You must log in to edit PetroWiki. Help with editing
Content of PetroWiki is intended for personal use only and to supplement, not replace, engineering judgment. SPE disclaims any and all liability for your use of such content. More information
Flow-after-flow tests for gas wells: Difference between revisions
No edit summary |
No edit summary |
||
| (2 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
This page discusses the implementation and analysis of flow-after-flow testing for [[ | This page discusses the implementation and analysis of flow-after-flow testing for [[Deliverability_testing_of_gas_wells|gas well deliverability]] assessment. Both the Rawlins and Schellhardt and Houpeurt analysis techniques are presented in terms of pseudopressures. | ||
==Flow-after-flow test procedure== | == Flow-after-flow test procedure == | ||
Flow-after-flow tests, sometimes called gas backpressure or four-point tests, are conducted by producing the well at a series of different stabilized flow rates and measuring the stabilized BHFP at the sandface. Each different flow rate is established in succession either with or without a very short intermediate shut-in period. Conventional flow-after-flow tests often are conducted with a sequence of increasing flow rates; however, if stabilized flow rates are attained, the rate sequence does not affect the test. <ref name="r1" /> The requirement that the flowing periods be continued until stabilization is a major limitation of the flow-after-flow test, especially in low-permeability formations that take long times to reach stabilized flowing conditions. '''Fig 1''' illustrates a flow-after-flow test. | |||
Flow-after-flow tests, sometimes called gas backpressure or four-point tests, are conducted by producing the well at a series of different stabilized flow rates and measuring the stabilized BHFP at the sandface. Each different flow rate is established in succession either with or without a very short intermediate shut-in period. Conventional flow-after-flow tests often are conducted with a sequence of increasing flow rates; however, if stabilized flow rates are attained, the rate sequence does not affect the test. <ref name="r1">Rawlins, E.L. and Schellhardt, M.A. 1935. Backpressure Data on Natural Gas Wells and Their Application to Production Practices, Vol. 7. Monograph Series, USBM.</ref> The requirement that the flowing periods be continued until stabilization is a major limitation of the flow-after-flow test, especially in low-permeability formations that take long times to reach stabilized flowing conditions. '''Fig 1''' illustrates a flow-after-flow test. | |||
<gallery widths="300px" heights="200px"> | <gallery widths="300px" heights="200px"> | ||
| Line 8: | Line 9: | ||
</gallery> | </gallery> | ||
==Rawlins-Schellhardt analysis technique== | == Rawlins-Schellhardt analysis technique == | ||
Recall the empirical equation that forms the basis for the Rawlins-Schellhardt analysis technique: | Recall the empirical equation that forms the basis for the Rawlins-Schellhardt analysis technique: | ||
[[File:Vol5 page 0845 eq 001.png]]....................(1) | [[File:Vol5 page 0845 eq 001.png|RTENOTITLE]]....................(1) | ||
Taking the logarithm of both sides of '''Eq. 1''' yields the equation that forms the basis for the Rawlins-Schellhardt analysis technique: | Taking the logarithm of both sides of '''Eq. 1''' yields the equation that forms the basis for the Rawlins-Schellhardt analysis technique: | ||
[[File:Vol5 page 0846 eq 001.png]]....................(2) | [[File:Vol5 page 0846 eq 001.png|RTENOTITLE]]....................(2) | ||
The form of '''Eq. 2''' suggests that a plot of log (Δ''p''<sub>''p''</sub>) vs. log (''q'') will yield a straight line of slope 1/''n'' and an intercept of {–1/''n''[log(''C'')]}. The AOF potential is estimated from the extrapolation of the straight line to Δ''p''<sub>''p''</sub> evaluated at a ''p''<sub>''wf''</sub> equal to atmospheric pressure (sometimes called base pressure). This analysis technique is illustrated with '''Example 1'''. | |||
== Houpert analysis technique == | |||
Flow-after-flow tests require stabilized data or data measured during [[Fluid_flow_through_permeable_media#Pseudosteady-state_flow|pseudosteady-state flow]]. Houpeurt<ref name="r2">Houpeurt, A. 1959. On the Flow of Gases in Porous Media. Revue de L’lnstitut Francais du Petrole 14 (11): 1468.</ref> gives the theoretical equation for pseudosteady-state flow, which was derived from the gas-diffusivity equation, as | |||
Flow-after-flow tests require stabilized data or data measured during [[ | |||
[[File:Vol5 page 0846 eq 002.png]]....................(3) | [[File:Vol5 page 0846 eq 002.png|RTENOTITLE]]....................(3) | ||
The coefficients ''a'' and ''b'' have theoretical bases and can be estimated if reservoir properties are known or they can be determined from flow-after-flow test data. Dividing both sides of '''Eq. 3''' by the flow rate, ''q'', and rearranging yields the equation that is the basis for the Houpeurt analysis technique: | The coefficients ''a'' and ''b'' have theoretical bases and can be estimated if reservoir properties are known or they can be determined from flow-after-flow test data. Dividing both sides of '''Eq. 3''' by the flow rate, ''q'', and rearranging yields the equation that is the basis for the Houpeurt analysis technique: | ||
[[File:Vol5 page 0846 eq 003.png]]....................(4) | [[File:Vol5 page 0846 eq 003.png|RTENOTITLE]]....................(4) | ||
The form of '''Eq. 4''' suggests that a plot Δ''p''<sub>''p''</sub>/''q'' vs. ''q'' will yield a straight line with a slope ''b'' and an intercept ''a''. The AOF is estimated in the Houpeurt deliverability analysis by solving '''Eq. 3''' for ''q'' = ''q''<sub>AOF</sub> at ''p''<sub>''wf''</sub> = ''p''<sub>''b''</sub>. | |||
== Example: Analysis of a flow-after-flow test == | |||
Estimate the initial stabilized AOF potential of a well<ref name="r3">Jennings, J. W. et al. 1989. Deliverability Testing of Natural Gas Wells. Prepared for the Texas Railroad Commission, Texas A&M U., College Station, Texas, August.</ref> with the well and reservoir properties listed. Use both the Rawlins-Schellhardt and the Houpeurt analysis techniques. In addition, estimate the AOF potential 10 years later when the static drainage area pressure has decreased to 350 psia. Evaluate the AOF potential at ''p''<sub>''b''</sub> = 14.65 psia. '''Table 1''' summarizes the flow-after-flow test data. ''L'' = 3,050 ft, ''r''<sub>''w''</sub> = 0.5 ft, ''M''<sub>''a''</sub> = 20.71 lbm/lbm-mole, ''T'' = 90°F = 555°R, ''A'' = 640 acres, ''ϕ'' = 0.25, ''C''<sub>''A''</sub> = 30.8828, and ''h'' =200 ft. | |||
Estimate the initial stabilized AOF potential of a well<ref name="r3" /> with the well and reservoir properties listed. Use both the Rawlins-Schellhardt and the Houpeurt analysis techniques. In addition, estimate the AOF potential 10 years later when the static drainage area pressure has decreased to 350 psia. Evaluate the AOF potential at ''p''<sub>''b''</sub> = 14.65 psia. '''Table 1''' summarizes the flow-after-flow test data. ''L'' = 3,050 ft, ''r''<sub>''w''</sub> = 0.5 ft, ''M''<sub>''a''</sub> = 20.71 lbm/lbm-mole, ''T'' = 90°F = 555°R, ''A'' = 640 acres, ''ϕ'' = 0.25, ''C''<sub>''A''</sub> = 30.8828, and ''h'' =200 ft. | |||
<gallery widths=300px heights=200px> | <gallery widths="300px" heights="200px"> | ||
File:Vol5 Page 0847 Image 0001.png|'''Table 1''' | File:Vol5 Page 0847 Image 0001.png|'''Table 1''' | ||
</gallery> | </gallery> | ||
Current [[File:Vol5 page 0781 inline 001.png]] = 407.6 psia, ''p''<sub>''p''</sub>( [[File:Vol5 page 0781 inline 001.png]] = 407.6) = 1.617 × 10<sup>7</sup> psia<sup>2</sup>/cp. [[File:Vol5 page 0781 inline 001.png]] after 10 years = 350 psia, ''p''<sub>''p''</sub>([[File:Vol5 page 0781 inline 001.png]] = 350) = 1.2239 × 10<sup>7</sup> psia<sup>2</sup>/cp. ''p''<sub>''b''</sub> = 14.65 psia, ''p''<sub>''p''</sub>(''p''<sub>''b''</sub>) = 2,674.8 psia<sup>2</sup>/cp. | Current [[File:Vol5 page 0781 inline 001.png|RTENOTITLE]] = 407.6 psia, ''p''<sub>''p''</sub>( [[File:Vol5 page 0781 inline 001.png|RTENOTITLE]] = 407.6) = 1.617 × 10<sup>7</sup> psia<sup>2</sup>/cp. [[File:Vol5 page 0781 inline 001.png|RTENOTITLE]] after 10 years = 350 psia, ''p''<sub>''p''</sub>([[File:Vol5 page 0781 inline 001.png|RTENOTITLE]] = 350) = 1.2239 × 10<sup>7</sup> psia<sup>2</sup>/cp. ''p''<sub>''b''</sub> = 14.65 psia, ''p''<sub>''p''</sub>(''p''<sub>''b''</sub>) = 2,674.8 psia<sup>2</sup>/cp. | ||
The pseudopressure in this example (and all others in this section) were calculated using the methods suggested by Al-Hussainy ''et al.''<ref name="r4" /> These methods, which involve numerical evaluation of the integral in '''Eq. 5''' and which require computational routines to estimate gas viscosity, ''μ'', and deviation factor, ''z'', are widely available in basic reservoir fluid flow analysis software. | The pseudopressure in this example (and all others in this section) were calculated using the methods suggested by Al-Hussainy ''et al.''<ref name="r4">Al-Hussainy, R., Jr., H.J.R., and Crawford, P.B. 1966. The Flow of Real Gases Through Porous Media. J Pet Technol 18 (5): 624-636. http://dx.doi.org/10.2118/1243-A-PA</ref> These methods, which involve numerical evaluation of the integral in '''Eq. 5''' and which require computational routines to estimate gas viscosity, ''μ'', and deviation factor, ''z'', are widely available in basic reservoir fluid flow analysis software. | ||
[[File:Vol5 page 0757 eq 002.png]]....................(5) | [[File:Vol5 page 0757 eq 002.png|RTENOTITLE]]....................(5) | ||
===Solution=== | === Solution === | ||
''Rawlins-Schellhardt analysis''. Plot Δ''p''<sub>''p''</sub> vs. ''q'' on log-log graph paper ('''Fig. 2'''). '''Table 2''' gives the plotting functions. Construct the best-fit line through the data points. All data points lie on the best-fit line and will be used for all subsequent calculations. | ''Rawlins-Schellhardt analysis''. Plot Δ''p''<sub>''p''</sub> vs. ''q'' on log-log graph paper ('''Fig. 2'''). '''Table 2''' gives the plotting functions. Construct the best-fit line through the data points. All data points lie on the best-fit line and will be used for all subsequent calculations. | ||
<gallery widths="300px" heights="200px"> | <gallery widths="300px" heights="200px"> | ||
| Line 55: | Line 59: | ||
Next, determine the deliverability exponent using least-squares regression analysis. Alternatively, because Points 1 and 4 both lie on the perceived "best" straight line through the test data, the reciprocal slope is estimated to be | Next, determine the deliverability exponent using least-squares regression analysis. Alternatively, because Points 1 and 4 both lie on the perceived "best" straight line through the test data, the reciprocal slope is estimated to be | ||
[[File:Vol5 page 0847 eq 001.png]] | [[File:Vol5 page 0847 eq 001.png|RTENOTITLE]] | ||
Now, calculate the AOF of the well. Because 0.5 ≤ ''n'' ≤ 1.0, calculate C using either regression analysis or a point from the best-fit straight line through the test data. Estimating C with regression analysis results in log(''C'') = ''α'' =-3.09 . Thus, | Now, calculate the AOF of the well. Because 0.5 ≤ ''n'' ≤ 1.0, calculate C using either regression analysis or a point from the best-fit straight line through the test data. Estimating C with regression analysis results in log(''C'') = ''α'' =-3.09 . Thus, | ||
[[File:Vol5 page 0847 eq 002.png]] | [[File:Vol5 page 0847 eq 002.png|RTENOTITLE]] | ||
Estimating ''C'' using Point 4 from the best-fit line and '''Eq. 1''': | Estimating ''C'' using Point 4 from the best-fit line and '''Eq. 1''': | ||
[[File:Vol5 page 0847 eq 003.png]] | [[File:Vol5 page 0847 eq 003.png|RTENOTITLE]] | ||
Therefore, the AOF potential of this well is | Therefore, the AOF potential of this well is | ||
[[File:Vol5 page 0848 eq 001.png]] | [[File:Vol5 page 0848 eq 001.png|RTENOTITLE]] | ||
To update the AOF to a new average reservoir pressure, recall that for pseudopressure analysis, neither ''C'' nor ''n'' changes as drainage area pressure decreases. The AOF for the new drainage area pressure becomes | To update the AOF to a new average reservoir pressure, recall that for pseudopressure analysis, neither ''C'' nor ''n'' changes as drainage area pressure decreases. The AOF for the new drainage area pressure becomes | ||
[[File:Vol5 page 0848 eq 002.png]] | [[File:Vol5 page 0848 eq 002.png|RTENOTITLE]] | ||
''Houpeurt analysis''. Plot Δ''p''<sub>''p''</sub>/''q'' vs. ''q'' on Cartesian graph paper ('''Fig. 3'''). '''Table 3''' gives the plotting functions. Construct the best-fit line through the last three data points. The first point, corresponding to the lowest flow rate, does not follow the trend and will be ignored in subsequent analyses. | ''Houpeurt analysis''. Plot Δ''p''<sub>''p''</sub>/''q'' vs. ''q'' on Cartesian graph paper ('''Fig. 3'''). '''Table 3''' gives the plotting functions. Construct the best-fit line through the last three data points. The first point, corresponding to the lowest flow rate, does not follow the trend and will be ignored in subsequent analyses. | ||
| Line 83: | Line 87: | ||
Determine the deliverability coefficients, ''a'' and ''b'', from a least-squares regression analysis, excluding the first point. The result is | Determine the deliverability coefficients, ''a'' and ''b'', from a least-squares regression analysis, excluding the first point. The result is | ||
[[File:Vol5 page 0849 eq 001.png]] | [[File:Vol5 page 0849 eq 001.png|RTENOTITLE]] | ||
Alternatively, use Points 2 and 4 from the line drawn through the test data to calculate ''a'' and ''b'': | Alternatively, use Points 2 and 4 from the line drawn through the test data to calculate ''a'' and ''b'': | ||
[[File:Vol5 page 0849 eq 002.png]] | [[File:Vol5 page 0849 eq 002.png|RTENOTITLE]] [[File:Vol5 page 0850 eq 001.png|RTENOTITLE]] | ||
[[File:Vol5 page 0850 eq 001.png]] | |||
Then, | Then, | ||
[[File:Vol5 page 0850 eq 002.png]] | [[File:Vol5 page 0850 eq 002.png|RTENOTITLE]] | ||
To update the AOF, note that for pseudopressure analysis neither ''a'' nor ''b'' changes as drainage area pressure changes. Therefore, the AOF for the new drainage area pressure is | To update the AOF, note that for pseudopressure analysis neither ''a'' nor ''b'' changes as drainage area pressure changes. Therefore, the AOF for the new drainage area pressure is | ||
[[File:Vol5 page 0850 eq 003.png]] | [[File:Vol5 page 0850 eq 003.png|RTENOTITLE]] | ||
A comparison ('''Fig. 4''') of the results from the two parts of this example shows that the Rawlins-Schellhardt equation appears to be valid for this range of test data; however, the line representing the Houpeurt equation deviates from the Rawlins-Schellhardt equation as BHFP decreases. Although the Rawlins-Schellhardt method is valid under many testing conditions, this deviation suggests that extrapolating the empirical equation over a large interval of pressure may not predict well behavior correctly. | A comparison ('''Fig. 4''') of the results from the two parts of this example shows that the Rawlins-Schellhardt equation appears to be valid for this range of test data; however, the line representing the Houpeurt equation deviates from the Rawlins-Schellhardt equation as BHFP decreases. Although the Rawlins-Schellhardt method is valid under many testing conditions, this deviation suggests that extrapolating the empirical equation over a large interval of pressure may not predict well behavior correctly. | ||
<gallery widths="300px" heights="200px"> | <gallery widths="300px" heights="200px"> | ||
| Line 105: | Line 108: | ||
== Nomenclature == | == Nomenclature == | ||
{| | {| | ||
|- | |- | ||
|'' | | ''a'' | ||
|= | | = | ||
|[[File:Vol5 page | | [[File:Vol5 page 0879 inline 001.png|RTENOTITLE]], stabilized deliverability coefficient, psia<sup>2</sup>-cp/MMscf-D | ||
|- | |- | ||
|'' | | ''b'' | ||
|= | | = | ||
| | | [[File:Vol5 page 0880 inline 001.png|RTENOTITLE]] (gas flow equation) | ||
|- | |- | ||
|'' | | ''C'' | ||
|= | | = | ||
| | | performance coefficient in gas-well deliverability equation, or wellbore storage coefficient, bbl/psi | ||
|- | |- | ||
|'' | | ''D'' | ||
|= | | = | ||
| | | non-Darcy flow constant, D/Mscf | ||
|- | |- | ||
|'' | | ''h'' | ||
|= | | = | ||
| | | net formation thickness, ft | ||
|- | |- | ||
|'' | | ''k''<sub>''g''</sub> | ||
|= | | = | ||
| | | permeability to gas, md | ||
|- | |- | ||
| | | ''p''<sub>''p''</sub> | ||
|= | | = | ||
| | | pseudopressure, psia<sup>2</sup>/cp | ||
|- | |- | ||
| | | [[File:Vol5 page 0781 inline 001.png|RTENOTITLE]] | ||
|= | | = | ||
| | | volumetric average or static drainage-area pressure, psi | ||
|- | |- | ||
|'' | | ''p''<sub>''wf''</sub> | ||
|= | | = | ||
| | | flowing BHP, psi | ||
|- | |- | ||
|''q'' | | ''q'' | ||
|= | | = | ||
| | | flow rate at surface, STB/D | ||
|- | |- | ||
|'' | | ''q''<sub>AOF</sub> | ||
|= | | = | ||
| | | absolute-open-flow potential, MMscf/D | ||
|- | |- | ||
| | | ''T'' | ||
|= | | = | ||
| | | reservoir temperature, °R | ||
|- | |- | ||
|''μ'' | | Δ''p''<sub>''p''</sub> | ||
|= | | = | ||
|viscosity, cp | | pseudopressure change since start of test, psia<sup>2</sup>/cp | ||
|- | |||
| ''μ'' | |||
| = | |||
| viscosity, cp | |||
|} | |} | ||
== References == | |||
< | <references /> | ||
== Noteworthy papers in OnePetro == | |||
Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read | Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read | ||
==External links== | == 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 == | ||
[[Deliverability testing of gas wells]] | |||
[[Deliverability_testing_of_gas_wells|Deliverability testing of gas wells]] | |||
[[Single-point_tests_for_gas_wells|Single-point tests for gas wells]] | |||
[[Isochronal_tests_for_gas_wells|Isochronal tests for gas wells]] | |||
[[ | [[Modified_isochronal_tests_for_gas_wells|Modified isochronal tests for gas wells]] | ||
[[ | [[Flow_equations_for_gas_and_multiphase_flow|Flow equations for gas and multiphase flow]] | ||
[[ | [[PEH:Fluid_Flow_Through_Permeable_Media]] | ||
==Category== | |||
[[ | [[Category:5.6.4 Drillstem or well testing]] [[Category:YR]] | ||
Latest revision as of 12:57, 6 July 2015
This page discusses the implementation and analysis of flow-after-flow testing for gas well deliverability assessment. Both the Rawlins and Schellhardt and Houpeurt analysis techniques are presented in terms of pseudopressures.
Flow-after-flow test procedure
Flow-after-flow tests, sometimes called gas backpressure or four-point tests, are conducted by producing the well at a series of different stabilized flow rates and measuring the stabilized BHFP at the sandface. Each different flow rate is established in succession either with or without a very short intermediate shut-in period. Conventional flow-after-flow tests often are conducted with a sequence of increasing flow rates; however, if stabilized flow rates are attained, the rate sequence does not affect the test. [1] The requirement that the flowing periods be continued until stabilization is a major limitation of the flow-after-flow test, especially in low-permeability formations that take long times to reach stabilized flowing conditions. Fig 1 illustrates a flow-after-flow test.
Fig. 1 – Pressure and flow rate history of a typical flow-after-flow test.
Rawlins-Schellhardt analysis technique
Recall the empirical equation that forms the basis for the Rawlins-Schellhardt analysis technique:
....................(1)
Taking the logarithm of both sides of Eq. 1 yields the equation that forms the basis for the Rawlins-Schellhardt analysis technique:
....................(2)
The form of Eq. 2 suggests that a plot of log (Δpp) vs. log (q) will yield a straight line of slope 1/n and an intercept of {–1/n[log(C)]}. The AOF potential is estimated from the extrapolation of the straight line to Δpp evaluated at a pwf equal to atmospheric pressure (sometimes called base pressure). This analysis technique is illustrated with Example 1.
Houpert analysis technique
Flow-after-flow tests require stabilized data or data measured during pseudosteady-state flow. Houpeurt[2] gives the theoretical equation for pseudosteady-state flow, which was derived from the gas-diffusivity equation, as
....................(3)
The coefficients a and b have theoretical bases and can be estimated if reservoir properties are known or they can be determined from flow-after-flow test data. Dividing both sides of Eq. 3 by the flow rate, q, and rearranging yields the equation that is the basis for the Houpeurt analysis technique:
....................(4)
The form of Eq. 4 suggests that a plot Δpp/q vs. q will yield a straight line with a slope b and an intercept a. The AOF is estimated in the Houpeurt deliverability analysis by solving Eq. 3 for q = qAOF at pwf = pb.
Example: Analysis of a flow-after-flow test
Estimate the initial stabilized AOF potential of a well[3] with the well and reservoir properties listed. Use both the Rawlins-Schellhardt and the Houpeurt analysis techniques. In addition, estimate the AOF potential 10 years later when the static drainage area pressure has decreased to 350 psia. Evaluate the AOF potential at pb = 14.65 psia. Table 1 summarizes the flow-after-flow test data. L = 3,050 ft, rw = 0.5 ft, Ma = 20.71 lbm/lbm-mole, T = 90°F = 555°R, A = 640 acres, ϕ = 0.25, CA = 30.8828, and h =200 ft.
Table 1
Current 
= 407.6 psia, pp( = 407.6) = 1.617 × 107 psia2/cp. after 10 years = 350 psia, pp( = 350) = 1.2239 × 107 psia2/cp. pb = 14.65 psia, pp(pb) = 2,674.8 psia2/cp.
The pseudopressure in this example (and all others in this section) were calculated using the methods suggested by Al-Hussainy et al.[4] These methods, which involve numerical evaluation of the integral in Eq. 5 and which require computational routines to estimate gas viscosity, μ, and deviation factor, z, are widely available in basic reservoir fluid flow analysis software.
....................(5)
Solution
Rawlins-Schellhardt analysis. Plot Δpp vs. q on log-log graph paper (Fig. 2). Table 2 gives the plotting functions. Construct the best-fit line through the data points. All data points lie on the best-fit line and will be used for all subsequent calculations.
Fig. 2 – Rawlins-Schellhardt analysis, Example 1.
Table 2
Next, determine the deliverability exponent using least-squares regression analysis. Alternatively, because Points 1 and 4 both lie on the perceived "best" straight line through the test data, the reciprocal slope is estimated to be
Now, calculate the AOF of the well. Because 0.5 ≤ n ≤ 1.0, calculate C using either regression analysis or a point from the best-fit straight line through the test data. Estimating C with regression analysis results in log(C) = α =-3.09 . Thus,
Estimating C using Point 4 from the best-fit line and Eq. 1:
Therefore, the AOF potential of this well is
To update the AOF to a new average reservoir pressure, recall that for pseudopressure analysis, neither C nor n changes as drainage area pressure decreases. The AOF for the new drainage area pressure becomes
Houpeurt analysis. Plot Δpp/q vs. q on Cartesian graph paper (Fig. 3). Table 3 gives the plotting functions. Construct the best-fit line through the last three data points. The first point, corresponding to the lowest flow rate, does not follow the trend and will be ignored in subsequent analyses.
Fig. 3 – Houpeurt analysis, Example 1.
Table 3
Determine the deliverability coefficients, a and b, from a least-squares regression analysis, excluding the first point. The result is
Alternatively, use Points 2 and 4 from the line drawn through the test data to calculate a and b:
Then,
To update the AOF, note that for pseudopressure analysis neither a nor b changes as drainage area pressure changes. Therefore, the AOF for the new drainage area pressure is
A comparison (Fig. 4) of the results from the two parts of this example shows that the Rawlins-Schellhardt equation appears to be valid for this range of test data; however, the line representing the Houpeurt equation deviates from the Rawlins-Schellhardt equation as BHFP decreases. Although the Rawlins-Schellhardt method is valid under many testing conditions, this deviation suggests that extrapolating the empirical equation over a large interval of pressure may not predict well behavior correctly.
Fig. 4 – Comparison of Rawlins-Schellhardt and Houpeurt methods.
Nomenclature
| a | = |  , stabilized deliverability coefficient, psia2-cp/MMscf-D
|
| b | = |  (gas flow equation)
|
| C | = | performance coefficient in gas-well deliverability equation, or wellbore storage coefficient, bbl/psi |
| D | = | non-Darcy flow constant, D/Mscf |
| h | = | net formation thickness, ft |
| kg | = | permeability to gas, md |
| pp | = | pseudopressure, psia2/cp |
|
|
= | volumetric average or static drainage-area pressure, psi |
| pwf | = | flowing BHP, psi |
| q | = | flow rate at surface, STB/D |
| qAOF | = | absolute-open-flow potential, MMscf/D |
| T | = | reservoir temperature, °R |
| Δpp | = | pseudopressure change since start of test, psia2/cp |
| μ | = | viscosity, cp |
References
- ↑ Rawlins, E.L. and Schellhardt, M.A. 1935. Backpressure Data on Natural Gas Wells and Their Application to Production Practices, Vol. 7. Monograph Series, USBM.
- ↑ Houpeurt, A. 1959. On the Flow of Gases in Porous Media. Revue de L’lnstitut Francais du Petrole 14 (11): 1468.
- ↑ Jennings, J. W. et al. 1989. Deliverability Testing of Natural Gas Wells. Prepared for the Texas Railroad Commission, Texas A&M U., College Station, Texas, August.
- ↑ Al-Hussainy, R., Jr., H.J.R., and Crawford, P.B. 1966. The Flow of Real Gases Through Porous Media. J Pet Technol 18 (5): 624-636. http://dx.doi.org/10.2118/1243-A-PA
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
Deliverability testing of gas wells
Single-point tests for gas wells
Isochronal tests for gas wells
Modified isochronal tests for gas wells
Flow equations for gas and multiphase flow
PEH:Fluid_Flow_Through_Permeable_Media