Part III - Well stimulation methods

Hydraulic fracturing

Absolute and effective stresses:
Stress and pressure scale	p
	Biot (poroelastic) constant:
Depth	1	K	1 cr
		K r	cb
p

Part III - Well stimulation methods

11

Hydraulic fracturing

Tensile failure of formation:

p f To

Breakdown pressure after Terzaghi:

pbd 3 h H To p

Part III - Well stimulation methods

12

Hydraulic fracturing

Hook’s law (1D case)

E1

Hook’s law in 3D case

i E1 i j k

Part III - Well stimulation methods

13

Hydraulic fracturing

In case of effective stresses (3D case)

1

(1)

i

E

i

j

k

Assuming no lateral displacement, i.e.:

i j h 0

i j h

0

1

(2)

h

v

E

h h

v

1

Part III - Well stimulation methods

14

Hydraulic fracturing

Relationships between horizontal and vertical effective and normal stresses:

h				v
	1

h			v	1 2	p
				1
1

Part III - Well stimulation methods

15

Hydraulic fracturing

Failure diagram (after Mohr)

- p p

p

-T0

- p

max

min

minmin

maxmax

Part III - Well stimulation methods

16

Hydraulic fracturing

Rock mechanic aspects of fracture propagation

The entire fracture design depends on the following fracturing parameters:

Fracture half-length, xf

Fracture width, w

Fracture conductivity, kfw/k

Fracture height, hf

Azimuth, shape or symmetry about the wellbore

Part III - Well stimulation methods

17

Hydraulic fracturing

Rock mechanic aspects of fracture propagation

Part III - Well stimulation methods

18

Hydraulic fracturing

Desired fracture half-length for different formation permeabilities

	5.0					Near
	Extremely		Very	Tight			Conventional
		tight	tight			tight
ft	4.0
1000
length,	3.0
half	2.0
Fracture	1.0
	0
	10 -4	10 -3		10 -2	10 -1	10 0	10 1	10 2

In-situ gas permeability, md

Part III - Well stimulation methods

19

Hydraulic fracturing

Material balance equation for fracture propagation

	x f	qit p
		2h f w CL rp	t p
			Fracture
	CL – leak-off coefficient
	rp = A/Af		Reservoir
			A

Part III - Well stimulation methods

20