Part IV - Well productivity estimating methods

Modern

Well Stimulation

Methods

Anatoly Zolotukhin

Part IV

Well productivity estimating methods

Performance comparison between vertical and horizontal wells

Most meaningful comparisons:

•Open hole or fully penetrated completions

•A vertical well with a vertical hydraulic fracture and a fully completed HW

•A vertical well with a vertical hydraulic fracture and a HW with one or more hydraulic fractures

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	methods (Gubkin - IFP program)

Forecasting Production

•Approaches and methods used in forecasting production

•Some examples

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	methods (Gubkin - IFP program)

Forecasting Production

Dupuit’s equation for production forecast of a single well…

PI	q						2kh
	p		B	o		o	ln(r	/ r ) S
							e	w

k – reservoir permeability h – net pay thickness

Bo – oil formation volume factoro – viscosity of oil

re – drainage area radius rw – well bore radius

S – skin factor

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	methods (Gubkin - IFP program)

Well production rate evaluation (steady state solutions)

•Fully penetrated vertical well: Dupuit (1863)

•Horizontal well: Merkulov (1958), Borisov (1964), Ciger (1983), Joshi (1986), Renard and Dupuy (1990)…

•Fully penetrated slant well: Cinco et al. (1975),

Van der Vlis et al. (1979)…

•Partly penetrated vertical well: Muskat (1937),

Brons and Marting (1961)…

•Partially penetrated slant well: not well described in literature

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	methods (Gubkin - IFP program)

Productivity of a horizontal well

Problem Set Up		Vertical section
	Top
Reservoir top		No cross-flow
	Bottom

	Plan view
Horizontal
well	pw = const
Reservoir bottom
Drainage area
contour	pe = const

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	methods (Gubkin - IFP program)

Productivity of a horizontal well

Mathematical Problem Set Up

2 p 0

Steady state conditions of flow

p

(x, y,

h

) 0

z

No cross-flow boundary conditions

2

p

(x, y,

h

)

0

at the reservoir top/bottom

z

2

p(x, y, z) p

at

( y2 z 2 r 2 );

L

x

L

w

w

2

2

p(x, y, z) p

at

(x2 y2 r 2 );

h

z

h

e

e

2

2

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	methods (Gubkin - IFP program)

Arbitrary Well as a Chain of Spheres

Spherical well

Horizontal well

Well with complex geometry

Well’s length: L=(2n+1)2rw

Michelevichius and Zolotukhin, 2003-2004

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	methods (Gubkin - IFP program)

Spherical well in an infinite reservoir

Pressure distribution:

Pressure distribution:

Production rate:

psxz

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	methods (Gubkin - IFP program)