Part IV - Well productivity estimating methods

A Fully Penetrated Slant Well

MZ-solution (2004):

2kh p

L sin h

2

r

h

L

L

B

e

1

ln

ln

L

2rw

2rw

h

q

2kh p

L sin h

2r

2

2r

L sin

h sin

h

e

e

B

ln

1

arctan

ln

L sin

L sin

2re

L

2erw

September 15, 2012	Part IV - Modern well stimulation	21
	methods (Gubkin - IFP program)

A Fully Penetrated Slant Well

Pressure distribution (MZ-solution):

x_z

y_z

x_y

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	methods (Gubkin - IFP program)

A Fully Penetrated Slant Well

Comparison of solutions (MZ, Cinco et al., Van der Vlis et al.):

0.05 70.06
0.04
q_ MZ2( h)
q_ CC( h)
q_ VV( h)
0.02
4.77 2 10 4
0	0	20	40	60	80	10 0
	2			h		10 0

September 15, 2012	Part IV - Modern well stimulation	23
	methods (Gubkin - IFP program)

A Partially Penetrated Vertical Well

Muscat (1937):

2kh p qMus B

		1
			2 ln
		2b

4h				4h
		(b)	ln
rw				re

(b) ln	(0.875b) (0.125b)
	(1 0.875b) (1 0.125b)

Brons and Marting (1961):

qBM

2 kh p

k

0.5

h

re

1

1

hD k

r

D

v

w

B ln

rw

b

ln h

G(b)

G(b) 2.948 7.363b 11.45b2

4.675b3

September 15, 2012	Part IV - Modern well stimulation	24
	methods (Gubkin - IFP program)

A Partially Penetrated Vertical Well

MZ-solution (2004):

q

2k h p

2

r

h

L

L

h

1

B

e

1

ln

ln

L

2rw

2L

2

h

2rw

September 15, 2012	Part IV - Modern well stimulation	25
	methods (Gubkin - IFP program)

A Partially Penetrated Vertical Well

Pressure distribution (MZ-solution):

x_z

y_z

x_y

September 15, 2012	Part IV - Modern well stimulation	26
	methods (Gubkin - IFP program)

A Partially Penetrated Vertical Well

Comparisons of results (MZ, Muskat, Brons and Marting):

1.693 10 3
		0.0015
q _M Z(L)
q _M US(L)
q _BM(L)
		0.001
5.239 10	4	10 4
	5
		1	2	3	4	5	6	7	8	9	10
		1					L				10

September 15, 2012	Part IV - Modern well stimulation	27
	methods (Gubkin - IFP program)

An Arbitrary Straight Well

MZ-solution (2004):

2kh p

L sin h

2

r

h

L

L

B

e

1

ln

ln

L

2rw

2rw

h

q

2kh p

L sin h

2r

2

2r

L sin

h sin

h

e

e

B

ln

1

arctan

ln

L sin

L sin

2re

L

2erw

September 15, 2012	Part IV - Modern well stimulation	28
	methods (Gubkin - IFP program)

Production Rate of an Arbitrary

Straight Well

Prod rate of different wells

	350
	300
m3/d	250					VW
	200					Slant, 45 degr
Rate,	150					HW
	100
	50
	0
	0	10	20	30	40	50

Well length, m

September 15, 2012	Part IV - Modern well stimulation	29
	methods (Gubkin - IFP program)

Production Rate of an Arbitrary

Straight Well

Prod rate of different wells

	400
	350
m3/d	300										HW
	250
	200
Rate,
	150
	100
	50
	0
	0	20	40	60	80	100	120	140	160	180	200

Well length, m

September 15, 2012	Part IV - Modern well stimulation	30
	methods (Gubkin - IFP program)