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Determination of flow efficiency and skin: Difference between revisions

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To quantify [[formation damage]] and understand its impact on hydrocarbon production, one must have reasonable estimates of the flow efficiency or skin factor. Several methods have been proposed to evaluate these quantities for oil and gas wells. The most common methods are:
To quantify [[Formation_damage|formation damage]] and understand its impact on hydrocarbon production, one must have reasonable estimates of the flow efficiency or skin factor. Several methods have been proposed to evaluate these quantities for oil and gas wells. The most common methods are:
 
*Multirate tests
*Multirate tests
*Isochronal gas-well tests
*Isochronal gas-well tests
*Transient well tests (pressure-buildup analysis)
*Transient well tests (pressure-buildup analysis)


==Multirate tests==
== Multirate tests ==
 
Multirate tests can be conducted on both oil and gas wells. In these tests, several stabilized flow rates, ''q<sub>i</sub>'' , are achieved at corresponding stabilized flowing bottomhole pressures, ''p''<sub>''wf''</sub>. The simplest analysis considers two different stabilized rates and pressures. The IPR can be written as
Multirate tests can be conducted on both oil and gas wells. In these tests, several stabilized flow rates, ''q<sub>i</sub>'' , are achieved at corresponding stabilized flowing bottomhole pressures, ''p''<sub>''wf''</sub>. The simplest analysis considers two different stabilized rates and pressures. The IPR can be written as


[[File:Vol4 page 0244 eq 001.png]]....................(1)
[[File:Vol4 page 0244 eq 001.png|RTENOTITLE]]....................(1)


Simplifying and solving for the flow efficiency, ''F'', we obtain
Simplifying and solving for the flow efficiency, ''F'', we obtain


[[File:Vol4 page 0244 eq 002.png]]....................(2)
[[File:Vol4 page 0244 eq 002.png|RTENOTITLE]]....................(2)


where ''x'' ≠ 0.  
where ''x'' ≠ 0.


The above equation clearly shows that it is possible to obtain flow efficiency rather simply with two stabilized bottomhole pressures and two stabilized flow rates. A similar analysis can be performed to obtain an expression for a linear IPR (''x'' = 0).
The above equation clearly shows that it is possible to obtain flow efficiency rather simply with two stabilized bottomhole pressures and two stabilized flow rates. A similar analysis can be performed to obtain an expression for a linear IPR (''x'' = 0).


==Multirate tests in gas wells: inertial effects==
== Multirate tests in gas wells: inertial effects ==
For many gas wells and some oil wells, flow rates are sufficiently high that turbulent or inertial pressure drops near the wellbore can be significant. In such cases, the additional pressure drop measured by the skin can be confused with the pressure drop because of non-Darcy or inertial flow. It is very important to separate out the pressure drop caused by turbulent flow from that caused by physical skin because it has a significant impact on the stimulation recommendations made on the well. To analyze high-rate gas or oil wells, the following equation is needed. <ref name="r1" />  
 
For many gas wells and some oil wells, flow rates are sufficiently high that turbulent or inertial pressure drops near the wellbore can be significant. In such cases, the additional pressure drop measured by the skin can be confused with the pressure drop because of non-Darcy or inertial flow. It is very important to separate out the pressure drop caused by turbulent flow from that caused by physical skin because it has a significant impact on the stimulation recommendations made on the well. To analyze high-rate gas or oil wells, the following equation is needed. <ref name="r1">Jones, L.G., Blount, E.M., and Glaze, O.H. 1976. Use of Short Term Multiple Rate Flow Tests To Predict Performance of Wells Having Turbulence. Presented at the SPE Annual Fall Technical Conference and Exhibition, New Orleans, Louisiana, 3-6 October 1976. SPE-6133-MS. http://dx.doi.org/10.2118/6133-MS</ref>


Darcy's law for high-rate gas wells can be written as
Darcy's law for high-rate gas wells can be written as


[[File:Vol4 page 0244 eq 003.png]]....................(3)
[[File:Vol4 page 0244 eq 003.png|RTENOTITLE]]....................(3)


Here,
Here,


[[File:Vol4 page 0244 eq 004.png]]....................(4)
[[File:Vol4 page 0244 eq 004.png|RTENOTITLE]]....................(4)


This equation can be rearranged to obtain
This equation can be rearranged to obtain


[[File:Vol4 page 0244 eq 005.png]]....................(5)
[[File:Vol4 page 0244 eq 005.png|RTENOTITLE]]....................(5)


Here, ''Aq''<sub>''sc''</sub> represents a laminar pressure drop and ''Bq''<sup>2</sup><sub>''sc''</sub> represents an inertial or non-Darcy pressure drop (sometimes referred to as a turbulent pressure drop). Note that ''A'' contains the physical skin, ''S'', and ''B'' is directly proportional to the non-Darcy coefficient, ''D''. By plotting multirate test data as a plot of [[File:Vol4 page 0245 inline 001.png]], we obtain ''A'' and ''B'' as an intercept and slope, respectively. It is then possible to compare the magnitude of the pressure drop caused by ''S'' with that caused by inertial effects, ''Dq''<sub>''sc''</sub>.  
Here, ''Aq''<sub>''sc''</sub> represents a laminar pressure drop and ''Bq''<sup>2</sup><sub>''sc''</sub> represents an inertial or non-Darcy pressure drop (sometimes referred to as a turbulent pressure drop). Note that ''A'' contains the physical skin, ''S'', and ''B'' is directly proportional to the non-Darcy coefficient, ''D''. By plotting multirate test data as a plot of [[File:Vol4 page 0245 inline 001.png|RTENOTITLE]], we obtain ''A'' and ''B'' as an intercept and slope, respectively. It is then possible to compare the magnitude of the pressure drop caused by ''S'' with that caused by inertial effects, ''Dq''<sub>''sc''</sub>.


If ''S''>''Dq''<sub>''sc''</sub>, a stimulation treatment would be recommended. However, if ''Dq''<sub>''sc''</sub> > ''S'', the well may need to be reperforated or fractured to increase the inflow area and to reduce inertial effects.
If ''S''>''Dq''<sub>''sc''</sub>, a stimulation treatment would be recommended. However, if ''Dq''<sub>''sc''</sub> > ''S'', the well may need to be reperforated or fractured to increase the inflow area and to reduce inertial effects.


==Isochronal test in gas wells==
== Isochronal test in gas wells ==
 
In gas wells in which it takes a long time to achieve stabilized rates, wells are shut in and produced for a fixed time interval (Δ''t'') at several different rates. These isochronal tests are then interpreted by the following "deliverability" relation,
In gas wells in which it takes a long time to achieve stabilized rates, wells are shut in and produced for a fixed time interval (Δ''t'') at several different rates. These isochronal tests are then interpreted by the following "deliverability" relation,


[[File:Vol4 page 0245 eq 001.png]]....................(6)
[[File:Vol4 page 0245 eq 001.png|RTENOTITLE]]....................(6)


where the exponent ''n'' lies between 0.5 and 1. An exponent closer to 0.5 indicates that non-Darcy effects are important; an exponent close to 1 indicates that they are not. <ref name="r2" />  
where the exponent ''n'' lies between 0.5 and 1. An exponent closer to 0.5 indicates that non-Darcy effects are important; an exponent close to 1 indicates that they are not. <ref name="r2">Matthews, C.S. and Russell, D.G. 1967. Pressure Buildup and Flow Tests in Wells, 1. Richardson, Texas: Monograph Series, SPE.</ref>


It should be noted that the "deliverability" equation is a variation of the equation derived in the previous section.
It should be noted that the "deliverability" equation is a variation of the equation derived in the previous section.


==Pressure-buildup analysis==
== Pressure-buildup analysis ==
The most common method for determining skin is a pressure-buildup test. <ref name="r2" /><ref name="r3" /> In this test, a well that has been producing for a time, ''t''<sub>''p''</sub>, is shut in for time Δ''t''. The pressure buildup is recorded as a function of time. By constructing a Horner plot<ref name="r2" /><ref name="r3" /> like the one shown in '''Fig. 1''', we can compute the skin and the product of the permeability and formation thickness, ''kh'', of the reservoir (in field units).


[[File:Vol4 page 0245 eq 002.png]]....................(7)
The most common method for determining skin is a pressure-buildup test. <ref name="r2">Matthews, C.S. and Russell, D.G. 1967. Pressure Buildup and Flow Tests in Wells, 1. Richardson, Texas: Monograph Series, SPE.</ref><ref name="r3">Horner, D.R. 1951. Pressure build-up in wells. Proc., 1951. . Proc., Third World Petroleum Congress, The Hague, Sec. II, 503–523.</ref> In this test, a well that has been producing for a time, ''t''<sub>''p''</sub>, is shut in for time Δ''t''. The pressure buildup is recorded as a function of time. By constructing a Horner plot<ref name="r2">Matthews, C.S. and Russell, D.G. 1967. Pressure Buildup and Flow Tests in Wells, 1. Richardson, Texas: Monograph Series, SPE.</ref><ref name="r3">Horner, D.R. 1951. Pressure build-up in wells. Proc., 1951. . Proc., Third World Petroleum Congress, The Hague, Sec. II, 503–523.</ref> like the one shown in '''Fig. 1''', we can compute the skin and the product of the permeability and formation thickness, ''kh'', of the reservoir (in field units).
 
[[File:Vol4 page 0245 eq 002.png|RTENOTITLE]]....................(7)


and
and


[[File:Vol4 page 0245 eq 003.png]]....................(8)
[[File:Vol4 page 0245 eq 003.png|RTENOTITLE]]....................(8)


Here, ''m'' is the slope of the straight-line portion of the Horner plot, and ''p''<sub>''ws'',1hr</sub> is the extrapolated shut-in pressure at a shut-in time of 1 hour.  
Here, ''m'' is the slope of the straight-line portion of the Horner plot, and ''p''<sub>''ws'',1hr</sub> is the extrapolated shut-in pressure at a shut-in time of 1 hour.


<gallery widths=300px heights=200px>
<gallery widths="300px" heights="200px">
File:Vol4 Page 246 Image 0001.png|'''Fig. 1—Horner plot from a pressure-buildup test.'''<ref name="r2" />
File:Vol4 Page 246 Image 0001.png|'''Fig. 1—Horner plot from a pressure-buildup test.'''<ref name="r2" />
</gallery>
</gallery>


It is also possible to obtain the average reservoir pressure with the Matthew, Brons, and Hazelbrook method from the pressure-buildup data. <ref name="r4" /> Knowing both the average reservoir pressure and skin, we can calculate the flow efficiency of the well. This method provides a direct and quantitative measure of the extent of formation damage in a well.  
It is also possible to obtain the average reservoir pressure with the Matthew, Brons, and Hazelbrook method from the pressure-buildup data. <ref name="r4">Matthews, C.S., Brons, F., and Hazelbrook, P. 1954. A Method for Determination of Average Pressure in a Bounded Reservoir. Trans., AIME, 201, 182–191.</ref> Knowing both the average reservoir pressure and skin, we can calculate the flow efficiency of the well. This method provides a direct and quantitative measure of the extent of formation damage in a well.


Methods following the same principle have been developed for deviated and horizontal wells. Equations for analysis are more complex and are not discussed in this page. The same methods can also be used to analyze data from gas wells and from wells on artificial lift.  
Methods following the same principle have been developed for deviated and horizontal wells. Equations for analysis are more complex and are not discussed in this page. The same methods can also be used to analyze data from gas wells and from wells on artificial lift.


The short discussion presented above shows how near-wellbore formation damage can be quantified by measurements made on oil and gas wells. Such measurements are essential for determining the extent and magnitude of the formation damage and its impact on hydrocarbon production. However, these measures do not provide us with any clues on the reasons for the formation damage.
The short discussion presented above shows how near-wellbore formation damage can be quantified by measurements made on oil and gas wells. Such measurements are essential for determining the extent and magnitude of the formation damage and its impact on hydrocarbon production. However, these measures do not provide us with any clues on the reasons for the formation damage.


== Nomenclature ==
== Nomenclature ==
{|
{|
|''Aq''<sub>''sc''</sub>
|=
|laminar pressure drop
|-
|-
|''B''  
| ''Aq''<sub>''sc''</sub>
|=  
| =
|proportional to the non-Darcy coefficient, ''D''
| laminar pressure drop
|-
|-
|''Bq''<sup>2</sup><sub>''sc''</sub>
| ''B''
|=  
| =
|inertial or non-Darcy pressure drop
| proportional to the non-Darcy coefficient, ''D''
|-
|-
|''c''  
| ''Bq''<sup>2</sup><sub>''sc''</sub>
|=  
| =
|compressibility
| inertial or non-Darcy pressure drop
|-
|-
|''Dq''<sub>''sc''</sub>
| ''c''
|=  
| =
|inertial effects
| compressibility
|-
|-
|''F''  
| ''Dq''<sub>''sc''</sub>
|=  
| =
|well flow efficiency
| inertial effects
|-
|-
|''k''  
| ''F''
|=  
| =
|overall permeability, md
| well flow efficiency
|-
|-
|''k''<sub>''I''</sub>
| ''k''
|=  
| =
|initial permeability, md  
| overall permeability, md
|-
|-
|''k''<sub>''h''</sub>  
| ''k''<sub>''I''</sub>
|=  
| =
|permeability and formation thickness
| initial permeability, md
|-
|-
|''m''  
| ''k''<sub>''h''</sub>
|=  
| =
|slope
| permeability and formation thickness
|-
|-
|''n''  
| ''m''
|=  
| =
|exponent
| slope
|-
|-
|''p''  
| ''n''
|=  
| =
|pressure
| exponent
|-
|-
|''p''<sub>''b''</sub>
| ''p''
|=  
| =
|bubblepoint pressure  
| pressure
|-
|-
|''p''<sub>''R''</sub>  
| ''p''<sub>''b''</sub>
|=  
| =
|average reservoir pressure  
| bubblepoint pressure
|-
|-
|''p''<sub>''wf''</sub>  
| ''p''<sub>''R''</sub>
|=  
| =
|flowing bottomhole pressure  
| average reservoir pressure
|-
|-
|''p''<sub>''ws,1hr''</sub>  
| ''p''<sub>''wf''</sub>
|=  
| =
|extrapolated shut-in pressure at a shut-in time of 1 hour
| flowing bottomhole pressure
|-
|-
|Δ''P''<sub>skin</sub>  
| ''p''<sub>''ws,1hr''</sub>
|=  
| =
|additional pressure drop caused by formation damage
| extrapolated shut-in pressure at a shut-in time of 1 hour
|-
|-
|''q''  
| Δ''P''<sub>skin</sub>
|=  
| =
|flow rate
| additional pressure drop caused by formation damage
|-
|-
|''q''<sub>''i''</sub>
| ''q''
|=  
| =
|flow rates
| flow rate
|-
|-
|''q''<sub>''sc''</sub>  
| ''q''<sub>''i''</sub>
|=  
| =
|volumetric flow rate, surface conditions
| flow rates
|-
|-
|''r''<sub>''e''</sub>  
| ''q''<sub>''sc''</sub>
|=  
| =
|external boundary radius
| volumetric flow rate, surface conditions
|-
|-
|''r''<sub>''w''</sub>
| ''r''<sub>''e''</sub>
|=  
| =
|well radius  
| external boundary radius
|-
|-
|''S''  
| ''r''<sub>''w''</sub>
|=  
| =
|skin factor
| well radius
|-
|-
|''T''  
| ''S''
|=  
| =
|temperature
| skin factor
|-
|-
|''t''  
| ''T''
|=  
| =
|time
| temperature
|-
|-
|Δ''t''  
| ''t''
|=  
| =
|fixed time interval
| time
|-
|-
|''z''  
| Δ''t''
|=  
| =
|real gas compressibility factor
| fixed time interval
|-
|-
|''μ''  
| ''z''
|=  
| =
|viscosity
| real gas compressibility factor
|-
|-
|''μ''<sub>''g''</sub>  
| ''μ''
|=  
| =
|gas viscosity  
| viscosity
|-
| ''μ''<sub>''g''</sub>
| =
| gas viscosity
|}
|}


==References==
== References ==
<references>
<ref name="r1" >Jones, L.G., Blount, E.M., and  Glaze, O.H. 1976. Use of Short Term Multiple Rate Flow Tests To Predict Performance of Wells Having Turbulence. Presented at the SPE Annual Fall Technical Conference and Exhibition, New Orleans, Louisiana, 3-6 October 1976. SPE-6133-MS. http://dx.doi.org/10.2118/6133-MS </ref>


<ref name="r2" >Matthews, C.S. and Russell, D.G. 1967. ''Pressure Buildup and Flow Tests in Wells'', 1. Richardson, Texas: Monograph Series, SPE.  </ref>
<references />


<ref name="r3" >Horner, D.R. 1951. Pressure build-up in wells. Proc., 1951. . Proc., Third World Petroleum Congress, The Hague, Sec. II, 503–523.</ref>
== Noteworthy papers in OnePetro ==


<ref name="r4" >Matthews, C.S., Brons, F., and Hazelbrook, P. 1954. A Method for Determination of Average Pressure in a Bounded Reservoir. Trans., AIME, 201, 182–191.</ref>
Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read
</references>


==Noteworthy papers in OnePetro==
== External links ==
Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read


==External links==
Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro
Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro


==See also==
== See also ==
[[Formation damage]]
 
[[Formation_damage|Formation damage]]
 
[[PEH:Formation_Damage]]


[[PEH:Formation Damage]]
== Category ==
[[Category:1.8 Formation damage]] [[Category:YR]]

Latest revision as of 10:51, 29 June 2015

To quantify formation damage and understand its impact on hydrocarbon production, one must have reasonable estimates of the flow efficiency or skin factor. Several methods have been proposed to evaluate these quantities for oil and gas wells. The most common methods are:

  • Multirate tests
  • Isochronal gas-well tests
  • Transient well tests (pressure-buildup analysis)

Multirate tests

Multirate tests can be conducted on both oil and gas wells. In these tests, several stabilized flow rates, qi , are achieved at corresponding stabilized flowing bottomhole pressures, pwf. The simplest analysis considers two different stabilized rates and pressures. The IPR can be written as

RTENOTITLE....................(1)

Simplifying and solving for the flow efficiency, F, we obtain

RTENOTITLE....................(2)

where x ≠ 0.

The above equation clearly shows that it is possible to obtain flow efficiency rather simply with two stabilized bottomhole pressures and two stabilized flow rates. A similar analysis can be performed to obtain an expression for a linear IPR (x = 0).

Multirate tests in gas wells: inertial effects

For many gas wells and some oil wells, flow rates are sufficiently high that turbulent or inertial pressure drops near the wellbore can be significant. In such cases, the additional pressure drop measured by the skin can be confused with the pressure drop because of non-Darcy or inertial flow. It is very important to separate out the pressure drop caused by turbulent flow from that caused by physical skin because it has a significant impact on the stimulation recommendations made on the well. To analyze high-rate gas or oil wells, the following equation is needed. [1]

Darcy's law for high-rate gas wells can be written as

RTENOTITLE....................(3)

Here,

RTENOTITLE....................(4)

This equation can be rearranged to obtain

RTENOTITLE....................(5)

Here, Aqsc represents a laminar pressure drop and Bq2sc represents an inertial or non-Darcy pressure drop (sometimes referred to as a turbulent pressure drop). Note that A contains the physical skin, S, and B is directly proportional to the non-Darcy coefficient, D. By plotting multirate test data as a plot of RTENOTITLE, we obtain A and B as an intercept and slope, respectively. It is then possible to compare the magnitude of the pressure drop caused by S with that caused by inertial effects, Dqsc.

If S>Dqsc, a stimulation treatment would be recommended. However, if Dqsc > S, the well may need to be reperforated or fractured to increase the inflow area and to reduce inertial effects.

Isochronal test in gas wells

In gas wells in which it takes a long time to achieve stabilized rates, wells are shut in and produced for a fixed time interval (Δt) at several different rates. These isochronal tests are then interpreted by the following "deliverability" relation,

RTENOTITLE....................(6)

where the exponent n lies between 0.5 and 1. An exponent closer to 0.5 indicates that non-Darcy effects are important; an exponent close to 1 indicates that they are not. [2]

It should be noted that the "deliverability" equation is a variation of the equation derived in the previous section.

Pressure-buildup analysis

The most common method for determining skin is a pressure-buildup test. [2][3] In this test, a well that has been producing for a time, tp, is shut in for time Δt. The pressure buildup is recorded as a function of time. By constructing a Horner plot[2][3] like the one shown in Fig. 1, we can compute the skin and the product of the permeability and formation thickness, kh, of the reservoir (in field units).

RTENOTITLE....................(7)

and

RTENOTITLE....................(8)

Here, m is the slope of the straight-line portion of the Horner plot, and pws,1hr is the extrapolated shut-in pressure at a shut-in time of 1 hour.

It is also possible to obtain the average reservoir pressure with the Matthew, Brons, and Hazelbrook method from the pressure-buildup data. [4] Knowing both the average reservoir pressure and skin, we can calculate the flow efficiency of the well. This method provides a direct and quantitative measure of the extent of formation damage in a well.

Methods following the same principle have been developed for deviated and horizontal wells. Equations for analysis are more complex and are not discussed in this page. The same methods can also be used to analyze data from gas wells and from wells on artificial lift.

The short discussion presented above shows how near-wellbore formation damage can be quantified by measurements made on oil and gas wells. Such measurements are essential for determining the extent and magnitude of the formation damage and its impact on hydrocarbon production. However, these measures do not provide us with any clues on the reasons for the formation damage.

Nomenclature

Aqsc = laminar pressure drop
B = proportional to the non-Darcy coefficient, D
Bq2sc = inertial or non-Darcy pressure drop
c = compressibility
Dqsc = inertial effects
F = well flow efficiency
k = overall permeability, md
kI = initial permeability, md
kh = permeability and formation thickness
m = slope
n = exponent
p = pressure
pb = bubblepoint pressure
pR = average reservoir pressure
pwf = flowing bottomhole pressure
pws,1hr = extrapolated shut-in pressure at a shut-in time of 1 hour
ΔPskin = additional pressure drop caused by formation damage
q = flow rate
qi = flow rates
qsc = volumetric flow rate, surface conditions
re = external boundary radius
rw = well radius
S = skin factor
T = temperature
t = time
Δt = fixed time interval
z = real gas compressibility factor
μ = viscosity
μg = gas viscosity

References

  1. Jones, L.G., Blount, E.M., and Glaze, O.H. 1976. Use of Short Term Multiple Rate Flow Tests To Predict Performance of Wells Having Turbulence. Presented at the SPE Annual Fall Technical Conference and Exhibition, New Orleans, Louisiana, 3-6 October 1976. SPE-6133-MS. http://dx.doi.org/10.2118/6133-MS
  2. 2.0 2.1 2.2 2.3 Matthews, C.S. and Russell, D.G. 1967. Pressure Buildup and Flow Tests in Wells, 1. Richardson, Texas: Monograph Series, SPE.
  3. 3.0 3.1 Horner, D.R. 1951. Pressure build-up in wells. Proc., 1951. . Proc., Third World Petroleum Congress, The Hague, Sec. II, 503–523.
  4. Matthews, C.S., Brons, F., and Hazelbrook, P. 1954. A Method for Determination of Average Pressure in a Bounded Reservoir. Trans., AIME, 201, 182–191.

Noteworthy papers in OnePetro

Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read

External links

Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro

See also

Formation damage

PEH:Formation_Damage

Category