PETROPHYSICS
Vol. 60, No. 1 February 2019
PETROPHYSICS February Vol. 60, No. 1 Contents
3 From the Editor
Th e Society of TUTORIAL Petrophysicists and 4 Organic-Mudstone Petrophysics: Workfl ow to Es mate Storage Capacity Well Log Analysts Kent Newsham, Joe Comisky and Roland Chemali
8866 Gulf Freeway, Suite 320 ARTICLES BEST OF THE 2018 SYMPOSIUM, PART 2 Houston, TX 77017, USA P: +1-713-947-8727 17 Defi ning Net-Pay Cutoff s in Carbonates Using Advanced Petrophysical Methods F: +1-713-947-7181 Mark Skalinski, Robert Mallan, Mason Edwards, Boqin Sun, Emmanuel Toumelin, Email: [email protected] Grant Kelly, Hazaretali Wushur, and Michael Sullivan [email protected] www.SPWLA.org 37 Frequency and Temperature Dependence of 2D NMR T1-T2 Maps of Shale Ravinath Kausik, Denise Freed, Kamilla Fellah, Ling Feng, Yanchun Ling, SPWLA Foundation. This fund and Gary Simpson supports scholarships in higher educa on 50 Maintaining and Reconstruc ng In-Situ Satura ons: A Comparison Between and research in formation evaluation. Whole Core, Sidewall Core, and Pressurized Sidewall Core in the Permian Basin Please send dona ons to: SPWLA, 8866 Aidan Blount, Adam McMullen, Melanie Durand, and Brian Driskill Gulf Freeway, Suite 320, Houston, TX 77017, USA 61 Novel Composite Cement for Improved Well Integrity Evalua on Hani Elshahawi, Shan Huang, Jacob Pollock, and Vinod Veedu ISSN 2641-4112 ARTICLES DEPTH CONTROL PETROPHYSICS is published bimonthly by the Society of Petrophysicists and Well Log Analysts 71 Depth: A Love and Hate Story (SPWLA). Subscription is included in Philippe Theys annual dues for members. Library Subscription cost is $250 (6-issues, 73 Connec ng the Dots—The Relevance of Proper Depth Control in the Discovery of Feb, April, June, Aug, Oct, Dec) Send the Groningen Field Subscription and member address Emile Fokkema and Clemens Visser changes to the SPWLA business office. Back issues if available are $35 each 76 Correc on of Driller’s Depth: Field Example Using Driller’s Way-Point Depth to members and $45 each to library Correc on Methodology subscribers. Harald Bolt
ADVERTISING RATES: (based on one-time, full color) Full Page: $1500, ARTICLES REGULAR SUBMISSIONS Half Page: $1200, Quarter Page: $1000. Additional fee for printing on 93 Modeling of Azimuthal Gamma-Ray Tools for Use in Geosteering in covers. Media kits are available by Unconven onal Reservoirs contacting the SPWLA business office Haijing Wang, Ed Stockhausen, Dennis F. Wya Jr., and Dean Gulick or by visiting the SPWLA website www.spwla.org. Responsibility: The 113 Feasibility and Design of Hydraulic Fracturing Stress Tests Using a Quan ta ve statements and opinions expressed Risk Assessment and Control Approach in PETROPHYSICS are those of the Thomas Bérard, Nikita Chugunov, Jean Desroches, and Romain Prioul authors and should not be construed as an official action or opinion of the 136 Neutron Generators as Alterna ves to Am-Be Sources in Well Logging: Society of Petrophysicists and Well An Assessment of Fundamentals Log Analysts, Inc. © Copyright 2017 Ahmed Badruzzaman, Andrea Schmidt, and Arlyn Antolak by the Society of Petrophysicists and Well Log Analysts, Inc. 171 Instruc ons to Authors
About the Cover The industry is beginning to use azimuthal Full-Color versions of all technical ar cles are available in the digital edi on of Petrophysics, GR tools for geosteering horizontal wells which is free to SPWLA members and can be found at Recent_Petrophysics_Journals.aspx. in unconven onal reservoirs. Theore cal analysis based on Monte Carlo nuclear As of Vol. 60 (1) 2019, modeling and case studies of fi eld data The Society of Petrophysicists and Well Log Analysts Petrophysics [ISSN: 2641-4112] from three horizontal wells are presented is dedicated to the advancement of the science of forma on in the ar cle by Wang et al. evalua on through well logging and other forma on evalua on is indexed and abstracted in techniques. SPWLA is dedicated to the applica on of these Thomson Reuters: techniques, to the explora on and exploita on of gas, oil and Scien fi c Cita on Index Expanded other minerals. PETROPHYSICS publishes original contribu ons Journal Cita on Report–Science on theore cal and applied aspects of forma on evalua on; par cularly well logging and petrophysics. Current Contents–Physical, Chemical, PRINTED IN USA ON ACID FREE PAPER and Earth Sciences
February 2019 PETROPHYSICS 1 PETROPHYSICS The Society of Petrophysicists and Well Log Analysts Editor Board of Directors 2018–2019
Carlos Torres-Verdin President VP Finance University of Texas at Aus n Zhipeng “Z” Liu Jennifer Market (+1) 512-471-4216 Kinder Morgan Lloyd’s Register cverdin@aus n.utexas.edu Houston, TX, USA Houston, TX, USA (+1) 713-369-8059 (+1) 713-302-8325 Associate Editors [email protected] [email protected] President-Elect VP Publica ons Jesus Salazar Carlos Torres-Verdin Acous cs and Rock Physics ConocoPhillips University of Texas at Aus n Richard Coates, Halliburton Houston, TX, USA Aus n, TX, USA (+1) 281-293-5237 (+1) 512-471-4216 [email protected] VP-Publica [email protected] VP Technology VP IT Core Analysis and Laboratory Petrophyiscs James Hemingway Mehrnoosh Saneifar Gary Beck, Cardinal Geosciences Consultant BHP Petroleum Manitou Springs, CO, USA Houston, TX, USA (+1) 281-433-5170 (+1) 832-600-4046 [email protected] [email protected]
Electromagne cs VP Educa on Fei Le, Baker Hughes Katerina Yared Consultant Highlands Ranch, CO, USA (+1) 720-431-7482 VP-Educa [email protected] Forma on Tes ng Mayank Malik, Chevron REGIONAL DIRECTORS
N. America 1 Middle East/Africa/India Adam Haecker Shouxiang (Mark) Ma Integrated Forma on Evalua on Con nental Saudi Aramco Chengbing Liu, Saudi Aramco Oklahoma City, OK, USA Dhahran, Saudi Arabia Wilfrido Solano, Chevron (+1) 979-587-1061 (+966) 3874 6931 [email protected] [email protected] N. America 2 Asia/Australia Doug Pa erson Rick Aldred Integrated Forma on Evalua on and Case Studies Baker Hughes Consultant Petrophysicist Hesham El-Sobky, ConocoPhillips Houston, TX, USA Queensland, Australia (+1) 713-879-4056 (+610) 408-453-351 [email protected] [email protected]
Magne c Resonance La n America Execu ve Director Nadege Bize-Forest Sharon Johnson Lalitha Venkataramaman, Schlumberger SPWLA Wim Looyes jn, Shell Schlumberger Rio de Janeiro, Brazil Houston, TX 77017 (+552) 197 45 45 772 (+1) 713-947-8727 [email protected] [email protected]
Nuclear Europe Pingjun Guo, ExxonMobil Michael Webster Produc on Petrophysics Ltd Aberdeen, Scotland, UK (+440) 7568-476931 [email protected] Petroleum Geochemistry Drew Pomerantz, Schlumberger
Well and Reservoir Surveillance Gerardo Cedillo, BP Managing Editor Publica on Manager Stephen Prensky Anna Tarlton (+1) 301-593-4966 InkSpot Prin ng Data-Driven Analy cs [email protected] 2301 S. Shaver Chicheng Xu, Aramco Services Pasadena, TX 77502, USA (+1) 713-472-1100 orders@inkspotprin ng.com
2 PETROPHYSICS February 2019 )5207+((',725
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DOI: 10.30632/PJV60N1-2019a9 Feasibility and Design of Hydraulic Fracturing Stress Tests Using a Quantitative Risk Assessment and Control Approach Thomas Bérard1, Nikita Chugunov1, Jean Desroches2, and Romain Prioul1 ABSTRACT Openhole microfracturing stress tests often fail at great success over this range. Finally, on test completion, we use depth because a fracture cannot be initiated, even with test results to reduce the uncertainty space. We illustrate the application of the equipment’s maximum pressure. This method with a synthetic case example. Uncertainties prove paper presents methodological developments enabling easily factored in and run-time is less than one second for feasibility assessment and design analysis of such tests adequate sampling of the uncertainty space. The analysis with respect to fracture initiation. Emphasis is put on informs on how successful or unsuccessful a planned test is quantitative risk assessment and control to account for the likely to be and, when necessary, on the most effective ways large uncertainty that generally prevails, before a test, in to improve the chance of success, including in terms of tool the in-situ conditions controlling the initiation pressure. con¿ guration, well and test design, and rock formation Given equipment’s pressure speci¿ cations, we calculate targets. Uncertainty reduction based on completed tests the probability of successfully initiating a fracture for a results should improve the success rate from one test, or range of in-situ conditions and design options. Global one test campaign, to the next. sensitivity analyses are carried out to map the chance of INTRODUCTION the equipment’s pressurization capacity. Failure to initiate a fracture leads to premature termination of the test and the Knowledge of the state of stress in the subsurface is of absence of measurement. The tool can then be moved to primary importance in all areas of geomechanics. Hydraulic another zone for another trial, but with no assurance that fracturing testing in boreholes is the only direct technique initiation will be achieved. Obtaining a pro¿ le of stresses available at great depth for measuring rock stress magnitude that samples the desired formations in the lithological (e.g., Haimson, 1993; Haimson and Cornet, 2003 and column thus becomes a challenge. references therein). Although more details will be provided When planning a stress test, the outcome with respect to in the next section, let us highlight that the ¿ rst step of such fracture initiation is dif¿ cult to forecast. This is partly because testing involves initiating a fracture from the borehole wall. the process of fracture initiation and early propagation is This may be achieved by increasing the À uid pressure within complex (Detournay and Carbonell, 1997; Papanastasiou an interval of the borehole sealed between a pair of packers et al., 1995; Lecampion, 2012a, 2012b; Lecampion et al., (hydraulic fracturing) or by increasing the À uid pressure 2013; Lecampion and Desroches, 2014; Lakirouhani et al., within a single packer (sleeve fracturing). However, fracture 2016; Lu et al., 2017). Models nonetheless exist that show initiation often proves dif¿ cult, if not impossible, to achieve very good agreement with laboratory experiments when at great depth (e.g., > 2 km), even with application of the material properties and boundary conditions are known equipment’s maximum pressure. Franquet et al. (2011), for accurately (Lecampion et al., 2017). In practice however, example, report on a series of seven attempts, of which three large uncertainty in the subsurface properties and conditions failed to initiate a fracture at maximum pressure. The same controlling the pressure required to initiate a fracture failure rate (3/7) is reported by Mishra et al. (2016). The generally prevails before a test. Notably, the initiation issue is more often noted at greater depth because the facture pressure depends on rock stress, which the test is precisely initiation pressure tends to increase over depth more rapidly meant to measure. As the initiation pressure is uncertain than the hydrostatic well pressure and eventually exceeds prior to a test, it is dif¿ cult to forecast whether it is within Manuscript received by the Editor June 5, 2018; revised manuscript received August 22, 2018; manuscript accepted August 29, 2018. 1Schlumberger, 1 Hampshire Street, Cambridge, MA 02139 USA; [email protected]; [email protected]; [email protected] 2Rocks Expert, 5153 chemin de Bertine, 04300 Saint Maime, France; [email protected] February 2019 PETROPHYSICS 113 Feasibility and Design of Hydraulic Fracturing Stress Tests Using a Quantitative Risk Assessment and Control Approach or beyond the equipment’s capabilities. For the same reason, it is dif¿ cult to forecast how effective any change in well or test design would be at improving the chance of success. This uncertainty is not factored in today’s feasibility assessment and design practices. The Hubbert and Willis (1957) or Haimson and Fairhurst (1967) analytical models are often used to estimate the initiation pressure and compare it to the tool’s pressure capability (e.g., Al Shehhi et al., 2015). However, because these models respectively have four and ¿ ve input parameters (including the minimum and maximum horizontal stresses), the overall level of uncertainty in the initiation pressure is very dif¿ cult to grasp. As a result, the risk of test failure tends to be poorly evaluated and, hence, poorly controlled. In this paper, we present methodological developments to assess the feasibility and improve the design of stress-testing operations under uncertainty. The proposed method adapts a general-purpose method for quantitative risk assessment and control (Vivalda and Jammes, 2008; Vivalda et al., 2009) to the context of fracture initiation in stress-testing operations. The overall workÀ ow is shown in Fig. 1. With reference to this ¿ gure, we ¿ rst de¿ ne a metric to gauge the risk of test Fig. 1—Overall workÀ ow for quantitative risk assessment and control of stress-testing operations. failure (criticality analysis). We then describe the model adopted to calculate this metric, and its input parameters. After this framework is in place, the feasibility assessment of the borehole itself. Let us note that hydraulic fracturing and design analysis of a particular, planned test involve for stress measurement is mostly performed in vertical data collection and consolidation for input uncertainty wells, assuming that the vertical stress is close to a principal assessment, uncertainty sampling and propagation for risk stress direction (within 10 to 15q) and that the direction assessment, as well as sensitivity analyses for risk control. of the least compressive principal stress is horizontal. We Finally, we discuss how, on test completion (successful shall restrict ourselves to such con¿ guration, as there are or not), input model parameters can be calibrated through numerous complexities arising in wells that do not meet history matching, thus allowing return of experience to be these restrictions (e.g., Weijers and de Pater, 1994). leveraged from one test, or one test campaign, to the next. Hydraulic fracturing stress testing can be performed After some background is provided on wireline formation in cased and perforated boreholes with a drillpipe and a stress testing, details for each step are presented in the packer arrangement prior to a hydraulic stimulation (Nolte, subsequent sections. In this paper, a synthetic case example 1979). Such implementation, known as a minifrac test, uses is used to illustrate the proposed workÀ ow. relatively large rates and volumes (7 to 30 L/min, several hundreds of liters, respectively) and creates a fracture with WIRELINE FORMATION STRESS TESTING an extent of the order of 10 m away from the well. There are several advantages to this con¿ guration. First, large Hydraulic fracturing stress testing relies on creating a surface pumps provide enough pressure to break down most hydraulic fracture and measuring the pressure at which it formations. Second, the fracture is propagated far away from opens or closes. This pressure is an estimate of the average the borehole. The technique has also several disadvantages, stress acting normal to the fracture surface. Because a the main one being that the created fracture is likely to span hydraulic fracture is expected to grow along the least- multiple formations bearing different stresses, thus only resistance path, i.e., perpendicular to the least-compressive providing an average estimate over these formations (for principal stress direction, the opening or closure pressures a discussion of a ¿ eld example, see Desroches and Woods, are estimates of the magnitude of the in-situ minimum 1995). Note that this can be turned into an advantage, if for principal stress averaged over the fracture surface, provided example, the application calls for a stress averaged over that the fracture is extended well beyond the near-borehole several formations to provide far-¿ eld boundary conditions region where the stress ¿ eld is perturbed by the presence to a particular geomechanical analysis. The other challenge 114 PETROPHYSICS February 2019 Bérard et al. is that the closure pressure may not be representative of the pressure in the tested interval in real time. The pressure in stress magnitude due to the complexity of the near-wellbore the packers is also monitored. When the test is completed, geometry (caused by the perforations and the casing/cement/ the packers can be deÀ ated and the toolstring can be moved rock interactions). to be set across the next interval to be tested. The pressure To achieve as close as possible a point-like measurement, in the packers is coupled with the pressure in the interval it is therefore preferable to create as small as possible to ensure a hydraulic seal with the minimum amount of a fracture. This has led to the development of the micro– differential pressure between the packers and the interval, hydraulic fracturing technique (Haimson, 1993; Haimson and thus limiting the risk of the fracture initiating behind the Cornet, 2003) of interest here. In this technique, a relatively packers or growing out of the sealed interval. short section of a borehole, usually about 1 m in length, is The pumpout module is used to inÀ ate the packer isolated with a straddle packer, and small injection rates and elements of the dual-packer module and to pressurize the small volumes (1 L/min, 1 to 10 L, respectively) are used test interval to create, propagate, and reopen the hydraulic to create and propagate the hydraulic fracture. However, fracture. The À ow rate delivered by the pump is, on average, the fracture still needs to be extended suf¿ ciently far away 1.1 L/min. Because the pump is downhole, wellbore storage from the wellbore, and several propagation/closure cycles effects are limited. are required to ensure that the fracture closure/reopening pressure has become insensitive to the near-wellbore stress perturbation (Desroches and Kurkjian, 1999). This technique is usually performed in uncased (open) boreholes. The ¿ rst advantage of this technique is that it tends to measure the stress only in the formation in front of the interval that is being tested. The second advantage, in open hole, is that the trace of the fracture at the borehole wall can be imaged to provide the direction of the maximum horizontal principal stress (e.g., Mosnier and Cornet, 1989; Cornet et al., 2003; Desroches et al., 2005; Zhao et al., 2015). The third advantage is that the straddle-packer arrangement can easily be moved within the wellbore, allowing tests to be conducted at multiple depths in the same run. However, this approach has disadvantages too. Using a small À ow rate may introduce an upper limit in the permeability of the formations that can be tested (if the rate is not large enough to overcome À uid leakoff into the formation, the interval pressure cannot be increased and no fracture can be created). The maximum pressure that can be reached with downhole tools is lower than that with surface equipment. If the pressure required to initiate and propagate the hydraulic fracture is above that limit, the test is terminated without any useful data acquired. The MDT modular formation dynamics tester is a wireline formation-testing tool (Zimmerman et al., 1990; Ireland et al., 1992). It consists of a series of modules, each designed to perform speci¿ c functions, which can be Fig. 2—Schematic of basic con¿ guration of the modular formation con¿ gured for the desired objectives. The tool is controlled dynamics tester tool for stress testing (after Thiercelin et al., 1994). in real time by software commands from the logging unit during the entire test sequence. The basic tool con¿ guration The standard testing procedure (Fig. 3), which we will for stress testing (Thiercelin and Desroches, 1993; Thiercelin refer to as HF for hydraulic fracturing, includes the steps et al., 1996), schematically shown in Fig. 2, is as follows. of positioning the tool, inÀ ating the packers to isolate an The dual-packer module has two inÀ atable straddle packers interval, and pumping À uid into the interval to build up that allow a section of a borehole, typically 1-m long, to pressure and, eventually, to initiate and propagate a hydraulic be isolated. This module is equipped with a dual-system of fracture. After pumping has stopped, pressure falloff is sensors (strain gauge and crystal quartz gauge) to measure monitored, either with or without À uid withdrawal from the February 2019 PETROPHYSICS 115 Feasibility and Design of Hydraulic Fracturing Stress Tests Using a Quantitative Risk Assessment and Control Approach interval. Further cycles of fracture reopening, propagation, and the straddle-packer arrangement of the tool positioned and pressure falloff are required to ensure that the wellbore so that the interval is in front of the created fracture. The inÀ uence on the measured closure pressure has vanished presence of a large preexisting defect created by the SF (Desroches and Kurkjian, 1999). process ensures that fracture extension will start at the interval level and at a pressure lower than if that preexisting defect was not present. The standard procedure can then be applied to obtain an estimate of the formation stress: packer inÀ ation and hydraulic fracturing cycles (which we will refer to as PS-HF for post-sleeve hydraulic fracturing). RISK CRITICALITY ANALYSIS To gauge the severity of the risk of test failure, a metric is de¿ ned herein as the difference between the theoretical pressure required to initiate a fracture, noted Pi , and the maximum downhole pressure that can be reached by the tool, noted Pmax: (1) Fig. 3—Schematic À ow rate and interval pressure versus time curves for the ¿ rst two injection cycles of a hydraulic fracturing stress test. When S is positive, fracture initiation is, in theory, Key pressure readings are annotated, including the hydrostatic mud impossible, and the difference indicates how much pressure (Pm), fracture initiation (or breakdown) pressure (Pi ), fracture propagation pressure, instantaneous shut-in pressure, closure pressure, pressure capacity is lacking to succeed. Conversely, when and fracture re-opening pressure, as well as pressures of interest in the S is negative, fracture initiation should be within reach, and context of this analysis (see text for details), including the maximum the difference indicates the surplus of pressure capacity differential pressure (ǻPmax), maximum permitted pressure (Pmax), and risk severity S = Pi –Pmax. The minimum in-situ stress magnitude is available, or “safety” margin. bracketed by the closure and propagation pressures. Adapted from The criticality of a risk depends on both the probability Malik et al. (2016). of an event and the severity of the consequences should the event occur (Kolluru and Brooks, 1995). The mapping If the mudcake is nearly impermeable, or if the of criticality as a function of severity and probability of formation itself is nearly impermeable, fracture initiation occurrence is the stakeholders’ responsibility. It reÀ ects their is not facilitated by any increase in pore pressure. In this objectives and concerns related to, e.g., safety, regulatory, or case, because the packer pressure is always higher than the business considerations. The resulting map of criticality as a interval pressure (to ensure a seal), the standard procedure function of severity and probability of occurrence is known may lead to fracture initiation under the packer elements and as the risk criticality matrix or risk matrix. It is customary hydraulic bypass of the packer. In other cases, the maximum to lump criticality levels into classes, such as acceptable, as possible interval pressure that the straddle-packer tool low as reasonably practicable (ALARP), and unacceptable con¿ guration can sustain is reached (and sometimes kept (Reed, 1994; Brereton and Altenbach, 1998). constant for a while) and yet no fracture is initiated. In either The criticality matrix de¿ ned for the present application one of such cases, the sleeve fracturing procedure (which is shown in Fig. 4. Note that Pi depends on how a fracture is we will refer to as SF for sleeve fracturing) can be followed initiated. As described above, we distinguish three operating to initiate a fracture (see Thiercelin and Desroches, 1993; modes: HF, SF, and PS-HF. Pmax depends on the equipment Thiercelin et al., 1994). Fluid is pumped into one packer used and may further depend on the hardware element under up to the maximum allowable inÀ atable pressure, which consideration. With the modular formation dynamics tester is typically larger than the maximum interval pressure that tool, Pmax may be controlled by the packers, the mandrel on can be reached in the straddle-packer con¿ guration (and which the packers are mounted, the pump, or the À owline. can be much larger for the models of packers dedicated to The latter refers to all the parts exposed to the high-pressure sleeve fracturing, see Khan et al., (2015). This may result in end of the pump (pressure gauges, stabber, etc.). Thus, there initiation of a stable longitudinal fracture in the formation are 12 different possible combinations of operating modes in contact with the packer. The packer can then be deÀ ated and hardware elements based on three fracturing modes (HF, 116 PETROPHYSICS February 2019 Bérard et al. SF, or PS-HF) and four hardware elements (packer, mandrel, at play, will be discussed further in the Discussion section. pump, or À owline). Any such combination will be hereafter We assume that a principal stress direction is vertical, that noted Mode | Element. The SF | Mandrel combination is the stress regime is either normal or strike-slip, and that the disregarded because the mandrel is not subjected to any borehole is vertical. load in SF mode. Each of these combinations may call for For the calculation of Pi we adopt the solution developed a dedicated criticality matrix. In the present analysis, the by Detournay and Cheng (1992), for which the fracture same criticality matrix is used regardless of the operating initiation pressure is given by mode. However, three different matrices are used for the packer, the mandrel/À owline, and the pump (see Fig. 4). (2) The criticality matrix for the mandrel/À owline elements is made more stringent than that for the packers. This is because the practical consequences of rupturing a mandrel Where ıh and ıH are, respectively, the minimum or bursting the À owline are far worse and because the and maximum horizontal stress magnitudes (positive in packers’ pressure speci¿ cations are, by experience, known compression); pp is the pore pressure; ıT is the rock tensile to be somewhat conservative. For the pump, a relief valve strength (positive); Ș is a poroelastic stress coef¿ cient given prevents the pressure from ever exceeding the maximum by Ș = Į(1–2Ȟ)/(2(1–Ȟ)), where Ȟ is the drained Poisson’s speci¿ ed pressure and, therefore, the risk criticality never ratio and Į is the Biot effective stress coef¿ cient; and H gets to be unacceptable. It is worth noting that high-severity is a function that depends on various factors including the events may still be acceptable provided that their probability pressurization rate. It is worth noting that H asymptotically of occurrence is low enough. tends to 0 and 1, and the above equation reduces to the Hubbert and Willis (1957) and Haimson and Fairhurst (1967) MODEL SELECTION equations, in the fast (H = 0) and slow (H = 1) pressurization regimes, respectively (Detournay and Cheng, 1992). For In this section, we describe the model adopted to simplicity, we substitute to H a scalar parameter h=1–H, calculate the severity metric S a-priori. The model is assumed ranging from 0 (full pressure equilibrium between the to be representative and accurate. Known limitations, well and the formation) to 1 (no pressure communication). especially about how much the model represents the physics This parameter h is hereafter referred to as the mudcake (a) (b) (c) Fig. 4—Criticality matrix for the packers (a), mandrels and À owline (b), and pumps (c) with probability displayed on a logarithmic (top row) and a linear (bottom row) scale. Unacceptable, as-low-as-reasonably-practicable, and acceptable criticality classes are shown in red, yellow, and green, respectively. Refer to the text for more explanation on how these criticality matrices are built. February 2019 PETROPHYSICS 117 Feasibility and Design of Hydraulic Fracturing Stress Tests Using a Quantitative Risk Assessment and Control Approach coef¿ cient. For SF mode, h is set equal to 1. For PS-HF magnitude over true vertical depth) to allow processing not mode, ıT is set equal to zero, because a fracture is supposed only depth points but also depth intervals. The maximum to have been initiated already. The initiation pressures for horizontal stress is de¿ ned by the ratio between the maximum HF SF SF-HF the HF, SF, and PS-HF modes are noted Pi , Pi , and Pi , and minimum horizontal stresses to explicitly ensure that the respectively. condition ıH ıh is satis¿ ed. Pmax is calculated as the sum of the well mud pressure, Table 1—Input Parameters to the P and P Models and Input Conditioning noted Pm, and the maximum additional pressure, known i max Parameters as the maximum differential pressure and noted ¨Pmax, that the tool element under consideration can deliver, or sustain, on top of the mud pressure: Pmax=Pm+¨Pmax. The mud pressure Pm is the pressure head of the hydrostatic mud column and is calculated as a function of depth and mud density Pm= ȡm gz, where ȡm is the average mud density, g is the acceleration due to gravity, and z is the true vertical depth. The maximum differential pressure ¨ Pmax is known from hardware speci¿ cations and, for certain elements, it depends on parameters such as the borehole diameter. For SF operations, ¨Pmax accounts for the imperfect pressure transmission of the packer pressure to the rock face. With the modular formation dynamics tester tool, various kinds psi of packers, mandrels, pumps, and À owlines exist with their psi/ft own differential pressure speci¿ cations. For the À owline, P is speci¿ ed in absolute, rather than differential, terms. The assigned values are used for illustration purposes; n/a – max nonapplicable. Refer to the Appendix for further details It is set to the maximum speci¿ ed pressure of the weakest part of the À owline, which depends on how the À owline The above parameters are assumed independent. is con¿ gured and on the speci¿ cations for each part. The However, the minimum horizontal stress may be expected, maximum speci¿ ed pressures for the packer, mandrel, and is often observed, to be strongly and approximately pump, and À owline elements are noted P packers, P mandrel, P pump, max max max linearly correlated with pore pressure (Breckels and Van and P À owline, respectively. The speci¿ ed P is assumed to be max max Eekelen, 1982; Engelder and Fisher, 1994; Hillis, 2001). In available in full. this case, the gradient of minimum horizontal stress may be calculated as INPUT PARAMETERS (3) Inputs to the above Pi and Pmax models are listed in Table 1 and comprise depth z, gradient of minimum horizontal stress G ( ), maximum/minimum horizontal stress ratio 0 ıh where G(ıh ) is the gradient of minimum horizontal stress / , gradient of pore pressure G (p ), rock tensile strength ıH ıh p at zero pore pressure, Ȗh is a poroelastic coupling parameter ıT, poroelastic coef¿ cient Ș, mudcake coef¿ cient h, gradient (sometimes referred to as the stress-path coef¿ cient), and s of mud pressure G(Pm), and borehole diameter Ø. Depth is represents a spread term, here assumed to follow a Gaussian treated as a parameter, and all pressure and stress inputs are distribution. An example of such built-in correlation is de¿ ned in terms of equivalent gradient (i.e., pressure or stress shown in Fig. 5. It is worth noting that Ȗh =2 Ș. 118 PETROPHYSICS February 2019 Bérard et al. This uncertainty space was chosen to resemble the conditions one may expect in a relaxed sedimentary basin. Note that the range assigned to the gradient of mud pressure ([0.5, 0.65] psi/ft or [9.6, 12.5] lbm/gal) is much wider than that of a well proposal (once the wellbore trajectory, casing points and mud program are decided). The intent is to assess the inÀ uence of this parameter on the risk level and, conversely, examine whether the risk of test failure could be mitigated by increasing the mud density. Fig. 5—Example of a built-in correlation between the gradient of minimum horizontal stress G(ıh) and that of pore pressure G(pp), as described by Eq. 3. The 2,000 samples are displayed with G(pp) drawn from its probability density function (here assumed to be uniform between 0.45 and 0.55 psi/ft) and G(ıh) calculated from Eq. 3 using the parameters displayed in the ¿ gure. The linear trend without any spread is shown by the dashed black line. As discussed in the Input Conditioning section, certain conditions may be enforced, which then introduce correlations, or more complex forms of dependencies Fig. 6—Probability density function (PDF, in red) and cumulative density function (CDF, in blue) for rock tensile strength ıT. The mean value is between parameters. highlighted in green. The values for the 5, 50, and 95% quantiles are The parameters corresponding to the tool con¿ guration highlighted in black. (kinds of packers, mandrels, pumps and À owline) and operating mode (HF, SF, or PS-HF) are discrete and selected Uncertainty assessment involves the sourcing of out of a list. information and its consolidation as parameter’s PDFs. For the set of parameters presented in Table 1, sources of UNCERTAINTY ASSESSMENT various types (including drilling and completion data, well-log data, laboratory and in-situ test data, and seismic Uncertainty in input parameters is described using data) and origins (e.g., offset wells and databases) are probability density functions (PDF). Considering how little generally used. These data may be further combined with is generally known before a test, only two values must be some a-priori knowledge, such as empirical relationships provided: a low value and a high value. If no additional between parameters or physical bounds. As an example, information is available, a uniform probability distribution the poroelastic coef¿ cient, Ș, is rarely measured. However, between the speci¿ ed limits is assumed. A “base case” value it can only vary between 0 and 0.5. In the absence of any may be assigned, in which case the probability distribution is available data to calibrate it, the full [0, 0.5] range can be built using generalized Gaussian functions with distribution used. Data availability and quality vary on a case-by-case parameters expanded by a shape factor controlling the skew basis. Data consolidation considers known variations in the of the distribution and the “base case” value treated as a data itself and the uncertainty arising, for example, from the median (Box and Tiao, 1992). An example is shown in Fig. lack of data, the lack of consistency between various pieces 6, for the rock tensile-strength parameter. It is also possible of data, or the questionable validity of the assumptions under to assign a single value, when an input parameter is known which the data were derived. This task can be particularly with certainty. dif¿ cult for in-situ parameters, for which data may be The uncertainty ranges assigned in Table 1 will be used scarce. On the other hand, when a rich dataset is available, as an illustrative example for the remainder of this paper. and when planning stress tests in different rock formations, February 2019 PETROPHYSICS 119 Feasibility and Design of Hydraulic Fracturing Stress Tests Using a Quantitative Risk Assessment and Control Approach it is advisable to treat separately the formations that are Stress conditions may also be bracketed based on stress expected to be represented by distinct uncertainty spaces regime or stress ellipticity, using the factor ੇ (Etchecopar or different correlations between parameters (depending on et al., 2013). This is illustrated in Fig. 7, where a strike- their lithology, for example). slip stress regime is enforced by imposing the condition Although there is no unique way to assess the uncertainty 1 ੇ ʹ. Finally, when the uncertainty range of mud and space, a few generic remarks may be made. First, it is pore pressure overlap, a further option is available to enforce advisable to assign too much uncertainty initially, rather than overbalanced conditions, namely, pm »pp RO, where RO is a too little. As explained later, sensitivity analysis results will minimum overbalance ratio. highlight which input parameters have the largest inÀ uence on the risk and should be better constrained, and which ones can be left more loosely constrained safely, because they have less signi¿ cant inÀ uence. Second, the consistency of the pore pressure and stress uncertainty space with respect to rock mass stability conditions and tectonics considerations can be evaluated and, if so desired, enforced, as described in the next section. Finally, history matching of past tests conducted in similar conditions, whenever available, is bene¿ cial. Such post-mortem analysis for model calibration will be discussed in a later section. INPUT CONDITIONING Conditions representing physical bounds or a-priori knowledge may be imposed on the values that the parameters can take within their respective uncertainty range. This is brieÀ y explained below. Please refer to the Appendix for further detail. Pore pressure and rock stress conditions may be made such that the rock mass is stable with regard to tensile failure Fig. 7—Examples of input conditioning based on stress regime using the condition 1 Q 2 to enforce a strike-slip stress regime (see the Appendix for the de¿ nition of Q). The 2,000 samples drawn from G(p ), (Murrell, 1964), (4) p G(ıh) and ıH / ıh probability density functions are displayed in a stress polygon diagram (Moos and Zoback, 1990) with accepted and rejected or shear failure stress samples shown in green and red, respectively. The overall compliance rate is also indicated. (5) (e.g., Brace and Kohlstedt, 1980), UNCERTAINTY SAMPLING AND PROPAGATION The uncertainty space is sampled using a Latin or both. In the above equations, ı1 and ı3 are the most- and hypercube sampling algorithm (Helton and Davis, 2003), least-compressive principal stresses, respectively, and ȝ is drawing a ¿ xed number of samples N. Considering the the friction coef¿ cient of the rock mass. We de¿ ne a tensile- number of uncertain parameters (nine), desired con¿ dence failure proximity factor T, and a shear-failure proximity levels in predicted probability of the outcomes, and global factor F, which can be used to impose a minimum and/or sensitivity analysis requirements, N is set to 2,000. When a maximum distance between the effective stress state and input conditioning is in use, samples are tested against the the critical stress state de¿ ned by, respectively, the tensile- selected conditioning criteria. When samples are drawn that and shear-failure criteria. Two additional parameters are do not meet the criteria, further samples are drawn until N required, namely, the gradient of overburden stress and the valid ones are found. The effect of varying N is examined in friction coef¿ cient of the rock mass. These two parameters Fig. 8b. are assumed to take ¿ xed values. 120 PETROPHYSICS February 2019 Bérard et al. Fig. 8—(a) Complementary cumulative density function 1–CDF of risk severity S, in continuous dark blue curve (with the 95% con¿ dence interval shown by dashed lines), overlaid on the risk criticality matrix, for the HF | Packers combination (with the IPCF-7-in.-PC packer type). The chance of success (COS) when operating at the maximum speci¿ ed pressure for the selected combination is highlighted by the white circle. The differential pressure (DP) capacity to get 50 and 95% COS are also highlighted. The uncertainty in the risk pro¿ le (dashed lines) reÀ ects the intensity of the sampling (see (b)). The pressure levels corresponding to the maximum speci¿ ed pressures for the HF | mandrel and the HF | pump combinations are highlighted in blue. (b) Same ¿ gure for various number of samples N (200, 2,000, and 20,000). The sampled sets of parameter values are run through RISK ASSESSMENT the model, and the results from all simulations are used to form the probability distribution of S for all 11 possible The probability density function of model output is one combinations of operating modes and hardware elements. representation of uncertainty. An equivalent representation Due to the analytical nature of the model, the simulation is the cumulative distribution function (CDF): run time is very small, and complete execution takes only a fraction of a second for adequate sampling of the risk. C c (6) February 2019 PETROPHYSICS 121 Feasibility and Design of Hydraulic Fracturing Stress Tests Using a Quantitative Risk Assessment and Control Approach where c stands for the PDF of Y. The CDF C(y) is thus to decrease from about 15% when N is equal to 200, down the probability that the output remains below y, while the to less than 1% when N is equal to 20,000. For the value probability of exceeding y is equal to 1–C(y). The latter chosen here (N =2,000), the maximum uncertainty is equal is more relevant when risk proceeds from exceeding a to about 5%, which is deemed small enough for the present threshold, as is the case in the present analysis (i.e., from application (as it involves small test series). As expected, exceeding pressure speci¿ cations). the overall range of S can be observed to increase with N, The risk pro¿ le corresponding to the input parameters as increasingly unlikely combinations of parameters get listed in Table 1 is shown in Fig. 8a. In this ¿ gure, the sampled. For the case presented here, the range increases complementary cumulative density function, 1–C(y), in towards higher values of S because the PDF assigned to the blue, is overlaid on the criticality matrix. It can be seen to rock tensile strength is highly skewed (Fig. 6). go through the ALARP and unacceptable risk criticality The risk pro¿ le shown in Fig. 8 is for the combination regions (colored in yellow and red, respectively). Three of HF operating mode and packers element (for a selected key readings can be inferred. The ¿ rst one is the probability kind of packers, namely the IPCF-7-in.-PC kind). The risk that the initiation pressure Pi is smaller than the maximum pro¿ le for all possible combinations of operating modes possible pressure Pmax. We refer to this probability as the and tool elements is obtained the same way. A summary is chance of success (COS) when operating at the maximum shown in Fig. 9 (for selected kinds of packer, mandrel, pump possible pressure. The second reading is the pressure and À owline). As mentioned previously, the mandrel is not capacity, relative to Pmax, required to achieve a certain COS. subjected to any tension by the packer in SF mode, which is This capacity is labeled “extra” or “lacking”, depending why this combination is not considered. In this example, the on whether it is below, or above, Pmax, respectively. In the HF | Packer combination (shown in Fig. 8) is the riskiest one. example presented in Fig. 8a, the COS is equal to about 60%, Such is often the case with the modular formation dynamics and about 1,300 psi pressure capacity is lacking to get a 95% tester tool in 8.5-in. diameter boreholes. For the SF mode, COS (even though, interestingly, the conditions chosen for the risk level is controlled by the packer element and is seen our case example correspond to relatively mild conditions). to be very low, with a COS of 100% and at least 4,400 psi Finally, the COS can be read at any pressure of interest. For extra pressure capacity at 95% COS. The risk level for PS- example, the COS when operating at 500 psi below Pmax (as HF operations is controlled by the packer element. The risk a precaution) can be seen to be equal to 40%. If, on the other level is lower than for the HF mode, with a COS of 80% hand, the tool was to be operated at 500 psi above Pmax, the (versus 60% for HF) and about 700 psi pressure capacity COS would be equal to nearly 80%. lacking to get a 95% COS (versus 1,300 psi for HF). Note We also show in Fig. 8a the maximum permitted that SF alone does not provide a measure of the stress; pressures for the hardware elements other than the element hydraulic fracturing of the fracture initiated by the sleeve currently considered (for the same operating mode). In the process is necessary in this case. Therefore, one must jointly present example, the maximum pressures for the mandrel consider SF and PS-HF modes to establish the risk pro¿ le and the pump elements are seen to be about 1,100 and 1,800 associated with the use of SF to measure rock stress. The psi above the maximum pressure for the packer element. analysis therefore allows us to identify the safest operating These limits indicate the relative ordering and pressure mode, the weakest hardware element for this mode, and the separation between the various hardware elements, for a risk level associated with this element. This is summarized given operating mode. in Fig.10. In Fig. 8b, we show the same risk pro¿ le generated using various numbers of samples (200, 2,000, and 20,000). The uncertainty of the risk pro¿ le is indicated by the dashed lines representing the 95% con¿ dence interval of the estimated CDF. The maximum uncertainty can be seen 122 PETROPHYSICS February 2019 Bérard et al. Fig. 9—Risk pro¿ les summary for all combinations of operating modes (HF, SF, and PS-HF, from left to right) and tool elements (packers, mandrel, pump, and À owline, from top to bottom), for selected types of elements. Fig.10—Risk pro¿ les for (a) hydraulic fracturing and combined sleeve, and (b) hydraulic fracturing. (a) is controlled by the dual-packer element; while (b) is governed by the hydraulic fracturing part of the combined operation and by the same element. February 2019 PETROPHYSICS 123 Feasibility and Design of Hydraulic Fracturing Stress Tests Using a Quantitative Risk Assessment and Control Approach SENSITIVITY ANALYSIS AND RISK CONTROL For the uncertain parameters, a global sensitivity analysis is performed (Saltelli et al., 2008). We ¿ rst assess The above analysis provides an initial assessment of the how the parameters contribute to the overall variability risk of test failure. We now examine whether and how such of the outcome of interest. Their relative contributions an initial risk may be controlled down to acceptable levels, depend on both the intrinsic sensitivity of the model and the when so required. uncertainty assigned to the parameters within the framework For job design parameters, the risk pro¿ le for the two of a particular study. The overall variability is reported as the different operating modes (HF or SF combined with PS-HF) standard deviation of the severity metric S. The parameters’ can be compared to identify which mode has the highest relative contributions are reported in a variance diagram. For COS, as discussed above and illustrated in Fig. 10. The risk the uncertainty ranges assigned in Table 1 and for the HF | pro¿ le for various kinds of packers, mandrels, pumps and Packers outcome presented in Fig. 8, the standard deviation À owline parts can similarly be compared to identify which is equal to about 900 psi, and the variance diagram is shown kinds of hardware elements provide the highest COS. In Fig. in Fig. 12. It can be seen that all parameters are not equally 11, we compare two different kinds of packers. The COS inÀ uential. Certain parameters have a large effect, such as with the IPCF-7-in.-PA packers is 8% while the COS with the gradient of minimum stress G(ıh) or the gradient of mud the IPCF-7-in.-PC packers is 60%, the latter being able to pressure G(Pm), whereas others contribute comparatively sustain about 1,500 psi more differential pressure than the little or very little. We also report the cumulative ¿ rst- former. Altogether, this allows identifying the operating order effect. If its value is close to 1, it indicates that the mode and tool con¿ guration with the highest COS. observed variance can be explained by a linear combination of the considered parameters. If it is larger than one, then some correlation between parameters exists. If it is small compared to 1, then there is some nonlinear contribution of parameters to the observed variance. In Fig. 12, the cumulative ¿ rst-order effect is close to 1, indicating that the considered parameters explain most of the variance without nonlinearity or cross-correlation. (a) Fig. 12—Variance diagram for the HF | Packers (IPCF-7-in.-PC) combination showing the relative contribution of the uncertain parameters to the variance of the severity metric S = Pi–Pmax. The standard deviation of S and the cumulative ¿ rst-order effect (FOE) are reported above. After the more inÀ uential parameters have been (b) identi¿ ed, the sensitivity of the risk to any parameter of interest can be further examined through trend analysis. We Fig. 11—Risk pro¿ les for two different types of packer, namely (a) the IPCF-7-in.-PA, and (b) the IPCF-7-in.-PC packers in hydraulic fracturing show in Fig. 13a to 13c the risk severity, risk criticality, and mode. COS trends, respectively, as functions of the parameters 124 PETROPHYSICS February 2019 Bérard et al. Fig. 13—(a) Risk severity, (b) risk criticality, and (c) COS trend plots as a function of the gradient of minimum stress G(ıh) and that of mud pressure G(Pm) (upper and lower panels, respectively), for the HF | Packers (IPCF-7-in.-PC) combination. (a) The severity trend plots map the PDF of the severity metric S (probability increasing from blue to red), with the P50% value and 95% con¿ dence interval highlighted in solid and dashed white lines, respectively. (b) The criticality trend plots map the risk criticality (acceptable, ALARP and unacceptable levels in green, yellow and red, respectively), with the same P50% value and 95% con¿ dence interval. (c) The COS trend plots show the COS when operating at the maximum possible pressure (black curve labeled “at spec”) or at 500 or 1,000 psi above and below it (dashed curves). G(ıh) and G(Pm) (top and bottom panels, respectively), trend is seen to increase from acceptable to ALARP to identi¿ ed above as being the two key contributors. The unacceptable levels over the same range of G(ıh), and the severity trend plot (Fig.13a) maps the PDF of the severity COS is seen to decrease from about 90 to 20%. The mud metric S = (Pi – Pmax), with probability increasing from blue pressure gradient has an opposite effect (lower set of panels to red. The 50% quantile (or P50%) value is highlighted in in Fig.), with the severity and criticality decreasing, and white with the 95% con¿ dence interval indicated by the the COS increasing from 30 to 80%, as the mud pressure dashed lines. The criticality trend plot (Fig. 13b) shows the gradient increases from 0.5 to 0.65 psi/ft. same P50% value and 95% con¿ dence interval, but this time Bivariate severity and criticality trend plots are also overlaid on the risk criticality maps. The criticality map produced to help understand how the risk is sensitive to any combines the severity PDF map (shown in the left panels) given pair of parameters. The severity surface shows the together with the criticality matrix de¿ ned beforehand (see value of S for the P50% quantile, and the criticality surface Fig. 4). The COS trend plot (Fig. 13c) is derived from the shows the P50% severity surface combined to the criticality severity plot at various levels of S: it reports the COS at the matrix. An example is shown in Fig. 14 for the gradient of maximum speci¿ ed pressure Pmax (thick black line labeled minimum stress G(ıh) and that of mud pressure G(Pm), for “at specs”) and at 500 and 1,000 psi above and below it (in the HF | Packers combination. As can be expected from the thin dashed lines). above single-variate trend analysis, the severity and criticality As can be seen in Fig. 13 (upper panels), the risk severity increase with higher values of G(ıh) and lower values of increases with increasing values of G(ıh), with P50% values of G(Pm). For example, it can be seen in the criticality trend S increasing from about í1,100 psi extra pressure capacity plot (right panel) that the risk of test failure in a formation when G(ıh) =0.7 psi/ft to about +700 psi lacking pressure with G(ıh) = 0.8 psi/ft is unacceptable if the gradient of mud capacity when G(ıh) = 0.8 psi/ft. Considering jointly the pressure is smaller than 0.58 psi/ft. severity and probability of occurrence, the P50% criticality February 2019 PETROPHYSICS 125 Feasibility and Design of Hydraulic Fracturing Stress Tests Using a Quantitative Risk Assessment and Control Approach (a) (b) Fig. 14—(a) Bivariate severity, and (b) criticality trend plots at the 50% severity metric quantile, as a function of the gradient of minimum stress G(ıh) and that of mud pressure G(pm), for the HF | Packers (IPCF-7-in.-PC) combination. In the severity plot, the (Pi - Pmax) = 0 contour is shown in white. Single or bivariate trend analyses enable deeper and quanti¿ ed understanding of the sensitivity of the risk to parameter(s) of interest, while accounting for the uncertainty of all other parameters. Such quanti¿ cation is particularly valuable considering that the most inÀ uential parameters often are the most uncertain ones. Sensitivity analyses allow identifying the conditions on any given parameter (or pair of parameters) for which the risk is either acceptable or unacceptable, regardless of the value that may be taken by the rest of the parameters. For example, it can be seen in Fig. 13b (upper panel) that the mean (P50%) outcome corresponds to an acceptable risk provided that the gradient of minimum stress G(ıh) is smaller than about 0.72 psi/ft, and an unacceptable risk if G(ıh) is larger than about 0.77 psi/ft, no matter what conditions are met on all other parameters. When the risk of test failure is high, sensitivity results may be used to understand whether the risk is controllable (e.g., based on the pressure capacity lacking to achieve a 95% COS) and, in the positive, to quantitatively assess the relative effectiveness of various risk-prevention measures. In practice, it is worth noting that only certain parameters are—more or less—under control. These parameters include borehole size, mud pressure gradient, and test target depth. They can, at least to a certain extent, be engineered to improve the COS. For example, a reduction in hole diameter from 12.25 to 8.5 in. may signi¿ cantly reduce the risk level (Fig. 15). This is because, in smaller boreholes, packers can deliver higher differential pressures and mandrels are subjected to less tension. An increase in mud density is another key lever to consider (see the lower set of panels in Fig. 15—Risk pro¿ les for (a) 8.5-in., and (b) 12.25-in. hole diameters for the HF | Packers combination. Note that, for the 12.25-in. case, the Fig.13). maximum possible pressure of the mandrel is about 500 psi lower than that of the packer, as indicated in red. 126 PETROPHYSICS February 2019 Bérard et al. The formation parameters (rock properties as well as seen in Fig. 16a, there is a 95% probability to have at least rock stress and pore pressure conditions) cannot be directly four successful tests and only 75% probability to obtain at engineered. However, because sensitivity results can be used least six successful tests in that series (i.e., even with a 60% to discriminate which conditions would lead to acceptable or COS, one is far from certain to obtain six successful tests unacceptable risk levels, one can focus prejob data collection out of 10, because 10 is a statistically small sample size). and/or acquisition efforts to reduce the uncertainty of the We also use null hypothesis testing with the Fisher’s exact input parameters seen to have the largest inÀ uence on the method (Fisher, 1934) and a con¿ dence level equal to 95% outcome. One may also try and identify rock formations to assess whether a signi¿ cant discrepancy exists between where the key in-situ conditions would appear to be more the predicted COS and any given actual (observed) success favorable, either within the target borehole (using core and rate. In Fig. 16b, the Fisher’s test decision (in purple) and log data acquired before the modular formation dynamics p-value (in black) are shown for the same case example (a tester tool is run) or in other boreholes located elsewhere in series of 10 tests with a COS of 60%). The test decision the ¿ eld. Stress measurements taken outside the formations is equal to 1 when there is strong-enough evidence to rule of interest (given the application at hand) are still valuable out the null hypothesis (i.e., conclude that the success rate in that they allow calibration of stress models that predict the is inconsistent with the predicted COS). It is equal to zero stress ¿ eld over the entire lithological column of interest. otherwise. The p-value is the probability of making a so- Finally, a calculated risk may be worth considering called Type-I error (i.e., reject the null hypothesis when it is when the maximum permitted pressure is controlled by the true). It can be observed that any number of successful tests packer element (as opposed to all other hardware elements) between three and nine included (out of 10 total) would be and it is seen that operating slightly above the maximum consistent with a COS of 60%. permitted pressure (and below the second weakest element’s maximum speci¿ ed pressure) would improve the COS signi¿ cantly. With reference to the risk pro¿ le shown in Fig. 8, for example, the COS would increase from 60% at the packers’ nominal pressure to 80 or 90% if the tool was to be operated 500 or 1,000 psi above it (the maximum speci¿ ed pressure of the mandrel, or second weakest element, is about 1,200 psi larger than that of the packers, see Fig. 8). However, such a decision must be carefully weighed as excessive pressures can reduce packer’s life expectation or even damage the packer element. It may also be possible to use a surface pump to increase the well pressure and provide this pressure addition to the mud pressure without exceeding tool service speci¿ cations, as long as the integrity of the wellbore is not compromised. Altogether, the presented sensitivity analysis provides practical insights to evaluate in a quantitative manner the relative merit of various risk prevention measures. This supports better-informed discussions on the best way Fig. 16—Example of PDF (in red) and CDF (in blue) of the number of successful tests (a) and null hypothesis test results (b) including the forward during the planning stage. It is worth noting that Fisher’s test decision (purple) and the p-value (in black), for a series of suf¿ cient time must be allowed between the design analysis 10 tests and a COS of 60%. and the stress-test operations to implement the most effective preventive measures. Similarly, the number of attempts needed to obtain The risk assessment also helps set or manage a given number of successful tests can be estimated, for a expectations—something that is not necessarily intuitive given COS. For example, using the same COS of 60% as to do because stress-test series tend to be relatively short, above, Fig. 17 shows the probability of getting at least ¿ ve statistically speaking (typically around 10 tests). For a given successful tests as a function of the number of attempts. It COS and a given number of planned attempts, we calculate can be seen that at least 12 tests must be attempted for this the probability of obtaining exactly, or at least, a certain probability to be 95% or more. This can be used to plan the number of successful tests. An example is shown in Fig. 16 number of attempts, accounting for the fact that some of for a series of 10 attempts with a COS of 60%. As can be them will likely fail. February 2019 PETROPHYSICS 127 Feasibility and Design of Hydraulic Fracturing Stress Tests Using a Quantitative Risk Assessment and Control Approach available after a test or a series of tests is completed can be leveraged to calibrate the model parameters. The consistency between a given uncertainty space and the measurements and observations made during a test is examined as follows. For each test, the risk pro¿ le is formed for the weakest tool element (given the test’s operating mode and equipment used), using the same workÀ ow described earlier. However, all input parameters measured for the test are ¿ xed to their measured value. From the resulting probabilistic distribution of S = (Pi – Pmax), we extract the 95% con¿ dence interval (between the P2.5% to P97.5% quantile values). We then compare the predicted con¿ dence interval against the observed value of S, noted Sobs. Sobs is the Fig. 17—Probability of getting at least ¿ ve successful tests as a function of the number of attempts, for a COS of 60%. difference between the maximum pressure reached during obs the test, Pi , and the maximum speci¿ ed pressure, Pmax. Note that P obs is not necessarily equal to P . For example, HISTORY MATCHING AND MODEL i max fracture initiation may occur before Pmax is reached, leakage CALIBRATION may take place preventing the pressure from being increased up to Pmax, or, in some cases, the pressure may be increased Upon completion of a test or a series of tests in a given somewhat beyond Pmax to try and force fracture initiation. borehole, the depth, mud pressure, borehole diameter, and obs For successful tests, Pi is the so-called breakdown pressure. maximum reached pressure are known for each of the tests, We assume the breakdown pressure is equal to the fracture together with the minimum horizontal stress magnitude for obs initiation pressure Pi. For unsuccessful tests, Pi only yields the tests successfully completed and interpreted. Also known obs a lower bound for Pi and, therefore, S is only a lower are the tool con¿ guration and operating mode, and whether bound for S. A successful test is deemed consistent with the fracture initiation was achieved or not. In many cases, pore risk prediction if Sobs is within the modeled 95% con¿ dence pressure measurements are taken in the same borehole, interval (equivalently, if the COS is between 2.5 and 97.5%). although not necessarily in the same formations or at the A failed test is deemed consistent if Sobs is not greater than exact same depths as the stress tests. Usually, no fresh data the modeled P97.5% quantile value (equivalently, if the COS is are available for the rest of the input parameters (rock tensile not greater than 97.5%). strength, stress anisotropy ratio, poroelastic coef¿ cient, and For illustration purposes, a synthetic dataset was created mudcake coef¿ cient), unless laboratory measurements are for a series of 15 stress tests (Table 2). We assumed that all made on core or some modeling work is undertaken, e.g., tests were conducted in HF mode and with the same and mechanical earth modeling (Bérard and Prioul, 2016). In known kinds of packers, mandrel, pump, and À owline. this section, we describe how the information that becomes Table 2—Synthetic Stress-Test Data z 128 PETROPHYSICS February 2019 Bérard et al. In Fig. 18, we crossplot the observed and predicted values of S for all tests. Successful and unsuccessful tests are color coded in green and red, respectively. The symbols are labeled according to the test number, as listed in Table 2. For unsuccessful tests, Sobs is a lower bound, as indicated by the horizontal bar. For the predicted values, the symbol is placed at the P50% value, and the 95% con¿ dence interval is shown by the vertical bar. Tests found consistent and inconsistent with the prediction have their symbol colored in white and orange, respectively. Figures 18a to 18c show the results before any calibration and at two successive stages of the calibration process. As can be seen in Fig. 18a, initially the risk prediction is only consistent with three tests out of 15. The plot further reveals that the prediction for all unsuccessful tests is too optimistic, whereas the prediction for many of the successful tests (six of nine) is too pessimistic. Tests 9 and 15 are examples of the former and latter cases, respectively, and their risk pro¿ les are shown in Fig. 19. Although there is more than one way to try bringing the predicted and observed values into closer agreement, we describe below how two adjustments could be made to this end. First, test failure was assumed to occur at least partially due to a relatively large minimum horizontal stress. The gradient of minimum horizontal stress was therefore increased for all unsuccessful tests, to increase their risk of test failure. A gradient of G(ıh) = 0.85 psi/ft, slightly larger than the largest measured gradient of 0.79 psi/ft (Test 2), was found adequate, as shown in Fig. 18b (compare also Figs. 19a and 19b for Test 15). At this point, the prediction becomes consistent with nine tests out of 15. The risk prediction was further calibrated by making the stress anisotropy ratio ıH /ıh a linear function of G(ıh) for all tests, with higher stress anisotropy corresponding to lower minimum horizontal stress and vice versa. An example of such anticorrelation can be seen in Wileveau et al. (2007). This second adjustment increases the risk of test failure when this risk was already relatively high and decreases it when it was already relatively low. The trend ıH /ıh = 1.01 + 0.35 (0.85 – G(ıh))/(0.85 – 0.686), with G(ıh) in psi/ft, was found adequate, as shown in Fig. 18c (compare also Figs. 19b and 19c for Tests 9 and 15). The calibrated prediction is now consistent with all tests. Fig. 18—Predicted versus observed Pi – Pmax. Successful and failed tests are displayed in green and red, respectively. The vertical bars show the 95% con¿ dence interval. The data label refers to the test number, as per Table 2. The results are shown for (a) the uncalibrated analysis, (b) after calibration of the minimum horizontal stress gradient for unsuccessful tests, and (c) after further calibration of the stress anisotropy ratio for all tests. February 2019 PETROPHYSICS 129 Feasibility and Design of Hydraulic Fracturing Stress Tests Using a Quantitative Risk Assessment and Control Approach (a) (b) (c) Fig. 19—Risk pro¿ le for Tests 9 and 15 (upper and lower panels, respectively) (a) before any calibration, and (b) and (c) at two successive stages of the calibration process. Although such calibration is subjective and the proposed initiation of an inclined mixed-mode shear-tensile fracture solution is far from unique, this example illustrates how may take place at a pressure lower than that required for a further insight may be gained by conducting postmortem longitudinal tensile fracture (Ramsey and Chester, 2004), analyses. The calibration may lead to revising the forecast leading to complex fracture shapes and, often, tests that are and the risk-prevention strategy from one test to the next very dif¿ cult to interpret. Another overlooked mechanism within a series in a single borehole, or from one test campaign is time-dependent, subcritical crack growth (e.g., Bunger to the next within a ¿ eld. and Lu, 2015; Lu et al., 2017), which can allow a decrease with time of the pressure required to initiate a fracture. DISCUSSION Addressing some of the above limitations would not only improve model accuracy but also provide practitioners with Because the model used for calculating (Pi – Pmax) additional options to design testing protocols with a higher is assumed to be accurate, the model assumptions and COS (by varying mud viscosity, loading (pump) rate, or potential sources of inaccuracy deserve some attention. With the duration at maximum pressure). One must also bear in respect to Pmax, the speci¿ ed differential pressure, ¨Pmax, is mind that the maximum pressure reached during the creation assumed to be available in full. This assumption may be and early propagation of a hydraulic fracture (the so-called violated in high-mobility cases (high-permeability rock breakdown pressure) can be higher than the fracture initiation and/or low-viscosity À uid) for which the À uid leakoff rate pressure (Zhao et al., 1996; Detournay and Carbonell, 1997) is greater than the pump’s À ow rate capacity to build up the and that, in some cases, fracture propagation requires higher pressure. Also, various factors known to impact hardware pressures than fracture initiation (for an in-depth discussion behavior are not fully accounted for in the speci¿ cations and examples, see Lecampion et al., 2017). Such cases are presently used (e.g., temperature, aging through cycles of not considered here. inÀ ation/deÀ ation, effect of exceeding packer pressure A key advantage of the retained, analytical model speci¿ cations, and borehole shape ovalization). With respect is computational speed—the entire execution of the to Pi, the solution by Detournay and Cheng (1992) does not proposed method takes only a fraction of a second for account for some of the complexities that may arise when adequate sampling of the risk. Moreover, it is our opinion pressurizing an openhole wellbore. First, plasticity may take that a simpli¿ ed model with fewer parameters is easier to place, preventing the rock from developing tensile tangential calibrate than, and therefore possibly preferable to, a more stresses (Papanastasiou et al., 1995; Bradford and Durban, sophisticated model with many parameters left completely 1998) and thus hindering the creation of a fracture at the unconstrained. A framework is in place to leverage return borehole wall. Such occurrences can be undetectable a-priori of experience, which will allow checking whether such but would lead to test failure. Plasticity may also increase the simpler models can indeed prove useful, once calibrated, pressure required to initiate a tensile fracture (Papanastasiou even with parameters whose value is set to numbers that et al., 1995). Finally, for some stress/rock con¿ gurations, may appear physically unreasonable. One such example is 130 PETROPHYSICS February 2019 Bérard et al. the rock tensile strength, which can be increased to values h = mudcake coef¿ cient, unitless much larger than its measured value and treated as a pure A = cumulative density function parameter into which many complex phenomena can be F = shear-failure proximity factor, unitless lumped. Fmin = minimum shear-failure proximity factor, unitless F = maximum shear-failure proximity factor, unitless CONCLUSIONS max G(pm) = equivalent depth gradient of mud pressure, psi/ft G(ı ) = Hydraulic fracturing stress tests often fail because a h equivalent depth gradient of minimum horizontal fracture cannot be initiated even at the equipment’s maximum stress magnitude, psi/ft G(ı ) = possible pressure. A method was developed for the feasibility v equivalent depth gradient of overburden stress assessment and design of such tests. The proposed method magnitude, psi/ft G(p ) = quanti¿ es the chance of achieving fracture initiation while p equivalent depth gradient of pore pressure, psi/ft G(ı 0) = allowing uncertainties in ambient conditions and design h equivalent depth gradient of minimum horizontal parameters to be factored in and analyzed in terms of risk of stress at zero pore pressure, psi/ft test failure. Furthermore, the method provides means for risk H = Detournay and Cheng (1992) function h(Ȗ), unitless control when the risk of test failure is deemed too high. The N = number of samples operating mode and tool con¿ guration with the highest COS Զ = probability P = are identi¿ ed. Sensitivity analyses are carried out to focus 50% 50% quantile value P = characterization efforts on the parameters having the largest max tool’s maximum speci¿ ed pressure, psi PÀ owline = À owline’s maximum speci¿ ed pressure, psi inÀ uence, to identify rock formations where the in-situ max P mandrel = mandrel’s maximum speci¿ ed pressure, psi conditions would appear to be more favorable, and to decide max P packers = packer maximum speci¿ ed pressure, psi on well design options that would prevent the risk most max P pump = pump maximum speci¿ ed pressure, psi effectively, such as a change in hole diameter or mud density. max P = fracture initiation (or breakdown) pressure, psi Finally, the proposed workÀ ow enables model parameters i Pobs = maximum pressure reached during a test, psi calibration through history matching of completed tests, i PHF = fracture initiation pressure for hydraulic thus providing a framework to capture and leverage return i fracturing, psi of experience and, hence, improve the success rate from one PSF = fracture initiation pressure for sleeve fracturing, psi test campaign to the next. i PS-HF fracture initiation pressure for post-sleeve Pi = hydraulic fracturing, psi ACKNOWLEDGMENTS well mud pressure, psi Pm = stress regime factor, unitless The authors are grateful to Schlumberger for permission to = = minimum stress regime factor, unitless publish this paper. maximum stress regime factor, unitless = NOMENCLATURE R = stress ellipticity factor, unitless overbalance ratio, unitless R0 = Abbreviations minimum overbalance ratio, unitless R0min = MDT = modular formation dynamics tester S = risk severity metric, psi HF = hydraulic fracturing S obs = risk severity reached during a test, psi SF = sleeve fracturing T = tensile-failure proximity factor, psi PS-HF = post-sleeve hydraulic fracturing minimum tensile-failure proximity factor, psi Tmin = ALARP = as low as reasonably practicable Į = Biot’s effective stress coef¿ cient, unitless COS = chance of success stress-path coef¿ cient, unitless Ȗh = PDF = probability density function Ș = poroelastic stress coef¿ cient, unitless FOE = ¿ rst-order effect ȝ = rock coef¿ cient of friction, unitless CDF = cumulative density function v = drained Poisson’s ratio, unitless average mud density, lbm/gal n/a = nonapplicable ȡm = maximum principal stress magnitude, psi ı1 = = intermediate principal stress magnitude, psi Symbols ı2 = minimum principal stress magnitude, psi Ø = borehole diameter, in. ı3 = minimum horizontal stress magnitude, psi a = probability density function ıh = maximum horizontal stress magnitude, psi g = acceleration due to gravity ıH = rock tensile strength, psi p = pore pressure, psi ıT p P = maximum differential pressure, psi s = spread term in stress-pressure coupling, unitless ¨ max z = true vertical depth, ft February 2019 PETROPHYSICS 131 Feasibility and Design of Hydraulic Fracturing Stress Tests Using a Quantitative Risk Assessment and Control Approach REFERENCES SPWLA 46th Annual Logging Symposium, New Orleans, Louisiana, USA, 26–29 June. 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I., Cañas, J., Garcia, G., Dumont, H., Rubio, N., Kayo, A., and Vivalda, C., and Jammes, L., 2008, Probabilistic Performance February 2019 PETROPHYSICS 133 Feasibility and Design of Hydraulic Fracturing Stress Tests Using a Quantitative Risk Assessment and Control Approach Assessment Methodology for Long Term Subsurface CO2 The shear-failure proximity factor F is de¿ ned as: Storage, presented at the PSAM9 Conference, Hong Kong, 17– 23 May. https://www.hkarms.org/ASUS_Server/psam9.sytes. netweb_resources_20080518_PSAM9/Parallel_Session/F_ Peony/Mon_1-3/F2_1330_1500/Probabilistic_Performance_ (A.1) Assessment_Methodology.pdf. Accessed January 3, 2019. Vivalda, C., Loizzo, M., and Lefebvre, Y., 2009, Building CO2 Storage Risk Pro¿ les with the Help of Quantitative Simulations, Energy Procedia, 1(1), 2471–2477. DOI: where , and . 10.1016/j.egypro.2009.02.009. F represents the distance between the effective stress state Weijers, L., and de Pater, C.J., 1994, Geometry of Hydraulic and the shear-failure envelope, the latter being given by a Fractures Induced From Horizontal Wellbores, Paper SPE- Mohr-Coulomb criterion with coef¿ cient of friction and 25049, SPE Production & Facilities, 9(2), 87–92. DOI: ȝ 10.2118/25049-PA. zero cohesion (Brace and Kohlstedt, 1980). Wileveau, Y., Cornet, F.-H., Desroches, J., and Blumling, P., 2007, Complete In Situ Stress Determination in an Argillite The tensile-failure proximity factor T is de¿ ned as: Sedimentary Formation, Physics and Chemistry of the Earth, Parts A/B.C, 32(8–14), 866–878. DOI: 10.1016/j. (A.2) pce.2006.03.018. Zhao, X.G., Wang, J., Qin, X.H., Cai, M., Su, R., He, J.G., Zong, Z.H., Ma, L.K., Ji, R.L., Zhang, M., Zhang, S., Yun, L., where T represents the distance between the least-compressive Chen, Q.C., Niu, L.L., and An, Q.M., 2015, In-Situ Stress effective stress and the rock tensile strength (reckoned Measurements and Regional Stress Field Assessment in ı3 ıT the Xinjiang Candidate Area for China’s HLW Disposal, positive). Engineering Geology, 197, 42–56. DOI: 10.1016/j. enggeo.2015.08.015. Finally, the overbalance ratio RO is de¿ ned as: Zhao, Z., Kim, H., and Haimson, B., 1996, Hydraulic Fracturing Initiation in Granite, Paper ARMA 96-1279 presented at the 2nd North American Rock Mechanics Symposium, Montréal, (A.3) Canada, 19–21 June. Zimmerman, T., MacInnis, J., Hoppe, J., Pop, J., and Long, T., 1990, Application of Emerging Wireline Formation For input conditioning purposes, , F, T, and R0 are Testing Technologies, Paper OSEA-90105 presented at the calculated for each sample. Accepted samples are such that 8th Offshore Southeast Asia Conference, Singapore, 4–7 the following conditions are met simultaneously: December. APPENDIX We de¿ ne the parameters Q, F, T, and R0 as follows. The stress regime and ellipticity shape factor Q is de¿ ned as: where Qmin, Qmax, Fmin, Fmax, Tmin, and R0min are user-de¿ ned thresholds such that: (i.e., we enforce a normal or strike-slip stress regime). where and ı1, ı2 , and ı3 are the magnitude of most- compressive, intermediate, and least-compressive principal א ) stresses, respectively. represents the stress regime [0;1] in a normal regime, [1;2] in a strike-slip regime, and [2;3] in a reverse regime) as well as the ellipticity shape factor R of the reduced stress tensor (Etchecopar et al., 2013; Cesaro et al., 2000). 134 PETROPHYSICS February 2019 Bérard et al. ABOUT THE AUTHORS USA, and Cambridge, Massachusetts, USA from 2003 to 2005. He became research Program Manager in 2007. He is Thomas Bérard is a Principal currently managing a team of researchers in geomechanics geomechanics engineer. He received his focused on geomechanics applications. Romain is a member PhD in rock mechanics in 2003 from of SPWLA, SPE, SEG, EAGE and ARMA. Institut de Physique du Globe de Paris, France. He joined Schlumberger in 2006 as Geomechanics Domain Head for CO2 storage. From 2010 to 2012, he was Senior geomechanics engineer with Data and Consulting Services, based in Pau, France, and from 2013 to 2015, he was Innovation Lead with the Reservoir Geomechanics Center of Excellence, based in Bracknell, UK. Since 2015, he is a Principal Research Scientist at Schlumberger-Doll Research, Cambridge, Massachusetts. His current research focuses on rock stress characterization. Nikita Chugunov is a Principal Scientist and a Program Manager with Schlumberger-Doll Research. He joined Schlumberger in 2006 as a postdoctoral scientist. His subsequent research focused on multiphysics modeling and inversion, optimization, and uncertainty quanti¿ cation with applications to monitoring program design, wellbore integrity, and measurements interpretation. He holds an MSc in Applied Physics and Mathematics from the Moscow Institute for Physics and Technology and a PhD in Applied Sciences from the Russian Academy of Sciences. Jean Desroches is Geomechanics Scienti¿ c Advisor with Rocks Expert, a rock mechanics consulting company. He received his PhD in rock mechanics from the Institut de Physique du Globe in Paris, France in 1990. He has held a number of R&D focused positions in Schlumberger in the UK, the US and France. His research interests encompass rock stress characterization, hydraulic fracturing, well integrity, reservoir stimulation, CO2 storage and hot dry rocks Romain Prioul is a Scienti¿ c Advisor and Program Manager at Schlumberger- Doll Research, Cambridge, Massachusetts. He received a PhD in 2000 in geophysics from the Institut de Physique du Globe de Paris, France. 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