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Practical considerations for diagnostic fracture injection test (DFIT) analysis
Accepted Manuscript Practical considerations for diagnostic fracture injection test (DFIT) analysis Guoqing Liu, Christine Ehlig-Economides PII:
S0920-4105(18)30701-0
DOI:
10.1016/j.petrol.2018.08.035
Reference:
PETROL 5215
To appear in:
Journal of Petroleum Science and Engineering
Received Date: 25 January 2018 Revised Date:
22 July 2018
Accepted Date: 12 August 2018
Please cite this article as: Liu, G., Ehlig-Economides, C., Practical considerations for diagnostic fracture injection test (DFIT) analysis, Journal of Petroleum Science and Engineering (2018), doi: 10.1016/ j.petrol.2018.08.035. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Practical Considerations for Diagnostic Fracture Injection Test (DFIT) Analysis Guoqing Liu and Christine Ehlig-Economides, University of Houston
Abstract
Introduction
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The diagnostic fracture injection test (DFIT) provides a way to estimate parameters critical to hydraulic fracture design. Existing published models for before-closure and after-closure behaviors rely on assumptions, and failure to honor important realities leads to parameter estimation errors that could degrade hydraulic fracturing design. This paper is to illustrate an accurate way to estimate parameters from the DFIT data, and then discuss how these parameters should be used in the hydraulic fracture design, and at last offer an alternative DFIT design approach. Two fundamental concepts underlying the proposed methodology are the material balance before fracture closure and the diffusive flow in the formation after closure. Before closure analysis must correctly address abnormal leakoff behaviors and near well friction losses. Likewise, accurate permeability and pore pressure estimation requires correct accounting for the leakoff rate into the formation. Strict attention to material balance yields estimations for instantaneous shut-in pressure (ISIP) and perforation and tortuosity friction losses that may, in turn, avoid apparent very high net pressure and stress shadowing. This work also underscores the importance of understanding surface and downhole volumes and rates both in the DFIT design and in the analysis. Further, for the DFIT case with pressure dependent leakoff (PDL), the fracture design for the subsequent hydraulic fracturing treatment should use the apparent leakoff rate associated with the first closure trend instead of the leakoff rate associated with the last closure trend derived from a normal leakoff model. Two successive DFITs in the same perforation, the first treated with low injection rate and small volume and then the second with high rate and large volume, are proved to be a good practice to obtain reliable estimation of formation properties. This paper demonstrates that DFIT parameters have often been misused. With the proposed methodology, the interpretation will be more accurate and reliable for formation evaluation and hydraulic fracture design.
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The diagnostic fracture injection test (DFIT), also termed as minifrac, fracture calibration test or fracture injection and falloff test, has been widely used to evaluate formation and obtain several key parameters for hydraulic fracture design (Feng and Gray 2016). The traditional interpretation methodology of a DFIT analysis is first to find the fracture closure pressure, and then divide the data into two portions: that occurring before closure (BC) and that occurring after closure (AC). Several BC analytical or semianalytical models have been proposed based on a series of assumptions since the pioneered model by Nolte (1979), including models by Nolte (1986), Hagoort (1981), Mayerhofer and Economides (1993), Craig and Blasingame (2006) and Liu and Ehlig-Economides (2015). All these BC models require a material balance ensuring that the sum of the fracture volume and the cumulative leakoff volume equal the total injected fluid volume. The total injection volume is usually calculated with the recorded rate and time, and could be taken as a known parameter. The core problem of the fracture modelling is therefore to connect the other two volumes in the material balance function: the fracture volume and the cumulative leakoff volume. All the above-mentioned BC models calculate the fracture volume during pressure falloff by assuming linear elasticity and a 2D fracture geometry. However, there are two ways to estimate the leakoff volume: one using a leakoff coefficient associated with the Cater leakoff model (Carter 1957; Nolte 1979, 1986; Liu and Ehlig-Economides 2015), and the other estimating permeability and skin based on the diffusive linear flow from the fracture into the matrix (Hagoort 1981; Mayerhofer and Economides 1993; Craig and Blasingame 2006). The commonly used AC models include Nolte AC model (Nolte et al. 1997; Nolte 1997), Soliman et al. (2005) model, Craig and Blasingame (2006) model and Liu et al. (2016) model. All AC models employ the diffusivity equation used for conventional pressure transient analysis.
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Except for the Liu and Ehlig-Economides (2015) model, all the above-mentioned BC models have been limited to ideal (normal) leakoff behavior. The ideal leakoff scenario is defined with the following assumptions (Nolte 1979, 1986): 1) Constant injection rate; 2) Constant fracture surface area after shut-in; 3) Only one main hydraulic fracture created without any secondary fracture; 4) Constant fracture compliance; 5) Constant fracture closure stress; 6) Negligible impact from the wellbore storage (WBS) so that all injected fluid at surface flows into the fracture before shut-in. The models presented by Hagoort (1981), Mayerhofer and Economides (1993), Craig and Blasingame (2006) rely on similar assumptions. Parameters quantified from the BC normal leakoff include a leakoff coefficient or permeability and skin, fluid efficiency, and fracture geometry. However, Craig et al. (2000) claimed that normal leakoff is rarely observed in the field. Barree and Mukherjee (1996) described several commonly observed abnormal leakoff phenomena, including pressure dependent leakoff (PDL), tip extension after shut-in, variable fracture compliance, height recession or transverse storage. Models that address abnormal leakoff include a numerical model by McClure et al. (2014) that addresses variable compliance and an analytical model introduced by Liu and EhligEconomides (2015) that consider variable compliance and many other abnormal leakoff behaviors. The Liu and Ehlig-Economides (2015) model addresses these abnormal leakoff behaviors by strictly applying a material balance function, and enables quantification of many more parameters. This paper uses a field case to illustrate quantification of parameters from each abnormal leakoff behavior. In addition to the modelling of BC abnormal leakoff behaviors (Liu and Ehlig-Economides 2015) and AC flow regimes (Liu et al. 2016), Liu and Ehlig-Economides (2017) builds a consistent model to match both the falloff, including BC and AC analyses, and the injection data. Many parameters are quantified that cannot be determined from other models, such as friction losses in wellbore, perforation and nearwellbore tortuosity, net pressure during and after shut-in, leakoff capacity and extension of secondary fractures, tip extension distance after shut-in. These parameters provide valuable insight into the hydraulic fracture behaviors and the formation properties. Furthermore, they can be used in the hydraulic fracture design. This paper shows how these parameters could improve the hydraulic fracture design. A final focus of this paper is the DFIT design. Historically, to obtain representative and reliable parameters for the subsequent hydraulic fracture design, the fracture calibration test would be pumped at a rate close to the planned rate of hydraulic fracture treatments, and minifrac tests in higher, but still quite low, permeability formations typically pumped the same volume as the anticipated pad of the hydraulic fracture treatment (Thompson and Church 1993). However, shale gas and tight oil formation permeability magnitudes are so low (Liu et al. 2018; Pang, et al. 2017) that the time to fracture closure might be excessive for injection of such large volumes. Hence, the DFIT design calls for a smaller injection volume that reduces the time to reach fracture closure and AC flow regimes. Marongiu-Porcu et al. (2014) recommended to create a short fracture using a short pumping time with a high pumping rate. Barree et al. (2014) suggested a DFIT should be pumped with at least 75% of the planned rate of the main hydraulic fracture treatment for 3-5 minutes, and then finished with a rapid step-down test. This paper recommends a new DFIT design that could provide reliable closure identification, short time to reach AC pseudo-linear and even pseudo-radial flow and fracture behavior representative of hydraulic fracture treatment.
Surface and Bottomhole Injection Rate and Volume DFIT injection rate, time, and pressure are usually recorded at the surface, and the rate may not be constant. Liu and Ehlig-Economides (2017) showed a methodology to build a consistent model for both
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pumping and falloff part of a DFIT. The bottomhole rate must be calculated to account for the wellbore storage (WBS) and the rate dependent friction losses occurring in the wellbore, perforations, in nearwellbore tortuosity. The pumping pressure climbs as a linear function of the cumulative injected fluid volume before the formation breakdown, and the slope of this linear trend represent the product of the total wellbore volume and the effective compressibility of the injected fluid and the wellbore string. To create a fracture, the injected fluid volume must exceed the volume required to pressurize the wellbore to the breakdown pressure. The minimum volume to ensure fracture creation must exceed −
), ..................................................................................................... (1)
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where, , is the minimum required fluid volume at surface to create a hydraulic fracture; is the combined compressibility of the injected fluid and wellbore string; is the wellbore volume at the start of injection; is the formation breakdown stress, and is the wellbore pressure before injection. At the final fracture closure, the total injected fluid volume flowing into the created fracture ( , ) can be calculated as
Material balance
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is the pumping volume at surface and is the final fracture closure stress. Depending where, , on the relative magnitude between the wellbore pressure before injection and the final fracture closure stress, the total fluid volume flowing into the created fracture could be bigger than, equal to or smaller than the recorded injection volume at surface. The total volume ( , ) is an important factor and should be accurately calculated because it is used in BC analysis to determine the leakoff coefficient, fracture geometry and fluid efficiency, and also used in AC analysis to calculate the average injection rate. Because of the wellbore storage effect, the bottomhole rate may not be equal to the surface pumping rate. Liu and Ehlig-Economides (2017) provided an equation to calculate the bottomhole rate using rate and pressure recorded at the surface. Both surface and bottomhole rates are used to calculate the wellbore friction, while only bottomhole rate is required to calculate friction losses in perforations and near-wellbore tortuosity. Consequently, both the recorded surface rate and the calibrated bottomhole rate in real time are required to match the injection pressure curve.
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All BC models are based on a material balance. However, all the above-mentioned BC analytical models except for the model by Liu and Ehlig-Economides (2015) are derived by assuming the normal leakoff condition. It requires that all the injected fluid is either stored in the hydraulic fracture or leaking off through the hydraulic fracture surface. Some abnormal leakoff behaviors render this assumption invalid. For instance, field case analyses by Liu and Ehlig-Economides (2016, 2017) suggest that some of the injected fluid may flow into secondary fractures activated by the created hydraulic fracture. Furthermore, fluid that flows into secondary fractures may continue to leak off the secondary fractures. These secondary fractures may have a higher activation or closure stress than the hydraulic fracture because the hydraulic fracture usually is expected to propagate against the minimum principal stress. The DFIT data therefore may present one or more closure events in the diagnostic plots. In such cases, the assumption of normal leakoff violates the material balance and leads to erroneous estimations of the leakoff coefficient, fluid efficiency and fracture geometry. A rigorous material balance must trace the fluid flow among the wellbore, hydraulic fracture, secondary fractures, and the formation matrix. At the final fracture closure, the cumulative fluid leakoff volume calculated from the leakoff side must be the same with that given by Eq. 2 calculated from the pumping side.
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Connections between BC and AC analysis
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AC analysis is to model the formation pressure response to the fluid leakoff during pumping and fracture closure. The BC leakoff history therefore should be considered in the AC analysis. Liu et al. (2016) proposed a AC model to calculate formation permeability with the AC linear flow by taking advantage of the fracture half-length estimated via the BC analysis. In this way, a consistent model can be generated to match both BC and AC data. Besides that, we are to illustrate two other impacts of the BC leakoff process on the AC modelling. When to estimate the formation permeability via the pseudo-linear or pseudo-radial model as suggested by Liu et al. (2016) and Ehlig-Economides and Liu (2017), the flow rate used in these equations should be calculated by dividing the total leakoff volume or the total effective pumping volume calculated with Eq. 2 by the injection time that used to generate diagnostic plots. The calculated rate may not be same with the average or the steady injection rate recorded at surface during the injection. This requires an accurate estimation of the total leakoff volume or the total injected fluid volume defined in Eq. 2. When to generate the forward global model including BC and AC, which is an essential step to match the field data, the leakoff process should also be simulated. According to the Carter leakoff model (Carter 1957), fluid leakoff rate through a fixed fracture area declines with the contact time. Therefore, from the perspective of formation matrix, the pumping and leakoff process can be viewed as an injection with variable rate. Then the AC model can be generated with the superposition of the whole leakoff rate history.
Hydraulic fracture design with parameters quantified from DFIT analysis
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Because DFITs are designed to provide input parameters for the hydraulic fracture design, the DFIT data should be interpreted in an accurate manner, and the calculated parameters should be used in a proper way in the hydraulic fracture design. As discussed above, the normal leakoff models in most cases are not adequate for DFIT analyses, so we use the Liu and Ehlig-Economides (2015) model to illustrate how the quantified parameters should be used in the hydraulic fracture design, and what difference could be made if the parameters are from the normal leakoff models. Three primary parameters, the leakoff coefficient, fluid efficiency and fracture closure stress, are quantified from the DFIT analysis and used in the hydraulic fracture design. Take the DFIT case with natural fracture related PDL for instance. BC Models derived from the normal leakoff assumption (Nolte 1986; Craig and Blasingame 2006) would suggest picking only the final closure trend and identify the hydraulic fracture closure at the deviation point off the trend (Barree et al. 2009). And then, the leakoff coefficient, fluid efficiency and fracture geometry are determined with the identified closure. We believe this methodology can provide a solid estimation of fracture closure stress, but an inaccurate estimation of the fluid leakoff coefficient and a poor estimation of the fluid efficiency because the leakoff computation does not account for the fluid loss into secondary fractures, which could be dominant over the hydraulic fracture. To include the leakoff through secondary fractures, Liu and Ehlig-Economides (2016) suggests labelling multiple closure trends, each of which represents a different fracture surface area. Then the fracture surface area under any pressures during fracture closing can be estimated together with the leakoff coefficient and fluid efficiency. By accounting for the leakoff into secondary fractures, the fluid efficiency could be much smaller than that determined from the Nolte solution (Nolte 1979, 1986), and should be used in the hydraulic fracture design. Otherwise, hydraulic fracture design with the overestimated fluid efficiency could lead to suboptimal hydraulic fracture performance because of the inadequate fracturing fluid volume. Also for the formation with secondary fractures, the multiple closure model by Liu and EhligEconomides (2015) enables quantification of the reopening stress, leakoff capacity and extension of each set of secondary fractures. With these results, it is possible to optimize hydraulic fracture design by promoting or preventing to reactivate these natural fractures. For instance, the DFIT may present PDL
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feature if the secondary fracture is permeable and connected with the hydraulic fracture. To take advantage of these secondary fractures, internal pressure of the hydraulic fracture (excluding friction losses) should be designed to be larger than their closure stress during the main hydraulic fracture treatment. King (2010), Zhu et al. (2016) and Bychina (2018) observed a positive correlation in tight formations among injection rate, fracture complexity and post treatment well productivity. In other words, high injection rate, or high injection pressure, is prone to create the complicated fracture system by connecting secondary fractures, and the fracture system with high complexity is preferred for the production from tight formations. According to Liu and Ehlig-Economides (2017), flow friction losses in wellbore, perforation and near-wellbore tortuosity can be determined separately from the DFIT with or without rate step-down test. It needs to be noted that the traditional method to estimate friction losses with the step-down test is unreliable because of the poor estimation of ISIP. The method to pick ISIP by drawing a straight line on the Cartesian pressure plot (Cramer and Nguyen 2013) or on the semi-log plot (Barree et al. 2014) is highly subjective and arbitrary because it has no consideration of the possible wellbore storage effect and lacks support from the physics theory. Therefore, we suggest determining friction losses with the model by Liu and Ehlig-Economides (2017). With the calculated friction losses, operations can be optimized. For instance, large friction in perforation could be reduced by adjusting perforation parameters like shot density, phase and hole diameters. While, for the case with large friction caused by the near-wellbore tortuosity, Wright et al. (1996) suggests pumping several small proppant slugs during pad to minimize the friction loss and to prevent the potential premature screenout.
DFIT design
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As to the DFITs, we recommend that they should be always injected in one single perforation cluster to avoid multiple fracture initiations. Otherwise, the DFIT data are uninterpretable because it is difficult to estimate the fluid distribution among perforation clusters and the potential stress shadowing effect among created fractures. Two major parameters that should be carefully addressed in the DFIT design are the injection rate and the volume. To mimic hydraulic fracture treatment, the same fracturing fluid planned for the main treatment should be pumped for the DFIT, and the pumping rate should be similar to the planned rate of one perforation cluster during the main treatment. Because of the relatively high pumping rate, the total injection volume for a DFIT may not be small, which may lead to the delayed hydraulic fracture closure and the long shut-in time required to reach AC flow regimes, especially the AC pseudo-radial flow.
Fig. 1 Composite G-function plots of two successive DFITs in one location (the left for the first DFIT and the right for the second DFIT) (Rizwan 2017)
Rizwan (2017) showed an informative field case with two successive DFITs through the same perforations in a tight gas formation. The first DFIT was pumped with a small volume (24.8 bbl) at a low rate (0.94 – 1.38 bpm). Its falloff presents a simple BC trend close to the normal leakoff following WBS (left graph of Fig. 1), from which the hydraulic fracture closure can be determined. According to
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Rizwan (2017), its AC clearly shows the pseudo-linear flow and even the pseudo-radial flow within 12.2 hours after shut-in. After the falloff of the first DFIT, the second DFIT was pumped with a larger volume (158 bbl) and at a higher rate (12.6 – 18.7 bpm). The second falloff presents complicated BC behaviors including WBS, PDL and apparent height recession (or transverse storage or variable fracture compliance) before the final closure, as shown in the right graph of Fig. 1. Several points can be learnt from the case. First, we may conclude that the difference in fracture closure behaviors is caused by different pumping rates and volumes. Specifically, low rate (also indicating the low pumping pressure, ISIP and net pressure) and small volume of the first injection may create a simple hydraulic fracture with limited extension, which shows a single closure trend close to the normal closure in its falloff data; while, much higher rate (also indicating the larger pumping pressure, ISIP and net pressure) and larger volume of the second injection may create a more complicated fracture system, in which scenario height recession or secondary fracture related transverse storage could occur. Secondly, Rizwan (2017) claimed that the data supports the holistic methodology (Barree et al. 2009) to pick the hydraulic fracture closure and contradicts the variable fracture compliance approach by McClure et al. (2014). The final fracture closure of the second DFIT picked with the holistic method is only 10 psi higher than that of the first DFIT, which is nearly the normal leakoff with a clear closure point. While, the difference is larger than 377 psi if the closure is picked with the variable fracture compliance approach. Thirdly, the case offers an alternative methodology to perform DFITs with two successive injections: the first one with low rate and small volume and the second with high rate and large volume. The simple and short hydraulic fracture created during the first injection provides the closure stress and AC pseudo-linear and pseudoradial flow within a relatively short shut-in time. The second test with the high rate and large volume provides insight on other possible fracture and formation behaviors, such as secondary fractures related phenomena and height recession, which are expected during the main hydraulic fracture pumping. The required shut-in time for the second DFIT could be relatively short because the its AC analysis is not a necessity with the formation pressure and permeability quantified from the previous DFIT. Besides the short shut-in time, another advantage of the design is that parameters quantified from both DFITs can be cross-checked for consistency. Two other similar but not same field cases are available in publications and should be mentioned as a comparison. Rohmer et al. (2015) showed two successive DFITs in the same well drilled in the Vaca Muerta Shale: the first injection with a small volume (20.8 bbl) and a low rate (≤ 5.5 bpm), and the second injection with a large volume (155 bbl) and a high rate (≤ 14 bpm). Diagnostic plots of both DFITs present abnormal leakoff behaviors but in distinctive features: the first one with obvious transverse storage/height recession and the second with short pressure dependent leakoff (PDL). The difference is unexpected. However, the final closures picked with the holistic methodology from the two DFITs are consistent. Nicholson et al. (2017) published another field case with two successive DFITs, which were tested in a shallow gas-shale formation with thrust fault setting, where the overburden stress is assumed to be the minimum principal stress. Different from cases demonstrated by Rizwan (2017) and Rohmer et al. (2015), the first injection in the Nicholson et al. (2017) case has a relatively large volume at 33.2 bbl and a high rate at 6.3 bpm compared with the second injection with an ultra-small volume at 0.82 bbl, which is only 2.5% of the first injection, and an ultra-low rate at 0.27 bpm. Diagnostic plots of the first falloff have a transverse storage/height recession feature, while the second falloff has a nearly normal leakoff behavior. This fits our previous discussion. However, the final closure picked from these two DFITs are not same. One possible reason is that the second injection may not totally reopen the hydraulic fracture created in the first injection because the size of the second injection is too small. It is a good case to demonstrate that the first injection in the two successive DFITs should be smaller than the later one.
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Case study
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In this section, we are to illustrate the bottomhole flow rate, leakoff rate during and after pumping, AC analysis, and then how these quantified parameters be used in the hydraulic fracture design. The DFIT was performed in the toe stage of a horizontal well completed with the slide sleeve. Wellbore was pressurized up to open the sleeve before the DFIT injection. Fluid was pumped into the formation through the first casing interval with an inner diameter (ID) of 6.09 inch and length of 10,500 ft and the second casing interval with an ID of 3.92 inch and length of 11,635 ft. The measured depth (MD) of perforations is at 22,135 ft. The surface injection rate was maintained flat at 5.6 bpm for one minute and then the step-down test was performed. Two rate steps, 4 and 3 bpm, are tested before the surface shutin, each for around 20 seconds. The stable pressure does not establish at neither of the steps. Approximately 13.75 bbl fresh water was injected into the well in 2.75 minutes with an average wellhead rate at 5.0 bbl/min, as shown in Fig. 2.
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Fig. 2 Injection profile
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The wellbore volume is calculated at 576 bbl, which is significantly larger than the injected fluid volume and the WBS effect cannot be neglected. Because the wellbore pressure declines from 13,823 psi at the start of pumping to 12380 psi at shut-in, an additional 3.32 bbl fluid flowed into the fracture by shut-in besides the surface injection volume at 13.75 bbl. Furthermore, by adding the after-flow volume after shut-in, a total of 26.6 bbl fluid finally flowed into the fracture and leaked off through the fracture surface at the final closure, which is almost 13 bbl more than or twice of the surface injection volume. The WBS effect therefore should be considered in the falloff analysis and the injection modelling.
Fig. 3 Bourdet derivative plot (Left) and composite G-function plot (Right).
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The left graph in Fig. 3 is the Bourdet derivative in log-log plot with markings indicating slope trends of interest. The fracture closure trend presents a 3/2-slope in the Bourdet derivative (Mohamed et al. 2011). The right graph of Fig. 3 shows the composite G-function plot displaying exactly the same closing trends. Two dashed lines in the lower right corner are guide lines with specific slopes: the red line with 3/2-slope and the green with unit slope. Briefly, the first behavior indicated by the green unit slope (marked as circle 1) in the Bourdet log-log plot is the indication of WBS with perforation friction dissipation. The next bump curve (circle 2) could be the tip extension after shut-in coupled with the near-wellbore friction dissipation. The end of tip extension can be picked at the bottom of the valley at around ∆t = 0.4 hours in the Bourdet derivative curve, or G = 8 in the Gdp/dG plot. The minimum fracture propagation pressure at the end of tip-extension is 8,668 psi. Then, the Bourdet derivative merge into a trend with 3/2-slope (circle 3), which corresponds to the straight trend indicated by the red dashed line in the Gdp/dG curve. The same closure is picked at the end of 3/2-slope in the Bourdet derivative curve with the derivation point from the straight trend in the Gdp/dG curve.
Fig. 4 Bourdet derivative plot (Left) and composite G-function plot (Right) without early behavior.
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For the case with tip extension and/or other early behaviors, Liu and Ehlig-Economides (2016) suggests starting the falloff analysis from the end of tip extension with an adjusted injection time equal to injection time ( ) plus tip extension time (∆ ). By excluding early WBS, friction and tip extension behaviors, new diagnostic plots are generated in Fig. 4. The new diagnostic plots show much clearer closure trend with little disturbance of the early behavior. Besides the final hydraulic fracture closure, a little hump (circle 1) above the final closure trend (circle 2) in the Gdp/dG curve indicates the pressure dependent leakoff (PDL) behavior, and the same closure point can be picked from the Bourdet derivative plot. Then, the final fracture geometry, formation leakoff coefficient, fluid efficiency and natural fracture surface area are estimated with the model introduced by Liu and Ehlig-Economides (2015). Table 1 Interpretation result of Well B
Injection and Falloff Feature , psi , bbl !, Vl, bbl ∆ , & , psi ∆ , psi , xf, initial, ft pp, min, psi
Injection
Friction losses at shut-in
Tip Extension
4.0×10-6 17.07 0.40 220 2,497 97 8,668
Closure 1
Closure 2
After-closure (data match)
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xf, final, ft , psi Total area of one-sided fracture, ft2 # , ft2 $% , ft/√min η k, md pi, psi
331 8,475 35,550 9,033
8,235 26,517 26,517
4.4 / 1023 0.97
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0.15 7,945
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Friction occurring in the wellbore and perforation, and near wellbore tortuosity, fracture geometry at shut-in are obtained by matching the early falloff behaviors and pumping data. The interpreted parameters are listed in Table 1. The result shows that the fracture half-length at shut-in is only 97 ft, and then the hydraulic fracture grows to 331 ft during tip extension after shut-in, which is 3.4 times as long as that at shut-in. The Bourdet derivative curve bends to flat soon after the closure (circle 4 in Fig. 3 or circle 3 in Fig. 4), leaving no room for the possible pseudo-linear flow. The flat is not solid and it starts drop because the pressure tends to be flat or even rises at the very end (no shown in this paper). Therefore, the apparent flat trend may not be a valid pseudo-radial flow. We then treat it as part of transition from the before-closure behavior to the after-closure flow regimes, and the final match provides formation permeability at approximately 0.15 md and formation initial pressure at 7,945 psi. The forward model then is generated based on the falloff analysis result, and it fits the falloff pressure and its derivatives well as shown in Fig. 5. And, the injection pressure can also be matched by slightly adjusting the area exponent, shown in Fig. 6.
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Fig. 5 Model match for falloff pressure behavior.
Fig. 6 Model match for injection and falloff pressure.
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Fig. 7 (A) presents the comparison between the surface injection rate and the bottomhole flow rate at the formation face. Because the injection pressure is not stable, the bottomhole rate is not constant even the surface rate is flat. Moreover, the bottomhole rate keeps declining at the step-down test and does not display any indication of “rate steps”. Therefore, the recorded rate at surface should not be used to determine the rate dependent friction. After step-down test, the surface rate drops to zero immediately after shut-in, while the after-flow lasts for much longer with a fading rate. Fig. 7 (B) shows the fracture internal pressure, bottomhole fracture face pressure, friction occurring in wellbore, perforation and near wellbore tortuosity, net pressure at the wellbore and the average net pressure. The result shows that friction accounts for the majority pressure drop after shut-in. While, the fracture average net pressure is approximately 1,000 psi at the shut-in but declines to 350 psi after the tip extension. And, the fracture internal pressure is relatively flat and does not have a large pressure drop after shut-in.
Fig. 7 (A) Surface injection rate and bottomhole flow rate; (B) Bottomhole pressure, fracture internal pressure, friction, net pressure at wellbore and average net pressure during injection and falloff.
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Our BC model is derived based on the material balance function. Components of material balance are shown in Fig. 8. The total injection fluid volume indicated by the green line grows from the pumped bottomhole volume at 17.07 bbl at shut-in to 26.6 bbl by adding the after-flow volume caused by the WBS. Its rapid growth occurs at early time after shut-in because the wellbore pressure declines rapidly during the time. The hydraulic fracture volume, indicated by the purple line, gains some extra volume after shut-in because of the fracture tip extension. Then, it declines gradually all the way to zero, which corresponds to fluid leakoff and fracture closure process. The cumulative leakoff volume, indicated by the blue line, increases from 0.4 bbl (leakoff volume during injection) to 26.6 bbl at the fracture final closure. The total injection volume should always equal to the sum of the cumulative leakoff volume and the hydraulic fracture volume. The only way to satisfy the material balance and build a plot like Fig. 8 is taking consideration of abnormal leakoff behaviors including secondary fractures, friction losses, WBS, etc.
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Fig. 8 The changes of hydraulic fracture volume, after-flow volume, cumulative leakoff volume and leakoff rate after shut-in.
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The fluid leakoff rate after shut-in is indicated by the red line in Fig. 8. It climbs to the highest point with tip extension when more fresh fracture surface is created for fluid leakoff. Then, it declines rapidly with the time. For one thing, part of the high leakoff rate is contributed by the natural fractures, while natural fractures are closing and losing their surface areas. For the other, the leakoff rate decline is rooted in the Carter leakoff model. The decline of leakoff rate at the late time is slowing down. From the decline curve, we can conclude that the leakoff process is not at constant rate. When to generate the forward model, we use the superposition of variable injection rates to model the AC pressure response. From above discussion, many more parameters are quantified in a more robust and accurate way. The next question will be how to use these parameters in the hydraulic fracture design. The first factor should be noted is the friction loss through the near-wellbore tortuosity, which is almost 2,500 psi at the end of pumping. As mentioned above, large tortuosity friction may lead to premature proppant screenout. One effective way to release the severe tortuosity is adding several 100-mesh proppant slugs during pad. Secondary fractures are another issue that should be considered in the hydraulic fracture design. The DFIT result reveals several major properties of secondary fractures: leakoff capacity, extension and reopening stress. These secondary fractures are permeable, which is learnt from the PDL behavior, so they are likely to contribute to the production if they are connected to the hydraulic fracture. However, DFIT results show that natural fracture has a limited extension, which is approximately one third of the hydraulic fracture surface area. To reactivate these natural fractures, the effective fracture internal pressure should be higher than 8,475 psi, or the required minimum net pressure along the hydraulic fracture is around 240 psi. It might be easy to satisfy the pressure requirement for the hydraulic fracture close to the wellbore, but could be challenging for the fracture into the far deep formation because of pressure loss along the fracture. Even higher net pressure is required if these natural fractures are designed to take proppant. Another potential impact of secondary fractures is the fluid leakoff. The leakoff through natural fractures could be calculated via the multiple closure model by Liu and Ehlig-Economides (2015). As to this field case, the fluid leakoff volume through natural fractures during pumping is minimal because of its limited surface area. However, for the case with massive connected natural fractures (Liu and Ehlig-Economides 2017), the amount of fluid leakoff volume through natural fractures could be dominated.
Conclusions This paper discusses several issues associated with the DFIT analysis. On the basis of the fracture behaviors in practice, we propose how to determine input parameters for both BC and AC DFIT models. Many parameters associated with abnormal leakoff behaviors can be quantified, and we show how these parameters can be used in the hydraulic fracture design. Also, we propose an alternative DFIT design. Several key conclusions are the following.
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1) Bottomhole rate should be calculated by considering the WBS effect. When to match the pumping data, both the surface rate and the calibrated bottomhole rate should be used. 2) The AC analysis is to model the pressure response after variable leakoff rate. The flow rate used in the AC analysis should be calculated by dividing the total effective injected volume defined in Eq. 2 by the injection time used to generate diagnostic plots. The AC forward model can be generated with the superposition of multiple leakoff rates. 3) The material balance function should be followed to quantitively model the abnormal leakoff behaviors, and then the associated parameters can be accurately estimated. 4) Secondary fracture properties (surface area, leakoff capacity and reopening stress) and friction losses (in wellbore, perforation and tortuosity) quantified from the DFIT analysis should be considered in the hydraulic fracture design. 5) A field case with two successive DFITs is proved to be an alternative DFIT design. The first DFIT is pumped at a low injection rate and small volume, while the second at a high rate and large volume. The case supports the holistic method to pick final fracture closure, and contradicts to the variable fracture compliance approach.
Acknowledgements
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The authors would like to thank operating companies for sharing data used in the case study.
Nomenclature
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Af = fracture one side surface area, L2 bpm = bbl per minute, L3/t CL = leakoff coefficient, L/√t G = G-function, dimensionless ISIP = instantaneous shut-in pressure, m/Lt2 k = permeability, L2 p = pressure, m/Lt2 pc = closure pressure, m/Lt2 pi = formation initial pressure, m/Lt2 pp, min = minimum fracture propagation pressure, m/Lt2 p’ = Bourdet pressure derivative, m/Lt2 q = flow rate, L3/t qaf = after-flow rate into the fracture caused by fluid expansion in the wellbore, L3/t t = time, t tp = pumping time, t V = volume, L3 Vp = pumping volume, L3 xf = fracture half-length, L xf，initial = fracture half-length at shut-in, L xf，final = fracture half-length after tip extension, L
Greek ∆ = difference, dimensionless η = fluid efficiency, percentage
Subscripts BH = Bottomhole c = closure f = fracture fric = friction
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inj = injection perf = perforation tort = near-wellbore fracture tortuosity te = tip extension w, wb = wellbore WBS = wellbore storage
References
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Barree, R.D. and Mukherjee, H. 1996. Determination of Pressure Dependent Leakoff and Its Effect on Fracture Geometry. Paper presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado. SPE-36424-MS. DOI: 10.2118/36424-MS. Barree, R.D., Barree, V.L., and Craig, D. 2009. Holistic Fracture Diagnostics: Consistent Interpretation of Prefrac Injection Tests Using Multiple Analysis Methods. SPE Production & Operations 24 (3): pp. 396-406. SPE-107877-PA. DOI: 10.2118/107877-PA Barree, R.D., Miskimins, J.L., and Gilbert, J.V. 2014. Diagnostic Fracture Injection Tests: Common Mistakes, Misfires, and Misdiagnoses. Paper presented at the SPE Western North American and Rocky Mountain Joint Meeting, Denver, Colorado. SPE-169539-MS. DOI: 10.2118/169539-MS. Bychina, M., Luo, G., Liu, G. et al. 2018. State of the Art for Multiple Transverse Fracture Horizontal Well Design. Hydraulic Fracturing Journal 5 (1): 53-68. Carter, R.D. 1957. Derivation of the General Equation for Estimating the Extent of the Fractured Area. In Appendix of "Optimum Fluid Characteristics for Fracture Extension", ed. Howard, G.C. and Fast, C.R., Drilling and Production Practices, New York: API. Cinco-Ley, H., Samaniego V, F., and Dominguez A, N. 1978. Transient Pressure Behavior for a Well with a FiniteConductivity Vertical Fracture. Society of Petroleum Engineers Journal 18 (04): 253 - 264. SPE-6014-PA. DOI: 10.2118/6014-PA Craig, D.P. and Blasingame, T.A. 2006. Application of a New Fracture-Injection/Falloff Model Accounting for Propagating, Dilated, and Closing Hydraulic Fractures. Paper presented at the SPE Gas Technology Symposium, Calgary, Alberta, Canada. SPE-100578-MS. DOI: 10.2118/100578-MS. Craig, D.P., Odegard, C.E., Pearson, W.C., Jr. et al. 2000. Case History: Observations from Diagnostic Injection Tests in Multiple Pay Sands of the Mamm Creek Field, Piceance Basin, Colorado. Paper presented at the SPE Rocky Mountain Regional/Low-Permeability Reservoirs Symposium and Exhibition, Denver, Colorado. SPE-60321-MS. DOI: 10.2118/60321-MS. Ehlig-Economides, C.A. and Liu, G. 2017. Comparison among Fracture Calibration Test Analysis Models. Paper presented at the SPE Hydraulic Fracturing Technology Conference and Exhibition, The Woodlands, Texas, USA. SPE-184866-MS. DOI: 10.2118/184866-MS. Feng, Y. and Gray, K. E. A Comparison Study of Extended Leak-off Tests in Permeable and Impermeable Formations. Paper presented at the 50th US Rock Mechanics / Geomechanics Symposium. Houston, Texas, USA, 2016. Gulrajani, S.N. and Nolte, K.G. 2000. Fracture Evaluation Using Pressure Diagnostics Ed Economides, M.J. and Nolte, K.G. Reservoir Stimulation (Third Edition). Chichester, England: John Wiley & Sons Ltd. Original edition. ISBN 0471491926. Hagoort, J. 1981. Waterflood-Induced Hydraulic Fracturing. PhD Thesis, Delft University. King, G.E. 2010. Thirty Years of Gas Shale Fracturing: What Have We Learned? Paper presented at the SPE Annual Technical Conference and Exhibition, Florence, Italy. SPE-133456-MS. DOI: 10.2118/133456-MS. Liu, G. and Ehlig-Economides, C. 2015. Comprehensive Global Model for before-Closure Analysis of an Injection Falloff Fracture Calibration Test. Paper presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, USA. SPE-174906-MS. DOI: 10.2118/174906-MS. Liu, G. and Ehlig-Economides, C. 2016. Interpretation Methodology for Fracture Calibration Test Before-Closure Analysis of Normal and Abnormal Leakoff Mechanisms. Paper presented at the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, USA. SPE-179176-MS. DOI: 10.2118/179176-MS. Liu, G., Ehlig-Economides, C., and Sun, J. 2016. Comprehensive Global Fracture Calibration Model. Paper presented at the SPE Asia Pacific Hydraulic Fracturing Conference, Beijing, China. SPE-181856-MS. DOI: 10.2118/181856-MS. Liu, G. and Ehlig-Economides, C. 2017. New Model for DFIT Fracture Injection and Falloff Pressure Match. Paper presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA. SPE-187191-MS. DOI: 10.2118/187191-MS. Liu, S., Li, H., & Valkó, P. P. 2018. A Markov-Chain-Based Method to Characterize Anomalous Diffusion Phenomenon in Unconventional Reservoir. In SPE Canada Unconventional Resources Conference, Calgary, Alberta, 13-14 March. SPE189809-MS. https://doi.org/10.2118/189809-MS
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Marongiu-Porcu, M., Retnanto, A., Economides, M.J. et al. 2014. Comprehensive Fracture Calibration Test Design. Paper presented at the Hydraulic Fracturing Technology Conference, The Woodlands, Texas. SPE-168634-MS. DOI: 10.2118/168634-MS. Mayerhofer, M.J. and Economides, M.J. 1993. Permeability Estimation from Fracture Calibration Treatments. Paper presented at the SPE Western Regional Meeting, Anchorage, Alaska. SPE-26039-MS. DOI: 10.2118/26039-MS. McClure, M.W., Blyton, C.A.J., Sharma, M.M. et al. 2014. The Effect of Changing Fracture Compliance on Pressure Transient Behavior During Diagnostic Fracture Injection Tests. Paper presented at the SPE Annual Technical Conference and Exhibition, Amsterdam, The Netherlands. SPE-170956-MS. DOI: 10.2118/170956-MS. Mohamed, I.M., Azmy, R.M., Sayed, M.A.I. et al. 2011. Evaluation of after-Closure Analysis Techniques for Tight and Shale Gas Formations. Paper presented at the North American Unconventional Gas Conference and Exhibition, The Woodlands, Texas. SPE-140136-MS. DOI: 10.2118/140136-MS. Nicholson, A.K., Bachman, R.C., and Hawkes, R.V. 2017. How Diagnostic Fracture Injection Tests (DFITs) Show Horizontal Plane Tensile and Shear Fractures in Various Stress Settings. Paper presented at the SPE/AAPG/SEG Unconventional Resources Technology Conference, Austin, Texas, USA. URTEC-2670018. DOI: 10.15530/URTEC2017-2670018. Nolte, K.G. 1979. Determination of Fracture Parameters from Fracturing Pressure Decline. Paper presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada. SPE-8341-MS. DOI: 10.2118/8341-MS. Nolte, K.G. 1986. A General Analysis of Fracturing Pressure Decline with Application to Three Models. SPE Formation Evaluation 1 (06): 571 - 583. SPE-12941-PA. DOI: 10.2118/12941-PA. Nolte, K.G. 1997. Background for after-Closure Analysis of Fracture Calibration Tests. SPE-39407-MS. Nolte, K.G., Maniere, J.L., and Owens, K.A. 1997. After-Closure Analysis of Fracture Calibration Tests. Paper presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas. SPE-38676-MS. DOI: 10.2118/38676-MS. Pang, Y., Soliman, M.Y., Deng, H. et al. 2017. Experimental and Analytical Investigation of Adsorption Effects on Shale Gas Transport in Organic Nanopores. Fuel 199: 272-288. DOI: https://doi.org/10.1016/j.fuel.2017.02.072 Rizwan, Y. 2017. Pressure Transient Analysis for Minifracs/DFIT and Waterflood Induced Fractures. Master degree Thesis, Delft University of Technology. Rohmer, B., Raverta, M., Boutaud de la Combe, J.L. et al. 2015. Minifrac Analysis Using Well Test Technique as Applied to the Vaca Muerta Shale Play. Paper presented at the EUROPEC 2015, Madrid, Spain. SPE-174380-MS. DOI: 10.2118/174380-MS. Soliman, M.Y., Craig, D.P., Bartko, K.M. et al. 2005. Post-Closure Analysis to Determine Formation Permeability, Reservoir Pressure, Residual Fracture Properties. Paper presented at the SPE Middle East Oil and Gas Show and Conference, Kingdom of Bahrain. SPE-93419-MS. DOI: 10.2118/93419-MS. Thompson, J.W. and Church, D.C. 1993. Design, Execution, and Evaluation of Minifracs in the Field: A Practical Approach and Case Study. Paper presented at the SPE Western Regional Meeting, Anchorage, Alaska. SPE-26034-MS. DOI: 10.2118/26034-MS. Wright, C.A., Weijers, L., Germani, G.A. et al. 1996. Fracture Treatment Design and Evaluation in the Pakenham Field: A Real-Data Approach. Paper presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado. SSPE-36471-MS. DOI: 10.2118/36471-MS. Zhu, H.Y., Jin, X. C., Guo, J. C., et al. 2016. Coupled flow, stress and damage modelling of interactions between hydraulic fractures and natural fractures in shale gas reservoirs. International Journal of Oil, Gas and Coal Technology 13 (4): pp. 359-390. DOI: 10.1504/IJOGCT.2016.080095.
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Highlights
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1. Bottomhole rate should be calculated by considering the WBS effect. 2. The AC analysis is to model the pressure response after variable leakoff rate. The flow rate used in the AC analysis should be calculated by dividing the total effective injected volume by the injection time used to generate diagnostic plots. 3. The material balance function should be followed to quantitively model the abnormal leakoff behaviors, and then the associated parameters can be accurately estimated. 4. Secondary fracture properties (surface area, leakoff capacity and reopening stress) and friction losses (in wellbore, perforation and tortuosity) quantified from the DFIT analysis should be considered in the hydraulic fracture design.
S0920-4105(18)30701-0
DOI:
10.1016/j.petrol.2018.08.035
Reference:
PETROL 5215
To appear in:
Journal of Petroleum Science and Engineering
Received Date: 25 January 2018 Revised Date:
22 July 2018
Accepted Date: 12 August 2018
Please cite this article as: Liu, G., Ehlig-Economides, C., Practical considerations for diagnostic fracture injection test (DFIT) analysis, Journal of Petroleum Science and Engineering (2018), doi: 10.1016/ j.petrol.2018.08.035. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Practical Considerations for Diagnostic Fracture Injection Test (DFIT) Analysis Guoqing Liu and Christine Ehlig-Economides, University of Houston
Abstract
Introduction
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The diagnostic fracture injection test (DFIT) provides a way to estimate parameters critical to hydraulic fracture design. Existing published models for before-closure and after-closure behaviors rely on assumptions, and failure to honor important realities leads to parameter estimation errors that could degrade hydraulic fracturing design. This paper is to illustrate an accurate way to estimate parameters from the DFIT data, and then discuss how these parameters should be used in the hydraulic fracture design, and at last offer an alternative DFIT design approach. Two fundamental concepts underlying the proposed methodology are the material balance before fracture closure and the diffusive flow in the formation after closure. Before closure analysis must correctly address abnormal leakoff behaviors and near well friction losses. Likewise, accurate permeability and pore pressure estimation requires correct accounting for the leakoff rate into the formation. Strict attention to material balance yields estimations for instantaneous shut-in pressure (ISIP) and perforation and tortuosity friction losses that may, in turn, avoid apparent very high net pressure and stress shadowing. This work also underscores the importance of understanding surface and downhole volumes and rates both in the DFIT design and in the analysis. Further, for the DFIT case with pressure dependent leakoff (PDL), the fracture design for the subsequent hydraulic fracturing treatment should use the apparent leakoff rate associated with the first closure trend instead of the leakoff rate associated with the last closure trend derived from a normal leakoff model. Two successive DFITs in the same perforation, the first treated with low injection rate and small volume and then the second with high rate and large volume, are proved to be a good practice to obtain reliable estimation of formation properties. This paper demonstrates that DFIT parameters have often been misused. With the proposed methodology, the interpretation will be more accurate and reliable for formation evaluation and hydraulic fracture design.
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The diagnostic fracture injection test (DFIT), also termed as minifrac, fracture calibration test or fracture injection and falloff test, has been widely used to evaluate formation and obtain several key parameters for hydraulic fracture design (Feng and Gray 2016). The traditional interpretation methodology of a DFIT analysis is first to find the fracture closure pressure, and then divide the data into two portions: that occurring before closure (BC) and that occurring after closure (AC). Several BC analytical or semianalytical models have been proposed based on a series of assumptions since the pioneered model by Nolte (1979), including models by Nolte (1986), Hagoort (1981), Mayerhofer and Economides (1993), Craig and Blasingame (2006) and Liu and Ehlig-Economides (2015). All these BC models require a material balance ensuring that the sum of the fracture volume and the cumulative leakoff volume equal the total injected fluid volume. The total injection volume is usually calculated with the recorded rate and time, and could be taken as a known parameter. The core problem of the fracture modelling is therefore to connect the other two volumes in the material balance function: the fracture volume and the cumulative leakoff volume. All the above-mentioned BC models calculate the fracture volume during pressure falloff by assuming linear elasticity and a 2D fracture geometry. However, there are two ways to estimate the leakoff volume: one using a leakoff coefficient associated with the Cater leakoff model (Carter 1957; Nolte 1979, 1986; Liu and Ehlig-Economides 2015), and the other estimating permeability and skin based on the diffusive linear flow from the fracture into the matrix (Hagoort 1981; Mayerhofer and Economides 1993; Craig and Blasingame 2006). The commonly used AC models include Nolte AC model (Nolte et al. 1997; Nolte 1997), Soliman et al. (2005) model, Craig and Blasingame (2006) model and Liu et al. (2016) model. All AC models employ the diffusivity equation used for conventional pressure transient analysis.
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Except for the Liu and Ehlig-Economides (2015) model, all the above-mentioned BC models have been limited to ideal (normal) leakoff behavior. The ideal leakoff scenario is defined with the following assumptions (Nolte 1979, 1986): 1) Constant injection rate; 2) Constant fracture surface area after shut-in; 3) Only one main hydraulic fracture created without any secondary fracture; 4) Constant fracture compliance; 5) Constant fracture closure stress; 6) Negligible impact from the wellbore storage (WBS) so that all injected fluid at surface flows into the fracture before shut-in. The models presented by Hagoort (1981), Mayerhofer and Economides (1993), Craig and Blasingame (2006) rely on similar assumptions. Parameters quantified from the BC normal leakoff include a leakoff coefficient or permeability and skin, fluid efficiency, and fracture geometry. However, Craig et al. (2000) claimed that normal leakoff is rarely observed in the field. Barree and Mukherjee (1996) described several commonly observed abnormal leakoff phenomena, including pressure dependent leakoff (PDL), tip extension after shut-in, variable fracture compliance, height recession or transverse storage. Models that address abnormal leakoff include a numerical model by McClure et al. (2014) that addresses variable compliance and an analytical model introduced by Liu and EhligEconomides (2015) that consider variable compliance and many other abnormal leakoff behaviors. The Liu and Ehlig-Economides (2015) model addresses these abnormal leakoff behaviors by strictly applying a material balance function, and enables quantification of many more parameters. This paper uses a field case to illustrate quantification of parameters from each abnormal leakoff behavior. In addition to the modelling of BC abnormal leakoff behaviors (Liu and Ehlig-Economides 2015) and AC flow regimes (Liu et al. 2016), Liu and Ehlig-Economides (2017) builds a consistent model to match both the falloff, including BC and AC analyses, and the injection data. Many parameters are quantified that cannot be determined from other models, such as friction losses in wellbore, perforation and nearwellbore tortuosity, net pressure during and after shut-in, leakoff capacity and extension of secondary fractures, tip extension distance after shut-in. These parameters provide valuable insight into the hydraulic fracture behaviors and the formation properties. Furthermore, they can be used in the hydraulic fracture design. This paper shows how these parameters could improve the hydraulic fracture design. A final focus of this paper is the DFIT design. Historically, to obtain representative and reliable parameters for the subsequent hydraulic fracture design, the fracture calibration test would be pumped at a rate close to the planned rate of hydraulic fracture treatments, and minifrac tests in higher, but still quite low, permeability formations typically pumped the same volume as the anticipated pad of the hydraulic fracture treatment (Thompson and Church 1993). However, shale gas and tight oil formation permeability magnitudes are so low (Liu et al. 2018; Pang, et al. 2017) that the time to fracture closure might be excessive for injection of such large volumes. Hence, the DFIT design calls for a smaller injection volume that reduces the time to reach fracture closure and AC flow regimes. Marongiu-Porcu et al. (2014) recommended to create a short fracture using a short pumping time with a high pumping rate. Barree et al. (2014) suggested a DFIT should be pumped with at least 75% of the planned rate of the main hydraulic fracture treatment for 3-5 minutes, and then finished with a rapid step-down test. This paper recommends a new DFIT design that could provide reliable closure identification, short time to reach AC pseudo-linear and even pseudo-radial flow and fracture behavior representative of hydraulic fracture treatment.
Surface and Bottomhole Injection Rate and Volume DFIT injection rate, time, and pressure are usually recorded at the surface, and the rate may not be constant. Liu and Ehlig-Economides (2017) showed a methodology to build a consistent model for both
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,
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pumping and falloff part of a DFIT. The bottomhole rate must be calculated to account for the wellbore storage (WBS) and the rate dependent friction losses occurring in the wellbore, perforations, in nearwellbore tortuosity. The pumping pressure climbs as a linear function of the cumulative injected fluid volume before the formation breakdown, and the slope of this linear trend represent the product of the total wellbore volume and the effective compressibility of the injected fluid and the wellbore string. To create a fracture, the injected fluid volume must exceed the volume required to pressurize the wellbore to the breakdown pressure. The minimum volume to ensure fracture creation must exceed −
), ..................................................................................................... (1)
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−
(
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where, , is the minimum required fluid volume at surface to create a hydraulic fracture; is the combined compressibility of the injected fluid and wellbore string; is the wellbore volume at the start of injection; is the formation breakdown stress, and is the wellbore pressure before injection. At the final fracture closure, the total injected fluid volume flowing into the created fracture ( , ) can be calculated as
Material balance
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is the pumping volume at surface and is the final fracture closure stress. Depending where, , on the relative magnitude between the wellbore pressure before injection and the final fracture closure stress, the total fluid volume flowing into the created fracture could be bigger than, equal to or smaller than the recorded injection volume at surface. The total volume ( , ) is an important factor and should be accurately calculated because it is used in BC analysis to determine the leakoff coefficient, fracture geometry and fluid efficiency, and also used in AC analysis to calculate the average injection rate. Because of the wellbore storage effect, the bottomhole rate may not be equal to the surface pumping rate. Liu and Ehlig-Economides (2017) provided an equation to calculate the bottomhole rate using rate and pressure recorded at the surface. Both surface and bottomhole rates are used to calculate the wellbore friction, while only bottomhole rate is required to calculate friction losses in perforations and near-wellbore tortuosity. Consequently, both the recorded surface rate and the calibrated bottomhole rate in real time are required to match the injection pressure curve.
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All BC models are based on a material balance. However, all the above-mentioned BC analytical models except for the model by Liu and Ehlig-Economides (2015) are derived by assuming the normal leakoff condition. It requires that all the injected fluid is either stored in the hydraulic fracture or leaking off through the hydraulic fracture surface. Some abnormal leakoff behaviors render this assumption invalid. For instance, field case analyses by Liu and Ehlig-Economides (2016, 2017) suggest that some of the injected fluid may flow into secondary fractures activated by the created hydraulic fracture. Furthermore, fluid that flows into secondary fractures may continue to leak off the secondary fractures. These secondary fractures may have a higher activation or closure stress than the hydraulic fracture because the hydraulic fracture usually is expected to propagate against the minimum principal stress. The DFIT data therefore may present one or more closure events in the diagnostic plots. In such cases, the assumption of normal leakoff violates the material balance and leads to erroneous estimations of the leakoff coefficient, fluid efficiency and fracture geometry. A rigorous material balance must trace the fluid flow among the wellbore, hydraulic fracture, secondary fractures, and the formation matrix. At the final fracture closure, the cumulative fluid leakoff volume calculated from the leakoff side must be the same with that given by Eq. 2 calculated from the pumping side.
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Connections between BC and AC analysis
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AC analysis is to model the formation pressure response to the fluid leakoff during pumping and fracture closure. The BC leakoff history therefore should be considered in the AC analysis. Liu et al. (2016) proposed a AC model to calculate formation permeability with the AC linear flow by taking advantage of the fracture half-length estimated via the BC analysis. In this way, a consistent model can be generated to match both BC and AC data. Besides that, we are to illustrate two other impacts of the BC leakoff process on the AC modelling. When to estimate the formation permeability via the pseudo-linear or pseudo-radial model as suggested by Liu et al. (2016) and Ehlig-Economides and Liu (2017), the flow rate used in these equations should be calculated by dividing the total leakoff volume or the total effective pumping volume calculated with Eq. 2 by the injection time that used to generate diagnostic plots. The calculated rate may not be same with the average or the steady injection rate recorded at surface during the injection. This requires an accurate estimation of the total leakoff volume or the total injected fluid volume defined in Eq. 2. When to generate the forward global model including BC and AC, which is an essential step to match the field data, the leakoff process should also be simulated. According to the Carter leakoff model (Carter 1957), fluid leakoff rate through a fixed fracture area declines with the contact time. Therefore, from the perspective of formation matrix, the pumping and leakoff process can be viewed as an injection with variable rate. Then the AC model can be generated with the superposition of the whole leakoff rate history.
Hydraulic fracture design with parameters quantified from DFIT analysis
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Because DFITs are designed to provide input parameters for the hydraulic fracture design, the DFIT data should be interpreted in an accurate manner, and the calculated parameters should be used in a proper way in the hydraulic fracture design. As discussed above, the normal leakoff models in most cases are not adequate for DFIT analyses, so we use the Liu and Ehlig-Economides (2015) model to illustrate how the quantified parameters should be used in the hydraulic fracture design, and what difference could be made if the parameters are from the normal leakoff models. Three primary parameters, the leakoff coefficient, fluid efficiency and fracture closure stress, are quantified from the DFIT analysis and used in the hydraulic fracture design. Take the DFIT case with natural fracture related PDL for instance. BC Models derived from the normal leakoff assumption (Nolte 1986; Craig and Blasingame 2006) would suggest picking only the final closure trend and identify the hydraulic fracture closure at the deviation point off the trend (Barree et al. 2009). And then, the leakoff coefficient, fluid efficiency and fracture geometry are determined with the identified closure. We believe this methodology can provide a solid estimation of fracture closure stress, but an inaccurate estimation of the fluid leakoff coefficient and a poor estimation of the fluid efficiency because the leakoff computation does not account for the fluid loss into secondary fractures, which could be dominant over the hydraulic fracture. To include the leakoff through secondary fractures, Liu and Ehlig-Economides (2016) suggests labelling multiple closure trends, each of which represents a different fracture surface area. Then the fracture surface area under any pressures during fracture closing can be estimated together with the leakoff coefficient and fluid efficiency. By accounting for the leakoff into secondary fractures, the fluid efficiency could be much smaller than that determined from the Nolte solution (Nolte 1979, 1986), and should be used in the hydraulic fracture design. Otherwise, hydraulic fracture design with the overestimated fluid efficiency could lead to suboptimal hydraulic fracture performance because of the inadequate fracturing fluid volume. Also for the formation with secondary fractures, the multiple closure model by Liu and EhligEconomides (2015) enables quantification of the reopening stress, leakoff capacity and extension of each set of secondary fractures. With these results, it is possible to optimize hydraulic fracture design by promoting or preventing to reactivate these natural fractures. For instance, the DFIT may present PDL
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feature if the secondary fracture is permeable and connected with the hydraulic fracture. To take advantage of these secondary fractures, internal pressure of the hydraulic fracture (excluding friction losses) should be designed to be larger than their closure stress during the main hydraulic fracture treatment. King (2010), Zhu et al. (2016) and Bychina (2018) observed a positive correlation in tight formations among injection rate, fracture complexity and post treatment well productivity. In other words, high injection rate, or high injection pressure, is prone to create the complicated fracture system by connecting secondary fractures, and the fracture system with high complexity is preferred for the production from tight formations. According to Liu and Ehlig-Economides (2017), flow friction losses in wellbore, perforation and near-wellbore tortuosity can be determined separately from the DFIT with or without rate step-down test. It needs to be noted that the traditional method to estimate friction losses with the step-down test is unreliable because of the poor estimation of ISIP. The method to pick ISIP by drawing a straight line on the Cartesian pressure plot (Cramer and Nguyen 2013) or on the semi-log plot (Barree et al. 2014) is highly subjective and arbitrary because it has no consideration of the possible wellbore storage effect and lacks support from the physics theory. Therefore, we suggest determining friction losses with the model by Liu and Ehlig-Economides (2017). With the calculated friction losses, operations can be optimized. For instance, large friction in perforation could be reduced by adjusting perforation parameters like shot density, phase and hole diameters. While, for the case with large friction caused by the near-wellbore tortuosity, Wright et al. (1996) suggests pumping several small proppant slugs during pad to minimize the friction loss and to prevent the potential premature screenout.
DFIT design
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As to the DFITs, we recommend that they should be always injected in one single perforation cluster to avoid multiple fracture initiations. Otherwise, the DFIT data are uninterpretable because it is difficult to estimate the fluid distribution among perforation clusters and the potential stress shadowing effect among created fractures. Two major parameters that should be carefully addressed in the DFIT design are the injection rate and the volume. To mimic hydraulic fracture treatment, the same fracturing fluid planned for the main treatment should be pumped for the DFIT, and the pumping rate should be similar to the planned rate of one perforation cluster during the main treatment. Because of the relatively high pumping rate, the total injection volume for a DFIT may not be small, which may lead to the delayed hydraulic fracture closure and the long shut-in time required to reach AC flow regimes, especially the AC pseudo-radial flow.
Fig. 1 Composite G-function plots of two successive DFITs in one location (the left for the first DFIT and the right for the second DFIT) (Rizwan 2017)
Rizwan (2017) showed an informative field case with two successive DFITs through the same perforations in a tight gas formation. The first DFIT was pumped with a small volume (24.8 bbl) at a low rate (0.94 – 1.38 bpm). Its falloff presents a simple BC trend close to the normal leakoff following WBS (left graph of Fig. 1), from which the hydraulic fracture closure can be determined. According to
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Rizwan (2017), its AC clearly shows the pseudo-linear flow and even the pseudo-radial flow within 12.2 hours after shut-in. After the falloff of the first DFIT, the second DFIT was pumped with a larger volume (158 bbl) and at a higher rate (12.6 – 18.7 bpm). The second falloff presents complicated BC behaviors including WBS, PDL and apparent height recession (or transverse storage or variable fracture compliance) before the final closure, as shown in the right graph of Fig. 1. Several points can be learnt from the case. First, we may conclude that the difference in fracture closure behaviors is caused by different pumping rates and volumes. Specifically, low rate (also indicating the low pumping pressure, ISIP and net pressure) and small volume of the first injection may create a simple hydraulic fracture with limited extension, which shows a single closure trend close to the normal closure in its falloff data; while, much higher rate (also indicating the larger pumping pressure, ISIP and net pressure) and larger volume of the second injection may create a more complicated fracture system, in which scenario height recession or secondary fracture related transverse storage could occur. Secondly, Rizwan (2017) claimed that the data supports the holistic methodology (Barree et al. 2009) to pick the hydraulic fracture closure and contradicts the variable fracture compliance approach by McClure et al. (2014). The final fracture closure of the second DFIT picked with the holistic method is only 10 psi higher than that of the first DFIT, which is nearly the normal leakoff with a clear closure point. While, the difference is larger than 377 psi if the closure is picked with the variable fracture compliance approach. Thirdly, the case offers an alternative methodology to perform DFITs with two successive injections: the first one with low rate and small volume and the second with high rate and large volume. The simple and short hydraulic fracture created during the first injection provides the closure stress and AC pseudo-linear and pseudoradial flow within a relatively short shut-in time. The second test with the high rate and large volume provides insight on other possible fracture and formation behaviors, such as secondary fractures related phenomena and height recession, which are expected during the main hydraulic fracture pumping. The required shut-in time for the second DFIT could be relatively short because the its AC analysis is not a necessity with the formation pressure and permeability quantified from the previous DFIT. Besides the short shut-in time, another advantage of the design is that parameters quantified from both DFITs can be cross-checked for consistency. Two other similar but not same field cases are available in publications and should be mentioned as a comparison. Rohmer et al. (2015) showed two successive DFITs in the same well drilled in the Vaca Muerta Shale: the first injection with a small volume (20.8 bbl) and a low rate (≤ 5.5 bpm), and the second injection with a large volume (155 bbl) and a high rate (≤ 14 bpm). Diagnostic plots of both DFITs present abnormal leakoff behaviors but in distinctive features: the first one with obvious transverse storage/height recession and the second with short pressure dependent leakoff (PDL). The difference is unexpected. However, the final closures picked with the holistic methodology from the two DFITs are consistent. Nicholson et al. (2017) published another field case with two successive DFITs, which were tested in a shallow gas-shale formation with thrust fault setting, where the overburden stress is assumed to be the minimum principal stress. Different from cases demonstrated by Rizwan (2017) and Rohmer et al. (2015), the first injection in the Nicholson et al. (2017) case has a relatively large volume at 33.2 bbl and a high rate at 6.3 bpm compared with the second injection with an ultra-small volume at 0.82 bbl, which is only 2.5% of the first injection, and an ultra-low rate at 0.27 bpm. Diagnostic plots of the first falloff have a transverse storage/height recession feature, while the second falloff has a nearly normal leakoff behavior. This fits our previous discussion. However, the final closure picked from these two DFITs are not same. One possible reason is that the second injection may not totally reopen the hydraulic fracture created in the first injection because the size of the second injection is too small. It is a good case to demonstrate that the first injection in the two successive DFITs should be smaller than the later one.
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Case study
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In this section, we are to illustrate the bottomhole flow rate, leakoff rate during and after pumping, AC analysis, and then how these quantified parameters be used in the hydraulic fracture design. The DFIT was performed in the toe stage of a horizontal well completed with the slide sleeve. Wellbore was pressurized up to open the sleeve before the DFIT injection. Fluid was pumped into the formation through the first casing interval with an inner diameter (ID) of 6.09 inch and length of 10,500 ft and the second casing interval with an ID of 3.92 inch and length of 11,635 ft. The measured depth (MD) of perforations is at 22,135 ft. The surface injection rate was maintained flat at 5.6 bpm for one minute and then the step-down test was performed. Two rate steps, 4 and 3 bpm, are tested before the surface shutin, each for around 20 seconds. The stable pressure does not establish at neither of the steps. Approximately 13.75 bbl fresh water was injected into the well in 2.75 minutes with an average wellhead rate at 5.0 bbl/min, as shown in Fig. 2.
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Fig. 2 Injection profile
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The wellbore volume is calculated at 576 bbl, which is significantly larger than the injected fluid volume and the WBS effect cannot be neglected. Because the wellbore pressure declines from 13,823 psi at the start of pumping to 12380 psi at shut-in, an additional 3.32 bbl fluid flowed into the fracture by shut-in besides the surface injection volume at 13.75 bbl. Furthermore, by adding the after-flow volume after shut-in, a total of 26.6 bbl fluid finally flowed into the fracture and leaked off through the fracture surface at the final closure, which is almost 13 bbl more than or twice of the surface injection volume. The WBS effect therefore should be considered in the falloff analysis and the injection modelling.
Fig. 3 Bourdet derivative plot (Left) and composite G-function plot (Right).
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The left graph in Fig. 3 is the Bourdet derivative in log-log plot with markings indicating slope trends of interest. The fracture closure trend presents a 3/2-slope in the Bourdet derivative (Mohamed et al. 2011). The right graph of Fig. 3 shows the composite G-function plot displaying exactly the same closing trends. Two dashed lines in the lower right corner are guide lines with specific slopes: the red line with 3/2-slope and the green with unit slope. Briefly, the first behavior indicated by the green unit slope (marked as circle 1) in the Bourdet log-log plot is the indication of WBS with perforation friction dissipation. The next bump curve (circle 2) could be the tip extension after shut-in coupled with the near-wellbore friction dissipation. The end of tip extension can be picked at the bottom of the valley at around ∆t = 0.4 hours in the Bourdet derivative curve, or G = 8 in the Gdp/dG plot. The minimum fracture propagation pressure at the end of tip-extension is 8,668 psi. Then, the Bourdet derivative merge into a trend with 3/2-slope (circle 3), which corresponds to the straight trend indicated by the red dashed line in the Gdp/dG curve. The same closure is picked at the end of 3/2-slope in the Bourdet derivative curve with the derivation point from the straight trend in the Gdp/dG curve.
Fig. 4 Bourdet derivative plot (Left) and composite G-function plot (Right) without early behavior.
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For the case with tip extension and/or other early behaviors, Liu and Ehlig-Economides (2016) suggests starting the falloff analysis from the end of tip extension with an adjusted injection time equal to injection time ( ) plus tip extension time (∆ ). By excluding early WBS, friction and tip extension behaviors, new diagnostic plots are generated in Fig. 4. The new diagnostic plots show much clearer closure trend with little disturbance of the early behavior. Besides the final hydraulic fracture closure, a little hump (circle 1) above the final closure trend (circle 2) in the Gdp/dG curve indicates the pressure dependent leakoff (PDL) behavior, and the same closure point can be picked from the Bourdet derivative plot. Then, the final fracture geometry, formation leakoff coefficient, fluid efficiency and natural fracture surface area are estimated with the model introduced by Liu and Ehlig-Economides (2015). Table 1 Interpretation result of Well B
Injection and Falloff Feature , psi , bbl !, Vl, bbl ∆ , & , psi ∆ , psi , xf, initial, ft pp, min, psi
Injection
Friction losses at shut-in
Tip Extension
4.0×10-6 17.07 0.40 220 2,497 97 8,668
Closure 1
Closure 2
After-closure (data match)
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xf, final, ft , psi Total area of one-sided fracture, ft2 # , ft2 $% , ft/√min η k, md pi, psi
331 8,475 35,550 9,033
8,235 26,517 26,517
4.4 / 1023 0.97
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0.15 7,945
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Friction occurring in the wellbore and perforation, and near wellbore tortuosity, fracture geometry at shut-in are obtained by matching the early falloff behaviors and pumping data. The interpreted parameters are listed in Table 1. The result shows that the fracture half-length at shut-in is only 97 ft, and then the hydraulic fracture grows to 331 ft during tip extension after shut-in, which is 3.4 times as long as that at shut-in. The Bourdet derivative curve bends to flat soon after the closure (circle 4 in Fig. 3 or circle 3 in Fig. 4), leaving no room for the possible pseudo-linear flow. The flat is not solid and it starts drop because the pressure tends to be flat or even rises at the very end (no shown in this paper). Therefore, the apparent flat trend may not be a valid pseudo-radial flow. We then treat it as part of transition from the before-closure behavior to the after-closure flow regimes, and the final match provides formation permeability at approximately 0.15 md and formation initial pressure at 7,945 psi. The forward model then is generated based on the falloff analysis result, and it fits the falloff pressure and its derivatives well as shown in Fig. 5. And, the injection pressure can also be matched by slightly adjusting the area exponent, shown in Fig. 6.
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Fig. 5 Model match for falloff pressure behavior.
Fig. 6 Model match for injection and falloff pressure.
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Fig. 7 (A) presents the comparison between the surface injection rate and the bottomhole flow rate at the formation face. Because the injection pressure is not stable, the bottomhole rate is not constant even the surface rate is flat. Moreover, the bottomhole rate keeps declining at the step-down test and does not display any indication of “rate steps”. Therefore, the recorded rate at surface should not be used to determine the rate dependent friction. After step-down test, the surface rate drops to zero immediately after shut-in, while the after-flow lasts for much longer with a fading rate. Fig. 7 (B) shows the fracture internal pressure, bottomhole fracture face pressure, friction occurring in wellbore, perforation and near wellbore tortuosity, net pressure at the wellbore and the average net pressure. The result shows that friction accounts for the majority pressure drop after shut-in. While, the fracture average net pressure is approximately 1,000 psi at the shut-in but declines to 350 psi after the tip extension. And, the fracture internal pressure is relatively flat and does not have a large pressure drop after shut-in.
Fig. 7 (A) Surface injection rate and bottomhole flow rate; (B) Bottomhole pressure, fracture internal pressure, friction, net pressure at wellbore and average net pressure during injection and falloff.
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Our BC model is derived based on the material balance function. Components of material balance are shown in Fig. 8. The total injection fluid volume indicated by the green line grows from the pumped bottomhole volume at 17.07 bbl at shut-in to 26.6 bbl by adding the after-flow volume caused by the WBS. Its rapid growth occurs at early time after shut-in because the wellbore pressure declines rapidly during the time. The hydraulic fracture volume, indicated by the purple line, gains some extra volume after shut-in because of the fracture tip extension. Then, it declines gradually all the way to zero, which corresponds to fluid leakoff and fracture closure process. The cumulative leakoff volume, indicated by the blue line, increases from 0.4 bbl (leakoff volume during injection) to 26.6 bbl at the fracture final closure. The total injection volume should always equal to the sum of the cumulative leakoff volume and the hydraulic fracture volume. The only way to satisfy the material balance and build a plot like Fig. 8 is taking consideration of abnormal leakoff behaviors including secondary fractures, friction losses, WBS, etc.
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Fig. 8 The changes of hydraulic fracture volume, after-flow volume, cumulative leakoff volume and leakoff rate after shut-in.
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The fluid leakoff rate after shut-in is indicated by the red line in Fig. 8. It climbs to the highest point with tip extension when more fresh fracture surface is created for fluid leakoff. Then, it declines rapidly with the time. For one thing, part of the high leakoff rate is contributed by the natural fractures, while natural fractures are closing and losing their surface areas. For the other, the leakoff rate decline is rooted in the Carter leakoff model. The decline of leakoff rate at the late time is slowing down. From the decline curve, we can conclude that the leakoff process is not at constant rate. When to generate the forward model, we use the superposition of variable injection rates to model the AC pressure response. From above discussion, many more parameters are quantified in a more robust and accurate way. The next question will be how to use these parameters in the hydraulic fracture design. The first factor should be noted is the friction loss through the near-wellbore tortuosity, which is almost 2,500 psi at the end of pumping. As mentioned above, large tortuosity friction may lead to premature proppant screenout. One effective way to release the severe tortuosity is adding several 100-mesh proppant slugs during pad. Secondary fractures are another issue that should be considered in the hydraulic fracture design. The DFIT result reveals several major properties of secondary fractures: leakoff capacity, extension and reopening stress. These secondary fractures are permeable, which is learnt from the PDL behavior, so they are likely to contribute to the production if they are connected to the hydraulic fracture. However, DFIT results show that natural fracture has a limited extension, which is approximately one third of the hydraulic fracture surface area. To reactivate these natural fractures, the effective fracture internal pressure should be higher than 8,475 psi, or the required minimum net pressure along the hydraulic fracture is around 240 psi. It might be easy to satisfy the pressure requirement for the hydraulic fracture close to the wellbore, but could be challenging for the fracture into the far deep formation because of pressure loss along the fracture. Even higher net pressure is required if these natural fractures are designed to take proppant. Another potential impact of secondary fractures is the fluid leakoff. The leakoff through natural fractures could be calculated via the multiple closure model by Liu and Ehlig-Economides (2015). As to this field case, the fluid leakoff volume through natural fractures during pumping is minimal because of its limited surface area. However, for the case with massive connected natural fractures (Liu and Ehlig-Economides 2017), the amount of fluid leakoff volume through natural fractures could be dominated.
Conclusions This paper discusses several issues associated with the DFIT analysis. On the basis of the fracture behaviors in practice, we propose how to determine input parameters for both BC and AC DFIT models. Many parameters associated with abnormal leakoff behaviors can be quantified, and we show how these parameters can be used in the hydraulic fracture design. Also, we propose an alternative DFIT design. Several key conclusions are the following.
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1) Bottomhole rate should be calculated by considering the WBS effect. When to match the pumping data, both the surface rate and the calibrated bottomhole rate should be used. 2) The AC analysis is to model the pressure response after variable leakoff rate. The flow rate used in the AC analysis should be calculated by dividing the total effective injected volume defined in Eq. 2 by the injection time used to generate diagnostic plots. The AC forward model can be generated with the superposition of multiple leakoff rates. 3) The material balance function should be followed to quantitively model the abnormal leakoff behaviors, and then the associated parameters can be accurately estimated. 4) Secondary fracture properties (surface area, leakoff capacity and reopening stress) and friction losses (in wellbore, perforation and tortuosity) quantified from the DFIT analysis should be considered in the hydraulic fracture design. 5) A field case with two successive DFITs is proved to be an alternative DFIT design. The first DFIT is pumped at a low injection rate and small volume, while the second at a high rate and large volume. The case supports the holistic method to pick final fracture closure, and contradicts to the variable fracture compliance approach.
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The authors would like to thank operating companies for sharing data used in the case study.
Nomenclature
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Af = fracture one side surface area, L2 bpm = bbl per minute, L3/t CL = leakoff coefficient, L/√t G = G-function, dimensionless ISIP = instantaneous shut-in pressure, m/Lt2 k = permeability, L2 p = pressure, m/Lt2 pc = closure pressure, m/Lt2 pi = formation initial pressure, m/Lt2 pp, min = minimum fracture propagation pressure, m/Lt2 p’ = Bourdet pressure derivative, m/Lt2 q = flow rate, L3/t qaf = after-flow rate into the fracture caused by fluid expansion in the wellbore, L3/t t = time, t tp = pumping time, t V = volume, L3 Vp = pumping volume, L3 xf = fracture half-length, L xf，initial = fracture half-length at shut-in, L xf，final = fracture half-length after tip extension, L
Greek ∆ = difference, dimensionless η = fluid efficiency, percentage
Subscripts BH = Bottomhole c = closure f = fracture fric = friction
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inj = injection perf = perforation tort = near-wellbore fracture tortuosity te = tip extension w, wb = wellbore WBS = wellbore storage
References
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Highlights
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1. Bottomhole rate should be calculated by considering the WBS effect. 2. The AC analysis is to model the pressure response after variable leakoff rate. The flow rate used in the AC analysis should be calculated by dividing the total effective injected volume by the injection time used to generate diagnostic plots. 3. The material balance function should be followed to quantitively model the abnormal leakoff behaviors, and then the associated parameters can be accurately estimated. 4. Secondary fracture properties (surface area, leakoff capacity and reopening stress) and friction losses (in wellbore, perforation and tortuosity) quantified from the DFIT analysis should be considered in the hydraulic fracture design.