Furui's IPR Model Correction and Its Application in Horizontal Well

0 downloads 7 Views 4MB Size Report
Aug 8, 2012 - Cresting Control & Inflow Control Device Installation ... Control Device (ICD) so that production from each zone is designed according to its ...
SPE 162944 Furui’s IPR Model Correction and its Application in Horizontal Well Cresting Control & Inflow Control Device Installation

Kareem Lateef, A. SPE* (King Fahd University of Petroleum and Minerals) & Omeke James Emeka, SPE. ! Copyright 2012, Society of Petroleum Engineers This paper was prepared for presentation at the Nigeria Annual International Conference and Exhibition held in Abuja, Nigeria, 6–8 August 2012. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract The problem of reservoir heterogeneity has made the continued use of Inflow Performance Relation (IPR) models developed on the assumption of homogeneity impractical. Furui in 2003 (and previously Butler in 1994) solved the problem using fully penetrating well idea so that the model can be applied to different sections of the reservoir. This paper corrects two errors in Furui’s model. The first error is the use of arithmetic mean of radii to evaluate the elliptic surface area of the well when an anisotropic reservoir is converted into an isotropic equivalent. This was corrected using an equivalent cylindrical surface area. The second error is the use of a planar isobaric surface at the end of the radial flow region instead of a circular one. These corrections gave the model a better performance-average of 99% against 96% by the original version, when compared with line source solution obtained by using Green function. Equating the hydrostatic and viscous pressure differences between the well and the water oil contact (WOC), a cresting equation that predicts the critical production rate and pressure drawdown for each zone needed to prevent water (or gas) encroachment was developed. Based the IPR and cresting equation, this work presents a mathematical concept on installation of Inflow Control Device (ICD) so that production from each zone is designed according to its requirements.

!

SPE 162944

2

!

Introduction Cresting impacts the worth of a well in two ways. Besides lowering the oil production rate and eventually the recovery, it also impose additional cost of treating produced water and exposes the production tubing to the corrosive action of the water. As a result cresting has thus considerably drawn attention of production and reservoir engineers. Large amount of effort has been dispensed at developing a good model to accurately describe cresting in horizontal wells. All the methods rely on one idea- predicting the critical rate of production below which the pressure drop will not be sufficient to initiate the movement of unwanted fluids. Since the idea require a connection between production rate and pressure drop, the inflow performance relation becomes an important tool in this quest.

! ! Literature review Efros (1963) proposed a critical flow rate based on the assumption that the critical rate is nearly independent of effective drainage radius. His correlation also neglected the effect of vertical mobility. Water cresting !!" ! !!!"#$!!"!!

!! !! ! !! ! ! ! ! !!

!

!! !! ! !! ! ! ! ! !!

!

!! !! !! !

Gas cresting !!" ! !!!"#$!!"!!

Where

!! !! !! !

!!! !

!!! !

! ! ! !! ! !"!!"#!!!! ! !!

! !! !

!! !

!! !

!! !

!

!

!! !!

Chaperson (1986) presented a simple estimate of critical rate under a steady or pseudo-steady state flow condition in an isotropic formation. Water cresting !!" ! !!!"#$!!"!!

!!!! !!

!! ! !!

!! ! ! ! ! !! !! !!

!

3

SPE 162944

!

Gas cresting !!" ! !!!"#$!!"!!

!!!! !!

!! ! !!

!! ! ! ! ! !! !! !!

!

Karcher (1986) proposed a correlation that is very similar to Efros’ equation. Water cresting

Gas cresting

Where

!!" ! !!!"#$!!"!!

!! !! ! !! ! ! ! ! ! ! !!! !! !! !! !!! !" !!

!

!!" ! !!!"#$!!"!!

!! !! ! !! ! ! ! ! ! ! !!! !! !" !! !! !! !!!

!

! ! ! ! !! !!"#!! ! ! ! !!

Joshi (1988) suggest the following relationship for determining critical oil flow rate in horizontal wells Water cresting !!" ! !!!"#$!!"!!

!! ! !! !! !! ! ! ! !! ! !! !! !" !! !!!

!

!!" ! !!!"#$!!"!!

!! ! !! !! !! ! ! ! !! ! !! !! !" !! !!!

!

Gas cresting

Where

!!! !

!!

!!!

! !!

! !! !!

!

! !!!

!

!

! !!"#!! ! !

!!! !

!!! !

!!!! !!!" ! !

!

!!!

!"#$%! !

All these models relied on IPR equations derived by looking at the plan view of a horizontal well and as such failed to consider the upper and lower no flow boundaries on the steady state equations. Butler (1994) and Furui et. al. (2003) solved this problem by deriving a model from the side view of the well, looking in the axial direction of the well and assuming that fluids produced from the well travel horizontally from the outer boundaries and radially in the vicinity of the well.

SPE 162944

4

!

Butler’s IPR !!

!!!"!!"!! !! !!!! ! !!" ! !! !!!"# !! !! !!"# !" ! ! ! !!!"!!"# ! !! !!"# ! !

!!

!!!"!!"!! !"!!! ! !!" ! !!! !!!"# !! !! !" ! ! !!!!" ! ! !!!"# !! !!"# ! !

Furui’s IPR

Where

!!

!! !! !!"#!!!"# !

!! !!

Sensitivity studies conducted with real well data have shown that Furui and Butler’s models match actual IPR in most case. Modelling a new IPR.

!! ! !

!!

!!!! !" !!"#!!"!!"#$%#&!'!!"#"!$%&! ! ! ! !!! !" !

!!! !!! !" ! ! ! !!!! !!"#!!"!!"#$%&'%(#)!!"#"!$%& ! ! !!! ! !! ! !! ! !"

5

SPE 162944

!

This will give an elliptic isobaric line (equipotential surfaces when!!! ! !! ). To simplify, we substitute !! ! !

Then

!! !! !!

!!"#!! ! ! !

!! !! !!

!!!!"!!! !

!! !!

!"! !! !! !"! !! !! ! !!"#! ! !" !" !! !!

Hence, !!

!!! !!! ! ! ! !! ! ! !! ! ! !! ! ! ! !! !! !" !!

Simplifying our substitution we get,

!

! !!

! ! ! !"! !! ! ! !"

!

! !!

! ! ! !! !!

!! ! !

!" !!! !!! ! ! ! ! ! ! !! ! ! !!!! ! ! ! !" ! !! !!

!! ! ! So, if we set

!

!!!

! !!!

!!"#!! ! ! !

!!"# ! We have, !! !

!

!!"#

!!

!

! !!

! ! ! !! !!

!! ! !

!!

!

!

!!! !

!!!

!! !!

!!"#!! ! ! ! !!"#

The effect of the transformation is that it replaces our reservoir with an isotropic equivalent with the vertical measurement scaled up by a factor of square root of Iani while the horizontal measurement is scaled down by the same factor.

The well bore is also affected and the shape is now an elliptic cylinder. Hence using the perimeter of an ellipse, the area open to flow at the well bore gives

SPE 162944

6

!

! !!" !

!!

!!"#

!

! !! !!"#

!

Comparing this with the area open to flow for an equivalent cylindrical well bore we have, !!"!!! ! !!" Hence our equivalent well bore radius gives

For radial flow,

!!! ! !!

!! !! !! !" !!"#

! !!"# ! !!!

!

!!

!!"#

!

! !! !!"#

!

! !!"# !! ! ! ! ! ! ! ! ! ! ! ! ! ! !!! !!!"#

!! !!"

Giving

! !

! !!"# ! !"

!!!

!

!

! !! !!

!!!"# !! !! !! !" ! !!"# !! ! !!"# !!

!!

!!

!"

! !! ! !! ! ! ! ! ! ! ! ! !

For the outer part of linear horizontal flow, we use two approaches 1. Assume vertical plane surface at a distance the circular equipotential surface of

! !!"#

! ! !!"# . radius!! !

from the well bore have the same pressure as

2. We take the pressure drop from the no-flow boundary to the equipotential surface of radius! For the first case,

! !!"# !

.

7

SPE 162944

!

!! !! !!

!!"! !!"# !! !! !!

!!"! !!"#

!!

!!"#

Combining equation (4) and (5)

!! ! !! ! !!

!

!! !!"# ! !!"# !

!!

!"

! !!"# ! !! ! !! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !

!! !! !! ! !!!"# !" ! !!" ! !! ! !!"# !! !! !! !"

!" !

!!

!!

!!"#

!!!"# ! ! !!"# !!

!

!

! !! ! ! ! !!"# !

! !!! ! !!!"# !

! !! ! !!

!!!!!!!!!!!!! !

For the second case, we take a strip of the reservoir having thickness !" at a height ! above the centre plane.

SPE 162944

8

! !! !! !!"

!!

!!"#

!! !! !!" !! ! !!

!! !! !! ! !!" !! ! !!

!!"

!!

!

!

!!! !

! !!"# !

!

! !!

! !!"# !

!!!

!!! ! !! ! !! !"

!! ! !!"#

!"

! !!"# !

! ! !!! ! !!!! ! !! !!"# ! !!! !"#!! !

! ! !!! ! !!!! ! !! !!"# ! !!! !"#!! ! ! !!!! ! !! !!"#

! !! !!!"# ! ! !! !!"#

!!!!

! !!!! ! !! !!"#

!! !! !!

!

! !! ! !! ! ! ! ! ! ! !!!

!!!"# ! ! !!! ! !! !!"!

Combining this with equation (5), we have, !! !! !! !" ! !" ! !! ! !! !!"#

Where

!" ! !" !" ! !

!!!"#

! !! ! !!"# !!

! ! !!!! ! !! !!"#

! ! !!! ! !!!! ! !! !!"# ! !!! !"#!!

!!!"# ! !!!! ! !! !!"#

!! !!"# ! !! ! !! ! !! !! !! !" ! !"

Recognizing that

! ! !!!

We can write !" ! !

! ! ! ! ! !! !!"#

! ! ! ! ! ! ! !! !!"# ! !! !"#!!

!!!"# ! ! !! !!"#

!!

9

SPE 162944

!

Converting to field units we have, !! ! !! ! !!

!! !! !"

!!

!!!!"!#!"

!!!"# ! ! !!"# !!

!

! !!! ! !!!"# !

! ! !!

!! !!!!"!#!" ! ! ! ! ! !! !! ! !! !! !! !" ! !"

To account for the effect of skin we have !! ! !! ! !!

!! !! !"

!!

!!!!"!#!"

!!!"# ! ! !!"# !!

! !!! ! ! !! !!!"# !

! ! !!

!! !!!!"!#!" ! ! ! !!!! !! ! !! !! !! !" ! !" ! ! Comparison with Butler’s and Furui’s models Horizontal Effective Well Length(Le),ft

3343

Assumed Drainage Width (2Yb or W),ft

8700

Wellbore Radius(rw),ft

0.26

Effective Drainage Radius(re),ft

3170

Net Pay Thickness(h),ft

180

Reservoir Pressure(Pe),psi

3000

Wellbore Flowing Pressure(Pwf),psi

2666

Horizontal Permeability (kh),md

784

0.62Vertical Permeability(kv),md

2.5

Formation Volume Factor(Bo),resbbl/STB

1.34

Skin Factor(s)

-3.5

Fluid Viscosity (µo), cp

0.62

Actual Productivity Index (PI), bbl/day/psi

2018.8

Using Butler’s IPR, !!

!!!"!!"!! !! ! !! !!!"# ! ! ! !!!"!!"# ! ! !! !! !!"# !" ! !! !!"# ! !

SPE 162944

10

! !!"# !

!! ! !!

!"# ! !"!!" !!!

!!!"!!"!! !! ! ! !!!!"!!"!! !!"#!!!"! ! !"##$!!"#!

!!"# !"

Using Furui’s IPR,

!!

!!!"# !! !!"# ! !

! !"!!"! !"

!"#!!"!!" !!!" !"!!" ! !

! !!"!!"#$

!!! !!!"#$ ! ! !"!!"#$ ! !"#

!!!!"!!"# ! ! ! !!!!"!!"!!" ! !!! ! !!"!!"#$

!"##$!!"#! ! !""!!!"#!!"#!!"# !!!"!!!!" !!"!!"#$ ! !"!!"#$ ! !"!!"#$ !!!"!!"!! !" !!! !!!"# ! ! !!!!" ! ! !! !! !" !!!"# !! !!"# ! !

!!

!!

!! !! ! ! ! !"#!!!! ! !!!!"

!!!"!!"!! !" ! !!!"!!"!! !!!!!"!!!"! ! !!"#$!!"#! !"

!!!"# !! !!"# ! !

! !"

!"#!!"!!" !!!" !"!!" ! !

!!! !!!"#$ ! ! !!!"#$ !!!"# !"#!!"!!"

! !!!"#$

!!!!!" ! ! ! !!!!!" ! !!! ! !!!!"#$ !!

!"#$!!"#! ! !"#!!!"#!!"#!!"# !!!"!!!!" !!!"#$ ! !!!"#$ ! !!!"#$

Using Equation 6b !!

!! !! !"

!!!"!!"!! !"

!!!"# ! !! ! !!"# !!

!

! !!! ! !! !!!"# !

!!!"!!"!! !" ! !!!"!!"!! !!!!!"!!!"! ! !"#$!!"#!!

!"

!!!"#

!! !

! !!"#

!!

! !"

!"#!!"!!"

!!!" ! !"!!"! ! !

! !!!"!"

11

SPE 162944

!

Using Equation 8b

!!

!!! !!!"#$ ! ! ! ! ! ! !!!"#$ !"#!!"!!" ! !!!"# !

!"#$!!"#!! ! !""!!!"#!!"#!!"# !!!"!!!!" !!!"!" ! !!!"#$ ! !!! !!

!!!!"!#!" !! !! !" ! !" ! !

!!!"!!"!! !" ! !!!"!!"!! !!!!!"!!!"! ! !"#$!!"#!!

!" ! !" !" ! !

!!!"#

!! !

! !!"#

! ! ! ! ! !! !!"#

!!

! ! ! ! ! ! ! !! !!"# ! !! !"#!!

! !!!"#$

! !"

!"#!!"!!"

!!!" ! !"!!"! ! !

!!!"# ! ! ! ! !! !!"#

!

! !!!"!" !!!"#$!!"

! !"## ! !"#$!!" ! !"#$$ !"#!!

!"#$!! !"#$!!"

!"#$!! ! !!"!!!"#!!"#!!"# !!!"#! !!!"!" ! !!!"#$ ! !!! !"#$!!!!" !"#!!

!"#$!! !!"!!"#$%#&!'!!"!!"#$"%& !"#$!!"

Applying the idea to cresting The minimum pressure drop between the well bore and the WOC to initiate migration of water into the oil zone is the pressure drop between the well bore and the equipotential surface whose radius is !

we have,

From Furui IPR,

!! ! !! !

!!!"" !! ! !! ! !"!!

! ! ! !!!!"#$ ! ! ! ! ! !

!!!"# !! ! !!" !! !!"# ! ! !! ! !! ! !!! !!!"# !" ! ! !!!!" !!!"# !! !!"# ! ! !"

Hence the maximum allowable pressure drawdown gives,

! !!"# !

so

SPE 162944

12

! !! ! !! ! !!!!"#$

!"

!!!"# !! !!"# ! !

!

!"

!!!"# !! !!"# ! !

!

!"

!!!"# ! !! ! !!"# !!

!!! ! !!!!" !! ! !! ! !!!"# ! ! !!!"# !" !! !!"# ! !

Similarly from Butler’s IPR,

!! ! !! ! !!!!"#$

!!! ! !!!" !! ! !! ! !!!"# ! !" !!!"# !" !! !!"# ! !

From our first IPR equation we have,

!! ! !! ! !!!!"#$

!"

!!

!

!!! ! ! !!!"# !

!!!"# ! ! !!"# !!

!! ! !! !

! !!!!

From the second IPR equation we have !! ! !! ! !!!!"#$

!" ! !" !! ! !! ! ! !" !"

From this we can determine the critical rate oil production and that will give !!" ! !! ! !! !

For Furui and Butler, we have !!" !

!!!"#$!!"!! !! ! !! !"! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !" !!!"# !! !! !" !! !!"# ! !

For our two equations, we have !!" !

!!!"#$!!"!! !! ! !! !"! !! !! !"

!!

!!!"# ! ! !!"# !!

! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !"

Skin due to formation damage around the well bore also affects the oil critical rate and maximum allowable pressure drawdown. So taking skin into consideration we have,

13

SPE 162944

!

Equation 9 gives

!! ! !! ! !!!!"#$

!"

!!!"# !! !!"! ! !

!!! ! !!!!" ! ! !!!"# !!!"# !" !! !! !!"# ! !

Equation 10 gives

!! ! !! ! !!!!"#$

!!!"# !! !!"# ! !

!

!!!"# ! !! ! !!"# !!

!

!"

!!! ! !!!" ! ! !!!"# !!!"# !" !! !! !!"# ! !

Equation 11 gives

!! ! !! ! !!!!"#$

!"

!

!"

Equation 12 becomes

!!

!!! ! ! !! !!!"# !

!!!"# ! ! !!"# !!

!!

!! ! !! ! !!!!"#$

Equation 13, gives

!! ! !! !

!! ! !! !

! ! ! ! ! ! ! ! ! ! ! !!!!

! ! ! ! ! ! ! ! ! ! ! ! !"!

! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !!!!!

!" ! !" ! ! !! ! !! ! !" ! !

! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !"!

!!" ! Equation 14 becomes !!" !

!! ! !! !

!!!"#$!!"!! !! ! !! !"! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !"! !!!"# !! !! !! !" !! !!"# ! !

!!!"#$!!"!! !! ! !! !"!

!! !! !"

!!

!!!"# ! ! !!"# !!

!!

! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !"!

To use the equation for gas conning calculation, we simply replace the water- oil density difference with gas – oil density difference.

SPE 162944

14

!

The design of ICD(s) and ICV(s)

These equipments are used to control inflow from different sections of a horizontal well in order to achieve effective sweep of the drainage volume. Proper use of the equipments requires the knowledge of critical flow rate and maximum allowable pressure draw down in the different sections of the reservoir. While and ICV can be adjusted continually during the life of the well, an ICD cannot. Hence it is important that the device is properly designed from the beginning of production.

An ICD/ICV can be designed as follows: 1. Determine the critical production rate per unit length of the well from different sections of the reservoir. 2. Select about 80% of the minimum value of the rates calculated in (1.) in order to allow for inaccuracies in the delineation of water-oil and gas-oil contact. 3. Using the value in (2), determine the corresponding production rate from other section using a uniform production rate per unit length (uniform flux).

15

!

SPE 162944

4. Convert this production rates to pressure drawdown(s) for other sections. 5. Calculate the additional drawdown(s) required through the openings of the ICD/ICV. 6. Calculate opening size needed for the pressure drop at the calculated flow rates.

Example: Horizontal section is 10,000' Permeability variation is as follow: Section 1: 500' Kh= 20 md Section 2: 500' Kh= 200 md Section 3: 1000' Kh= 50 md Section 4: 1500' Kh= 150 md Section 5: 1000' Kh= 40 md Section 6: 1500' Kh= 10 md Section 7: 200' Kh= 400 md Section 8: 800' Kh= 80 md Section 9: 400' Kh= 60 md Section 10: 600' Kh= 40 md Section 11: 300' Kh= 600 md Section 12: 700' Kh= 70 md Section 13: 250' Kh= 50 md Section 14: 450' Kh= 35 md Section 15: 300' Kh= 15 md Anisotropic factor Kv/Kh=0.1 The reservoir thickness = 200' The reservoir width =2500’ The wellbore radius is 6" Oil viscosity = 2cp Formation Volume Factor = 1.2STB/bbl Oil API = 45.4

o

Solution. Critical rate per unit length !!" !!!"#$!!"!! !! ! !! !! !!!"#$!!"!! !! ! !! !! ! ! ! ! !!!"# !!!"# !! !! !" !!"# !! !! !" ! ! !! ! !!"# ! ! !! ! !!"# !!

Among the parameters needed to calculate the critical rate per unit length, only the horizontal permeability varies from one section to the other. The region with the smallest critical rate per unit length is the region with the lowest horizontal permeability.

SPE 162944

16

! !! ! !!

!!"# !

! ! !" ! !!!"# !!!

!"!!!!!! !"!!!!!"!! ! ! !"!!" !" !" ! !"# ! !"!!! !"!! ! !"!!!

!! !

!!" !!!"#$!!"!! !! ! !! !! ! !!!"#$!!"!! !"!! ! !"!!" !!""!! ! ! ! !!!!"#$%!! !"#!! ! !" ! !!!"# !""!!!!"# !!!"#!!!!!! !" !!"# !! !! !" ! !!! ! !" ! ! !! ! !!"# !!

The minimum value of

!!" !

occur at the section having 10md permeability !!" !

!"#

! !!!!"#$%!!" ! !!!"#$%!"#!! ! !"

With 80% of this value, we calculate the pressure drop through the reservoir in other section when they are producing at the same rate per unit length.

!! ! !! ! !"!!!!!"# !! !! !" ! !" !" !

!!!"#

!! !

! ! ! ! ! !! !!"#

! !!"#

! ! ! ! ! ! ! !! !!"# ! !! !"#!!

! !!!"#

! !"

!!

!!" !

!""!!!!"#

!!! ! !" ! !

!!!"# ! ! !! !!"#

!!

!

!"#!! !!

! !!!"# !"#$!!"!

! !""" ! !"#$!!" ! !""" !"#!!

! !"!!!!!!!"#!!!!!!!!!!"#$%&! !

!" ! !" !!

!!!"# ! !!!"# !!

We can now tabulate what each section will produce and the corresponding pressure drop. Secti on

Lengt h(ft)

Permeability (md)

1 2 3 4 5 6 7 8

500 500 1000 1500 1000 1500 200 800

20 200 50 150 40 10 400 80

Allocated production rate (STB/day) !! ! !!!"#$%&!!

!"#$%& !"#$%& '(#)*& )+#"(& '(#)*& )+#"(& *#'!& $%#$(&

Pressure drop (psia) !"#!! !! ! !! ! !!

!"#$'& !#"$& *#$%& $#+'& %#!!& '(#+)& ,#%!& +#)(&

!"#!!" !"#$!!"

17

SPE 162944

! 9

400

60

10 11 12 13 14 15

600 300 700 250 450 300

40 600 70 50 35 15

!+#('& $!#%+& !,#%*& $)#(,& %#!+& !(#+(& !,#%*&

(#,"& %#!!& ,#(!& )#$!& *#$%& !,#+!& $+#',&

Using section #6 with the highest pressure drop across the reservoir, we can now calculated the additional pressure drop required across the ICV/ICD

Section

Length(ft)

Permeability (md)

1 2 3 4 5 6 7 8

500 500 1000 1500 1000 1500 200 800

20 200 50 150 40 10 400 80

9

400

60

10 11 12 13 14 15

600 300 700 250 450 300

40 600 70 50 35 15

Allocated production rate (STB/day) !! ! !!!"#$%&!!

!"#$%& !"#$%& '(#)*& )+#"(& '(#)*& )+#"(& *#'!& $%#$(& !+#('& $!#%+& !,#%*& $)#(,& %#!+& !(#+(& !,#%*&

Pressure drop (psia) !"#!! !! ! !! ! !!

!"#$'& !#"$& *#$%& $#+'& %#!!& '(#+)& ,#%!& +#)(& (#,"& %#!!& ,#(!& )#$!& *#$%& !,#+!& $+#',&

Required pressure drop across valves (psia) ! !"!!" ! !! ! !!

!"#$'& '+#('& $%#!(& '+#,$& $*#'+& ,#,,& ')#)+& '!#"%& ',#'*& $*#'+& ')#"+& '!#$+& $%#!(& $(#,+& !$#!)&

The diameter of the valve required for the required pressure drop at the calculated production rates is ! ! !! !!! !!

!!!"

!

!!!"!!!!!"!!!!"#$%&'#!!"! !"#$%&'(!!"#$%&!

!"#$%!!"!!"#$!%&$%'(!!"#$%&%'!!"!!"!#!!"#$%&%'!!

!"#!!"#$%&"!!"#$%&'(! !!!"#$%!!"!! ! !!!!""#$%!!" ! !"#$!!!" !

!!" !"#

!!!

!!!"#!!"!!"#$!

SPE 162944

18

!

If the specific gravity of the fluid is known. In this case 0.8, we can calculate the opening sizes

Section

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Allocated production rate (STB/day) !! ! !!!"#$%&!!

!"#$%& !"#$%& '(#)*& )+#"(& '(#)*& )+#"(& *#'!& $%#$(& !+#('& $!#%+& !,#%*& $)#(,& %#!+& !(#+(& !,#%*&

Required pressure drop across valves (psia) ! !"!!" ! !! ! !!

!"#$'& '+#('& $%#!(& '+#,$& $*#'+& ,#,,& ')#)+& '!#"%& ',#'*& $*#'+& ')#"+& '!#$+& $%#!(& $(#,+& !$#!)&

Required Valve opening d (inches) !!!

! ! !! !!

!!!"

"#"$$%&! "#"'$''! "#"(%)*! "#"&(%*! "#"()(%! +,--!./01213! "#"%''4! "#"*%"4! "#"'44$! "#"$'*5! "#")%)4! "#"$($'! "#")5*%! "#"'*$5! "#"'$&"!

Even in a case where we are producing above the critical rate, this concept can also be applied to ensure uniform flux and simultaneous water breakthrough along the entire length of the horizontal section. RECOMMENDATIONS AND CONCLUSIONS 1. The equations so derived are applicable to water and gas cresting for a well that is centrally located with respect to the reservoir boundary. 2. The equations are based on steady state model, so gives the delta P between the wellbore and the boundary 3. More works need to be done to account for eccentricity with respect to boundaries. 4. Butlers IPR should be used in the form !!!"!!"!! !! !!!! ! !!" ! !! !! !!!"# ! ! ! ! ! !!!" !!"# !! !! !!"# !" ! !! !!"# ! !

19

!

SPE 162944

REFERENCES 1. Bournazel, C., and Jeanson, B., “Fast Water Coning Evaluation,” SPE Paper 3628 presented at the SPE 46th Annual Fall Meeting, New Orleans, Oct.3–6, 1971. 2. Calhoun, John, Fundamentals of Reservoir Engineering. Norman, OK: The University of Oklahoma Press, 1960. 3. Chaney, P. E. et al., “How to Perforate Your Well to Prevent Water and Gas Coning,” OGJ, May 1956, p. 108. 4. Chaperson, I., “Theoretical Study of Coning Toward Horizontal and Vertical Wells in Anisotropic st Formations: Subcritical and Critical Rates,” SPE Paper 15377, SPE 61 Annual Fall Meeting, New Orleans, LA, Oct. 5–8, 1986. 5. Butler, R.M.: Horizontal Wells for the Recovery of Oil, Gas and Bitumen, Petroleum Monograph, Petroleum Society of CIM (1994) 2. 6. Furui, K., Zhu, D. and Hill, A.D.: “A Rigorous Formation Damage Skin Factor and Reservoir Inflow Model for a Horizontal Well,” SPEPF (August 2003) 151. 7. Babu, D.K. and Odeh A.S.: “Productivity of a Horizontal Well,” SPE Reservoir Engineering (November 1989) 417. 8. Penmatcha, V.R. and Aziz K.: “Comprehensive Reservoir/Wellbore Model for Horizontal Wells,” SPEJ (September 1999) 224. 9. Brigham, W.E.: “Discussion of Productivity of a Horizontal Well,” SPE Reservoir Engineering (May 1990) 254. 10. Joshi, S. D., “Augmentation of Well Productivity Using Slant and Horizontal Wells,” J. of Petroleum Technology, June 1988, pp. 729–739. 11. Joshi, S., Horizontal Well Technology. Tulsa, OK: Pennwell Publishing Company, 1991. 12. Ozkan, E., and Raghavan, R., “Performance of Horizontal Wells Subject to Bottom Water Drive,” SPE Paper 18545, presented at the SPE Eastern Regional Meeting, Charleston, West Virginia, Nov. 2–4, 1988. 13. Papatzacos, P., Herring, T. U., Martinsen, R., and Skjaeveland, S. M., “Cone Breakthrough Time for Horizontal Wells,” SPE Paper 19822, presented at the 64th SPE Annual Conference and Exhibition, San Antonio, TX, Oct.8–11, 1989. 14. Pirson, S. J., Oil Reservoir Engineering. Huntington, NY: Robert E. Krieger Publishing Company, 1977. 15. Schols, R. S., “An Empirical Formula for the Critical Oil Production Rate,” Erdoel Erdgas, A., January 1972, Vol. 88, No. 1, pp. 6–11.

SPE 162944

!

20

NOMENCLATURES

! !! ! !"#$%&"'%($&&!!!"#!!"##!!"#$%$&'()

! ! !"#$ ! !"#$%!!"#$!!"!!"!!""#$%&#'("!!"#$%#&'!!"#$%&!!!"! ! ! !"#$!!!"#$%!

! ! !"#$%&'%(#)!!"#$%&

! ! !"#$%&'(!!"#$%$&'()!!"#$""%!!!!!!"##!!"#!!!!!!"#!!"#!!"#$%!$!!!"! !! ! !"#!!"#$%&'"(!!"#$%&!!"#$%&!!!"!!"#!

!! ! !"#$%&'(!!"#$%$&'()!!"#$""%!!!!!!"##!!"#!!!!!!"#$%!!"#!!"#$%!$!!!"! !! ! !"#$%&'(!!"#$%$&'()!!"#$""%!!!!!!"##!!"#!!!!!!"#!!"#!!"#$%!$!!!"!

! ! !"#"$%&'$!!!!"#$%&&!!!"!

! ! !"#$%"&'()!!"##!!"#$%!!!!"!

! ! !"#$"%&'(!!"#$!!"!!"#$%&'(!!"#!!!"#$!%&'(!!"#$"%&'(')*!!!"! !! ! !"#$%"&'()!!"#$"%&'(')*!!!"!

!! ! !"#$%&'(!!"#$"%&!"!#$!!!"! !! ! !"#$%&'!!"!!"#!!!"!!" ! !

!! ! !"#$%&'!!"!!"#!!!"!!" ! !

!! ! !"#$%&'!!"!!"#$%!!!"!!" ! !

!!" ! !"#$#%&'!!"#$!!"!!"#!!"#$%&'(#)!!!"#!!"#! !!! ! !"#$%!"#$%&!!!!"#$#!%&!!"#!!"#$!

!!! ! !""#$%&'#!!"#"!$%&!!!"#$%&!!!"! !! ! !"##$%&"!!"#$%&!!!"!

! ! !"#$%&'(!!"#$%$&'()!!"#$""%!!!!!!"##!!"#!!!!!!"#$%!!"!!!"#$%!$!!!"! ! ! !"#$!!!"!!!!!!"#"!$%&!!!!"! !!! ! !"#$!!"#"!$%&!!!"#$!!!!"!

!

Suggest Documents