Fracture Closure Stress: Reexamining Field and Laboratory Experiments of Fracture Closure Using Modern Interpretation Methodologies

Transcription

1 SPE MS Fracture Closure Stress: Reexamining Field and Laboratory Experiments of Fracture Closure Using Modern Interpretation Methodologies D. P. Craig, DFITpro.com; R. D. Barree, Barree & Assocs. LLC; N. R. Warpinski, Retired and T. A. Blasingame, Texas A&M University Copyright 2017, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in San Antonio, Texas, USA, 9-11 October 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 During the 1990s, field and laboratory experiments measured hydraulic fracture creation, propagation, and closure, and the archived data represent the finest collection of measurements that can be used to evaluate fracture models and fracture closure interpretation methodologies. None of the current fracture closure interpretation methods, including G-function derivative analysis, log-log storage diagnostics, and the changing-compliance method have been evaluated versus the field and laboratory measured data. Recent papers have proposed fracture closure pressure interpretations that differ from established methodologies, and under some circumstances, will result in a closure pressure that is higher than traditionally accepted. Thus, it seems an opportune time to reexamine the field and laboratory fracture closure data using interpretation methodologies developed over the last twenty years. Additional issues cloud closure pressure interpretations, including different definitions of fracture closure used in numerous publications, like mechanical fracture closure, hydraulic fracture closure, progressive fracture closure, and complete fracture closure. Evidence from downhole tiltmeters and finely-instrumented laboratory experiments of fracture propagation and closure all demonstrate that residual width is retained after closure. Consequently, closure is somewhat of a misnomer, and if a "closed" fracture remains open, the relationship between what we interpret as fracture closure and the minimum horizontal stress needs to be clearly defined based on measurements as opposed to simulation. Based on field tiltmeter deformation and pressure measurements in hard rock formations, we find that G-function derivative analysis and the log-log storage diagnostic plot interpretations together provide a fracture closure pressure that is consistent with the minimum horizontal stress identified using tiltmetermeasured rock deformation. Additionally, the closure pressure interpretations, and corresponding minimum horizontal stress, are invariant over multiple injection/falloff sequences of varying volume and time. Field experiments exhibiting variable-storage/changing-compliance signatures were also observed, and the changing-compliance method interpretations of fracture closure pressure are inconsistent with tiltmetermeasured rock deformation. Finally, we find the fracture re-opening pressure identified using tiltmeter deformation and the fracture closure pressure interpreted using pressure falloff data are essentially equal.

2 2 SPE MS Based on laboratory measurements of fracture closure and pressure, we find that G-function derivative analysis and the log-log storage diagnostic plot together provide a fracture closure interpretation generally consistent with measured fracture closure, but despite attempts to define an objective closure identification methodology, fracture closure signatures are often non-distinct and interpretations are subjective. In soft rock reservoirs, like unconsolidated sand, the fracture closure pressure interpretation does not correspond to the minimum horizontal stress, but in hard rock reservoirs, the fracture closure pressure identified using G-function derivative analysis and log-log storage diagnostic interpretations are approximately equal to the imposed minimum horizontal stress. Introduction Hydraulic fracture closure has been studied for decades by researchers inside and outside of the petroleum industry. Even after decades of study, opinions vary widely with respect to the fracture closure process, the identification of fracture closure pressure, and the relationship between hydraulic fracture closure pressure and the minimum horizontal stress. Hydraulic fracture closure pressure is typically inferred from pressure data during fracture initiation, re-opening, or falloff. While we recognize small-volume stress tests, fracture step-rate tests, fracture-injection/flow back tests, and fracture pulse tests are all used to infer closure pressure, we focus our study on fracture closure interpretations from the analysis of pressure and time data during a fracture-injection/falloff test (DFIT). Numerous models and methods exist for identifying fracture closure pressure from pressure versus time data recorded during injection/falloff sequences. In geophysics and rock engineering, Hayashi and Haimson (1991) provided a summary of commonly-used methods outside of petroleum engineering, and the authors described a fracture closure process based on observations of laboratory fracture closure experiments. Hayashi and Haimson suggested a 3-stage fracture closure process during the shut-in period following a fracture inducing or dilating injection. Stage 1 of the process begins at the end of fracture-tip extension after shut-in and as aperture along the entire fracture half-length decreases. According to Hayashi and Haimson, fracture closure begins at the fracture tip, which defines Stage 2 of the closure process, and continues as the open width and fracture length decrease from the fracture tip back to the wellbore. Stage 3 of the process is defined by "complete" closure of the hydraulic fracture, where complete closure allows for the possibility of residual fracture width. Hayashi and Haimson define the pressure observed at fracture-tip closure (Stage 2) as the minimum horizontal stress. Although Hayashi and Haimson based their model on observed field and laboratory closure data, they did not present fracture dimensions during closure to validate their proposed fracture closure process. Several derivative works have followed from the work of Hayashi and Haimson (1991), notably Raaen, Skomedal, Kjørholt, Markstead, and Økland (2001) who recognized that a change in fracture compliance should be observed as fracture closure begins at the fracture tip, and suggested a fracture-injection/flow back test and interpretation methodology to identify closure pressure from a change in fracture compliance. McClure, Jung, Cramer, and Sharma (2015) extended the work of Raaen et al., and using simulations of synthetic cases and interpretations of field data, described a changing fracture-compliance method for identifying fracture closure from pressure falloff data in the absence of flow back. Recently, Zanganeh, Clarkson, and Hawkes (2017) have suggested a fracture closure process and closure pressure identification analogous to that of Hayashi and Haimson (1991). Zanganeh, Clarkson, and Hawkes also suggest that the fracture closure pressure corresponding to the minimum horizontal stress is observed at the start of tip closure, and base their conclusions on finite-element modeling of synthetic cases and interpretations of field data. Classical fracture closure pressure interpretation methods include plotting the shut-in pressure and pressure derivative versus the square root of time, which have been described by Middlebrook, Aud, Harkrider, and Hansen (1997). Perhaps the best known fracture closure pressure interpretation methodology

3 SPE MS 3 is G-function analysis, which was initially presented by Nolte (1979), and expanded to include G-function derivative analysis by Castillo (1987) and Barree and Mukherjee (1996). A "holistic" approach to fracture closure interpretation that included a square-root of time plot, G-function derivative analysis, and a log-log storage diagnostic plot was also presented by Barree, Barree, and Craig (2009). We assume for the purposes of this research that the de facto standard for closure pressure interpretation from fracture-injection/falloff data is G-function derivative analysis combined with the log-log storage diagnostic plot. The G-function is defined as follows where the dimensionless loss-volume function at the end of pumping is defined by Valkó and Economides (1999) as and α N is Nolte's power-model growth exponent (½ α N 1) and Γ is the Euler gamma function. The dimensionless loss-volume function is defined at any time after the end of pumping and written as where F is the hypergeometric function, dimensionless time is defined as Δt D = (t t e )/t e, and t e is the time at the end of pumping. Closure Interpretation and Leakoff Types G-function derivative analysis requires a Cartesian plot of three curves: bottomhole pressure versus the G- function; the derivative, dp w /dg, versus the G-function, and the derivative, Gdp w /dg, versus the G-function. G-function derivative analysis can be used to identify hydraulic fracture closure and has been classically used to identify several non-ideal leakoff types, including pressure-dependent leakoff, fracture-height recession/transverse or variable storage, and fracture tip extension. Examples of the leakoff types commonly observed have been provided by Barree, Barree, and Craig (2009) and Craig, Eberhard, and Barree (2000). Fig. 1 contains graphs of the four common leakoff types and has been updated from that of Craig, Eberhard, and Barree to include variable storage/changing compliance. A brief review of the classical leakoff types is as follows. Normal leakoff behavior occurs when fracture area is constant during shut-in and leakoff is through a homogeneous rock matrix. With G-function derivative analysis, normal leakoff is indicated by a constant derivative and when the derivative Gdp w /dg lies on a straight line extending from the origin. Fracture closure is identified when the Gdp w /dg data deviate downward from the straight line. Pressure-dependent leakoff from dilated fractures/fissures is indicated by a characteristic "hump" in the Gdp w /dg derivative that lies above an extrapolated straight line from the origin through the normal leakoff data. The fissure opening pressure is identified at the end of the hump when the Gdp w /dg derivative data begin to follow the extrapolated straight line. A period of normal leakoff behavior is generally observed before fracture closure is identified when the Gdp w /dg derivative data deviate downward from the extrapolated straight line. Fracture height recession or transverse storage or variable storage or changing compliance during shut-in are indicated by G-function derivative analysis when the Gdp w /dg derivative data fall below a straight line extrapolated through the normal leakoff data. Traditionally, hydraulic fracture closure (1) (2) (3)

4 4 SPE MS is identified when the Gdp w /dg derivative data deviate downward from the straight line; however, McClure, Jung, Cramer, and Sharma (2015) argue that fracture closure should be identified as the pressure corresponding to the beginning of variable storage or changing compliance. Storage and compliance are related to system stiffness by a reciprocal relationship. For example, Craig and Blasingame (2005, 2006) and Craig (2014) define storage during fracture propagation and closure as (4) where C is the storage coefficient, c w is the wellbore-fluid compressibility, c f is fracture-fluid compressibility, V w is the volume of the wellbore, V f is the volume of one wing of the fracture, A f is the area of one wing of the fracture, and S f is the fracture stiffness, which can be written in a general form for 2D-analytical expressions of fracture stiffness as where c is constant, E' is the plane-strain modulus, and L c is a characteristic length. McClure, Jung, Cramer, and Sharma (2015) frame their discussion of closure around system stiffness, which is the reciprocal of storage, that is, using the definitions of storage in Eq. 4, system stiffness is defined as (5) (6) where S eff is a system stiffness. In another recent work, van den Hoek (2016) frames his discussion of fracture closure in terms of total compliance, which using the definitions in Eq. 4, he defines as (7) where C t is a system compliance and C f is a time-dependent fracture compliance, which van den Hoek defined as where h is the fracture height, L is the fracture half length, and E(m) is complete elliptical integral. van den Hoek (2016) provided an interesting modification in that he allowed a time-dependent fracture compliance during the falloff. In other words, van den Hoek's solution, which was formulated based on laboratory experiments of fracture closure, explicitly allows fracture height and or length recession before hydraulic fracture closure is observed. It should be clear that discussions of variable storage, effective stiffness, and changing total compliance all refer to the same phenomena during a fracture-injection/falloff sequence. In Fig. 1, the graph labeled "Fracture Height Recession/Transverse or Variable Storage" illustrates the Gdp w /dg derivative response during the closure process with variable storage, compliance, or (8)

5 SPE MS 5 stiffness. Additionally, the figure illustrates the different interpretations of fracture closure based on the changing fracture compliance method or the classical Gdp w /dg derivative interpretation a difference of about 500 psi between the two interpretations in the Fig. 1 example. Fracture tip extension, which occurs when a fracture continues to grow after injection is stopped, is indicated when the Gdp w /dg derivative data lie along a straight line that extrapolates above the origin. Figure 1 Classical G-function derivative analysis qualitative interpretations. As noted, Fig. 1 shows the traditional interpretation of leakoff types during a falloff, but other effects can result in a non-linear Gdp w /dg derivative response. Barree and Miskimins (2016) summarized several additional possibilities to explain Gdp w /dg derivative deviation from a normal leakoff signature, and in some cases, the root cause of the Gdp w /dg derivative deviation from normal leakoff may be either unknown or ambiguous. Additionally, combinations of the above leakoff-types can be observed in some data sets. Fracture-injection/falloff tests conducted at the toe of horizontal wells predominately exhibit variable storage or changing compliance during the falloff, so the correct fracture closure interpretation is important for determining a representative minimum horizontal stress. The holistic analysis method (Barree, Barree, and Craig 2009) also requires a log-log plot of the derivative td[p e p w (t)]/dt plotted versus time, t, which we refer to here as the log-log storage diagnostic. Craig (2014) has proved that the derivative td[p e p w (t)]/dt is related to a constant-rate pressure transient solution as follows. (9)

6 6 SPE MS where p i is the initial reservoir pressure, p wsd is the slug-test pressure difference, and dimensionless pressure, dimensionless time, and the dimensionless storage coefficient are defined as (10) (11) The fracture closure process is a storage phenomenon, so storage consists of both wellbore and fracture storage components. In general, an observed deviation of the Gdp w /dg derivative off of the extrapolated straight line, for example, pressure-dependent leakoff, will result in an observed deviation of the td[p e p w (t)]/dt derivative on the log-log storage diagnostic plot, which signals a change in fracture storage. Additionally, the deviation of the Gdp w /dg derivative identified as fracture closure coincides with dissipation of storage distortion of the pressure falloff data identified by the log-log storage diagnostic in soft and hard rock types. The above discussion of the fracture closure process and fracture closure identification are all based on analytical or numerical models, and although the models are based on fundamental physics and sound principles, their validation is often based on interpretation, which can be ambiguous. Both laboratory and field experiments of hydraulic fracture propagation and closure have been completed over the last two decades; however, the results of fracture closure models have not been routinely tested against the experimental observation. Analysis and Interpretation of Data We examined both field and laboratory data with the intent of validating fracture closure interpretation models and methodologies with known or carefully measured results. The field data include virtually all the time, rate, pressure, and deformation measurements from the M-Site project that has been summarized by Peterson, et al (1996) and Warpinski, et al (1998). We recognize that we are not the first to analyze all, or portions, of the M-Site field measurements. The original interpretations relied on fracture closure identification methods that preceded the development of G-function derivative analysis and the log-log storage diagnostics; consequently, the original interpretations were often inconsistent between data sets and analysts. Subsequent analysis of the M-Site field data, for example, the study presented by Gulrajani, Nolte, and Romero (2001), also noted inconsistent interpretations of the multiple data sets, which the authors rationalized was caused by repeated injections of increasing volume connecting higher-stress reservoir rock to the wellbore. Our intent is to provide a consistent interpretation of all relevant time, rate, pressure, and deformation data recorded at the M-Site. Additionally, our objective is to use the downhole tiltmeter fracture re-opening and fracture closing deformation measurements to define the minimum horizontal stress. With the minimum horizontal stress defined independently, we then compare fracture closure pressure interpretations from the different methodologies to validate a closure model. Many laboratory experiments have also been completed of hydraulic fracture creation, propagation, and closure. We use publicly-available laboratory data, where the minimum horizontal stress is experimentally imposed, to compare fracture closure pressure interpretations with the known solution to validate a closure model. Additionally, some publicly available data includes measurements of fracture dimensions that were recorded during closure, so the effect of changing storage (or changing compliance) can be evaluated with respect to the fracture closure interpretations. Finally, we include a never-published laboratory experiment (12)

7 SPE MS 7 where the minimum horizontal stress is experimentally imposed, and a blind test is used to compare the interpreted fracture closure pressure to the known minimum horizontal stress. Field Experiments of Fracture Closure Perhaps the most comprehensive, best-documented, and publicly available field data set of fracture closure was recorded at the M-Site in the mid-1990s. While the scope of the M-Site project was much more comprehensive than simply fracture closure determination, two separate hard rock, tight-gas sandstone formations were tested during the field experiments, and the results provide insight into the fracture closure process and fracture closure pressure determination. Experiments in both sands included multiple injections of varying injection volume, injection rate, falloff time, flow back periods, time between injections, and observations of hydraulic fracture closure. Many injections were monitored by downhole tiltmeters cemented in place in an offset wellbore along with microseismic imaging of fracture propagation from two arrays in adjacent wellbores. Fig. 2 shows a plan view of the surface location of the M-Site wells. The Monitor Well shown in Fig. 2 held six tiltmeters and a microseismic array cemented in place while a wireline-run microseismic array monitored events from MWX-3. Fig. 3 contains the location and orientation of the tiltmeters in the Monitor Well along with the location of the triaxial seismic receivers with respect to the B-Sand and C-Sand in the MWX-2 treatment well. Within Fig. 3, the measurementaxis orientation is shown for each tiltmeter, and for all tiltmeters the y-axis is essentially normal to the primary fracture orientation in the treatment well, which is shown in Fig. 2. With the tiltmeter y-axes essentially normal to the primary fracture plane, the tiltmeters have proven to be extremely sensitive to the rock deformation resulting from small fracture-width changes in the treatment well. Additionally, the deformation and tiltmeter response is virtually immediate with respect to rate or pressure changes in the treatment well once the treating pressure exceeds the minimum horizontal stress. Additional M-Site wellbore configuration, experimental measurements, and experimental procedures have been exhaustively documented by numerous authors, including Warpinski et al (1995, 1996, 1997, 1998), Peterson, et al (1996), and Branagan, et al (1996a, 1996b, 1997a, 1997b). Figure 2 Plan view of M-Site, including locations of treatment well (MWX-2) and Monitor Well (downhole tiltmeters). After Branagan, et al

8 8 SPE MS Figure 3 Tiltmeter placement within Monitor Well, and tiltmeter axis orientation. After Branagan et al. (1996). For the purposes of this paper, the pressure, rate, and time data recorded during the injection/falloff sequences are interpreted using G-function derivative analysis and the log-log storage diagnostic plot to infer hydraulic fracture closure, and where relevant tiltmeter measurements are available, closurestress interpretations are compared with tiltmeter-measured rock deformation. As noted, the downhole tiltmeters are extremely sensitive to deformation created by an opening or closing fracture; thus, the tiltmeter measurements provide the best direct indication of hydraulic fracture width changes in field experiments. Injection/falloff sequences were completed in both the B-sand and the C-sand. In the B-sand, a total of 10 injection/falloff, or injection/falloff/flowback, sequences were recorded over a period of nine months with different fluid types, volumes, injection rates, falloff period, and flowback period. The first three injection/falloff sequences were three small volume and low rate classical stress tests to establish an estimated minimum horizontal stress. In the C-sand, a total of 8 injection/falloff, or injection/falloff/ flowback, sequences were recorded with different fluid types, volumes, injection rates, falloff period, and flowback period. No small-volume stress tests were pumped in the C-sand in the MWX-2 wellbore. Fracture re-opening experiments were pumped in both the B-Sand (Injection 4B) and the C-Sand (Injection 4C). Prior injections in both sands had created and propagated a hydraulic fracture, so the reopening experiments were pumped at very low rates to observe the dilation of an existing fracture, which would be indicated by the rock deformation measured by the tiltmeters. As previously noted, an existing fracture should dilate (open) as the pressure within the fracture exceeds the minimum horizontal stress. Conversely, an existing fracture should contract (close) during a falloff to a residual-width. In hard rock (E > psi [12.5 GPa]), the pressure observed at fracture closure (residual width) corresponds to the minimum horizontal stress. Thus, in both the B-Sand (E = psi [31.5 GPa]) and C-Sand (E = 5.25

9 SPE MS psi [36.2 GPa]) fracture re-opening and fracture closure should occur at the same pressure, which is equivalent to the minimum horizontal stress (within experimental error). In soft rock (E < psi [5.0 GPa]), which includes unconsolidated sand formations, fracture closure to a residual width can be observed at a pressure below the minimum horizontal stress (Dong and de Pater 2007). B-Sand Stress Tests and Fracture Closure Experiments B-Sand experiments at the M-Site began with three stress tests in November Fig. 4 shows graphs for each of the three stress tests, which are labeled within each graph "Stress Test #1," "Stress Test #2," and "Stress Test #3." For each injection/falloff sequence, Fig. 4 shows graphs of bottomhole pressure and injection rate versus time; bottomhole pressure, the derivative of bottomhole pressure with respect to the G- function, dp w /dg, and the product of the G-function and the derivative of bottomhole pressure with respect to the G-function, Gdp w /dg, plotted versus the G-function during the shut-in period; and a log-log storage diagnostic graph of the fracture-pressure difference, p e p w (t), and the product of time and the derivative of the fracture-pressure difference with respect to time, td[p e p w (t)]/dt, plotted versus time since the beginning of the injection. Figure 4 MWX-2 stress tests recorded in November 1994.

10 10 SPE MS Stress Test #1 was a very small injection of 41-gal of water pumped at injection rates of less than 20 gal/min. For Stress Test #1 the 1994 interpretation of closure of (p c ) 1994 = 3,020 psi is shown along with a new interpretation of the fissure-opening pressure, (p fis ) 2017 = 2,941 psi, and fracture closure pressure, (p c ) 2017 = 2,886 psi using G-function derivative analysis. The log-log storage diagnostic graph shows that the fracture closure time interpreted using G-function derivative analysis corresponds to the dissipation of storage distortion of the pressure falloff data. Stress Test #2 was a slightly larger injection of 47-gal of water pumped at injection rates of less than 20 gal/min. For Stress Test #2, the new interpretation includes a fissure opening pressure of (p fis ) 2017 = 2,915 psi, and hydraulic fracture closure pressure of (p c ) 2017 = 2,893 psi. Stress Test #3 was again a slightly larger injection of 51-gal of water pumped at injection rates of less than 20-gal/min, but the test included a step-down in injection rates. G-function derivative analysis shows a fissure-opening pressure, (p fis ) 2017 = 2,960 psi, but the final recorded pressure during the falloff was (p w ) final = 2,938 psi, and G-function derivative analysis confirms that hydraulic fracture closure was not observed, which is indicated by the increasing Gdp w /dg derivative through the end of the recorded pressure data. The log-log storage diagnostic also demonstrates that the end of storage distortion was not observed during the recorded falloff, which is also indicated by the increasing derivative, td[p e p w (t)]/dt. After a 19-bbl borate crosslinked-gel injection (Injection 1C) was completed, the fracture diagnostics continued with Injection 2B, Injection 3B, and Injection 4B, and the fracture closure diagnostic graphs are shown in Fig. 5 with each injection/falloff sequence labeled "Injection 2B," "Injection 3B," and "Injection 4B," respectively. Injection 2B consisted of 27.1 bbl of 2% KCl-treated water injected in step rates up to 3.3 bbl/min. There are several important features of Injection 2B to note. First, the step-rate injection can theoretically be used to interpret fracture closure pressure from a graph of bottomhole pressure versus injection rate; however, close examination of the bottomhole pressure and injection rate versus time graph for Injection 2B clearly shows the pressure response was not smooth or constant at the lowest injection rate of 0.5-bbl/min; consequently, an interpretation of the fracture closure stress from the step-rate pressure data, like that presented by Gulrajani, Nolte, and Romero (2001), is highly questionable.

11 SPE MS 11 Figure 5 MWX-2 Injections 2B (27 bbl), 3B (104 bbl), 4B (215 bbl) April Second, the G-function derivative analysis graph clearly shows the "sudden" appearance of variable storage or changing compliance during the falloff, which was not observed in any of the stress tests recorded before the crosslinked-gel Injection 1B. The fracture-compliance method interpretation suggests a fracture closure pressure of (p c ) ΔCbc = 3,208 psi, where the subscript ΔCbc denotes variable storage/compliance before closure. Since the final recorded pressure before beginning flow back was (p w ) final = 2,893 psi, fracture closure was not observed during the falloff based G-function derivative analysis. Additionally, the loglog storage diagnostic clearly shows storage distortion is observed through the end of the recorded falloff data; thus, hydraulic fracture closure was also not observed during the falloff based on the log-log storage diagnostic. Injection 3B was a 104-bbl injection of 2% KCl-treated water, which except for a brief shut-down early in the test, was injected at a constant rate. The bottomhole pressure and injection rate versus time plot shows the final recorded pressure during the falloff was (p w ) final = 2,972 psi. The G-function derivative analysis graph once again suggests variable storage/changing compliance was observed during the falloff. Using the fracture-compliance method, the fracture closure is (p c ) ΔCbc = 3,308 psi. Fracture closure was not observed

12 12 SPE MS based on G-function derivative analysis as indicated by the increasing derivative, Gdp w /dg, and based on the log-log storage diagnostic plot, which shows an increasing derivative, td[p e p w (t)]/dt, and corresponding storage distortion of the pressure falloff. Injection 4B was a bbl injection of 2% KCl-treated water with a brief shut-down during the injection, but with a hydraulic fracture re-opening experiment included at the beginning of the injection. As was observed in Injection 2B and Injection 3B, the G-function derivative analysis plot shows a strong indication of variable storage/changing compliance, and the fracture-compliance method closure pressure is (p c ) ΔCbc = 3,330 psi. Conversely, fracture closure was not observed based on G-function derivative analysis and the log-log storage diagnostic plots, which both show increasing derivatives, Gdp w /dg and td[p e p w (t)]/ dt, respectively, through the end of the falloff data. Although the low-volume stress tests should have established a fracture closure pressure corresponding to the minimum horizontal stress, the test analyses remain pressure interpretations of fracture closure and are not a direct observation of closure. The tiltmeters, however, are a measurement of rock deformation as a function of increasing hydraulic fracture width. Consequently, a re-opening experiment where 2% KCl-treated water is slowly injected into an existing fracture, and the pressure gradually increases, should indicate measurable rock deformation as the pressure within the fracture exceeds the minimum horizontal stress (closure pressure) and the hydraulic fracture dilates. Fig. 6 contains plots of bottomhole pressure and y-axis deformation of the tiltmeters at 4,628-ft (below the B-Sand), 4,558-ft (within the B-Sand), 4,487-ft (above the B-Sand). In each figure, the tiltmeter measurements are essentially constant before the injection begins and as pressure starts to increase. As bottomhole pressure exceeds approximately 2,800 psi, deformation is observed in every tiltmeter. The tiltmeter measurements suggest existing-fracture dilation begins at approximately (p c ) ReOpen 2,800 psi, which may be the fracture opening pressure corresponding to the minimum horizontal stress. Each figure shows a vertical red dashed line that corresponds to the fracture closure pressure interpreted from the stresstest data, 2,855 psi (p c ) ,893 psi and the black dashed line corresponds to the fracture closure stress interpreted using the fracture-compliance method, which is 3,208 psi (p c ) ΔCbc 3,330 psi. Figure 6 MWX-2 B-Sand Injection 4B re-opening experiment tiltmeters identifying deformation and fracture opening. Unfortunately, tiltmeter re-opening experiments also have uncertainty, for example, if the re-opening injection rate is too high, deformation may be observed before reopening. The tiltmeter measurements are, however, consistent with the fracture closure pressure interpreted from G-function derivative analysis and log-log storage diagnostic. Additionally, the tiltmeter measurements seem to validate that the fracture closure pressure interpretations based on identifying the dissipation of storage distortion correspond to the minimum horizontal stress. Conversely, the tiltmeter measurements are inconsistent with the findings of the fracture-compliance method for closure identification, that is, the fracture-compliance method interpreted closure pressure may not correspond to the minimum horizontal stress. Fig. 6 does show a significant

13 SPE MS 13 increase in deformation as the pressure exceeds approximately 3,100 psi, but the initial deformation is observed as bottomhole pressure increases above approximately (p c ) ReOpen 2,800 psi. Injections 5B and 6B were both 400-bbl 40-lb/1,000-gal linear gel injections, and the pressure falloff did not extend through hydraulic fracture closure for either injection/falloff sequence. Injection 7B consisted of the final KCl-treated water injection/falloff in the B-Sand, and the falloff did extend through hydraulic fracture closure. Fig. 7 shows the Injection 7B diagnostic plots, and the bottomhole pressure and injection rate versus time graph show that the injection consisted of 30.5-bbl of 2% KCl treated water at injection rates up to 19 bbl/min. Unlike Injection 2B, Injection 3B, and Injection 4B, but like the three stress tests, the leakoff-off type identified using G-function derivative analysis is pressure-dependent leakoff with a fissureopening pressure of (p fis ) 2017 = 2,893 psi. G-function derivative analysis shows no indication of variable storage/changing compliance, but it does indicate fracture closure was observed at (p c ) 2017 = 2,855 psi, which is consistent with the three stress tests and validated by the tiltmeter measurements from the Injection 4B reopening experiment. The log-log storage diagnostic also shows storage distortion dissipates as the fracture closes, which is indicated by the decreasing derivative td[p e p w (t)]/dt, after closure. Figure 7 MWX-2 B-Sand Injection 7B bbl KCl water prefrac DFIT August The tiltmeter measurements during the re-opening experiment provided a clear indication of hydraulic fracture re-opening and dilation during the injection, but the measurements are not as definitive during closure. For example, Fig. 8 contains a graph of bottomhole pressure and tiltmeter deformation recorded during the pressure falloff for the tiltmeter located at 4,487-ft (above the B-Sand). Notice that as bottomhole pressure falls below the re-opening pressure and falloff-interpreted fracture closure pressure, the tiltmeter measurements continue to show decreasing deformation, which suggests fracture width continues to decrease. Examination of the tiltmeter measurements also shows that the data are relatively noisy; however, the shape of the tiltmeter-measured deformation curve is similar to the pressure falloff curve, and the tiltmeter-measured deformation might follow relationships known to exist for fracture pressure falloff data.

14 14 SPE MS Figure 8 MWX-2 B-Sand Injection 7B bottomhole pressure and tiltmeter (4,487 ft) falloff during shut-in. As previously noted, Craig (2014) demonstrated that the derivative, td[p e p w (t)]/dt, is related to a general pressure transient solution as follows. Generally, an analytical solution for a fractured well is used to generate the pressure transient derivative, and the observed DFIT data are matched to an appropriate solution. The method is general, and any appropriate transient solution, including flow from an infinite- or finite-conductivity fracture, dual porosity reservoir, anisotropic reservoir, multiple producing fractures, etc., can be used in the matching process. For the purposes of the current paper, it's important to note the behavior of the pressure-transient derivative, which is shown in Fig. 9. In Fig. 9, the increasing derivative is indicative of wellbore and fracture storage distortion. Wellbore and fracture storage distortion dissipates as the curve reaches the apex and begins to fall. A closing fracture is a type of storage (Craig and Blasingame 2005, 2006), and in most cases, fracture storage affects the falloff data long after wellbore storage has dissipated. Thus, when the derivative, td[p e p w (t)]/dt, is increasing, the fracture is still closing. (13) Figure 9 Pressure transient solution derivative versus dimensionless time.

15 SPE MS 15 In terms of the tiltmeter response, tiltmeter measurements peaked at the end of pumping, that is, the hydraulic fracture maximum width was observed at the end of pumping and pressure p e. Since tiltmeter deformation is proportional to the fracture width, and the fracture width changes over time are a function of pressure, it's anticipated that the tiltmeter deformation-difference derivative, td[(u y ) e u y (t)]/dt, curve should mirror the fracture pressure-difference derivative curve. In other words, we postulate that in a homogeneous reservoir with normal leakoff, the tiltmeter deformation-difference derivative, td[(u y ) e u y (t)]/ dt, will increase through hydraulic fracture closure. Similarly, if pressure-dependent leakoff is observed, the tiltmeter deformation-difference derivative should show a positive "hump," like the fracture pressuredifference derivative. One issue, however, in attempting derivative analysis of tiltmeter data is the noise noted in Fig. 8. If finitedifference differentiation of the noisy tiltmeter data is attempted, the noise will be amplified by the derivative calculation, and the derivative may be of limited value. An alternative technique for calculating a "noiseless" underlying derivative of noisy experimental data was developed by Chartrand (2011) and is called total variation regularization. Fig. 10 illustrates the derivative calculation of the tiltmeter measurements (4,487 ft) using both "smoothed" central-difference calculations and total variation regularization. With a smooth derivative calculation, the tiltmeter deformation-difference derivative, td[(u y ) e u y (t)]/dt, should show trends similar to the fracture pressure-difference derivative, td[p e p w (t)]/dt. Figure 10 MWX-2 B-Sand Injection 7B tiltmeter du y /dt derivative calculated with central-difference and total variation regularization. Fig. 11 shows a log-log graph of the tiltmeter deformation-difference derivative versus time since the beginning of pumping for the tiltmeters at 4,487-ft (above B-Sand), 4,558-ft (within B-Sand), and 4,628- ft (below B-Sand). All three tiltmeter derivative curves have a similar behavior that includes a pressuredependent leakoff "hump" followed by an increasing derivative until fracture closure is observed. Fig. 11 also contains a log-log plot of both the fracture pressure-difference derivative and the tiltmeter deformationdifference derivative (4,558-ft within B-Sand), and shows how both exhibit a pressure dependent hump and an increasing derivative before hydraulic fracture closure is interpreted. Figs. 10 and 11 demonstrate that a characteristic tiltmeter deformation-derivative signature was observed and is consistent with pressureinferred hydraulic fracture closure. While the tiltmeter deformation-derivative curves may not provide an easily-identified and definitive closure event, the tiltmeter deformation-difference derivative interpretation along with the analog fracture pressure-difference derivative methodology provide convincing evidence of hydraulic fracture closure, and the closure pressure is consistent with the fracture re-opening and pressure-

16 16 SPE MS falloff inferred fracture closure pressure. To our knowledge, a relationship between the deformationdifference derivative and the pressure-difference derivative has not been studied. The trends observed in the tiltmeter and pressure data suggest additional research is warranted to mathematically define a relationship if one exists. Figure 11 Comparison of tiltmeter deformation-difference derivatives, td[(u y ) e -u y (t)]/dt, and comparison of tiltmeter deformation-difference derivative (4,558 ft) with observed fracture pressure-difference derivative, tdδp/dt. Fracture Re-Opening Experiment C-Sand The C-Sand is located between 4,303-ft and 4,390-ft in the MWX-2 wellbore, and the experiments of interest for the present paper are Injection 3C and Injection 4C, which includes a fracture re-opening experiment. Injection 1C, like Injection 1B in the B-Sand, was a 95-bbl injection of 40-lb/1,000-gal borate-crosslinked gel, and Injection 2C was a 40-lb/1,000-gal linear gel injection. Injection 3C was a 247-bbl injection of 40-lb/1,000-gal linear gel, with a significant falloff period; however, fracture closure cannot be interpreted from the falloff data using G-function derivative analysis and the log-log storage diagnostic plot. Fig. 12 contains a graph of bottomhole pressure and injection rate versus time, the G-function derivative analysis plot, and the log-log storage diagnostic graph. The graph of bottomhole pressure and injection rate versus time shows a maximum injection rate of 19-bbl/min and a falloff that was recorded through a final bottomhole pressure of (p w ) final = 2,956 psi. G-function derivative analysis suggests fracture closure was not observed through the end of the falloff, and the log-log storage diagnostic also shows an increasing fracture pressure-difference derivative through the end of the falloff, which confirms storage was still distorting the pressure falloff and suggests the fracture was still closing.

17 SPE MS 17 Figure 12 MWX-2 C-Sand Injection 3C DFIT Analysis. A fracture re-opening experiment was also conducted in the C-Sand, and Fig. 13 contains a graph of bottomhole pressure and injection rate during the re-opening. The injection rates were kept lower during re-opening as compared to the B-Sand re-opening experiment; thus, the tiltmeter re-opening deformation measurements may provide a more definitive fracture re-opening pressure. As shown in Fig. 13, the injection rates were maintained at generally less than 10-gal/min until fracture opening was observed. Fig. 14 contains graphs of bottomhole pressure and tiltmeter deformation for the tiltmeters at 4,418-ft (below the C-Sand), 4,348-ft (within the C-Sand), and 4,273-ft (above the C-Sand). Even with the noise in the tiltmeter-recorded deformation, a fracture re-opening pressure of approximately (p c ) ReOpen 2,900 psi was observed. Pressure falloff analysis of the entire Injection 4C injection/falloff sequence is shown in Fig. 15. The final recorded pressure during the falloff was (p w ) final = 3,108 psi, which is clearly above the hydraulic fracture re-opening stress, and both G-function derivative analysis and the log-log storage diagnostic confirm that hydraulic fracture closure was not observed during the falloff, which is indicated by the increasing derivatives, Gdp w / dg and td[p e p w (t)]/dt, respectively, through the end of the falloff data. Figure 13 MWX-2 C-Sand Injection 4C Reopening Experiment.

18 18 SPE MS Figure 14 MWX-2 C-Sand Injection 4C Reopening Experiment. Figure 15 MWX-2 C-Sand Injection 4C DFIT Analysis Summarizing the findings from both the B-Sand and C-Sand injection/falloff and fracture re-opening experiments, we observed the following. Fracture re-opening experiments using bottomhole pressure and tiltmeter deformation measurements suggest a B-Sand fracture re-opening pressure of (p c ) ReOpen 2,800 psi and a C-Sand re-opening pressure of (p c ) ReOpen 2,900 psi. Fracture closure pressure interpretations using G-function derivative analysis and the log-log storage diagnostic suggest a fracture closure pressure approximately equivalent to the fracture reopening pressure. In the B-Sand, the falloff-interpreted closure pressure was 2,855 psi (p c ) ,893 psi. However, the C-Sand injection/falloff sequences did not allow bottomhole pressure to decline below p w (t) = 2,956 psi, but we can confidently state that the falloff analysis in the C-Sand suggests a fracture closure pressure of (p c ) C-Sand < 2,956 psi. Fracture closure pressure when interpreted using G-function derivative analysis and the loglog storage diagnostic was invariant over multiple injection/falloff sequences, including different fluids, fluid volumes, and rates, and invariant over time. The fracture-compliance method interpretations of the G-function derivative, Gdp w/dg, in the B- Sand injections suggested a fracture closure pressure of 3,208 psi (p c ) ΔCbc 3,330 psi, which are inconsistent with the small-volume stress tests, holistic G-function derivative analysis, and the fracture re-opening experiments. Tiltmeter measurements during a pressure falloff do not exhibit an easily-identifiable and definitive closure event.

19 SPE MS 19 Tiltmeter deformation-difference derivative curves are generally similar in shape and behavior to fracture pressure-difference derivatives; consequently, the deformation-difference derivative can potentially validate fracture closure and the end of storage distortion identified using G-function derivative analysis and the log-log storage diagnostic. Laboratory Experiments of Fracture Closure Numerous researchers have reported experiments of fracture propagation and closure under controlled laboratory conditions. Cheung and Haimson (1989) looked at existing fracture closure interpretation techniques, while also developing a new model of their own, for identifying fracture closure pressure from pressure falloff data. Their experimental method required multiple injection-falloff sequences with the wellbore pressure falling to below 1 MPa before each subsequent injection, and their experiments focused as much on identifying the fracture re-opening pressure as the fracture closure pressure. Fig. 16 contains a graph of pressure and the Gdp w /dg derivative for injection a of Test #10 for a Niagara dolomite (E > psi [43.7 GPa]) fracture closure experiment. Injection a was the first fracture-injection/ falloff in the sample, and it was the only injection/falloff sequence with sufficient analyzable beforeclosure data. For example, only about 10 seconds of before-closure pressure data are available for analysis in Fig. 16, which is barely sufficient to identify trends. The raw experimental data were not available; however, Cheung and Haimson's Fig. 2 was digitized using publicly-available software (Rohatgi 2017), which provided the pressure and time data required to construct Fig. 16. While digitizing historical publiclyavailable experimental data is sometimes necessary (and worthwhile), there is inevitably a loss of resolution; consequently, the data scatter shown in Fig. 16 may not have existed in the original raw pressure and time recording. Figure 16 Niagara Dolomite Test #10 Injection a. After Cheung and Haimson (1989). The graph illustrates a clear "hump" in the Gdp w /dg derivative, which based on Fig. 1, is interpreted as pressure-dependent leakoff. de Pater et al (1994) have found pressure-dependent leakoff in laboratory fracturing experiments of moderately hard sandstone, so the result is anticipated even though the sample contains no obvious natural fractures or fissures. The closure pressure is interpreted to be 13.2 MPa, which is within 12% of the imposed 15 MPa minimum horizontal stress. While the interpretation reasonable, it is nonunique because of limited before-closure data and a noisy Gdp w /dg derivative. With very few beforeclosure data points, and since virtually all the before-closure data is affected by pressure-dependent leakoff, the log-log storage diagnostic is of limited value for a fracture closure interpretation in this case.

20 20 SPE MS When reviewing laboratory data, it is useful to have fracture dimensions measured during closure to help correlate the pressure falloff to measured fracture dimensions. While Cheung and Haimson reported acoustic emissions during closure, fracture dimensions during closure were not reported. de Pater, Desroches, Groenenboom, and Weijers (1996) presented measurements of both pressure falloff and fracture dimensions with respect to time for both sandstone (E psi [20.4 GPa]) and cement paste. Fig. 17 contains a graph of pressure, dp w /dg, and Gdp w /dg versus the G-function and a graph of fracture width at the wellbore, fracture radius, and Gdp w /dg versus the G-function. The data were digitized from Fig. 3 and Fig. 10 of de Pater, Desroches, Groenenboom, and Weijers (1996) for the sandstone sample. Figure 17 G-function derivative analysis and fracture dimensions during closure for SNV03. After de Pater, et al (1996). G-function derivative analysis suggests fracture closure was not observed through the end of the recorded pressure falloff data as indicated by the Gdp w /dg derivative following a straight line extrapolated from the origin. The imposed stress was 23 MPa, which coincides with the last recorded pressure. A definitive closure identification using G-function derivative analysis would have required recording the pressure falloff below 23 MPa; however, the Gdp w /dg derivative curve is consistent with the observed closure. In other words, closure was not observed during the falloff, which is confirmed by the Gdp w /dg derivative curve. Pressure-dependent leakoff is once again indicated during the falloff of the sandstone sample by the Gdp w /dg derivative "hump." Fig. 17 also shows that during the Gdp w /dg derivative pressure-dependent leakoff signature, both the fracture width and fracture radius were decreasing. As previously discussed, a decreasing radius during the falloff increases fracture stiffness, which should result in decreasing storage and a changing compliance signature of the Gdp w /dg derivative, which is opposite of what is observed. In both the Niagara dolomite and the Colton sandstone samples, any variable storage/changing compliance signature that should be observed in the Gdp w /dg derivative, is masked by the pressure-dependent leakoff. The fracture width change and radius change during closure confirm that the fracture was indeed closing from the fracture tip back to the wellbore, which is consistent with the closure process defined by Hayashi and Haimson (1991) and "progressive fracture closure" as defined Zanganeh, Clarkson, and Hawkes (2017). However, the experiment also clearly shows that the minimum horizontal stress is not equivalent to the pressure at tip-closure. At fracture-tip closure, the experimental data show a pressure of about 30 MPa, but the imposed horizontal stress was only 23 MPa; thus, the conclusions of Zanganeh, Clarkson, and Hawkes are not supported by experimental data in a hard rock sample. In hard rock, a fracture closure pressure

21 SPE MS 21 corresponding to the minimum horizontal stress is correctly identified by the traditional Gdp w /dg derivative interpretation and the log-log storage diagnostic when the fracture closes to essentially the residual width at the wellbore. Dong and de Pater (2007) presented a fracture closure experiment of a soft unconsolidated sand (E 250,000 psi [1.7 GPa]), which makes a very interesting comparison with the hard-rock cases noted above. Fig. 18 contains a graph of p w, dp w /dg, and Gdp w /dg versus the G-function along with a log-log graph of the td[p e p w (t)]/dt derivative versus time. A Gdp w /dg derivative interpretation suggests fracture closure is observed at G = 2.09 and a closure pressure of 3 MPa after periods of pressure-dependent and normal leakoff; however, the imposed stress during the experiment was 7 MPa. The td[p e p w (t)]/dt derivative also shows the effects of pressure-dependent leakoff and fracture storage distortion until fracture closure was observed. Fig. 19 is reproduced from Dong and de Pater (2007) and shows several CT scans of the hydraulic fracture during the pressure falloff. The CT scans shows that the fracture remains open with perhaps a small decrease in aperture as the pressure declines below the imposed horizontal stress; however, it also shows that the fracture closes as the pressure decreases to about 3 MPa. After the pressure falls below the imposed minimum horizontal stress, fracture closure begins at the tip and proceeds back to the wellbore until a residual fracture width is observed. The CT scans graphically demonstrate that the Gdp w /dg derivative and the log-log td[p e p w (t)]/dt derivative accurately reflect fracture closure, that is, the methods can identify the decrease to a residual fracture width and volume, but for soft rock, the closure pressure does not correspond to the minimum horizontal stress. Figure 18 Soft unconsolidated sand closure experiment CTC08. After Dong and de Pater 2007.

22 22 SPE MS Figure 19 CT scans of fracture closure in a soft unconsolidated sand. After Dong and de Pater (2007). Fig. 19 is also an excellent visualization of fracture-storage distortion. As previously noted, during a fracture-injection/falloff test, storage has both wellbore and fracture components. In the laboratory experiments, wellbore storage is minimized, so the primary contributor to storage distortion of the falloff data is fracture closure when fluid is "squeezed" from the fracture into the formation as closure proceeds. Figs. 18 and Fig. 19 viewed in conjunction demonstrate that the storage distortion observed in the td[p e p w (t)]/dt derivative is purely a function of the closing fracture. When the fracture finally closes, storage distortion of the pressure falloff dissipates. The observation holds for field and laboratory data and is independent of rock hardness. Fig. 20 is an example provided by van Dam and de Pater (2017) of a closure experiment in a harder sample (E psi [8.9 GPa]). The example was provided as a "blind test" where the imposed stress remained unknown until after an analysis was completed, and the examples illustrates the difficulty of interpreting fracture closure from laboratory data. The Gdp w /dg derivative shows a pressure-dependent "hump," a variable storage/changing compliance "dip," and a period of normal leakoff. A changingcompliance interpretation results in a closure pressure of MPa, which is 26% too high, and as was demonstrated in the field experiments, a strict changing-compliance closure interpretation as advocated by McClure, Jung, Cramer, and Sharma (2015), does not provide the correct closure pressure and minimum horizontal stress. A classical interpretation resulted in a closure pressure of MPa, and while the classical interpretation is within 10.5% of the correct answer (16 MPa), it illustrates the difficulty in drawing the correct Gdp w /dg derivative straight line during a G-function derivative analysis without a clear and distinct deviation of the Gdp w /dg derivative off the straight line. It also shows that picking the end of storage distortion using the td[p e p w (t)]/dt derivative is helpful, but it is also not distinct since closure is observed as storage distortion dissipates and not necessarily at the apex of the td[p e p w (t)]/dt derivative. In other words, despite all attempts to make fracture closure identification objective using the Gdp w /dg and td[p e p w (t)]/dt derivatives, the pressure falloff trends from laboratory experiments are often non-distinct and the interpretation subjective, which can introduce some interpretation error for example, 12.5% for the hard dolomite and 10.5% for the hard sandstone.