Pre Frac Injection Tests - Barree
76
Pre‐Frac Injection Tests R.D. Barree
Transcript of Pre Frac Injection Tests - Barree
Pre‐Frac Injection Tests
R.D. Barree
Presenter
Presentation Notes
Pre-frac injection/falloff tests provide one of the most useful methods for determining stresses, pore pressure, and leakoff data. The correct execution and interpretation of these tests is critical to fracture design and is considered a part of the GOHFER® process.
© 2009
In this session …
• Discuss DFIT requirements and procedures– Look at SRT Analysis
– Pressure loss at Perfs
– Near‐Wellbore Pressure Loss
– Look at Post Shut‐In Analysis
– discuss G‐function analysis in detail• Importance of correct determination of closure
• Pore pressure and permeability
• Efficiency and Leakoff
• Discuss the effects of Variable Storage and Tip Extension
Presenter
Presentation Notes
In this section we will discuss the requirements for diagnostic fracture injection tests (DFIT) including step-rate test (SRT) analysis, falloff prior to fracture closure, and after-closure pressure transient decline analysis. Various methods for analysis will be presented with special emphasis on the dimensionless G-function.
© 2009
Diagnostic Fracture Injection Test:
DFITRequirements:• Data Acquisition
– 0.01‐0.1 psi resolution surface gauge
– Record all rates and pressures at 1/sec sampling rate
– Injection schedule must be precisely recorded
• Use Newtonian, non‐wall building fluid (water, oil, or N2).
Procedure:• Bring rate to max• Pump for 2‐5 minutes• Rapid step‐down to get WHP at each rate
• Isolate wellhead• Shut‐down for 90 minutes (minimum) or up to 48 hrs
Presenter
Presentation Notes
The key requirements for the pre-frac injection test are outlined above. High resolution pressure recording is mandatory. Normal service company resolution of 5 to 10 psi is unacceptable. The actual rate versus time is critical to match the simulator results with the observed pressures. A minimum shut-in time is required to analyze the injection test. A shut-in time of 10 times the injection time gives a G value of ~10 which is sufficient to see closure in most reservoirs. Longer is better. Work by Chu at Marathon has shown that, if closure is confirmed, then traditional pressure transient analysis of impulse tests may be used to determine reservoir properties. This is one of the main reasons to specify that the tests be conducted with Newtonian, non-wall building fluids. The reservoir properties in the vicinity of the wellbore are the primary factors that we wish to determine from the pre-frac treatment and not the instantaneous leak-off that we can achieve with various fluid additives. In fact, this is a second issue which will be addressed in the future: If we understand the reservoir then we can evaluate the use of fluid additives to systematically alter the fluid flow characteristics in the reservoir. Nothing precludes the application of this approach today other than the time and costs associated with additional injection tests in the reservoir. The first step is to inject a fluid that investigates the basic reservoir characteristics and second is how to modify these properties with fluid additives.
© 2009
Pre‐Frac Injection/Falloff Tests
Why pre‐frac test?
• obtain specific data
– Characterize the reservoir and completion
• every pump‐in carries risk of damage
– testing procedure must be designed to minimize damage
Types:• Step‐rate injections
– pipe and near‐well friction
– # of effective perfs open– frac extension pressure
• Pressure falloff after shut‐in– frac closure pressure– fluid efficiency and leakoff coefficient
– fracture closure mechanism
Presenter
Presentation Notes
Pre-frac testing is conducted to provide specific diagnostic information about the reservoir, wellbore, fluid, and completion geometry. Various data can be obtained from different types of tests. The testing procedure must be designed to provide the maximum amount of critical data for the least cost, in terms of induced fluid damage and perturbation of the reservoir system. Every injection carries the risk of inducing some damage or alteration in the native stress and saturation state. The more complex and potentially damaging the fluid system becomes, the more the chance to overwhelm the data that is being extracted increases. In the past, pre-frac testing has been directed toward characterizing the frac fluid itself. The philosophy recommended here attempts to characterize the reservoir and completion, while sacrificing information about the fluid.
© 2009
Application of Pre‐Frac Tests
• Calibration of logs:– Total closure stress
• Mechanical properties
• Tectonic strain and stress
• Net fracture extension pressure– Frac width– Height containment– Created fracture length and width
• Leakoff– Pad volume requirements
– Maximum sand concentration
• Overall design– Expected pack concentration
– Final fracture conductivity
– Necessary frac length for optimum stimulation
If you’re going to do this, you’d better do it right!
Presenter
Presentation Notes
As Ken Nolte pointed out in his keynote address in College Station (Feb 2007), the results of pre-frac tests determine practically every input and output of our fracture design process. They determine the expected frac geometry, conductivity, formation flow capacity, and optimum frac design as well as the means necessary to place the design. Because these parameters are so critical, it is imperative that the analysis is done correctly. In my personal experience, there are far too many self-avowed experts doing the analysis incorrectly and adding tremendous doubt and confusion to the fracturing industry, as well as casting doubt on the validity of the analysis methods and fracture design modeling in general.
© 2009
Pre‐Frac Step‐Rate Injection Test
Presenter
Presentation Notes
The plot shows actual data from an extended injection/falloff test. This test was somewhat longer than usual but shows the main features of the step-rate test (SRT) and falloff.
© 2009
Traditional Step Rate Test(SRT) Analysis
Presenter
Presentation Notes
The conventional step-rate test (SRT) analysis plots observed pressure versus pump rate. A break in the curve indicates fracture extension pressure. The slope of the curve after breakdown indicates overall friction in the fracture and wellbore. In this case, the data are plotted for both increasing and decreasing rates. The hysteresis in the curve illustrates changes in net pressure and fracture extension conditions that occurred during pumping.
© 2009
System Friction Analysis from SRT Data
• Step‐down data preferred– pressure response to rate changes should be related to frictional components
• Requires accurate pipe friction estimate
• Additional rate‐dependent pressure drop caused by– perforation
• Square of the rate
– near‐well flow restriction• Square root of rate
Presenter
Presentation Notes
There are various ways to analyze step-down data to determine perforation and near-well friction. The step-down data are preferred since the fracture is created and fully inflated, and the dynamic pressure response to rate changes should be related almost completely to frictional components. Any step-down analysis conducted on surface pressure data requires an accurate pipe friction estimate first. Once this is accounted for, any additional rate-dependent pressure drop is caused by perforation and near-well flow restrictions. Perf pressure drop is related to the square of rate while tortuosity is generally related to the square-root of rate. This allows the two effects to be separated when multiple rate data are available.
© 2009
Presenter
Presentation Notes
The model above shows a discrete match of each frictional component over the entire step-rate test.
© 2009
Resolving Components of Friction
• Pipe friction– Generally varies with rate^2 in turbulent flow– Must know the pipe friction to separate it from BH and near‐well friction
• Perf friction– Varies with rate^2– Changes with sand injection
• CD change and perf rounding• Diameter change and perf erosion
• Tortuosity– Varies with rate^0.5 (or some other factor)– Some restriction that dissipates with injection rate
Presenter
Presentation Notes
The observed surface pressure is removed from the actual fracture pressure by various frictional components, as well as hydrostatic head. The first priority in understanding near-well pressure drop is to accurately characterize the pipe friction. This is important because the pipe friction increases generally with the square of pump rate, the same as perforation friction. So, unless the pipe friction can be accurately determined, there will be a direct error in the “holes open” calculation stemming from the result. Near-well tortuosity is easier since it tends to increase more slowly as rate increases. Generally a 0.5 power is applied, although sometime a variable exponent is used.
© 2009
Pipe Friction Estimates
WaterSlick-water (FR)20# Linear gel
40# gelGelled Oil
70Q N2 Foam
Data calculated for 2-7/8” tubing
Presenter
Presentation Notes
Pipe friction estimates can be made from many models. The data above come from a correlation that is still under development. This model is based on the power-law parameters of the fluid and has been used successfully for many fluid systems. The shape of the curves shows the characteristic shift from laminar to turbulent behavior at low rate.
© 2009
Perforation Restriction Causes Large Pressure Drop
• Correct number & size of perfs can be estimated
• Pressure drop should be at least 100‐200 psi more than the confining stress between zones
• Also depends on coefficient of discharge (CD)– Jet perfs: 0.754; Bullets: 0.822
– higher value indicates more efficient perf
psidNCq
PppD
fpf ;
975.1422
2ρ=
Presenter
Presentation Notes
Pressure drop through the perfs can be a significant part of the total pressure drop experienced in the flow system. In limited entry fracturing operations, the correct number and size of perforations can be estimated so that injected fluid is distributed over several sets of perforations. Efficient fluid diversion can be accomplished by designing for a pressure drop of around 400 psi through the perforations, depending on the difference in confining stress between the various zones being treated. Ideally, the pressure drop through the perforation should be at least 100-200 psi more than the stress contrast between zones. In some cases, the perforation size and number may be selected to deliver a desired fraction of the total rate to each zone. On average, a pressure drop of this magnitude requires about 1-3 bpm injection rate per perforation for average perforation sizes. The pressure drop through the perfs also depends strongly on the coefficient of discharge CD. Perforation entry coefficients have been estimated for various types of perforators. Jet perforations have a reported entry coefficient of 0.754, compared to 0.822 for bullets. A higher value of the entry coefficient indicates a more efficient perforation. Some authors have reported values as low as 0.5 for jets and 0.7 for bullets. Remember that a minimum perforation size must be maintained to prevent proppant bridging. In the equation above: Ppf = Pressure drop at perfs, psi q = the total pump rate, bpm f = the slurry density, g/cc CD = the perforation coefficient Np = the number of open perforations dp = the perf diameter, inches
© 2009
Tortuosity:Near‐Wellbore Pressure Loss
• Stress halo around perf• Flow around cement micro‐annulus
• Perforation interference• Narrow fracture width• Fracture turning and branching (multiples)
• Off‐vertical fractures• Pulverized cement debris• Charge debris• Leakoff into drilling and perf induced fracs
Presenter
Presentation Notes
A common practical problem associated with fissured or fractured reservoirs is near-wellbore pressure loss or “tortuosity” effects. These include a variety of mechanisms that result in excess injection pressure and an apparently severe restriction to fluid entry from the wellbore to the propagating fracture. The figure illustrates several of the possible causes for this effect. Numerous published experimental studies indicate that hydraulic fractures initiated in cased, cemented, and perforated completions do not extend from the perforation tips. Instead, the injected fluid generally flows around a cement-formation micro-annulus and initiates the fracture at an intersected plane of weakness, or in the orientation defined by the principal in-situ stress field. Frequently the near-wellbore area is also the site of numerous fractures induced by the drilling and completion process. These fractures can complicate the near-well environment including the fracture initiation orientation and local fluid flow.
© 2009
Current SRT Spreadsheet
Presenter
Presentation Notes
Rather than analyzing the entire injection test second-by-second, a more common technique uses only the points when rate and pressure are held constant at each step-down. The analysis is currently conducted in a spreadsheet program installed with GOHFER®. This analysis will be described in the exercises and will be incorporated into GOHFER® in future versions.
© 2009
Post Shut‐In:What is G‐function Analysis?
• Post shut‐in pressure decline analysis using dimensionless function
• Extends the analysis through use of the first derivative and semi‐log derivative of BHP (dP/dG and GdP/dG)
• Also uses the characteristic shapes of derivative curves to locate specific modes of pressure decline
• Extension to After‐Closure Analysis (ACA) to define reservoir linear and pseudo‐radial flow
Presenter
Presentation Notes
Post shut-in pressure decline analysis can be accomplished using several techniques. One method that minimizes ambiguity and provides a large amount of information about the leakoff mechanism and in-situ stress state is the G-function derivative analysis approach. This process uses a dimensionless falloff time and various derivative curves to identify leakoff mechanisms and closure stresses from characteristic shapes of the curves. The method can also be used to identify transient flow regimes so that additional after-closure analysis can be performed on select data.
© 2009
G‐function Analysis inPre‐Completion Decision Making
• Estimate pore pressure– Is the zone depleted, normally pressured or over‐pressured
– Impacts reserve estimates and cleanup
• Detection of natural fractures– Significance to fracture placement– Do they impact flow performance?
• Estimation of permeability• Determine leakoff mechanism and magnitude• Combine reservoir and fracture data to make realistic estimates of post‐frac rate
Presenter
Presentation Notes
The relatively simple pre-frac injection test can provide information on reservoir pressure, permeability and reservoir characteristics. Putting these together with realistic fracture cleanup and conductivity estimates allows forecasting of post-frac performance. This method can be used to make economic decisions regarding completion and stimulation of questionable zones and allows high-grading of completion options.
© 2009
Algebraic Definition of the G‐Function
G-function is a dimensionless function of shut-in time normalized to pumping time:
( ) ( )( )04 gtgtG DD −Δ=Δπ
( ) ppD tttt −=Δ
Presenter
Presentation Notes
Pressure decline analysis after fracturing has traditionally been accomplished through some shut-in time-function. The G-function is a dimensionless time function relating shut-in time (t) to total pumping time (tp) (at an assumed constant rate).
© 2009
G‐Function: Two limiting cases•Low Leakoff, high efficiency
•Fracture area open varies approximately linear w/time
(α = 1.0 )
•High leakoff, low efficiency
•Fracture area varies w/ square‐root of time
(α = 0.5)
( ) ( )( )5.15.1134
DDD tttg Δ−Δ+=Δ
( ) ( ) ( )( ) 5.05.01 1sin1 DDDD ttttg Δ+Δ+Δ+=Δ −−
Presenter
Presentation Notes
Two limiting cases for the G-function are shown here. The case of a=1.0 is for low leakoff, or high efficiency where the fracture area open after shut-in varies approximately linearly with time. The equation for a=0.5 is for high leakoff, or low efficiency fluids, where the fracture surface area varies with the square-root of time after shut-in. The value of g0 is the computed value of g at shut-in. The basic G function calculations are conducted with the equations given above. One of the key variables identified by Nolte is the difference between a high efficiency (upper limit) and a low efficiency (lower limit) leak-off condition. One of the surprises is the small effect that these two conditions have on the qualitative shape of the curves.
© 2009
Falloff Analysis Methods
• Observed shut‐in pressure versus square‐root of shut‐in time (Sqrt(t) Plot)– Use of diagnostic
derivatives on Sqrt(t) plot
• G‐Function and its diagnostic derivatives
• Log‐Log plot of pressure change after shut‐in versus time after shut‐in
After Closure analyses to define reservoir properties:
– Flow regime identification
– Horner analysis– Talley‐Nolte method
Presenter
Presentation Notes
Post shut-in pressure decline analysis can be accomplished using several techniques. The most commonly used (and mis-used) has been the pressure vs. Sqrt(t) plot. While this plot can be very useful, it is frequently misinterpreted and has led to many errors in closure determination and endless arguments about the actual net pressure required to extend a fracture. By using the plot correctly, and in concert with other analysis methods, the correct closure can be determined with minimal ambiguity (in most cases). The various analysis methods listed will be described in detail. A correct closure pick must satisfy all the diagnostics simultaneously and consistently. Once closure is correctly identified, various methods are available to determine reservoir properties such as transmissibility and reservoir pressure. Using these methods accurately first requires identification of the reservoir transient flow regimes that occur after closure.
© 2009
Evaluated Pressure Falloff Cases
1. Fracture extension after shut‐in
2. Constant leakoff in a well‐confined fracture with tip recession during closure
3. Pressure dependent leakoff
4. Pressure dependent leakoff and modulus
5. Leakoff with variable storage or fracture compliance (transverse storage)
Presenter
Presentation Notes
Five basic cases, which are listed above, were analyzed to determine the pressure decline signature which would result on a G-function plot. Each was found to exhibit a specific and identifiable response on the G-function vs. Pressure plot or one of its derivatives. Some additional cases have been added since the original work of Barree and Mukherjee was completed. These will be described later.
© 2009
Ambiguous Closure Using Sqrt(t) Analysis
Sqrt(Shut-in Time)
Pre
ssur
e 1
2
3
4
5
6
Which one is closure?
Presenter
Presentation Notes
The problem with any analysis technique is that the signature for closure has not been rigorously defined, or if it has, it has not been universally accepted. At the 2007 SPE Hydraulic Fracturing Conference in College Station, Texas, Ken Nolte showed a similar figure to illustrate the various “closure” points used by different practitioners in the industry. There is only one correct closure pressure and time. Unfortunately, there are many possible incorrect results that can, and are, frequently used. For normal constant-fracture-area, matrix-dominated leakoff the inflection point (3) is the correct closure. Use of the first derivative of pressure wrt. Sqrt(t) is helpful in locating the inflection point; but this method does not provide the correct closure in all cases, as will be shown. The same ambiguities can exist with any diagnostic plot for closure determination. A consistent method, using all diagnostic methods in concert, is needed to determine the correct closure point without ambiguity.
© 2009
Normal Leakoff G‐Function
Presenter
Presentation Notes
The G-function analysis of the previous data shows as close to ideal constant matrix leakoff as can usually be seen in a real field case. Note the linear response of the superposition derivative curve throughout most of the leakoff, up until closure. The derivative is influenced by non-linear transients, and possible slight PDL, out to a G-function value of about 1.5. After that it indicates a constant leakoff, as expected. Fracture closure occurs at about a G-function value of 2.5 as shown by the departure of the superposition curve from the straight line through the origin and the change in slope of the dP/dG curve. The tangent to the semi-log derivative must intercept the origin at G=0.
© 2009
Sqrt(t) Plot for Normal LeakoffP
ress
ure
Der
ivat
ives
Time
Presenter
Presentation Notes
Closure is indicated on the Sqrt(t) plot by the inflection point, as determined by the peak of the first derivative. The early slight PDL or afterflow generates a double hump on the first derivative. The semi-log derivative helps to clarify the behavior and indicates the correct closure
© 2009
Log‐Log Plot for Normal Leakoff
2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 90.1 1 10 100 1000
Time (0 = 8.15)
2
3
4
5
6789
2
3
4
5
6789
2
3
4
10
100
1000
(m = -1)
(m = 0.632)
BH ISIP = 9998 psi 1
Del
ta-P
ress
ure
and
Der
ivat
ive
Presenter
Presentation Notes
The log-log plot of the change in pressure with change in time after shut-in for the normal leakoff case is shown. This plot is extremely powerful in that it can be used to determine fracture closure, leakoff mechanism and transient flow regime, and after-closure transient flow regimes in the reservoir. The fracture closure from the previous G-function and Sqrt(t) plots is shown by [1]. Note that the pressure derivative and pressure difference curves are parallel and approximately ½ slope up until closure. This corresponds to the formation linear flow period and is consistent with the typical model of fracture fluid leakoff under one-dimensional linear flow with constant pressure boundary conditions. The reservoir pseudo-linear flow regime (not present in this test) is shown after closure by a -1/2 slope of the derivative. The reservoir pseudo-radial flow regime is indicated by a -1 slope of the derivative.
© 2009
Summary of Characteristic Slopes on Log‐Log Plot
Presenter
Presentation Notes
The table summarizes the characteristic slopes of the curves on the log-log plot for each flow regime. Cases have been observed where the pressure derivative maintains a near-zero slope after closure. The flow regime responsible for this signature has not yet been identified.
© 2009
Fracture and Reservoir Transient Flow Regimes
Fracture Linear Flow(Tip-Extension, ½ slope)
Bi-Linear Flow (Before closure, ¼ slopeAfter closure, -3/4 slope)
Pseudo-Radial Flow(After closure, -1 slope)
Formation Linear Flow(Before closure, ½ slopeAfter closure, -½ slope)
Presenter
Presentation Notes
For a vertical fractured well various transient flow regimes will be encountered after the injection test, during leakoff to closure, after closure, and during production: Fracture linear flow represents a flow regime dominated by fracture storage. Most of the flow comes from expansion of the fluid in the fracture or change in fracture width during closure. Bilinear flow represents fluid flowing from the fracture along linear flow paths normal to the fracture face and linearly along the fracture. Formation linear flow represents a period of linear flow when the predominant flow paths in the formation are normal to the fracture plane. Pressure gradients within the fracture are negligible during this time. The radius of investigation of the pressure transient has not progressed far enough into the reservoir to behave as a radial flow geometry. In pseudo radial flow, the effects of the fracture are not felt and the transient performance resembles a radial flow geometry. In this flow regime the far-field reservoir properties can be determined from the dissipation of the pressure transient.
© 2009
After‐Closure Flow Regime Plot
2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 90.001 0.01 0.1 1
Square Linear Flow (FL^2)
2
3
4
56789
2
3
4
56789
2
3
4
56789
10
100
1000
10000
(m = 1)
Del
ta-P
ress
ure
and
Der
ivat
ive
ΔP=(pw-pr)
Start of Radial Flow
ΔP vs. FL2
FL2 dΔP/dFL
2 vs. FL2
Presenter
Presentation Notes
The log-log plot of pressure minus assumed reservoir pressure, versus the square of the linear flow time function can be used to identify the after-closure flow regimes. The analysis depends on an accurate closure pick. The pressure difference curve is completely dependent on the value of reservoir pore pressure used, but the pressure derivative is insensitive to the pressure estimate. For this reason the method is iterative and the pressure derivative should be used for all initial analyses. On the plot the linear flow period is identified by a ½ slope of the pressure derivative. If the correct pore pressure is used then the pressure difference curve will also fall on a ½ slope and be 2x higher in magnitude than the derivative. During the radial flow period, both curves will lie on the same unit slope line if the pressure estimate used for the pressure difference function is correct. In this example, there is no reservoir pseudo-linear flow regime and the system transitions from closure directly to radial flow.
© 2009
After‐Closure Analysis
Vi: bblsk: mdtc: minMR: psi-1h: ftμ: cp
Pre
ssur
e
Radial flow time function
RESULTS:Reservoir Pressure = 7475.68 psi
Transmissibility, kh/μ =298.94991 md*ft/cpkh=7.94014 md*ft
Permeability, k = 0.0968Start of Pseudo Radial Time = 2.15 hours
⎥⎦
⎤⎢⎣
⎡=
cR
i
tMVkh 000,251
μ
Presenter
Presentation Notes
Once the radial flow regime has been identified, the Cartesian plot of pressure versus the radial flow time function can be constructed. A straight line through the appropriate data in the radial flow period is constructed. The intercept gives pore pressure. The slope is related to transmissibility as shown previously. In this case, the pore pressure is 7475 psi and kh/m =300 md-ft/cp. Note that the far-field transient is dominated by the reservoir fluid viscosity as the radial-flow regime is far outside the area invaded by the injected fluid. Knowing net pay height and reservoir fluid viscosity, the permeability can be determined.
© 2009
Horner Analysis: Only Valid in Pseudo‐Radial Flow
2 31
Horner Time
7250
7500
7750
8000
8250
8500
8750
9000
9250
9500
9750
(m = 14411)
(Reservoir = 7476)
1
P*=7476 psikh/μ=298 md-ft/cpkh=7.9 md-ftk=0.097 md
( )Hm
qkh 14406.162=
μ
q: bpmk: mdmH: psi-1h: ftμ: cp
Presenter
Presentation Notes
If a pseudo-radial flow regime is identified on either the Talley-Nolte plot or the log-log pressure derivative plot, then the Horner analysis can be used directly to obtain pore pressure and transmissibility. In the figure, the Horner slope through the radial flow data is 14411 psi. Using an average pump rate of 18.4 bpm, kh/m = 298 md-ft/cp. For the assumed gas viscosity kh=7.9 md-ft. Using the same assumed net gives k=0.097 md. This result is consistent with the ACA results. The conventional Horner analysis uses a Cartesian plot of observed pressure versus Horner time, (tp + Dt)/Dt, with all times in consistent units. The fracture propagation time is tp and the elapsed shut-in time is Dt. As shut-in time approaches infinity the Horner time function approaches 1. A straight-line extrapolation of the Horner plot to the intercept at a Horner time of 1.0 gives an estimate of reservoir pressure. The slope of the correct straight-line extrapolation, mH, can be used to estimate reservoir transmissibility: The flow rate in the equation is assumed to be in barrels per minute and is the average rate for the time the fracture was extending. The viscosity is the far-field mobile fluid viscosity. The propagation of the transient in pseudoradial flow occurs at a great distance from the fracture and is not affected by the injected fluid viscosity. The major problem with the Horner analysis is that the results are only valid if the data used to extrapolate the apparent straight line are actually in fully developed pseudoradial flow. There is no way to determine the validity of the Horner analysis or to determine the flow regime within the Horner plot itself.
© 2009
Permeability Estimation from G at Closure (Gc)
• Good estimate when after‐closure radial‐flow data not available
96.1
038.0
01.00086.0
⎟⎠⎞
⎜⎝⎛
=pc
t
z
rEGc
Pk
φ
μ
Where:k = effective perm, mdμ = viscosity, cpPz = process zone stress
or net pressureφ = porosity, fraction
ct = total compressibility, 1/psiE = Young’s Modulus, MMpsirp = leakoff height to gross frac height ratio
Presenter
Presentation Notes
If a relationship between G-function and flow rate exists, then it is reasonable to expect a correlation between permeability and G-function. The equation shown was developed empirically but has been tested in many cases and gives a good estimate of permeability when after-closure radial-flow data are not available. Note that formation height and frac length do not appear in the equation. The dimensionless time to closure is a function of the volumetric efficiency of the fluid and the volume to surface area ratio of the created frac. The surface area can be a large H and small Xf or the inverse and the closure results will be the same. Things that change the rate of fracture surface-area growth, like process-zone stress, modulus, and net-to-gross ratio are important. The value returned from the relation is k and not kh.
© 2009
Permeability Estimate from G‐at‐Closure ‐ Illustrated
Per
mea
bilit
y, m
d
Gc
Estimated Permeability = 0.0974 md
Presenter
Presentation Notes
Using the data from the example, the permeability is estimated to be 0.097 md. This is in close agreement with the more direct measurements. Note that the viscosity used in this analysis is an approximation of the injected fluid viscosity corrected for relative permeability effects in the invaded region around the fracture. Leakoff up until closure is dominated by the mobility of the injected fluid more than the far-field reservoir properties. The reservoir effects are handled through the compressive storage term made up of porosity and total reservoir compressibility (Ct). The reservoir compressibility includes pore volume compressibility and all fluids, adjusted for their saturations. The variable Pz is defined as the process-zone stress or net fracture extension pressure. It is obtained from the observed ISIP minus the closure pressure for the fracture. Higher values of Pz imply increased resistance to fracture extension and greater width with less surface area generated per volume of fluid injected. This leads to more stored fluid in the fracture at shut-in and less permeable area available for leakoff. The result is that closure time is longer than for the same permeability reservoir and injected fluid volume with a lower Pz value.
© 2009
Computation of
Efficiency and Leakoff Coefficient• Efficiency is given by:
• Leak‐off is given by:
c
c
GG+
=2
η
dGdP
tErhC
ppL π
2=
These equations are only valid with nopressure dependent behavior during closure.
Presenter
Presentation Notes
For constant leakoff, with no pressure dependence, efficiency can be estimated from the value of the G-function at closure (usually an extrapolation of a straight line portion of the pressure falloff curve). Also, for constant fracture height, constant modulus, and constant leakoff, the overall leakoff coefficient can be estimated from the equation shown. In this equation h=frac height (ft), rp=permeable area/total frac area, E=Young’s Modulus (psi), tp=pumping time (minutes), and dP/dG has already been defined as the value of the pressure versus G derivative.
© 2009
Typical PDL Behavior of G‐Function Derivatives
P vs. G
Fracture Closure
GdP/dG vs. G
End PDL
dP/dG vs. G
Pre
ssur
e
Der
ivat
ives
Presenter
Presentation Notes
This example illustrates a typical case of moderate pressure dependent leakoff (PDL). The total main-fracture closure stress is 9150 psi at G=2.45. The fissure opening pressure is 9300 psi at G=2.1. The fissure opening pressure is clearly indicated by the sharp break in the pressure derivative curve. This break corresponds to the end of a “hump” on the semi-log derivative curve, following which the pressure data become linear with G. This early-time hump above the extrapolated straight-line on the superposition curve, along with the sharply curving pressure derivative, is a clear signature for pressure dependent leakoff. After fissure closure the pressure derivative is constant, and the superposition curve (semi-log derivative) is linear (constant slope), both indicating constant leakoff coefficient. The pressure data alone provide a much less clear indication of the end of pressure dependent leakoff.
© 2009
Log‐Log Plot for PDL Example
2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 90.1 1 10 100 1000
Time (0 = 9.133333)
2
3
4
5
6789
2
3
4
5
6789
2
10
100
1000
(m = 0.5)
(m = -1)
(m = -0.5)
BH ISIP = 10000 psi 1
ΔP vs. Δt
ΔtdΔP/dΔt vs. Δt
Fracture closure
Linear Flow
Radial Flow
Pre
ssur
e D
iffer
ence
and
Der
ivat
ive
Presenter
Presentation Notes
The linear-flow dominated leakoff transient after the end of PDL is shown on the log-log plot by the ½ slope of the pressure derivative. Closure of the main fracture falls at the end of the ½ slope line. After closure the far-field transient behavior is not affected by the fissure leakoff as all secondary fractures are closed and the system permeability is constant. As with normal leakoff the reservoir linear flow period is shown by a -1/2 slope of the derivative and pseudo-radial reservoir flow is indicated by a -1 slope.
© 2009
Sqrt(t) Plot for PDL Example
1/24/200700:20 00:40 01:00 01:20 01:40
1/24/200702:00
Time
8250
8500
8750
9000
9250
9500
9750
10000
10250
0
100
200
300
400
5001False Closure
Pre
ssur
e
Der
ivat
ives
P vs. √t
√tdP/d√t vs. √t
dP/d√t vs. √t
Fracture Closure
Presenter
Presentation Notes
The first derivative peak, or inflection point on the P vs. Sqrt(t) plot responds primarily to the PDL event and does not give an accurate indication of fracture closure. The false closure is indicated on the plot. If the semi-log derivative is constructed for the Sqrt(t) plot then the PDL “hump” is clearly identified and the false early closure pick can be avoided. Actual closure, synchronized in time to the G-function closure, is clearly indicated by the departure from the straight-line through the origin on the derivative axis. The Sqrt(t) semi-log derivative also shows the characteristic PDL hump and the fissure opening pressure. The Sqrt(t) first-derivative analysis frequently leads to incorrect estimates of closure stress and net fracture extension pressure in PDL cases. In this case the first derivative is nearly useless in determining closure.
© 2009
Estimation of PDL Coefficient from Falloff Data
CC
dPdG
dPdG
orCC
C P
p
o P P P P
p
odp
fo fo
= ⎛⎝⎜
⎞⎠⎟
⎛⎝⎜
⎞⎠⎟
⎛⎝⎜
⎞⎠⎟ =
> <
ln Δ
Leakoff coefficient can be estimatedfrom the ratio of dP/dG before and
after fissure closure
Cdp
Presenter
Presentation Notes
During the pressure-dependent leakoff phase of closure, the observed magnitude of the pressure derivative (dP/dG) is an indication of the relationship between leakoff coefficient and pressure. Once the fissure opening pressure (Pfo) is determined from the end of pressure-dependent behavior, a plot of effective leakoff coefficient at any pressure (Cp) divided by stabilized constant leakoff after fissure closure (Co) can be made as a function of pressure or pressure differential above Pfo. If the data are plotted as ln(Cp/Co) vs dP the slope of the line gives the coefficient for pressure dependent leakoff (Cdp).
© 2009
Determination of PDL Coefficient
9300 9400 9500 9600 9700 9800 9900 10000 10100 10200 10300Bottom Hole Pressure (psi)
-1
0
1
2
3
4
5
6
(Fissure Opening Pressure = 9311)
(PDL Coefficient = 0.0019)
ln(Cp/Co)
Ln(L
eako
ff R
atio
)
Presenter
Presentation Notes
For this example the slope of the leakoff ratio plot is not linear. This indicates that the PDL character is changing and does not exactly match the exponential model. In many cases a near-perfect straight line is observed. In other cases two straight lines of clearly different slope are observed. This behavior probably indicates multiple conjugate fracture sets with different opening pressures ad flow capacities. In this case the flow capacity of the composite fissure system continuously changes with pressure.
© 2009
Natural Fracture System in Hard‐Rock
σΗmin
σΗmax
Presenter
Presentation Notes
One conceptual model of pressure dependent leakoff in hard, naturally fractured reservoirs is shown here. A hydraulic fracture initiated at a wellbore may cut across a series of pre-existing natural fractures, or may begin propagating along an existing fracture which is roughly parallel to the preferred stress orientation for fracture growth. Pressurized fluid which leaks-off from the propagating fracture preferentially flows along the high conductivity channels formed by the existing natural fractures. If the fluid pressure in the fractures reaches the normal stress on the cracks they will tend to open. Because fracture flow rate is related to the cube of aperture, flow rate or apparent leakoff rate will increase dramatically when pressure exceeds the critical fissure opening pressure (Pfo). If fluid pressure is admitted to a series of fractures paralleling the propagating hydraulic fracture the stiffness, or apparent modulus of the system may increase.
© 2009
Typical leakoff volume:
0.05 ft3/ft2 each face
3” depth in 20% φ rock
10’ depth in 1/2% φ fractures
df
( )( )
dx
P ST S
f
f
f h
h≤
−+
⎡
⎣⎢⎢
⎤
⎦⎥⎥
12
2
SH
Sh
Fissures Opened By Tensile Stress Field
Presenter
Presentation Notes
Delaney, et al, have also presented a theoretical analysis of the tensile stress region surrounding the tip of a propagating fracture. Their work indicates that a series of parallel fractures can be created in the tip process zone. Their analysis is supported by field descriptions of magmatic dikes surrounded by swarms of parallel fractures which are not related to pre-existing natural fracture directions. These parallel fracture sets appear to be closely related to the multiple fracture swarms observed in the M-site observation well and other fracture over-coring studies. While some of the fractures can be invaded by the injected fluid, as observed in coring studies and surface expressions of dikes, the presence and number of multiple fractures does not appear to influence net treating pressure. This finding is also supported by the M-site observation well pressure data. The width of the fracture, hence the number of parallel fractures created, is causally related to the excess net pressure in the hydraulic fracture. High net pressures tend to produce wider fracture zones. Weaker rocks, with low tensile strength (T), and low closure stresses (Sh) also contribute to wider fracture zones. The width, hence volume, of the fracture zone may be critically important to leakoff calculations. For a typical fracture treatment, a total fluid volume of about 0.05 ft3/ft2 is lost at closure. In a 20% porosity rock this equates to a 3” depth of invasion. In a 0.5% porosity fracture system, the invaded zone depth can be 10’. This fracture zone width is consistent with the process zone width predicted, and observed in dike outcrops.
© 2009
Width of Fracture Zone for Various Half‐Lengths (Sh=5000 psi, Tn=1000 psi)
Fracture Half-Length
Presenter
Presentation Notes
The plot shows the computed width of the fracture zone based on some assumed input parameters. Note that for an average created fracture length of about 800 feet and a net pressure of 1000 psi the fracture zone width is slightly more than 20 feet.
© 2009
Using best straight-line extrapolation to closure:Computed efficiency = 0.48Actual efficiency (simulator) = 0.28
Using 75% rule:Computed efficiency = 0.35
η =+GGc
c2
Estimated Efficiency with PDL
0.75*(ISIP-Pclosure)
Presenter
Presentation Notes
The previously illustrated method of computing fracture fluid efficiency fro the G-function at closure is not valid if pressure dependent leakoff exists. In the example shown, the pressure falloff rate after fissure closure yields an efficiency estimate of 0.48 compared to an actual efficiency of 0.28 at the end of pumping, as determined from material balance in the numerical simulator with PDL. Nolte has suggested a “75% rule” to adjust the efficiency estimate for this case. In the 75% rule a tangent to the G-function curve is drawn at a point 75% of the pressure between ISIP and closure. Using the 75% rule decreases the efficiency estimate to 0.35, which is still too high. From a physical standpoint this makes sense. By applying the efficiency analysis to the linear part of the pressure falloff we are analyzing the rate of fluid loss in a matrix system after all fissures have closed. However, the entire frac job was pumped at a pressure above the fissure opening pressure, so leakoff during pumping was much greater (in this case as much as 10 times greater) than that observed during the linear pressure falloff. Under these conditions the only way to accurately model leakoff conditions during the job is to identify the existence and magnitude of the pressure dependent leakoff function, and model it correctly.
© 2009
G‐Function Analysis for Leakoff with Variable Storage
Pre
ssur
e
Der
ivat
ives
Presenter
Presentation Notes
The pressure vs. G-function curve shows the characteristic slow initial decline after shut-in with the slope increasing as closure approaches. The semi-log derivative clearly shows the characteristic “belly” in the curve below the straight-line through the origin. Main fracture closure is indicated by the departure from the straight-line, as before.
© 2009
Sqrt(t) Plot for Leakoff with Variable Storage
Pre
ssur
e
Der
ivat
ives
Time
Presenter
Presentation Notes
In the case of variable storage the first derivative analysis of the Sqrt(t) plot (inflection point) gives the correct closure point. Closure can also be found from the semi-log derivative departure from the straight-line through the origin. The semi-log derivative also shows the “belly” indicating the duration of variable storage.
© 2009
Variable Storage Signature on the Log‐Log Plot
Del
ta-P
ress
ure
and
Der
ivat
ive
Presenter
Presentation Notes
The main fracture closure occurs at the point where the pressure derivative breaks off the positive slope, as in the previous cases. With variable fracture storage the slope of the derivative is much higher than ½ before closure. A slope approaching 1 indicates storage on a conventional type-curve analysis, and the same is true here. The separation between the pressure difference and derivative curves in the near-unit-slope region is caused by the changing storage. After closur,e the far-field reservoir transients are not affected by storage, except that the time to reach closure is extended because of the excess fluid that must be leaked-off to achieve closure. In this example there is an extended transition period before reservoir pseudo-linear flow is established.
© 2009
Fracture Height Recession and Transverse Storage
Leakoff through a thin permeable layer:Decreasing storage relative to leakoff rate
accelerates pressure decay
Expulsion of fluid from transverse fractures:
Maintains pressure in fracture until fissures close
Presenter
Presentation Notes
Previously, Nolte and others have identified fracture height recession as a leakoff mechanism characterized by slow initial pressure decline after shut-in, with the rate of pressure decay increasing with time after shut-in. The process is driven by a large storage volume of fluid in a fracture with out-of-zone growth across impermeable layers. Initially the leakoff rate is small compared to the volume of fluid stored in the fracture, so the pressure decline is slow. As the fracture closes the remaining storage volume decreases and the leakoff rate accelerates with respect to the remaining compliant fracture volume and the pressure decline rate increases. The same effect can be obtained in a system of transverse fractures opening against a higher stress than the minimum in-situ principal stress normal to the main fracture plane. After shut-in, the transverse fractures close first, acted upon by higher net stress. As they close they can expel fluid back into the main fracture, supporting its pressure and decreasing the rate of pressure decay. As the transverse fractures close the rate of fluid expulsion and pressure support decreases and the rate of pressure decay in the main fracture increases to normal matrix-dominated rate. In this case this mechanism is another aspect of PDL. In cases of PDL, the leakoff from the fracture system is accelerated. In the case of transverse storage, the compliant volume of the secondary fractures is large compared to the increase in leakoff. For this reason, the storage mechanism dominates the PDL signature. This leakoff character has been observed in cases with no height growth, as indicated by micro-seismic and tilt mapping.
© 2009
Closure‐Time Correction for Variable Storage
Pre
ssur
e D
eriv
ativ
e
Presenter
Presentation Notes
For a normal constant-area fracture, the time required to reach closure through normal leakoff is proportional to the volume of fluid stored in the fracture at shut-down and the surface area open to leakoff, adjusted for fracture compliance. In the case of variable storage, there is a much larger volume of fluid in the fracture at shut-in than would be the case for a constant-height planar fracture. For this reason, the time required to reach closure is delayed in proportion to the excess fluid storage ratio. A correction factor (rp) must be applied to correct the observed closure time to the appropriate closure time for a planar constant height geometry fracture. Nolte describes rp as the net-to-gross ratio of the fracture to the leakoff zone for the height recession case. For general variable storage (recession or transverse fractures) rp is here called simply the variable storage correction factor. It can be approximated by the ratio of the area under the semi-log derivative of the G-function up until closure, to the area under the right triangle formed by the tangent line to the semi-log derivative and passing through the origin. The equation in the inset mathematically defines the area ratio. For the example, the ratio is approximately 0.85.
© 2009
Permeability Estimate with Storage Correction
Data Inputrp 0.85φ 0.08 V/Vct 6.00E-05 psi-1
E 5 Mpsiμ 1 cp
Gc 3Pz 944.0 psi
Mini-Frac Permeability = 0.0617 md
Presenter
Presentation Notes
Without the storage ratio correction, the permeability estimate for the observed closure time would be approximately 0.04 md. With the correction, the perm estimate is 0.061 md. Because pseudo-radial flow was not established in the test, it is not possible to accurately determine permeability from the after-closure analysis. In some cases, the storage ratio can be 0.5 or less and the permeability estimate error introduced by missing the correction can be severe.
© 2009
Tip‐Extension G‐Function AnalysisP
ress
ure
Der
ivat
ives
Presenter
Presentation Notes
The data show the expected signature for fracture extension after shut-in. Note that there appears to be a late-time straight-line with what will be shown is a pressure dependent leakoff signature. Using the G-function and its derivatives alone can lead to errors in interpretation of the correct closure mechanism. The vertical dashed line [1] is positioned at the end of the data but there is no actual closure in this test. The fracture tip-extension behavior implies fairly low permeability (or at least, low leakoff). Note that the dP/dG curve never becomes a horizontal line, indicating that the apparent leakoff continues to change throughout closure, as seen in the hypothetical example.
© 2009
Sqrt(t) Plot for Tip‐ExtensionP
ress
ure
Der
ivat
ives
Presenter
Presentation Notes
The typical analysis of the Sqrt(t) plot gives an inaccurate closure indication for the tip-extension case. In the figure, the dashed magenta line is the first derivative of the pressure curve. A large derivative maximum (inflection point) occurs shortly after shut-in. This point is commonly picked as closure but is not correct. If the semi-log derivative of pressure wrt Sqrt(t) is plotted, a signature similar to the G-function semi-log derivative is obtained. As long as this derivative is still rising, the fracture has not yet closed (in general). The tangent to the semi-log derivative is an artifact and does not define a true straight-line. Nolte has pointed out that the Sqrt(t) and G-function plots would be functionally equivalent if the fracture were created instantaneously. The G-function corrects for the superposition of leakoff transient of various durations generated during fracture growth
© 2009
Log‐Log Plot for Tip‐ExtensionD
elta
-Pre
ssur
e an
d D
eriv
ativ
e
Presenter
Presentation Notes
The log-log plot provides the most definitive indication of tip-extension. Because the pressure transient along the length of the fracture continues to dominate the pressure decline, while some leakoff to the formation may occur, the tip-extension phenomenon exhibits a ¼ slope of the pressure derivative on the log-log plot. The pressure difference curve follows a parallel ¼ slope offset by 4x from the derivative. If the derivative is still rising, the fracture has not yet closed. Obviously, no after-closure analysis can be performed.
© 2009
Potential Problems in Pressure Diagnostics
• Bad ISIP– Extreme perf restriction– Wellbore fluid expansion
• Zero surface pressure during falloff– Falling fluid level– Non‐zero sandface rate– Partial vacuum above fluid column
• Gas entry to closed wellbore– Phase segregation
• Use of gelled (wall‐building) fluid– Disruption of after‐closure pressure gradients– Masking of reservoir flow capacity
Presenter
Presentation Notes
When dealing with actual field data, things can happen to make the data less than ideal and can interfere with interpretation of the data. The list of things that can cause problems in falloff analysis is far from complete, but these represent fairly common problems that may be encountered. If the problem is recognized it may be possible to avoid making inaccurate conclusions based on erroneous data. Often the data itself cannot be corrected and the test may ultimately be compromised. In this section the typical character of the data is described for each potential problem using typical field examples. Suggestions are offered to improve interpretation of the data, where possible. In many cases the test data used for analysis must be truncated and the useless data ignored.
© 2009
Example of Ambiguous ISIP Caused by Near‐Well Restriction
GohWin Pumping Diagnostic Analysis ToolkitJob Data
3/20/200700:00 00:05 00:10 00:15
3/20/200700:20
Time
30000
40000
50000
60000
70000
80000
90000A
0.0
0.2
0.4
0.6
0.8
1.0
1.2B
(ISIP = 56975)
Bottom Hole Pressure (kPa)Slurry Rate (m³/min)
AB
21
Minifrac Events
1
2
3
Start
Shut In
Stop
Time00:05:45
00:10:31
04:37:46
BHP78547
57469
45868
SR0.990
0.000
0.000
ISIP=80000
Presenter
Presentation Notes
In cases with severe near-well restrictions, due to perfs or tortuosity, the ISIP is difficult to determine because of wellbore fluid expansion and afterflow. The example shows actual BH gauge data for an injection test. Note the raid and large pressure decay at shut-in with no clear indication of an instantaneous shut-in pressure. Within one minute after surface shut-in the BHP drops more than 20,000 kPa (2900 psi). The selection of the ISIP used for analysis has a large impact on the interpretation of results.
© 2009
BHP G‐function for Early ISIP Shows Apparent “PDL”
GohWin Pumping Diagnostic Analysis ToolkitMinifrac - G Function
5 10 15 20G(Time)
45000
50000
55000
60000
65000
70000
75000
80000A
0
2500
5000
7500
10000
12500
15000D
(0.002, 0)
(m = 333.3)
(20.05, 6681)
(Y = 0)
Bottom Hole Pressure (kPa)Smoothed Pressure (kPa)1st Derivative (kPa)G*dP/dG (kPa)
AADD
1
1 End of TestTime20.29
BHP45908
SP45907
DP25457
FE91.53
Presenter
Presentation Notes
Using the early ISIP estimate, the G-function derivative shows leakoff with massive PDL during the initial decline. Fracture closure does not occur before the end of the test. The early derivative hump, that can be interpreted as PDL, is probably due to afterflow and wellbore fluid expansion caused by the abnormally high near-well pressure drop at shut down. The excess near-well pressure drop also affects the apparent net fracture extension pressure of 25.4 MPa (3695 psi).
© 2009
Late ISIP G‐Function Suppresses “PDL Hump”
GohWin Pumping Diagnostic Analysis ToolkitMinifrac - G Function
2 4 6 8 10 12 14 16 18
G(Time)
44000
46000
48000
50000
52000
54000
56000
58000A
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000D
(0.002, 0)
(m = 302)
(19.65, 5933
(Y = 0)
Bottom Hole Pressure (kPa)1st Derivative (kPa)G*dP/dG (kPa)
ADD
1
1 ClosureTime19.43
BHP45928
SP45924
DP11047
FE91.19
Presenter
Presentation Notes
Using a later ISIP estimate suppresses the apparent PDL hump but does not change the interpretation of the late-time data. The apparent fracture extension pressure is much lower (1600 psi) using the later ISIP value.
© 2009
Early ISIP Log‐Log Plot Shows Increased Separation and Long Negative Derivative Slope
GohWin Pumping Diagnostic Analysis ToolkitMinifrac - Log Log
2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 20.1 1 10 100
Time (0 = 9.283333)
2
3
4
56789
2
3
4
56789
2
3
100
1000
10000
A
-2000
0
2000
4000
6000
8000
10000
12000
14000B
(0.29, 6408)
(m = 0.506)
(3.255, 21772)
(Y = 3734)
(82.06, 2319) (m = 0.254)
(250.5, 3079)
(Y = 421.8)
(Y = 3134)
Delta Bottom Hole Calc Pressure (kPa)Delta Smoothed Pressure (kPa)Smoothed Adaptive 1st Derivative (kPa/min)Adaptive DTdDP/dDT (kPa)
AABA
BH ISIP = 71366 kPa 1
1 End of TestTime264.72
DBHCP25457
DSP25458
FE91.53
7x Separation
Presenter
Presentation Notes
Using the early ISIP affects the log-log diagnostic plot because the change in pressure from ISIP is the primary variable. In this analysis the 0.25 slope of the log derivative curve at the end of the test implies that fracture tip extension is still occurring. However, the 7x separation between the derivative and pressure difference curves is not consistent with the bi-linear flow result. The incorrect ISIP drives the abnormaly large separation and causes a prolonged negative derivative slope in the middle-range data.
© 2009
Late ISIP Log‐Log Plot Gives Consistent Separation
GohWin Pumping Diagnostic Analysis ToolkitMinifrac - Log Log
2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 20.1 1 10 100
Time (0 = 10.5)
2
3
456789
2
3
456789
2
3
456789
2
10
100
1000
10000
(41.34, 1853) (m = 0.25)
(254
(Y = 410.3)
(Y = 2956)
Delta Bottom Hole Calc Pressure (kPa)Delta Smoothed Pressure (kPa)Smoothed Adaptive 1st Derivative (kPa/min)Adaptive DTdDP/dDT (kPa)
BH ISIP = 56975 kPa 1
1 ClosureTime260.51
DBHCP11037
DSP11037
FE91.17
4x
Presenter
Presentation Notes
The late ISIP analysis ends with the same ¼ slope of the derivative but the separation of the curves is reduced to 4x, as required for bi-linear flow and fracture tip extension. In many cases ISIP is difficult to determine and is frequently not “instantaneous”.
© 2009
BHP Gauge Data with Falling Fluid Level
GohWin Pumping Diagnostic Analysis ToolkitJob Data
10/2/200619:00 20:00 21:00 22:00 23:00
10/3/200600:00 01:00 02:00
10/3/200603:00
Time
2500
3000
3500
4000
4500
5000
5500
6000
6500A
0
1
2
3
4
5
6
7B
(ISIP = 4366)
BH Gauge Pressure (psi)Slurry Rate (bpm)
AB
321
1
2
3
Start
Shut In
Stop
Time10/2/2006 19:19:03
10/2/2006 19:35:34
10/2/2006 23:23:40
BGP6393
4368
3027
SR6.100
0.000
0.000
Presenter
Presentation Notes
The plot shows the early part of a recorded injection and falloff using bottomhole gauges. The pressure declines fairly steadily for the first 4 hours then levels-off abruptly. The vertical line (3) intersects the pressure at BHP=3027 psi, the hydrostatic head of the wellbore fluid column. Any data after this time, which is most of the 5-day falloff, is essentially useless for the analysis as it represents falling fluid level in the wellbore. The reservoir pore pressure appears to be substantially below the head but a bottomhole shut-in device was not used for the test.
© 2009
Long‐Term Falloff with BHP Gauges and Falling Fluid Level
GohWin Pumping Diagnostic Analysis ToolkitJob Data
10/3/2006 10/4/2006 10/5/2006 10/6/2006 10/7/2006Time
2500
3000
3500
4000
4500
5000
5500
6000
6500A
0
1
2
3
4
5
6
7B
(ISIP = 4367)
BH Gauge Pressure (psi)Slurry Rate (bpm)
AB
321
Minifrac Events
1
2
3
Start
Shut In
Stop
Time10/2/2006 19:19:03
10/2/2006 19:35:34
10/2/2006 23:23:39
BGP6393
4368
3027
SR6.100
0.000
0.000
Presenter
Presentation Notes
In this example test, the BHP declines very slowly after the well goes “on vacuum” at surface. The wellbore fluid column is partially supported by the low pressure, essentially vapor pressure of water, at the surface below the closed wellhead. The effect is the same that holds water in a water-cooler or manometer. The pressure decline rate does not reflect the flow capacity of the reservoir and is not related to reservoir pressure or permeability. Also, any analysis method based on a shut-in assumption is invalid because the sand-face flow rate is not zero during the period when the wellbore fluid level is falling. Flow from the wellbore guarantees a small positive injection rate at the perforations.
© 2009
Effect of Falling Fluid Level on G‐Function Derivative Plot
GohWin Pumping Diagnostic Analysis ToolkitMinifrac - G Function
10 20 30 40
G(Time)
2600
2800
3000
3200
3400
3600
3800
4000
4200
4400A
0
200
400
600
800
1000
1200
1400
1600
1800
2000D
(0.002, 0)
(m = 211.4)
(7.373, 1558)
(Y = 0)
BH Gauge Pressure (psi)Smoothed Adaptive 1st Derivative (psi)Smoothed Adaptive G*dP/dG (psi)
ADD
1
1 ClosureTime
5.36BGP3423
SP3439
DP913.5
FE73.99
Presenter
Presentation Notes
The G-function derivatives are also invalid when the well goes on vacuum. The sharp break in the pressure trend makes the first derivative go to almost zero and causes a sharp drop in the semi-log derivative that can easily be mistaken for massive PDL. The late-time semi-log derivative continues to climb slowly and can be mistaken for a lack of closure.
© 2009
Effect of Falling Fluid Level on Log‐Log Diagnostic Plot
GohWin Pumping Diagnostic Analysis ToolkitMinifrac - Log Log
2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 60.1 1 10 100 1000
Time (0 = 1175.566667)
2
3
4
5
6789
2
3
4
5
6789
2
10
100
1000
(32.69, 246.3)
(m = 0.912)
(168.5, 1099)
Delta Bottom Hole Calc Pressure (psi)Smoothed Adaptive 1st Derivative (psi/min)Adaptive DTdDP/dDT (psi)
BH ISIP = 4352 psi 1
1 ClosureTime123.46
DBHCP929.1
DSP912.6
FE73.99
Presenter
Presentation Notes
The falling fluid level also invalidates the log-log diagnostic analysis. The derivative shows a high negative slope followed by a positive ½ slope that can be mistaken as an indicator that the fracture is still open. This is consistent with the G-function derivative but is an incorrect physical interpretation.
© 2009
Effect of Falling Fluid Level on ACA Log‐Log Linear Plot
GohWin Pumping Diagnostic Analysis ToolkitACA - Log Log Linear
6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 90.01 0.1 1
Square Linear Flow (FL^2)
2
3
456789
2
3
456789
2
3
456789
10
100
1000
10000
(m = 1)
(m = 0.5)
(p-pi) (psi)Moving Avg Of Slope (psi)
ResultsStart of Pseudo Linear Time = 71.87 minEnd of Pseudo Linear Time = 98.57 minStart of Pseudo Radial Time = 110.06 hours
123
Analysis Events
3
2
1
Start of Pseudoradial Flow
End of Pseudolinear Flow
Start of Pseudolinear Flow
SLF0.01
0.32
0.37
BGP2777
3028
3093
Slope0.000
0.000
0.000
(p-pi)478.0
728.3
793.1
Presenter
Presentation Notes
The pressure difference curve on the ACA log-log linear plot breaks up and away from the derivative during periods of falling fluid level. The derivative may have a slope much higher than 1 and may reverse at late time, as in this example. None of these data are valid for analysis after the wellhead pressure approaches zero.
© 2009
Effect of Falling Fluid Level on ACA Linear Flow Plot
GohWin Pumping Diagnostic Analysis ToolkitACA - Cartesian Pseudolinear
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Linear Flow Time Function
2700
2800
2900
3000
3100
3200
3300
3400
3500
(m = 1297.8)
BH Gauge Pressure (psi)
ResultsReservoir Pressure = 2296.52 psiStart of Pseudo Linear Time = 71.87 minEnd of Pseudo Linear Time = 98.57 min12
Analysis Events
2
1End of Pseudolinear Flow
Start of Pseudolinear Flow
LFTF0.56
0.61
BGP3028
3093
Presenter
Presentation Notes
Extrapolation of the pressure trend on the ACA Linear Flow plot can be misleading in this case. The pressure trend typically deflects above the correct extrapolation and may describe a reverse “S” curve that eventually may stabilize at the actual reservoir pressure after an extremely long time.
© 2009
Pressure Increase Caused by Gas Entry and Phase Segregation
3/22/200322:00
3/23/200300:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00
3/23/200318:00
Time
0
1000
2000
3000
4000
5000
6000A
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5BWellhead Pressure (psi) Slurry Rate (bpm)A B
Presenter
Presentation Notes
The complete data set for a long-term injection test in an over-pressured formation is shown. The minimum pressure recorded at surface was 743 psi after 2.5 hours of falloff. The pressure increases after that time until about 9 hours of falloff. For purposes of analysis, the end of the valid data occurs before the minimum pressure point at 2.5 hours. The later pressure rise is caused by entry of small gas bubbles at the perforations which rise in the wellbore fluid column. The low permeability and slow leakoff restrict expansion of the gas bubbles and hold their volume nearly constant as they rise.
© 2009
Pressure Increase from Rising Gas Bubbles
Phead=0.45 psi/ft
VzNRTPP head ==1
VzNRTPP == 12
Presenter
Presentation Notes
For the ideal case of a sealed wellbore under isothermal conditions, the volume of the gas bubble remains constant as it rises. With no mass transfer from the gas to the wellbore fluid, the moles of gas in the bubble remains constant, therefore its pressure remains constant as it rises. If a single gas bubble floats from the perfs to the surface under these conditions the surface pressure will rise to the original BHP and the pressure at the perfs will double. In reality, leakoff from the well is not identically zero, the increased pressure generated by the rising bubble causes an increase in leakoff rate, the gas temperature decreases somewhat during transit, and some gas may dissolve in the wellbore fluid. Still, a very small gas bubble entering at the perforations can cause a large pressure upset.
© 2009
Early‐Time WHP G‐function Analysis
GohWin Pumping Diagnostic Analysis ToolkitMinifrac - G Function
1 2 3 4 5 6G(Time)
5000
5500
6000
6500
7000
7500
8000
8500A
0
200
400
600
800
1000
1200
1400
1600
1800
2000D
(0.002, 0)
(m = 1218)
(1.316, 1600)
(Y = 0)
Bottom Hole Calc Pressure (psi)Smoothed Pressure (psi)1st Derivative (psi)G*dP/dG (psi)
AADD
1
1 ClosureTime
1.00BHCP
7192SP7202
DP1182
FE34.54
Presenter
Presentation Notes
The G-function derivative shows fracture closure occurs at Gc= 1.0 and WHP= 2836.8 psi. This gives a BHP of 7192 psi or 0.72 psi/ft as fracture closure gradient. Fluid efficiency for the water injection was 34.5%. The net fracture extension pressure was 1182 psi above closure. As long as closure occurs before phase segregation becomes dominant, the results are useable. Generally, gas entry does not occur until after closure when the BHP approaches pore pressure and counter-current gravity segregation allows gas to enter the well.
© 2009
Effect of Gas Entry and Phase Segregation on G‐Function
GohWin Pumping Diagnostic Analysis ToolkitMinifrac - G Function
5 10 15 20 25G(Time)
5000
5500
6000
6500
7000
7500
8000
8500A
0
200
400
600
800
1000
1200
1400
1600
1800
2000D
(0.002, 0)
(m = 1218)
(1.316, 1600)
(Y = 0)
Bottom Hole Calc Pressure (psi)Smoothed Pressure (psi)1st Derivative (psi)G*dP/dG (psi)
AADD
1
1 ClosureTime
1.00BHCP
7192SP7212
DP1190
FE34.54
Presenter
Presentation Notes
The entire G-function plot is shown to illustrate what happens to the derivatives during the phase segregation period. Note that both derivatives become negative as the pressure rebounds. The late-time “normal” pressure decline, with positive derivatives, cannot be analyzed for reservoir flow capacity. It may be possible to extrapolate to a valid reservoir pressure if phase segregation stops, and if the final liquid level in the well can be determined accurately. This process is risky and not recommended. The best approach is to truncate the test at the first pressure minimum.
© 2009
Effect of Gas Entry and Phase Segregation on Log‐Log Plot
GohWin Pumping Diagnostic Analysis ToolkitMinifrac - Log Log
2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 90.1 1 10 100 1000
Time (0 = 12.666667)
2
3
4
56789
2
3
4
56789
2
3
4
10
100
1000 (11.41, 922.9)
(m = -0.5)
(77.1, 355)
(Y = 96.55)
Delta Bottom Hole Calc Pressure (psi)Delta Smoothed Pressure (psi)1st Derivative (psi/min)DTdDP/dDT (psi)
BH ISIP = 8377 psi 1
1 ClosureTime
5.31DBHCP
1185DSP1175
FE34.54
Presenter
Presentation Notes
After closure there is a long period of -1/2 slope indicating a linear reservoir transient flow period. Once phase segregation begins the derivative drops radically. Any further analysis attempt is useless.
© 2009
Effect of Gas Entry and Phase Segregation on ACA Log‐Log Plot
ACA - Log Log Linear
2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 90.001 0.01 0.1 1
Square Linear Flow (FL^2)
2
3
456789
2
3
456789
2
3
456789
10
100
1000
10000
(m = 1)
(m = 0.5)
Slope (psi)(p-pi) (psi)
ResultsStart of Pseudo Linear Time = 11.88 minEnd of Pseudo Linear Time = 28.70 minStart of Pseudo Radial Time = 17.37 hours
123
Analysis Events
3
2
1
Start of Pseudoradial Flow
End of Pseudolinear Flow
Start of Pseudolinear Flow
SLF0.01
0.14
0.27
BHCP5280
5617
6103
Slope297.5
652.2
913.1
(p-pi)999.9
1337
1823
Presenter
Presentation Notes
The linear flow period is apparent on the ACA log-log plot. When segregation begins the pressure difference curve deviated upward and the derivative drops precipitously. Any late-time trend is essentially meaningless.
© 2009
Effect of Gas Entry and Phase Segregation on ACA Linear Plot
GohWin Pumping Diagnostic Analysis ToolkitACA - Cartesian Pseudolinear
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Linear Flow Time Function
5000
5250
5500
5750
6000
6250
6500
6750
7000
7250
(m = 3541.8)
Bottom Hole Calc Pressure (psi)
ResultsReservoir Pressure = 4279.89 psiStart of Pseudo Linear Time = 11.88 minEnd of Pseudo Linear Time = 28.70 min12
Analysis Events
2
1End of Pseudolinear Flow
Start of Pseudolinear Flow
LFTF0.38
0.52
BHCP5617
6103
Presenter
Presentation Notes
On the ACA Linear Flow Plot the pressure trend reverses at the start of phase segregation. Obviously, any extrapolation of this trend is meaningless. Even the start of gas entry causes the slope of the pressure curve to deviate upward, leading to an erroneously high estimate of reservoir pressure.
© 2009
Effect of Gas Entry and Phase Segregation on ACA Radial Plot
GohWin Pumping Diagnostic Analysis ToolkitACA - Cartesian Pseudoradial
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8Radial Flow Time Function
4750
5000
5250
5500
5750
6000
6250
6500
6750
7000
7250
(m = 5638.5)
Bottom Hole Calc Pressure (psi)
ResultsReservoir Pressure = 4894.94 psiTransmissibility, kh/µ = 87.73613 md*ft/cpkh = 2.07706 md*ftPermeability, k = 0.0495 mdStart of Pseudo Radial Time = 17.37 hours1
Analysis Events
1 Start of Pseudoradial FlowRFTF0.01
BHCP5280
Presenter
Presentation Notes
A similar trend is seem on the Radial Flow Plot, but the time scale is more compressed.
© 2009
Pressure Decay without Filter‐Cake: One‐Dimensional Transient Flow
Pfrac
PporeDistance from frac face
Presenter
Presentation Notes
The conventional fluid loss model is a one-dimensional solution for linear transient flow with constant pressure boundary conditions. The frac pressure at the fracture face is assumed constant with time and the far-field pore pressure is assumed to be constant. Initially the pressure gradient, and the leakoff rate, is very high. With time, the transient moves further into the reservoir and the gradient (and rate) decrease. The solution give rate decreasing linearly with the square-root of time.
© 2009
Impact of Resistances in Series
K=1 K=0.001
ΔP3=L3/k3 ΔP2=L2/k2ΔPTΔP1=L1/k1 =+ +
10 2 0.5
K=100
Kavg=Lt/(L1/k1+ L2/k2+ L3/k3)=0.025
Presenter
Presentation Notes
Leakoff is modeled as a combination of series flows. The figure roughly describes a high permeability far-field reservoir zone, a near-fracture invaded zone, and a thin wall filter-cake zone. In series flow the total pressure drop through the system is the sum of the pressure drops through each zone. Using Darcy’s Law, each pressure drop can be determined from the length and permeability of each zone. When even a thin film of very high flow resistance is present, such as the filter-cake, the flow capacity of the least conductive region dominates the system.
© 2009
Frac Fluid Loss: Discontinuous Pressure Gradient with Filtercake
Pfrac
PporeDistance from frac face
With filtercake pressure gradient is discontinuous and far-field gradient is not related to leakoff rate through reservoir permeability
Presenter
Presentation Notes
When a filter-cake is deposited on the fracture wall, most of the pressure drop is taken across the filter-cake during leakoff. The far-field pressure gradient is much less than expected, when computed based on the leakoff rate. The after-closure analysis yields an estimate of reservoir flow capacity that is much too high and is inconsistent with the observed closure time.
© 2009
Recall: Complete Stress Equation
• Pc = closure pressure, psi• ν = Poisson’s Ratio• Pob = Overburden
Pressure• αv = vertical Biot’s
poroelastic constant• αh = horizontal Biot’s
poroelastic constant
( )[ ] txphpvobc EPPPP σεααν
ν+++−
−=
1
• Pp = Pore Pressure• εx = regional horizontal
strain, microstrains• E = Young’s Modulus,
million psi• σt = regional horizontal
tectonic stress
Presenter
Presentation Notes
The total fracture closure stress equation, as implemented in GOHFER, is shown above. The equation, as written, includes most of the unknowns that make up the stress profile as separate explicit variables. The interaction among all the variables and the sources of data for each must be understood to appreciate the difficulty in estimating a physically consistent and reasonably accurate stress profile. When the measured closure stress is known, estimates for elastic properties can be input and an estimate of pore pressure derived.
© 2009
Estimation of Pore Pressure & Flow Capacity
• Horner plot is only valid in pseudo‐radial flow
• Short‐term after‐closure data can be misleading
• In linear flow, ½ slope and 2x factor between DP and DP’ is diagnostic
• Pore pressure can be obtained from the linear flow period
• Reservoir kh can be determined when radial flow is identified
• Pore pressure is related to closure stress
Presenter
Presentation Notes
To define reservoir flow capacity, the most important flow regime to identify is the pseudo-radial reservoir flow transient. In this regime, the Horner analysis is valid to define pore pressure and flow capacity. When insufficient data is available to define closure and after closure regimes, incorrect conclusions can be reached. Extrapolation of the Horner plot may appear to be based on a straight-line, but can give inaccurate pressure estimates and slope values. The methods for identifying linear and radial flow periods have been outlined. The linear flow period can be used to obtain an estimate of pore pressure before the onset of radial flow. If radial flow is identified, then reservoir kh can be defined by both the Horner and ACA radial floe plot. In cases where only short-term falloff data are available ,an estimate of pore pressure can be made from the closure stress using the complete stress equation and log derived elastic properties.
© 2009
Conclusions:
• G‐function response in low perm, hard rock is definitive and relatively easily interpreted
• Closure pressure and leakoff mechanism can be defined
• Natural fractures and their stress state can be determined
• Closure pressure is related to reservoir pore pressure
• Correlations between Gc and production can be developed for clean fluid (acid and/or water) injection tests
• Extended falloff data can be used for pseudo radial flow analysis of perm
Presenter
Presentation Notes
Analysis of the pre-frac falloff test can provide invaluable information about fracture closure stress, net extension pressure, pore pressure, reservoir flow capacity, the presence and stress state of natural fractures, leakoff magnitude and mechanism and may other parameters important in design. These tests, when correctly designed and interpreted are the single most valuable source of data.
