Well Performance Course

Reservoir Engineering I

Well Performance

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Arron Singhe

Well Performance Introduction

OUTLINE SKIN EFFECT  Definition  Example

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PRODUCTIVITY INDEX  Definition

Well Performance Introduction

STATEMENT OF PROBLEM Van EVERDINGEN and HURST noticed:

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“at a given flow rate, the measured bottom hole flowing pressure, pwf, is less than the calculated one from theory”

This observation indicated the existence of an additional pressure drop around the well bore. This additional pressure drop is called a skin effect The Local Content People

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Well Performance Introduction

SKIN FACTOR

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It is not unusual for materials such as mud filtrate, cement slurry, or clay particles to enter the formation during drilling, completion or Workover operations

 Those effects may reduce the permeability around the wellbore

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It is referred to as wellbore damage and the region of altered permeability is called the skin zone

 The skin zone can extend from a few inches to several feet into the

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On the other hand, many wells are hydraulically fractured which will also cause a change in the near wellbore permeability

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formation

Well Performance Introduction

INTRODUCTION OF THE SKIN EFFECT

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Near the wellbore, the permeability of the layer changed due to the skin effect

s

kh (p) skin p  141.2   qo Bo   s skin  kh  141.2q o Bo  

Field units: ft, bbl/d, mD, psia, cp

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Skin is dimensionless Skin zone is a zone of changed permeability due to mud filtrate invasion or cement during drilling or completion of the well

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Well Performance Introduction

EFFECT OF THE SKIN EFFECT Skin can be

 Positive

□ In this case in the reservoir the permeability decreased around the well □ reason: overbalanced drilling, closing the pores, swelling of the shale etc.

□ In this case the permeability increased around the well. □ reason: well stimulation

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 Negative

Well Performance Introduction

SKIN EFFECT

 The pressure drop across the skin zone is the difference between the actual pressure in the well when it is flowing and the pressure that would have been seen, if the well were undamaged.

 Assuming radius of the skin zone, rs with reduced permeability ks, then the skin can be calculated from (Hawkins, 1956)

 Or the skin can be described in terms of effective well-bore radius

rweff  rwe

s

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k  rs s    1 ln  k s  rw

Well Performance Introduction

EXAMPLE

Use the following equations:

k   rs  s    1  ln    k s   rw 

rweff  rw  e

s

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Example 10.1: A 6 inch (0.5 ft) diameter hole has a damaged region 24 inches (2 ft) deep measured from the well center. The permeability of the damaged zone is one tenth that of the undamaged region (i.e ks = 0.1*k). A) What is the skin? B) What is the effective wellbore radius? C) What, if the 24 inch deep zone was stimulated and the permeability was 10 times larger (i.e ks = 10 * k)?

Well Performance Introduction

SOLUTION What is the skin? Calculate rw and rs

rw  0.25 ft rs  2 ft k  r s    1 ln s  k s  rw 2  10  1 ln  18.7 0.25

What is the effective wellbore radius?

rweff  rwe  s  0.25e 18.7  1.9 x10 9 ft

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Calculate skin for damaged zone

Well Performance Introduction

SOLUTION What is the skin for the stimulated case?

k  rs s    1 ln  k s  rw 2  0.1  1 ln  1.9 0.25

rweff  rwe  s  0.25e1.9  1.67 ft

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Calculate the effective wellbore radius?

Well Performance Introduction

SKIN FACTOR Example 10.2: Calculate the pressure drops in the skin zones in a vertical well and for a 1000 ft long horizontal well. The skin factor is 1. h=25 ft; Bo= 1.06; kv= kh=10 mD, o=0.8 cp, qo = 1000 STB/d

 q B  pskin  141.2   o o   s  kh  Vertical well

141.2  qo  o Bo s kh( well length ) 141.2 1000  0.8 1.06  1 10 1000  12 psi

pskin 

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141.2  qo  o Bo pskin  s kh 141.2 1000  0.8 1.06  1 10  25  479 psi

Horizontal well

Well Performance Introduction

WELL DELIVERABILITY EXAMPLE Example 10.3: The following data is available for a production well: k = 0.01 D pe = 2000 psia pwf = 500 psia o = 0.5 cP h = 40 ft re = 1000 ft Bo = 1.25 The well production rate is 738 bbl/d

rw = 0.35 ft

7.078 khP q re  o Bo ln , rw rw,  rw e  s

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What is the effective wellbore radius, r‘w and the skin factor?

Well Performance Introduction

WELL DELIVERABILITY EXAMPLE Example 10.3: The following data is available for a production well: k = 0.01 D pe = 2000 psia pwf = 500 psia o = 0.5 cP h = 40 ft re = 1000 ft Bo = 1.25 The well production rate is 738 bbl/d

rw = 0.35 ft

q

ln

7.078khP 7.078  0.01 40  (2000  500) 6794 .9    738 re re 1000 ln ,  o Bo ln , 0.5 1.25  ln , rw rw rw

1000 6794 .9 1000 ,   9 . 20718  r   0.1 ft w , 9.20718 rw 738 e

rw, 0.1 r  rw exp( s )   s  ln  ln  1.25  s  1.25 rw 0.35 , w

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What is the effective wellbore radius, r‘w and the skin factor?

Well Performance Introduction

PRODUCTIVITY INDEX (PI or J)

 A well produces or injects with a rate q.  As a consequence, there is a pressure difference between the bottom hole and any other point in the formation:

p  pwf  pr 

 The rate is a function of the pressure difference and goes to  q   J  lim  p 0 p   

 A productivity index PI or J is defined as q J p

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zero, if the pressure difference goes to zero