Part IV - Well productivity estimating methods

Spherical well in a finite reservoir

Exact solution for pressure distribution:

	B					qi
p(x, y, z)
				(x x0 )	2	( y y0 )	2	2
	4 k	j						z jh z0

Pressure distribution:

psxy

psyz

psxz

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	methods (Gubkin - IFP program)

Spherical well in a finite reservoir

Exact solution for production rate:

			1					1
j		2	2	2				2
		rw	jh				re	jh

Final approximation:

F. Domanuyck, 2010

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	methods (Gubkin - IFP program)

Horizontal Well

Ciger (1983):

qC

2 kh h p

r

r

2

(L / 2)

2

h

h

B

e

e

ln

L / 2

L

ln

2 rw

Joshi (1986):

qJ

2 kh h p

a b

h

h

B ln

ln

L / 2

L

2r

w

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	methods (Gubkin - IFP program)

Horizontal Well

Michelevichius, Zolotukhin (MZ-solution), 2004:

q

MZ

2kh p

L h

r

h

2

L

L

B

ln

e

ln

1

h

L

2rw

2rw

2πkhp

L h

2r

2

2r

L

h

h

μB ln

e

1

e

arctan

ln

L

L

2re

L

2erw

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	methods (Gubkin - IFP program)

Horizontal Well

Pressure distribution (MZ-solution):

x_z

y_z

x_y

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	methods (Gubkin - IFP program)

Horizontal Well

Pressure distribution in the near wellbore zone (MZ-solution):

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	methods (Gubkin - IFP program)

psxz

Horizontal Well

Comparison of solutions (MZ, Joshi, Ciger):

1.52 5 10320 00

15 00 q_ MZ(L)

q_ C(L) 10 00 q_ J(L)

50 0

	26 4.358
		0 0			50 0		10 00		15 00		20 00
		50						L			2 10		3

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	methods (Gubkin - IFP program)

Horizontal Well

Comparison of solutions (MZ, Joshi, Ciger):

3.38	9 10 30.00 4
	0.00 3
q_ MZ(L)
q_ C(L) 0.00 2
q_ J(L)
	0.00 1
1.24	6 10 4
	0 0	2	4	6	8	10
	0.5			L		10

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	methods (Gubkin - IFP program)

A Fully Penetrated Vertical Well

Dupuit (1863): MZ-solution (2004):

qD	2 kh p			q	2 kh p
		re
						r
				MZ
	B ln rw				B ln r
						e
						w

Pressure distribution:

psxy

psyz

psxz

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	methods (Gubkin - IFP program)

A Fully Penetrated Slant Well

Cinco et al. (1975):

qCC

2 kh p

2.06

1.865

h

SCC

log

re

B ln

SCC

41

56

100rw

rw

Van der Vlis et al. (1979):

2 kh p

0

cos

h

rw

qVV

SVV

0.454sin

360

re

B ln

SVV

4 cos

h

rw

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	methods (Gubkin - IFP program)