Factors effecting PI Factors effecting PI The expression for PI for for an oil well including skin effect, can be written as [ ] dp B k s r r P P h k J R wf P P o o ro w e wf R ∫ + − − = µ 75 . 0 ) / ln( ) ( 00708 . 0 It can be observed from above equation that the following factors can effect the behavior of PI : • Phase behavior of the reservoir fluids • Relative permeability behavior • Oil viscosity behavior • Oil formation volume factor behavior 50
Transcript
Factors effecting PIFactors effecting PI
The expression for PI for for an oil well including skin effect, can be written as
[ ] dpBk
srrPPhk
J R
wf
P
Poo
ro
wewfR∫+−−
=µ75.0)/ln()(
00708.0
It can be observed from above equation that the following factors can effect the behavior of PI :
• Phase behavior of the reservoir fluids
• Relative permeability behavior
• Oil viscosity behavior
• Oil formation volume factor behavior50
Saturation dependency of Saturation dependency of kkroro
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Pressure dependency of Pressure dependency of µµoo
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Pressure dependency of BPressure dependency of Boo
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Factors affecting IPRFactors affecting IPR
1. A decrease in kro as gas saturation increases
2. An increase in oil viscosity as pressure decreases and gas is evolved
3. Shrinkage of the oil as gas is evolved when pressure on the oil decreases
4. Formation damage or stimulation around the wellbore
5. An increase in turbulence with increasing oil rate
These factors can change either as a result of drawdown change at a constant value of PR or as PR declines because of depletion.
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Effects of drive mechanisms on IPEffects of drive mechanisms on IP
The source of energy to move oil and gas into the wellbore has asubstantial effect on both the performance of the reservoir and the total production. The basic drive mechanisms are
• Dissolved gas drive
• Gas cap drive
• Water drive
• Combination drive
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Dissolved gas driveDissolved gas drive
A dissolved gas drive reservoir is closed to any outside source of energy. The only source of material to replace the produced fluids is the expansion of the fluids remaining in the reservoir. Its pressure is usually at or above bubble point pressure and therefore no free gas exists. Some small but usually negligible expansion of the connate water and rock may also occur.
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Dissolved gas drive performanceDissolved gas drive performance
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Dissolved gas drive performance (continued)Dissolved gas drive performance (continued)
The reservoir pressure declines rapidly with production until PR=Pb , since the only mechanism to move oil is fluid expansion. During this period producing gas/oil ratio will be constant at Rs=Rsi . Since there is no free gas in the reservoir, f(PR) remains fairly constant.
Once PR declines below Pb , free gas will be available to expand, and PR will decline less rapidly. As a result of free gas, R and f(PR) will change rapidly in reverse directions.
Recovery at abandonment conditions will range between 5 to 30% of original oil in place.
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Gas cap driveGas cap drive
A gas cap drive reservoir is also closed from any outside source of energy. But there is a gas cap over the oil formation. As oil is produced the gas cap will expand and help to maintain the reservoir pressure. Also, as the reservoir pressure declines due to production, gas will be evolved from the saturated oil.
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Gas cap drive performanceGas cap drive performance
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Gas cap drive performance (continued)Gas cap drive performance (continued)
The reservoir pressure will decline more slowly than for a dissolved gas drive, but as the free gas cap expands, some of the upstructure wells will produce at high gas/oil ratios. Under primary conditions, the recovery may be between 20 to 40% of the original oil in place.
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Water driveWater drive
In a water drive reservoir, the oil zone is in contact with an aquifer that can supply the energy by replenishing the produced material. Usually the aquifer is connected to a surface outcrop. The oil will be undersaturated initially, formation of free gas will help the oil production.
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Water drive performanceWater drive performance
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Water drive performance (continued)Water drive performance (continued)
The recovery to be expected from a water drive reservoir may vary from 35 to 75% of the original oil in place. If the production rate is low enough to allow full water encouragement, recovery may be even higher.
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Combination driveCombination drive
In many cases, an oil reservoir will be both saturated and in contact with an aquifer. In this case all previously mentioned drive mechanisms will be contributing to oil production.
It is almost impossible to generalize on the expected recovery and performance of a combination drive reservoir because of the wide variety of combinations of aquifer and gas cap sizes.
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Comparison of formation pressure changeComparison of formation pressure change
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Comparison of GOR changeComparison of GOR change
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Present time Present time IPRIPR’’ss for oil wellsfor oil wells
Up to this point we talked about theoretical inflow equations. If all of the variables in the inflow equation could be available accurately, Darcy’s law cold be used to quantify the IPR. Unfortunately, sufficient information rarely exists especially at the earlier life of the reservoir to accomplish this. Therefore, empirical methods must be used to predict the pressure-inflow rate for a well.
We will mainly discuss Vogel and Vogel and FetkovichFetkovich equations and their modifications for future IPR predictions. Basic forms of the equations account for the effects of drawdown only. This means PR is assumed constant.
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VogelVogel’’s equations equation
Vogel reported the results of his study in which he used numerical simulation model to calculate IPR for oil wells producing from saturated reservoirs. The final equation for Vogel’s method was based on calculations made for 21 reservoir conditions21 reservoir conditions.
Although the method was proposed for saturated, dissolved gas saturated, dissolved gas drive reservoirs onlydrive reservoirs only, it has been found to apply for any reservoir in which gas saturation increases as pressure is decreased.
Vogel’s results are summarized in the following slides.
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IPR change with depletionIPR change with depletion
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Dimensionless IPR for depletion Dimensionless IPR for depletion
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IPR change with reservoir conditions IPR change with reservoir conditions
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Dimensionless IPR for changing res. conditions Dimensionless IPR for changing res. conditions
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VogelVogel’’s equations equation
After plotting dimensionless IPR curves for all the cases considered, Vogel arrived at the following relationship between dimensionless flow rate and dimensionless pressure (must be ratio of gauge pressuresmust be ratio of gauge pressures) :
2
max,
8.02.01
−
−=
R
wf
R
wf
o
o
PP
PP
qq
where
qo inflow rate corresponding to Pwf
qo,max inflow rate corresponding to zero wellbore flowing pressure
PR average reservoir pressure existing at the time of interest74
Vogel pointed out that in most applications of his method the error in inflow rate is less than 10%. But the error could be as high as 20% during the late stage of depletion. If the constant productivity index version of the equation
−=
R
wf
o
o
PP
qq 1max,
is used, the error increases to 70% to 80% at low values of Pwf . It has also been shown that Vogel’s method can be applied to wells producing water, oil, and gas with a small modification (qL=qo+qw) :
2
max,
8.02.01
−
−=
R
wf
R
wf
L
L
PP
PP
qq
Example #2 : VogelExample #2 : Vogel’’s method (s=0) s method (s=0)
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A well is producing from a reservoir having an average reservoirpressure of 2085 psig. A stabilized (pseudosteady state) production test on the well resulted in a producing rate of 282 STB/day when theflowing bottomhole pressure was 1765 psig. The bubble point pressure is 2100 psig. Using Vogel’s method, calculate :
a. The producing rate if Pwf is reduced to zero (qo,max)
b. The producing rate if Pwf is reduced to 1485 psig
c. The bottomhole pressure necessary to obtain an inflow rate of 400STB/day.
If we compare the results for both straight line and Vogel approaches, the difference is pronounceable at high flow rates :
1097109718481848qqo,maxo,max
1618161816451645PPwfwf @ q=400@ q=400
496496528528q @ q @ PPwfwf=1485 psig=1485 psig
VogelVogelConstant JConstant J
VogelVogel’’s method for s method for undersaturatedundersaturated reservoirsreservoirs
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Two different approaches must be considered to apply Vogel’s method to single phase reservoirs. Depending on the test flow rate and corresponding bottomhole flowing pressure, a test can be conducted either at PPwfwf ≥≥ PPbb (Test case #1) or PPwfwf < < PPbb (Test case #2) :
VogelVogel’’s method for s method for undersaturatedundersaturated reservoirsreservoirs
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Applying Vogel’s equation for any flow rate greater than the rate qb
(Pwf = Pb) :
( )
−
−−+=
−
−=
−−
2
max,
2
max,
8.02.01
8.02.01
b
wf
b
wfbobo
b
wf
b
wf
bo
bo
PP
PP
qqqq
PP
PP
qqqq
The reciprocal slope is defined as the change in flow rate with respect to the change in Pwf :
( )
−−−−=
∂∂−≡ 2max,
6.12.0
b
wf
bbo
wf
o
PP
Pqq
PqJ
VogelVogel’’s method for s method for undersaturatedundersaturated reservoirsreservoirs
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Evaluating the expression for J @ Pwf = Pb gives
( )b
bo
Pqq
J−
= max,8.1
This equation also establishes a relationship between J and qo,max for saturated reservoirs (Pb = PR and qb = 0),
8.1max,R
oPJq =
VogelVogel’’s method for s method for undersaturatedundersaturated reservoirsreservoirs
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Substituting the expression for qo,max in the main equation gives :
−
−+=
2
8.02.018.1 b
wf
b
wfbbo P
PPPPJqq
Once a value of J at Pwf ≥ Pb is determined, above equation can be used to generate an IPR.
Procedure for test case #1 (Procedure for test case #1 (PPwfwf ≥≥ PPbb))
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1. Calculate J using test data in
wfR
o
PPqJ−
=
( )bRb PPJq −=
2. Calculate qb using
3. Generate IPR for values of Pwf < Pb using
−
−+=
2
8.02.018.1 b
wf
b
wfbbo P
PPPPJqq
4. The IPR for Pwf ≥ Pb is linear.
Example #3 : Example #3 : UndersaturatedUndersaturated reservoir reservoir PPwfwf > > PPbb
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The following data pertain an unsaturated reservoir :
PR = 4000 psig
Pb = 2000 psig
S = 0
Stabilized flow test results are
Pwf = 3000 psig
qo = 200 STB/day
Generate IPR behavior of the reservoir using Vogel’s model.
In the previous slides we defined flow efficiency as
drawdownactualdrawdownideal
PPPP
EwfR
wfRF =
−−
='
'
'
JJE
JqJq
E
F
F
=
=
In terms of productivity index flow efficiency becomes
Vogel method with sVogel method with s≠≠0 (continued)0 (continued)
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Vogel’s equation may be written using previous definitions as
2''
1max,
8.02.01
−
−==
R
wf
R
wfEo
o
PP
PP
qqF
where qo,max term is the maximum inflow which could be obtained for the well if EF = 1 or S = 0.
From the definition of EF, we can find the following equation :
+−=
R
wfFF
R
wf
PP
EEPP
1'
VogelVogel’’s IPR as a function of Es IPR as a function of EFF
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Vogel method with sVogel method with s≠≠0 (continued)0 (continued)
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The previous graph can be put into equation form as
22
max,
1)(8.018.1
−−
−=
R
wfF
R
wfF
o
o
PP
EPP
Eqq
Because of the restriction that Pwf’≥ 0, above equation is valid only if
−≥≤ =
FRwf
Eoo E
PPorqq F111
max,
This restriction will always be satisfied if EF ≤ 1.
Vogel method with sVogel method with s≠≠0 (continued)0 (continued)
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For values of EF > 1, calculations at higher drawdown must be checked if the criteria holds. If not then the following approximation may be used to calculate the maximum flow rate :
( )FEoo Eqq F 376.0624.01max,max, += =
For the case of EF = 1 (Pwf = Pwf’ ),
derived equation is identical to Vogel’s equation.
Example #4 : StandingExample #4 : Standing’’s modificationss modifications
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Use the following data and construct an IPR for this well for the present conditions and for a possible value after a successful frac job :
Complex flow regimes existing around the wellbore may not be predicted by Vogel equation. Bendaklia and Aziz used a complex reservoir model to generate IPR’s for a number of wells and found that the Vogel equation would fit the generated data if expressed as
n
R
wf
R
wf
o
o
PP
VPP
Vqq
−−
−=
2
max,
)1(1
In order to apply this equation at least three stabilized tests are required to evaluate the three unknowns, qqo,maxo,max ,V ,V and nn.
FetkovichFetkovich methodmethod
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Fetkovich proposed a method for calculating inflow performance for oil wells using the same type of equation that has been used foranalyzing gas wells for many years. The procedure was verified by analyzing isochronal and flow-after-flow tests conducted in reservoirs with permeabilities ranging from 6 md to greater than 1000 md. Pressure conditions ranged from highly unsaturated to saturated at initial pressure and to a partially depleted field with a gas saturation above the critical. In all cases oil-well backpressure curves were found to follow the same general equation :
nwfRo PPCq )( 22 −=
where
C is the flow coefficientn is exponent depending on well characteristics
The value of n ranged from 0.568 to 1.000 for the 40 field tests. It is understood today that the exponent n accounts for the effect of n accounts for the effect of highhigh--velocity flowvelocity flow and pressure squared function accounts for pressure squared function accounts for the effect of simultaneous twothe effect of simultaneous two--phase flowphase flow.
The applicability of Fetkovich’s equation to oil wells was justified by writing Darcy’s equation in integral form :
