en0ineers 5or mo!ern ana+-sis. *hereas the- are use! on hi0h temerature 3e++s an! e+ectrica+ 0au0es are not recommen!e! 5or such hi0h temeratures. E+ectronic 0au0es are 3i!e+- use! !ue to the hi0h accurac- (ut the- are e9ensi)e than the mechanica+ one. ,hree main e+ectrica+ 0au0es are use! as a ressure sensors i.e. 1= uart cr-sta+ 0au0e are more accurate 0au0es 3or;s 3hen caacitance chan0es 3ith the a+ie!  ressure.it has t3o 8uart cr-sta+s sensor an! re5erence cr-sta+. &= Caacitance 0au0e simi+ar to the 8uart cr-sta+ 0au0e on+- !i55erence is that it uses 8uart su(strate instea! o5 cr-sta+ more accurate than the a(o)e 0au0e an! /= Strain e+ectrica+ 0au0es 3or;s on the !e5+ection o5 !iahra0m 3hich is measure! an! con)erte! into ressure. Other t-es o5 0au0es are ,u(in0 con)e-e! 0au0e
1.0 ressure -uild u% Test: 2ui+!4u test is con!ucte! (- usin0 the 5o++o3in0 metho! initia++- 3e++ is a++o3e! to ro!uce to cause !ra34!o3n i.e. constant rate 8 5or a sometime then 3e++ is shut4!o3n to (ui+! u or increase (ac; the ressure near to the ori0ina+Breser)oir ressure an! this test can (e ana+-se!  (- A0ar3a+>s metho! an! t-e cur)e metho!. 2ui+! u cur)e can (e !i)i!e! in to three re0ions 1= Ear+- ,ime re0ion
1.5 ressure Dra'do'n Test# In this test the (ottom4ho+e ressure is ana+-se! !urin0 the constant rate <3e++ is ro!ucin0= 3e++ is com+ete+- shut !o3n rior the !ra34!o3n test unti+ the ressure is reache! to the initia+ ressure an! (ecome sta(i+ies throu0hout the 5ormation.it can (e !i)i!e! in to three ones 5or ana+-sis i.e. ,ransient one or ear+- 5+o3 erio! 5+o3 characteristics can (e e9amine!.&= Late transient erio!./= Semi stea!- state use! to test the reser)oir +imit.
Fi0ure &: Pressure (ui+!4u an! !ra3!o3n cur)es

1. Tec&nical %re%aration for t&e 'ell testing# 1. E8uiment 5or 3e++ testin0 at the sur5ace shou+! (e esta(+ishe! an! ressure teste! as  er the stan!ar!s. &. At ie !es; the DS, too+s shou+! (e chec;e! /. Ma;e sure !o3n4ho+e comonents o5 the test strin0 are as er the re8uirement inner an! outer !iameters threa!s an! co++ars. Assure a++ items shou+! (e c+eane! an! 5ree 5rom !irt rust
1.2 b!ecti"es# ,he o(ecti)e o5 the reort is to resent the 5in!in0s o5 the 3e++ test ana+-sis that ha)e (een con!ucte! in oi+ reser)oir usin0 )arious metho!s. ,he initia+ (ui+! u test 3as ana+-se! usin0

A0ar3a+>s metho! 5or semi4+o0 ana+-sis. *hereas !ra3!o3n test 3as con!ucte! an! ana+-se! usin0 the semi4+o0 0rah o5 ressure )ersus time. Secon! (ui+!4u test 3as ana+-se! usin0 2our!et>s t-e cur)e match. Fina++- a 3e++ test ana+-sis so5t3are 3as use! <"aa Sahir= to ana+-se an! comare the resu+ts 5rom the manua+ ca+cu+ations. ,hese metho!s 3ere use! to ca+cu+ate the ermea(i+it- <;= initia+ ressure
$.

3et&odology ,o er5orm the 3e++ test ana+-sis the !ata 3as 0i)en <,a(+e &= 3hich consists o5 a t3o4hour c+ean4u inter)a+ suerse!e! (- 1 st (ui+!4u inter)a+ 5or three hours !ra3!o3n inter)a+ 5or & hrs at constant rate o5 ro!uction an! 5ina++- & n! (ui+!4u inter)a+ 5or ' hrs. 3hich can (e summarise! in ,a(+e / (e+o3. ,a(+e &: *e++ test !ata

Paramete rs #alues

Porosity φ .1-

h (ft) #1-

Well dia (in) /.-

Bo (bbl/STB) 1.#-

Ct (psi ! ) 1.#-E( -

" (cp) .0

,a(+e /: F+o3rate sche!u+e

$peration &uration (hrs) 'lo rate (STB/&)

Clean up 2 #0

!st build up # 

Productio n 2 -

%nd build up 0 

A (est 5it +ine 3as constructe! to 5in! out the in5inite actin0 ra!ia+ 5+o3 re0ion 3hi+e !ra3in0 the semi +o0 0rah s t-e cur)e an! +o04+o0 cur)e in or!er to ca+cu+ate the  ermea(i+it- s;in 5actor an! the 3e++ (ore stora0e usin0 E8uation # to E8uation 1%.

/. *esults# ,he ,a(+e  sho3s the resu+ts o5 manua+ an! so5t3are ca+cu+ation 5or (oth 1 st an! &n! (ui+!4u an! !ra34!o3n re0ions an! these re0ions can a+so (e seen Fi0ure / an! Fi0ure .

Pressure vs Time -1 - 

Pressure, psi

0 / 3 -



1

2

#



-

 Time, !rs

Fi0ure /: *e++ test ressure )s time +ot

3

/

0



Production rate vs time 3

-



Production rate 4 st"%

#

2

1

 

1

2

#



-

 Time !rs

Fi0ure : Pro!uction rate )s time 5or the 3e++ test

,he 1st (ui+!4u re0ion has the sma++est )a+ues o5 the ermea(i+it- an! s;in 5actor 3hen comare! to the other )a+ues an! & n! (ui+! u re0ion reresents the hi0hest )a+ue 5or the 3e++  (ore stora0e. In so5t3are no massi)e !i55erence in )a+ues has (een o(ser)e! !urin0 the ana+-sis o5 the three re0ions. In (oth ca+cu+ations the #%%%4si ressure has (een o(ser)e! 3hich is e8ua+ to the initia+ reser)oir ressure. Permea(i+it- )a+ues 5a++s un!er the satis5actorran0e. Positi)e )a+ues ha)e (een o(ser)e! 5or the s;in 5actor i.e. 5rom .'/4$.? 3hich in!icates the 3e++(ore !ama0e. Norma++- 3e++(ore stora0e coe55icient 5or the )ertica+ 3e++ is %.%%1((+Bsi an! this )a+ue can (e cut !o3n (- !o3n4ho+e shut4in to %.%%1((+Bsi 3e++ (ore stora0e coe55icient increases 3ith the hi0her comressi(i+it- or 5+ui! )o+ume an! s+oe o5 the strai0ht +ine 3ou+! (e shi5te! to3ar!s the +ater times
Properties

nits/symb

!st Build

&ra

%nd build

*appa

3

/

+radient Permeability ,nitial Pressure S-in factor Wellbore stora.e

ols m md%5 Psi%Pi

up 1.32 11#.1 -.

don 21.-# 12.3 (

up ( 1#0.#1 (

Saphir ( 12 -

s ""l%psi

.0# (

-./1 .2/-

3. .13

-.- .1

,o o(ser)e the e55ects o5 a+terin0 the s;in 3e++ (ore stora0e an! ermea(i+it- on the ressure +o04+o0 +ot a sensiti)it- ana+-sis has (een con!ucte!. Di55erent )a+ues
Paramete r nit 0odel value Sensitivit y values

C

s-in

(bbl/ps i) .1

-.-

.2 .# . .1

 (-.# 11

-h (mdft ) #//.  1 1- 3 0

Fi0ure #: Sensiti)it- ana+-sis 0rahs 5or 3e++(ore stora0e ermea(i+it- an! s;in 5actor resecti)e+- <5rom +e5t to ri0ht=

0. 4ncertainty Analysis 1. It is not ossi(+e to ;ee the 5+o3 rate constant !urin0 the !ra34!o3n test !ue to the cho;e 3hich contro+s the 5+o3 rate an! 3or;s in stes there5ore constant 5+o3 rate !oes not achie)a(+e. &. ,here are more uncertaint- in the !ata 3hen 3e++ test runs 5or the shorter erio! o5 time as comare! to the 3e++ test runs 5or the +on0er erio! o5 time 3hich re!uces the uncertaint-. /. Chances o5 h-sica+ error in the ressure !ata !ue to noise temerature an! time shi5t. . 7ncertaint- a(out ca+cu+atin0 the arameters +i;e ermea(i+it- 3hich !een!s on the )iscosit- an! comressi(i+it- these roerties are not )er- accurate 3hich mi0ht a55ect the estimation o5 reser)oir arameters. #. Human error is the (i00est 5actor 3hi+e se+ectin0 the (est match !urin0 the 2our!et>s t-e cur)e matches 3hich can !ou(t the estimation. Fo++o3in0 are the common 3e++ testin0 Pro(+ems: 1. Imroer !esi0n 5or 3e++ testin0. &. Same test ro0ram use! 5or a++ reser)oirs /. 7na(+e to un!erstan! the test concet test !ata. . Ana+-sis o5 3e++ test !ata !esi0n an! oeration (- )arious team or ersons. #. Com+e9 mo!e+ eas- 3e++ test ractice an! )ice )ersa $. Fau+t- instrumentsB0au0es <hen0 &%%#=

5. onclusion# ,he 3e++ test !ata 3as e9amine! (- (oth manua++- an! throu0h so5t3are A0ar3a+>s e8ui)a+ent time metho! MDH metho! an! 2our!et>s t-e cur)e match 3ere use! to  er5orme! the manua+ ca+cu+ations on the other han! "aa Sahire so5t3are 3as use! to estimate the (oth !ra34!o3n an! (ui+!4u !ata (ut the resu+ts 3ere rett- much simi+ar in  (oth cases. Durin0 the test )arious arameters 3ere ca+cu+ate! +i;e ermea(i+it- s;in 5actor an! 3e++ (ore stora0e. Sensiti)it- ana+-sis 3ere er5orme! 3hi+e se+ectin0 the ar(itrar)a+ues 5or the ermea(i+it- s;in 5actor an! 3e++ (ore stora0e an! recor!e! the !i55erent  (eha)iours o5 the cur)es an! conc+u!e! that the reser)oir is homo0enous has constant 3e++(ore stora0e )ertica+ in shae 3ith in5inite (oun!ar-. 7ncertaint- in our mo!e+ are cause! (- ina(i+it- to ;ee 5+o3rate constant !urin0 !ra3!o3n the short test time o5 the 5irst (ui+!4u noise in ressure !ata uncertaint- in)o+)e! in !etermination o5 5+ui! an! roc; roerties an! 5ina++- human error.

-ibliogra%&y Ahme! ,. &%1%. Reservoir Engineering Handbook. s.+.:s.n. Anon. n.!. Test Wells. On+ine Accesse! &' %& &%16. Chau!hr- A. 7. &%%. Oil well testing handbook. A!)ance! ,*PSOM Petro+eum S-stems Inc. Houston ,e9as: Gu+5 Pro5essiona+ Pu(+ishin0 is an imrint o5 E+se)ier. Lee J. 1?'&. Well Testing. ,e9as: SPE te9t (oo; series o+ume 1.  Ne+ techno+o0-  &%1#. National Maesurement System, G+as0o3: ,7 S7D Limite!. Petro*i;i PEH &%1#. etroWiki! Well test. On+ine A)ai+a(+e at: htt:BBetro3i;i.or0B*e++Ktest Accesse! &6 Fe(ruar- &%16. S.P.A ENI 1???. Well test ro"edure, s.+.: s.n. hen0 S.4@. a. C. &%%#. *e++ ,estin0. #est ra"ti"e, . '.

E6uations used# m= 162.6 (

 μq Bo  Kh

)

E4uation 1

s =1.151

[

 P ws ( ∆ t e =1 hr )− P ws ( ∆ t =0 )

s =1.151

[

 P i − P 1 hr

C =

m

m

−log

k  2

 + 3.23

φμ ct  r w

qB 24 mWBS

 P M match=

− log

]

k   μ c r

∅

 + 3.23

2 t  w

]

E4uation 2

E4uation #

E4uation 

P D E4uation -

∆P

( ) t  D

T M match =

C  D

∆ t 

141.2 qBμ k =

( ) P D

 P M match

∆P

E4uation /

h

C = 0.000295

C  D =

E4uation 3

( )

 kh ∆ t  T M match  μ t  D C  D

E4uation 0

0.8936 C  ∅

E4uation 

2

c t  h r w

s =0.5 ln

(

2 s

C  D e match C  D

)

E4uation 1

A%%endi7 A

Fi0ure $: Grah +otte! 5or A0ar3a+>s metho! 5or the 5irst (ui+!u

alculations For 1 st -uildu% Inter"al#

1. 2est 5it e8uation o5 +ine 5rom semi4+o0 +ot o5 e8ui)a+ent time
(

 )=

0.8 x 3980 x 1.35 19.6240 x 315

113.10 md

. Ca+cu+ate the s;in 5actor (- usin0 the e8 s = 1.151 [

 P ws ( ∆ t e =1 hr )− P ws ( ∆ t =0 ) m

− log

(

k  2

φμr w C t 

)

+ 3.23 ]

,o ca+cu+ate the  P ws ( ∆t e = 1 hr )  su(stitute the )a+ue o5 91 in (est 5it e8 3hereas +o0<%=  % 3i++ 0et -??.# For  Pws ( ∆ t =0 )   '%1.6 +ast 5+o3in0 ressure su(stitute a++ the )a+ues in a(o)e e8 to 0et the s;in 5actor s = 1.151 [

(

 4994.5 − 4801.7   113.1 − log 2 19.6240 0.15 x 0.8 x 0.3125  x 1.35E-5

)+

3.23 ]

S = 4.83 #. ,o ca+cu+ate the initia+ ressure Pi at tet & hrs +u0 in (est 5it +ine e8 3i++ 0et  y =8.5226 ln ( 2 ) + 4994.5   #%%%.# sia

A%%endi7 -

Fi0ure 6: MDH semi4+o0 ana+-sis 5or !ra3!o3n

Fi0ure ': Chan0e in ressure )s teste! time 5or 3e++(ore stora0e

alculations for dra'do'n Inter"al

1. 2est 5it e8uation o5 +ine 5rom semi4+o0 +ot o5 e8ui)a+ent time <5rom Fi0ure 6= is  y =−9.351 ln ( x )+ 4754.9 &. Con)ert the natura+ +o0 to +o0 1% (- re+acin0 +n<9= 3ith +n<1%=9+o0<9= a(o)e e8  (ecomes -  4&1.#/1+o0<9=  6#.? an! comare it 3ith -  m9c 0i)es m  0ra!ient 4&1.#/1 an! -4intercet  6#.? /.

Ca+cu+ate the Permea(i+it- (rearran0in0 the a(o)e E8uation 1  μq Bo ) k =162.6 ( mh

 K =162.6

(

0.8 x 5000 x 1.35 21.531 x 315

)=

129.46 md

. Ca+cu+ate the s;in 5actor (- usin0 the e8 s = 1.151 [

 P i− P1 hr m

−log

(

k  2

φμ r w C t 

)

+ 3.23 ]

*hereas  Pi=5000.4 psi ¿ the ist buidup i!ter"a # to ca+cu+ate the

 P 1 hr  ut )a+ue

o5 91 in (est 5it e8uation 3hereas +o0<%=  % 3i++ 0et -6#.? su(stitute a++ the )a+ues in a(o)e e8uation to 0et the s;in 5actor s = 1.151 [

(

 5000.4 − 4754.9   129.46 −log 2 21.531 0.15 x 0.8 x 0.3125  x 1.35E-5

)+

3.23 ]

S =5.71 #. ,o ca+cu+ate the 3e++(ore stora0e use the 0rah o5 t an! P <= the e8uation o5 (est 5it  y =10213 x  3e ha)e 0ra!ient  +ine
3e++(ore stora0e can (e ca+cu+ate! throu0h the E8uation ' 5000 x 1.35 = 0.0275 bb / psi C = 24 x 10213

A%%endi7 

Fi0ure ?: Lo0 4+o0 +ot 5or 5ina+ (ui+!u

alculations For $ nd buildu% Inter"al#

1. Match the (est cur)e o5 the 2our!et>s t-e cur)es 3ith the +o04+o0 +ot cur)e
8

. t  p

&. ,he a+ues 5or  C    an!  P D  are 1% an! &% resecti)e+- a5ter se+ectin0 the  D ran!om oint on 0rah. /. ,he )a+ues 5or ∆ P  an!

∆ t   are /#% an! %.%1 correson!ence to the a(o)e4

mentione! )a+ues on the +o04+o0 3ithout mo)in0 the 2our!et>s t-e cur)es. . Ca+cu+ate the )a+ues 5or  PM match  an! TM match  3ith the he+ o5 the E8uation # an! E8uation $ as 5o++o3s

TM match=

 PM match=

10 0.01   1%%%

20

  %.%#61

350

#. Ca+cu+ate ermea(i+it- (- usin0 E8uation 6  K =

141.2 x 5000 x 1.35 x 0.8 x 0.0571 315

 1/'./1 mD

$. Ca+cu+ation 5or *e++(ore stora0e (- usin0 the E8uation ' 138.31 x 315 x 0.01 C =0.000295  %.%1$ ((+Bsi 0.8 x 10 6. 1st o5 a++ ca+cu+ate the !imension+ess stora0e CD rior to ca+cu+ate the s;in 5actor (  0.8936 x 0.016 C  D = 2 usin0 the E8uation ?  &&?.#& 0.15 x 1.35E-5 x 315 x 0.3125 '. Ca+cu+ate the s;in 5actor (- usin0 the E8uation 1%

(

8

10 s =0.5 ln 229.52

)=

6.49