4. Solusi Persamaan aliran radial silindris dibawah pengaruh Wellbore Storage dan SkinSelama sumur ditutup, tekanan reservoir akan menopang kolom fluida di lubang bor sebatas mana ditentukan oleh kesetimbangan antara tekanan formasi dan berat kolom fluida.

Apabila sumur tersebut diproduksikan dengan membuka kerangan di permukaan, mula-mula minyak yang diproduksikan hanya berasal dari apa yang ada di lubang bor, sedangkan laju produksi mula-mula dari formasinya sendiri sama dengan nol.

Dengan bertambahnya waktu aliran, laju aliran didasar sumur akan berangsur-angsur sama dengan laju aliran dipermukaan.

Fluid-Filled Wellbore - Unloading

Rat

e

Time

Bottomhole Rate

Surface Rate

wbwb

sfw

cVBqq

dtdp

24

q

qsf

q = laju alir di permukaanqsf = laju alir di muka formasi

Berdasarkan persamaan kesetimbangan materi di lubang sumur dan laju akumulasi fluida di lubang sumur adalah :

Dengan anggapan luas luabnag sumur sama disemua tempat dan faktor volume formasi konstan maka dapat dituliskan persamaan kesetimbangan :

Fluid-Filled Wellbore - Afterflow

Rat

e

Time

Bottomhole Rate

t=0

Surface Rate

wbwb

sfw

cVBqq

dtdp

24

q

qsf

dtdPC1qq w

Dsf

Pada saat persamaan diatas akan menjadi : 0qqsf

dtdPC1 w

D

atau DD tlogdPlogClog

Characterizing Damage and Stimulation

Characterizing Damage and StimulationInstructional Objectives

1. List causes of damage skin2. List causes of geometric skin3. Calculate skin from pressure drop4. Calculate flow efficiency from skin5. Calculate skin factor and wellbore radius 6. Convert skin to fracture half-length

Damage Caused by Drilling Fluid

Mud filtrateinvasion

Damage Caused by Production

p < pb p > pb

Damage Caused by Injection

“dirty”water

incompatiblewater

Reservoir Model of Skin Effect

Bulkformation

h

rw

ka

ra

k

Alteredzone

Reservoir Pressure Profile

500

1000

1500

2000

1 10 100 1000 10000Distance from center of wellbore, ft

Pres

sure

, psi

ps

Skin and Pressure Drop

spqB

hk00708.0s

Skin and Pressure Drop

skh

qB2.141ps

Skin Factor and Properties of the Altered Zone

w

a

a rrln1

kks

Skin Factor and Properties of the Altered Zone

wa

a

rrlns1

kk

Effective Wellbore Radius

w

warrlns

swwa err

Minimum Skin Factor

w

emin r

rlns

Minimum Skin Factor Example

3.75.0

745lnrrlnsw

emin

Geometric Skin - Converging Flow to Perforations

Geometric Skin - Partial Penetration

h

hp

Partial Penetration

hp

ht

h1

pdp

t sshhs

Partial PenetrationApparent Skin Factor

21

11

2ln1

2ln11

BA

hh

hrhs

pD

pD

pDDpDp

21

h

v

t

wD k

khrr

tppD hhh

tD hhh 11

41

1 pDD hhA

431

1 pDD hhB

Geometric Skin - Deviated Wellbore

sechh

sss d

Deviated Wellbore Apparent Skin Factor

100log

5641

865.1'06.2'Dww hs

wh

vw k

k tantan 1'

v

h

wD k

krhh

Geometric Skin - Well With Hydraulic Fracture

Lf

Skin Factor and Fractured Wells

2Lr f

wa

waf r2L

Completion Skin

dpdp ssss

d

R

dp

R

p

dp

pdp k

kkk

rr

nLhs ln

rdp

Lp

kR

kdp

kd

rp

rd

rw

After McLeod, JPT (Jan. 1983) p. 32.

Gravel Pack Skin

Lg

Cement

22 pgp

gRgp rnk

hLks

Productivity Index

wfppqJ

Flow Efficiency

wfswf

idealactual

f ppppp

JJE

Flow Efficiency and Rate

foldfnew

oldnew EEqq