SPE 166132 Make Decision on the Fly: A New Method to Interpret Pressure-Time Data during Fracturing – Application to Frac Pack Elias Pirayesh, Mohamed Y. Soliman, Mehdi Rafiee, Texas Tech University
Copyright Copyright 2013, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in New Orleans, Louisiana, USA, 30 September –2 October 2013. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.
Abstract Real time analysis of fracturing data is an invaluable tool for determining whether a fracturing job is progressing as planned. Therefore since the early days, understanding of fracturing pressure as a readily available diagnostic tool has been emphasized and practiced by the industry. Theories and techniques were developed for the interpretation of such data e.g. Nolte-Smith (1981). The well-known well-known Nolte-Smith method (1981) analyzes the pressure response of a formation during pumping, in order to predict the fracture geometry being created. Although this technique provides a highly reliable tool in terms of interpreting fracturing events, but in real time practices, it can take this technique quite a long time to detect a change in fracture behavior. This is partly due to the data compression associated with the Nolte-Smith log-log plot. Also Nolte-Smith technique necessitates prior knowledge of closure pressure of the formation which is not always known. In this paper, we present a new method to analyze and interpret pressure-time data during fracturing. This method, which is based on a modification of Nolte-Smith technique, has proven effective in precisely interpreting fracturing behavior while the job is being carried out. Additionally it eliminates the short-comings of the original technique, as discussed above; meaning that the proposed method permits quick and accurate interpretation of fracturing data plus it needs no prior knowledge of formation in-situ stresses. This has been reached by a new innovative moving-reference-point concept assembled with a mathematical mathematical manipulation of the power-law fracture propagation theory. Application of the new technique in the analysis of a variety of field cases including several frac packs and regular fracturing treatments has proven quite successful. First accurate pressure-time matches were obtained and then using these matches, the Nolte-Smith parameters were determined which in part allowed detection of fracture behavior changes (e.g. propagation to width-gain) width-gain) usually in less than a minute and sometimes even in a few seconds of the start of the event.
Introduction Using the fracture propagation model developed by Perkins and Kern (1961) and (1961) and refined by Nordgren by Nordgren (1972), (1972) , the fracturing pressure at the wellbore may be written written as a power function of time as given in equation 1.
pnet
e
t ,
1
8
e
1 5
1
A large exponent is an indication of low leak-off rate, in other words more of fluid is maintained inside the fracture and contributing to fracture propagation. The bounds given in equation 1 are based on a Newtonian fluid, which was generalized, by Nolte by Nolte (1979) to (1979) to the following form: 1 4n 4
e
1 2n 3
2
Using dimensional analysis Nolte analysis Nolte and Smith (1981) reached (1981) reached the conclusion that there are four modes of fracture propagation.
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Beginning with the start of the fracturing treatment, each of those modes is defined by a specific slope on a plot of log of pnet vs. log of time. The two basic modes are 1) a mode where a small positive slope on the log-log plot is observed and indicates that the fracture is propagating normally and 2) a mode where a unit slope on the log-log plot is observed is identified to mean a screen-out mode (Fig. 1). The other two modes include 3) a mode when pressure drops rapidly and is usually the sign of uncontained fracture height growth and 4) an elongated flat pressure (i.e. critical pressure) for which there is no definite explanation. Based on the succeeding pressure trend, several interpretations are possible for the latter mode which include rapid height growth, increasing fracture compliance and opening of fissures 2000
Net Pressure (psi)
200 0.1
1
10
100
time (min) Figure 1- Nolte-Smith analysis of a frac pack treatment In addition to the basic assumptions as noted by Nolte and Smith (1981), the analysis has two additional implied assumptions. The first assumption is that the injection rate is constant. The second assumption is that the fracture propagation is continuous (smooth function of time). Furthermore, to ensure correct interpretation of fracturing events, Nolte-Smith analysis necessitates precise knowledge of formation closure pr essure. This requires conducting of pre-fracturing tests such as minifrac test that are not routinely performed in every fracturing job. This issue is furthered with the increasing application of multi-stage multicluster fracturing schemes where the subsequent fracturing stages experience higher ISIP’s and thus higher closure stresses (Mayerhofer et al., 2011; Soliman et al., 2008).
New Approach: Moving Reference Point Technique (MRP) The approach we have developed builds on the work of Nolte and Smith by coupling the fracture propagation theory to basic testing technology. The original Nolte-Smith analysis assumes that the fracture continuously and smoothly propagates with time. Some of the recent field observations through microseismic monitoring especially in fractured shale formations imply that a fracture may grow in spurts. This sporadic fracture growth implies that a fracture m ight go through periods of ballooning followed by periods of growth. Identifying the periods of ballooning and growth will help in diagnosing problems and identifying potential sand out very early. In the new approach, the reference point is not the time of the start of injection but rather changes (vide infra). This change in reference points makes the identification of potential error quicker. The basic Nolte-Smith technique depends on the power law equation for propagation of a hydraulic fracture given below as equation 3.
log p pclosure
e log t
3
Nolte-Smith technique assumes that the fracture passes through various phases and each phase is continuous. Thus, it assumes that the log-log plot of the net pressure versus time should yield a straight line with slope e . The value of the slope e depends on the fracturing fluid flow-behavior-index, n. It has been observed that the assumption of continuous propagation, although helpful, may not be always accurate. As noted above, fracture propagation may consist of periods of ballooning followed by periods of spurt growth. These periods of ballooning and growth may alternate through the injection period. Identifying of periods of spurt growth may be very helpful and is described in the following analysis. Jeffrey et al. (2009) present a 2-D numerical simulator that is built around this idea where a fracture may balloon when it intersect a natural fracture. Figure 2 shows a mined fracture that was created in a coal bed methane formation. The figure shows that a fracture
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followed a plane of weakness (cleat) that in turn intersected the created hydraulic fracture. In such shallow formation, however, the stress level is very low and the stress anisotropy between the two horizontal stresses may be very low or nonexistent and may yield behavior inconsistent with deep formation fracturing.
Figure 2- Offsets in hydraulic fracture exposed by mining; propped fracture trace is shown in roof rock above mined coal seam, Jeffrey et al. (2009) Assuming that the reference point is t i , equation 4 is the general power law equation of fracture growth. In Nolte-Smith Analysis the reference point, t i is set as zero. In this analysis, this reference time is the start of a growth period. As shown below equations 5 and 6 may be derived from equation 4.
p pi
p t
e
t ti
p t
C t ti
C t ti
e
4
e 1
e Ct ti
5 e
6
Taking the logarithm of equations 4-6, we get equations 7-9.
log p pi log C e log t ti
p log e C e 1 log t t i t p log e C e log t ti log t t i t
log
Equations 4 and 6 may be combined to yield the following equation.
7 8 9
4
SPE 166132
p
t ti
t
e (p pi )
10
If the fracture is propagating then the exponent e will generally have a value of range determined using equation 2, the value of e will usually being 0.25 . If the fracture is ballooning, the exponent will be 1, similar to what one would observe in any storage situation. In the case of fracture ballooning equation 10 becomes equation 11.
t ti
p t
pt
11
Equations 4-6 take the following format.
p pi
p t
(t t i )
p t
C t
ti
12
C
C
13
(t t i )
14
Numerical Procedure
Analysis of fracturing pressure with MRP is done according to the data analysis flow chart presented in fig. 3.
START
Pick a new reference point
Pick the next Point
Plot e vs. time Report interpretation
YES
NO Find
Find Find
Is ɛ
< Threshold?
Figure 3 - Data analysis flow chart To begin the analysis, an initial reference point
(t ref , pref )i which meets the following criteria is picked:
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I. II.
5
For intact formations, the first reference point must be picked after the formation breakdown has occurred. For formations with existing flaws such as small cracks resulting from minifrac tests, the first reference point can be picked at any time after the existing crack has been reopened. The sandstone formation of example 1 which was previously subject to minifrac and step-rate tests falls into this category.
To obtain meaningful results it is recommended that the first few points of pressure data be omitted from analysis as such data usually contain severe fluctuations and are usually affected by formation breakdown/ fracture re-opening. After having picked the reference point, analysis continues by selecting (t ,p) pairs and then by calculating e using equation 10. Values of e are then plotted vs. time and used for fracturing behavior interpretation. In every time step, an average E and C are also calculated using equations 19a and 19b, respectively. E and C are subsequently used to estimate BHPest. (equation 20).
E C
t
1 t ti
e dt
(a)
t
ti
15
t
1 t ti
c dt
(b)
t
ti
BHPest.
p ref
C.(t tref ) E
16
If the different between the BHPest. and the observed bottomhole pressure i.e. p(t) exceeds a pre-determined threshold, then the next point in time is chosen as the new reference point and this way the entire process is repeated until injection stops .
Application to Homogeneous Formations If the formation is homogeneous and isotropic it is expected that the fracture growth would be continuous and the slope of the net pressure with time would follow the theory developed by Nolte and Smith (1981). This may be the case in hard sandstone rocks; however, this is not expected to happen in many reservoirs and definitely not in heterogeneous and shale formations. Application of the Moving Reference Point technique in the fracturing pressure analysis of two frac pack examples will be provided in the subsequent sections.
Application to Heterogeneous Formations If the formation contains various heterogeneity, natural fractures and planes of weaknesses, it is expected that the fracture growth would consist of periods of propagation and ballooning. Basically, the fracture propagates following the established theory until the fracture tip hits a region of heterogeneity. Once the fracture reaches the region of heterogeneity, it may start ballooning causing an increase in pressure. During this ballooning period it is expected that the fracture volume increases and includes the increase in the volume of the natural fracture. The ballooning effect is similar to the tip screen out effect discussed by Nolte and Smith. The volume of the fracture and natural fracture may be calculated using the following equation. p
0.041665
t
Cff Vf
17
Equation 15 is easily derived from basic well testing equation for storage period. One may also use the equation developed by Nolte and Smith which is based on the compliance of the fracture. p
2 qi
t
ql
E
2
h L
18
If the leak-off rate is negligible compared to the injection rate, equation 16 may be simplified as given in equation 17. p
t
E
2 q i E
2
h L
E 2
1
19 20
As Nolte and Smith (1981) have suggested, equation 17 may be used to estimate the distance to the restriction and
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consequently determining whether the restriction is due to tip screen out or near wellbore restriction. Equation 15 may be used in the same fashion to determine the distance to obstruction. Calculating the volume of the fracture using equation 15 at different times during the process of creating the fracture may be taken as a measure of fracture complexity.
Examples Application of the moving reference point (MRP) technique is illustrated through two examples. In addition to an introduction to the formation geologies and fracture designs, each example presents analysis results in the form of a pressure match and a plot of e vs. time. The pressure match shows how closely the numerical procedure (fig. 3) follows the observed data and thus is an indicator of the level of accuracy of the performed analysis. The e vs. time plot is the ultimate outcome of our analysis and using the criteria introduced subsequently this plot can be used to interpret fracturing pressure and to identify fracturing events. The four fracturing modes introduced by Nolte and Smith (1981) can be used with an e vs. time plot to monitor the behavior of 1
fractures during pumping. Values of e in the range of
4n 4
e
1 2n 3
indicate that the created fracture is
propagating under the assumptions of Perkins and Kern (1981) which are confined height, constant fracture compliance, and unresticted extension. e 1 usually means that fracture propagation has decreased significantly and instead fluid storage is taking place in the form of increasing fracture average pressure and average width. In addition, a rapid pressure drop i.e. e 0 is the sign of rapid height growth. No certain explanation exists for a constant fracturing pressure trend (i.e. e 0 ) and based on the succeeding pressure behavior, several interpretations are possible, including rapid height growth, increasing fracture compliance and opening of fissures. Due to the uncertainties associated with this period and the potential undesirable consequences of it, Nolte and Smith (1981) named this constant pressure “Critical Pressure” and provided guidelines for treating it. Example 1: High Perm Oil Well Frac Pack
Frac packs are normally high-rate treatments designed to create infinite conductivty (or very high conductivity) fractures to bypass the skin damage in high permeability formations. Due to high rates of injection, full packing of fractures can start and lead to pressures much beyond the allowable levels in a matter of minues or sometimes even even in fraction of a minute. Therefore quick identification of the onset of fracture-packing is of utmost importance to prevent both intolerable pressure levels and over-flushinng of proppants . Currenly, real-time fracturing diagnostic techniques include Nolte-Smith analysis and numerical simulation; however fracturing simulators are not fully capable of replicating fracturing behavior in real time. Fig. 4 compares the net pressures of two fracturing treatments with those predicted by three commercial fracturing simulators. In the first case (fig. 4a) all the simulators overestimated the average net pressure, but this is not nearly as serious as failiure to predict screenouts. Fig. 4b shows the net pressure observed during a frac pack that reached catastrophic levels whereas two out of three fracturing simulators did not see a screenout coming. It may be noted that the nature of the log-log plot of the original technique by Nolte and Smith tends to compress data. The technique presented in this paper corrects this problem. Two frac pack examples are presented here to illustrate how the Moving Reference Point technique can be used in different geologies to obtain a more detailed understanding of fracture behavior as well as to accelerate identification of fracturing problems. The two frac packs are vastly different from each other in size and in their subjected geologies. With an injected volume of 37K gallons of slurry, the first treatment is almost twice the size of the second one which injected 21K gallons of slurry. Also the first treatment was done in a relatively thin sandstone which was only 40 ft. in height whereas the second one pumped into 215 ft. of perforated interval spanning through several layers of high perm sandstone and also shale and silty sand. Results of fracture analysis studies with a three-dimensional fracturing simulator indicate that the first treatment creates a length fracture with a ratio of about 4.65, a perfect PKN-type fracture. The same ratio for the second treatment is only about height 0.75.
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Simulator 1
Simulator 2
Simulator 1
Simulator 2
Simulator 3
Observed
Simulator 3
Observed
900
6000
800 ) i s p ( e r u s s e r P t e N
5000 ) i s p 4000 ( e r u s 3000 s e r P t e 2000 N
700 600 500 400 300 200
1000
100 0
0 -10
10
30
50
0
20
Time (min)
40
60
Time (min)
(a) (b) Figure 4 - Net pressure matches obtained by commercial fracturing simulators. Job Design
A FracPack performed in a high perm sandstone formation (fig. 5) pumped 37,000 gallons of a 25 lb seawater-based fracturing fluid (fig. 6) and 54,000 pounds of a 12/18 light weight synthetic proppant. While a constant slurry injection rate of 25 BPM was maintained throughout the treatment, proppant injection started at t 18.4min and continued till the end of the treatment when the fracture could be packed no more (fig. 7). Minifrac test results show that the sandstone formation which has been highlighted in yellow on fig. 5 has an average closure stress of 5,022 psi, 200-250 psi lower than the surrounding shale barrier. This along with a modouli of elasticity in the order of the modouli of the surrounding shale and a relatively small fracture toughness are expected to lead to confined height fracture growth. As seen in fig. 6, the fracturing fluid has a flow behavior index of 0.5 for which the fracture propagation or mode I
slope ranges from
1 6
to
1 5
.
Figure 5 – Example 1 : Geology
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n' 1000 c e s / 1 0 750 7 1 @ 500 p c , y t i s 250 o c s i V 0
K'
0.75
0.2
0.5 0.1 K'
n' 0.25
0 0
0.5
1
1.5
0 0
0.5
1
1.5
Time (hours) at formation temperature (200˚f)
Time (hours) at formation temperature (200 ˚f )
(a) (b) Figure 6- Rheological properties of the fracturing fluid
Bottomhole Pressure
Slurry Rate
Proppant Concentration
7000
50 40
6000 30 BHP (psi)
Slurry Rate (BPM)
20 Proppant Concentration (PPG)
5000
10 4000
0 0
10
20
30
40
50
Time, min
Figure 7- Example 1: treatment schedule Analysis
Nolte-Smith Technique The log-log plot of P net vs. time of examples 1 ( fig 8a) matches case 2 of Nolte-Smith (1981) (fig. 8b) and is comprised of two distinct periods, including I.
II.
t
20min : The slope of this period matches that of mode I i.e.
1 6
to
1 5
and thus indicates that fracture
propagation is the predominant event of this period. t 20 min : With a slope of 1+ , this period fits the definition of mode III i.e. 1, the most possible interpretation of which is creation of a substatial flow barri er somewhere in the fracture. For this specfic example, this barrier if full-packing of fracture by the injected proppants.
So in summary, fracturing modes I and I II were identified on the Nolte-Smith chart of example 1 which helped determine the onset of fracture packing at about 25 min.
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2,000
Net Pressure, (psi)
200 0.1
1
10
100
Time (min)
(a) (b) Figure 8 - (a) Example 1: Net pressure vs. time (b) Examples with the different characteristic Slopes (Nolte & Smith, 1981) Moving Reference Point Technique The MRP analysis performed here uses a small threshold of 10 psi which permitted achieving a close match with the observed pressure (fig. 9a). A plot of Error defined here as
ABS(BHPest. p(t)) shown in fig. 9b demonstrates how close the
achieved pressure match is. Next in line is using the plot of e vs. time to interpret fracturing events. Observed Bottomhole Pressure Estimated Bottomhole Pressure 7000
50 40
BHP 6000 (psi)
Error (psi)
30 20 10
5000
0 0
10
20
30
Time (min)
(a)
40
50
0
10
20
30
40
Time (min)
(b)
Figure 9 – Example 1 (a) Pressure match obtained with MRP (b) Error in BHP estimation using MRP
As shown in fig. 10, analysis with MRP confirms the results achieved by Nolte-Smith technique, meaning that a period of overall fracture propagation i.e.
1 6
e
1 5
(on the e-time plots, this range will be highlighted in green) is followed by a period
during which continued fluid storage resulting from sand injection seems to be the predominant event (on the e-time plots, this range will be highlighted in red). Fig. 10 also shows that from time zero to t=20 min, the created fracture has gone through periods of ballooning and growth. Marked by signs on fig. 10, periods of ballooning have formed two peaks reaching almost into the red zone. This agrees with the observations made using fracture monitoring methods such as microseismic mapping which show that rather than growing continuously fractures actually tend to grow in spurts. As previously discussed, quick detection of the beginning of fracture packing and screenouts is very significant in fracturing
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treatments, especially in FracPacks. For the example in hand, MRP’ response to f luid storage starts by as early as t = 21 min (marked by an orange circle on fig. 10) when the curvature of the plot changes from positive to negative or by t= 23 min (marked by a red circle on fig. 10) when the plot has fallen well within the red zone. Application of Nolte-Smith analysis in real time is such that after ob serving a unit slope line on the Nolte -Smith chart, fracking engineer needs to wait at least quarter of a log cycle (of time) to confirm fracturing mode III. In case of example 1, this necessary precaution will delay recognition of fracture packing till t=35.6 min. Table 1 which compares the frac-packing identification times of Nolte-Smith and MRP techniques shows that MRP took about 1/4 of the time taken by Nolte-Smith to detect the onset of fluid storage resulting from the introduction of proppants into the fracture. In summary, use of MRP technique in the analysis of fracturing pressure gives a much more accurate description of fracture behavior during pumping plus it permits almost instantaneous identification of fracturing problems such as screenouts. In case of example 1, a comparison made between Nolte-Smith and MRP techniques showed that MRP cuts problem recognition time by a factor of about 4. 1.5 1.25 1
e
0.75 0.5 0.25 0 0
5
10
15
20
25
30
35
40
Time (min) Figure 10 - Example 1: analysis with Moving Reference Point Technique (M RP) Table 1: frcture packing identification times (a)
(b)
Since the beginning of injection
Since the beginning of proppant schedule ( t 18.4min )
Nolte-Smith
Moving Reference Point
Nolte-Smith
Moving Reference Point
35.6 min
23 min
17.2 min
4.6 min
Example 2: High Perm Gas Well FracPack Job Design
A FracPack treatment performed in a high permeability sandstone formation (fig. 11) consumed 21,000 gallons of a 25# seawater-based fracturing fluid (fig. 6) and 90,600 pounds of a 12/18 light weight synthetic proppant. A constant injection rate of 18 BPM was maintained throughout the treatment and the proppant was injected in a ramped manner as described in fig. 12. Bound by two thick shale layers, the pay zone consists of two high leakoff sandstone layers separated from each other by several layers of shale and silty sand. From fig. 11 and as confirmed by a minifrac test, the closure stress of the pay zone is about 6,500 psi which is substantially lower than the closure stresses of the bounding shales.
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The fracturing fluid here is the same as example 1 and thus fracturing mode I (i.e. PKN-type propagation) is expected to happen in the same condition as was discussed before i.e. Nolte-Smith slopes ranging from
1
to
6
1 5
.
Figure 11- Example 2 : Geology
Bottomhole Pressure
BHP (psi)
Slurry Rate
Proppant Concentration
9000
40
8000
30
7000
20
Slurry Rate (BPM) Proppant Concentration (PPG)
6000
10
5000
0 0
10
20
30
Time (min)
Figure 12- Example 2: treatment schedule Analysis
On the log-log plot of pnet vs. time of this example (fig. 13 ), three distinct periods can be identified, including, I. II.
t < 1 min: Pressure grows with a small slope of 0.1 and so the major fracking event of this short period is PKN-type fracture propagation. 1 min < t < 3 min and 3 min < t < 9 min: With a slope of about -0.35 and -0.1, respectively, these periods meet the conditions of mode IV i.e. fracture height growth (fig. 8b ).
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III.
t > 10 min: During this period, pressure increases with a slope larger than unity which indicates blockage of fluid flow paths by the injected proppants.
Results of analysis with MRP (fig. 14) agree with the findings of Nolte-Smith technique; meaning that an elongated period with an average e of about -0.70 prevails through the first 10 minutes of injection. This period of major fracture height growth is followed by a prolonged period of fluid storage with an e of about 1 which lasts till the end of injection. These interpretations are in accordance with the results of our fracturing simulation study which gave a good match with the length observed net pressure. Figure 14a shows that the created fracture has a ratio of about 0.75, proving the predominance height of height growth during the first 9 minutes of injection. Fig. 14b shows that the fracture profile has remained almost constant from t 9 min till the end of the FracPack. It also shows that the major event during this period is fluid storage in the form of rapid increase in pressure and fracture width. High Resolution MRP Analysis In order to obtain a more detailed understanding of the fracture behavior, we adjusted the parameters of the numerical procedure outlined in the data analysis flow chart (fig. 3). This gave a higher accuracy e vs. time plot which is shown in fig. 16. As seen in this figure, fracturing behavior is not as simple as previously thought, for example, there is a short period of constant pressure i.e. e 0 that took place right in middle of the initial pressure decline period; this point is marked by a sign on fig. 16. The physical meaning of this constant pressure is not exactly known to us yet, but it could mark propagation through the two close together shale layers that separate the top and bottom sandstone formations. Also, the last part of the FracPack that based on Nolte-Smith analysis was thought to be purely of fluid storage nature actually includes some short periods of fracture propagation and also constant pressure. These short periods are marked by signs on the fig. 16. More importantly, fig. 16 permits accurate determination of the onset of fracture packing. On the MRP analysis chart, conception of fracture packing is identified at t = 8 min when the plot falls completely in the red zone (on fig. 16, this point is marked with a sign). On the other hand, if this example were a real time Nolte-Smith analysis, to establish fracture-packing the fracking engineer would have had to wait at least till t = 17.8 min. Table 2 which compares Nolte-Smith and MRP techniques in terms of the time of identification of fracture packing shows that MRP took less than 1/6 of the time taken by Nolte-Smith to detect the inception of the new fracturing event.
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13
Net Pressure (psi)
1000
100 0.1
1
10
100
time (min) Figure 13- Example 2: Nolte-Smith Analysis 1.5 1 0.5
e
0 0
5
10
15
20
25
30
-0.5 -1 -1.5 time (min) Figure 14- Example 2: MRP analysis
(a) t 9 min (b) t 27.89 min Figure 15- Example 2: Results of fracturing simulation study confirm that no/ negligible fracture propagation has taken place form t 9 min till the end of the treatment.
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1.5 1 0.5
e
0 0
5
10
15
20
25
30
-0.5 -1 -1.5 Time (min)
Figure 16- Example 2: a higher resolution MRP analysis
Table 2: frcture packing identification times (a)
(b)
Since the beginning of injection
Since the beginning of proppant schedule (t = 6.25 min)
Nolte-Smith
Moving Reference Point
Nolte-Smith
Moving Reference Point
17.8 min
8 min
11.55 min
1.75 min
Discussion The FracPack examples provided here showed that the Moving Reference Point technique is in complete accord with NolteSmith technique. More importantly, MRP offers substantial improvements upon some of the major disadvantages associated with Nolte-Smith technique which include data compressions and loss of sensitivity to minor fracturing events that could help understand fracture behavior and also in the diagnosis of fracturing problems. Knowledge of fracture closure stress was necessary for the Nolte-Smith analyses of both examples and any inaccuracies in its amount can lead to flawed analysis and false interpretations of fracturing events. This major concern with Nolte-Smith analysis has been completely eliminated by the MRP technique meaning that although knowledge of formation breakdown/ reopening is necessary for starting MRP analysis, but for the rest of the treatment, formation closure stress is need not to be known at all. In fact, MRP owes its accuracy to elimination of a fixed reference point. As shown in the above examples, a more precise informative understanding of fracturing behavior can be obtained by adjusting the parameters of the MRP numerical procedure. This enhanced understanding lead to verification of some field observations such as growth of fractures in spurts and also penetration of fractures into separated shale layers. Of course, if more field data were analyzed using the MRP technique, more fracturing events that used to go unnoticed by Nolte-Smith technique would have been revealed here. Finally, the MRP numerical procedure itself can too be improved and optimized to get more accurate results. It can also be customized to work with different types of treatments including foam-fracking, acid-fracking and etc.
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Measuring Downhole Pressure It is strongly recommended that a downhole gauge with surface read-out be used to monitor pressure changes. This type of pressure monitoring gives accurate representations of the periods of growth and ballooning. Surface pressure gauges may be less expensive to implement, however, they do not reflect an accurate measure of the fine changes in p ressures.
Summary of Conclusions
— Nolte-Smith technique relies on assumptions such as continuous fracture propagation and fixed injection rate which do not necessarily hold true in all fracturing operations. In addition, Nolte-Smith technique requires prior accurate knowledge of formation closure stress. These along with compression of data by the log-log plot of this technique make fracture behavior interpretation rather slow and quite insensitive to minor fracturing events.
— In this paper, by taking derivative of PKN fracture propagation model, the Moving Reference Point technique (MRP) was developed. While offering the same advantages as Nolte-Smith technique does, the new method eliminates some of the limitations of the older method, for example, with MRP no prior knowledge of formation in-situ stresses is needed. Application of the new technique in the analysis of two FracPacks proved a success; meaning that in addition to providing a comprehensive understanding of fracture behavior, MRP can also help accelerate identification of fracturing problems. The new technique employs a numerical procedure to analyze fracturing pressure and due to computational intensity it needs to be implemented using computer programming. First the procedure obtains an accurate match with the observed pressure and then using this match, the exponent of the PKN fracture propagation equation i.e. e is found. Studying the changes of e with time allows identification of the changes in fracture behavior. The MRP numerical procedure itself can be subject to further improvement and optimization.
Nomenclature C
Constant
Cf f
Fracturing fluid compressibility, psi
e
Time exponent
E
Young’s modulus, psi
E'
Plane strain modulus, psi
K IC
Fractur e toughness, psi in
L
Fracture length tip to tip
n
Flow behavior index
p
Net pressure, psi
p cl
Closure stress, psi
qi
Injection rate into one fracture wing, ft3 / min
ql
Leal off rate of one fracture wing, ft 3 / min
t
Time, min
ti
Time of start of a new period, min
Vf
Fracture volume, ft 3
1
Poisson’s ratio
References Jeffrey, Robert G. , Zhang, Xi , & Thiercelin, Marc J. (2009). Hydraulic Fracture Offsetting in Naturally Fractured Reservoirs: Quantifying a Long-Recognized Process. Paper SPE 119351 presented at the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, 19-21 January 2009. http://dx.doi.org/10.2118/119351-ms. Mayerhofer, Michael J, Stegent, Neil Alan, Barth, James O, & Ryan, Kevin M. (2011). Integrating Fracture Diagnostics and
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Engineering Data in the Marcellus Shale. Paper SPE 145463 presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, USA, 30 October -2 November. http://dx.doi.org/10.2118/145463-ms. Nolte, K.G. (1979). DETERMINATION OF FRACTURE PARAMETERS FROM FRACTURING PRESSURE DECLINE . Paper SPE 8341 presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, 23-26 September. http://dx.doi.org/10.2118/8341-ms. Nolte, K.G., & Smith, MB. (1981). Interpretation of Fracturing Pressures. Journal of Petroleum Technology, 33(9): 17671775. SPE 8297. http://dx.doi.org/10.2118/8297-PA. Nordgren, R.P. (1972). Propagation of a Vertical Hydraulic Fracture. Society of Petroleum Engineers Journal, 12 (4): 306-314. SPE 3009. http://dx.doi.org/10.2118/3009-pa. Perkins, T.K., & Kern, L.R. (1961). Widths of Hydraulic Fractures. Journal of Petroleum Technology, 13(9): 937-949. SPE 89. http://dx.doi.org/10.2118/89-pa. Soliman, M.Y., East, Loyd, & Adams, David. (2008). Geomechanics Aspects of Multiple Fracturing of Horizontal and Vertical Wells. SPE Drilling & Completion, 23 (3): 217-228. SPE 86992. http://dx.doi.org/10.2118/86992-pa.
