Part IV - Well productivity estimating methods

An Infinite Conductivity

Vertical Fracture

MZ-solution (2004):

q

2 kh p

2

L / 2

2

2re

L

re

B

ln

2

2

L / 2

arctan

rw

L

2re

Asymptotic behavior:

								2khL p
L		L
	arctan					qF		Bre
		2re			2
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	methods (Gubkin - IFP program)

A Long Horizontal Well

MZ-solution (2004):

qHW

2 kh p

2re

2

2re

L

h

h

B ln

1

arctan

ln

L

L

L

2re

2rwe

	L		L
Asymptotic behavior:
		arctan
			2re			2

qHW				2khL p
					h		h
	B		r			ln
			e				2r	e
							w

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	methods (Gubkin - IFP program)

A Long Horizontal Well vs Infinite Conductivity Long Vertical Fracture

Asymptotic behavior:					L
	qF			h		h
			1					1
				r
	q	HW			ln	2r e
				e		w

If h = 10 m, re = 100 m, rw = 0.1 m, then 0.0927

qF 1 0.0927 1.0927

qHW

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	methods (Gubkin - IFP program)

Well Performance Comparisons

Production rate calculations (MZ-solution)

	500
m3/d	400
rate,	300						VW
Production	200						SW
							HW
	100						FW
	0
	0	20	40	60	80	100	120
				Well lengh, m

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	methods (Gubkin - IFP program)

Well Interference

a)

Wells in line

b) Wells in grid

D

D

D

re

re

- vertical well

- horizontal well

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	methods (Gubkin - IFP program)

Vertical Wells in Line

Total inflow into (2n+1) vertical wells with a distance D between them:

q

2k h p(2n 1)

2

nD

2

2re

nD

rw

re

B

2n 1 ln

ln

1.85

2

nD

2

arctan

re

rw

D

D

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	methods (Gubkin - IFP program)

Vertical Wells in Line

Pressure distribution for 2 horizontal wells in line:

psxy	psyz	psxz

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	methods (Gubkin - IFP program)

Vertical Wells in Grid

Total inflow into (2n+1) vertical wells with a distance D between them:

	q		2kh p(2n 1)2
			2		2.9re			2.9rw
		B 2n 1					ln
				ln
					(2n 1)D			D

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	methods (Gubkin - IFP program)

Vertical Wells in Grid

Pressure distribution for 3x3 horizontal wells in grid:

psxy	psyz	psxz

September 15, 2012	Part IV - Modern well stimulation	39
	methods (Gubkin - IFP program)

Effect of well interference on total

production
	Total production rate vs number of wells						Input data:
							h = 10 m
Sm3/d	10000						re= 5000 m
					Without interference
	8000
rate,
	6000
production
	4000				With interference
	2000
Total	0
	0	10	20	30	40	50	60

Number of w ells

Q(15 wells without interference) = Q(26 wells with interference)

September 15, 2012	Part IV - Modern well stimulation	40
	methods (Gubkin - IFP program)