Hong

AADE-08-DF-HO-04 Geomechanics Modeling for Better Drilling Performance Hong (Max) Wang, Mohamed Y. Soliman, Zhaohui Shan, Halliburton; Brian F. Towler, University of Wyoming Copyright 2008, AADE This paper was prepared for presentation at the 2008 AADE Fluids Conference and Exhibition held at the Wyndam Greenspoint Hotel, Houston, Texas, April 8-9, 2008. This conference was sponsored by the Houston Chapter of the American Association of Drilling Engineers. The information presented in this paper does not reflect any position, claim or endorsement made or implied by the American Association of Drilling Engineers, their officers or members. Questions concerning the content of this paper should be directed to the individuals listed as authors of this work. Abstract Geomechanics modeling is very important for optimizing drilling performance by increasing rate of penetration (ROP) and minimizing non-productive time (NPT). It provides the basis for bit selection and drilling parameter optimization, wellbore stability analysis, and lost circulation prevention and control. Because of difficulties accessing the rock formation, the modeling largely relies on the data availability and quality. To narrow down the error bar during the process, a vast amount of data may be needed for cross-checking the modeling quality. Using a real case from a cuttings injection project, it is demonstrated what data are needed, which documents contain the data and how the raw data are processed to obtain the needed parameters for further engineering simulation. Introduction Rotary drilling has long been the major means to access hydrocarbon reserves. During the drilling process and the penetration of subterranean rock formations, rock will be constantly exposed to alterations due to mechanical and chemical interactions. Attempts to improve drilling efficiency without integrating geomechanics will not reach the optimum. However, due to the difficulty of accessing the rock insitu, the cost of knowing the rock properties is generally very high. Gaining knowledge of the rock requires acquisition of a batch of data and processing the data for rock properties. Further, simulations are needed to understand the rock behavior under certain drilling conditions. With the development of computer technologies, the data acquisition and processing cost has gone down and the value created out of understanding the rock behavior has gone up. Especially as rig costs increase, the value of understanding rock is tremendous. This trend has created opportunities for operation optimization and drilling process innovation as well. The major role of geomechanics in drilling currently includes the following: • Drilling method selection (underbalanced/managed pressure drilling, conventional drilling, casing drilling, etc.) • Well design for optimized well trajectories and casing programs; • Drill bit customization and selection for improved ROP and borehole quality; • • • Drilling parameters optimization for high ROP; Wellbore stability indicators for drilling fluid selection and optimization; Wellbore strengthening for higher wellbore pressure containment and coping with lost circulation. Well design starts with understanding the subterranean stress and pressure profiles and lithologies. Selecting the best method of drilling can significantly reduce well construction costs, as demonstrated by a progressive reduction in total drilling days in a new drilling area. The number of drilling days required can be greatly shortened after a number of wells have been drilled and performance has been analyzed for better well designs. Better designs also include optimized casing points and well trajectories including wellbore deviation and azimuth with an understanding of the effects of stress, strength and pressure environments. Drill bit design, selection and usage should all be tied to the understanding of geomechanics1 including the lithology, rock strength, shale plasticity, formation pressure, abrasiveness, etc. Bit selection software programs have been created to allow engineers to select the best bit for an interval based on the geomechanical properties of the formations to penetrate. Understanding rock properties is also necessary to help ensure the bit achieves the optimal ROP and to diagnose improper usage of a drill bit. Wellbore stability analysis has long been performed for obtaining a minimum mud weight for critical drilling projects. In addition to the mud weight, understanding of the hole collapse mechanisms is equally important for correct mud chemistry, such as selecting the right mud type, preparing an optimized water phase salinity, etc.2,3 The stress and pressure environment, as well as the rock strength, also play important roles. Because wellbore stability is strongly related to the wellbore orientation, the proposed wellbore deviation and azimuth are needed as well. Rock sensitivity to water and various cations, shale water activities, CEC (Cation Exchange Capacity), etc. together with rock mechanical properties are all necessary to depict the rock behavior under wellbore stability conditions. Wellbore strengthening is a new concept4,5,6 that has led to a series of studies7,8,9,10 and subsequent field successes.11,12,13 Wellbore strengthening techniques can help operators achieve 2 H. Wang, M. Soliman, Z. Shan, B. Towler higher wellbore pressure containment and contribute to studies to understand why some wellbores are weaker than others.8 Similar to wellbore stability analysis, designing a wellbore strengthening job (sometimes referred to as stress cage) requires knowing almost the same types of data as wellbore stability analysis. Knowing the rock parameters, etc. allows us to perform simulations to understand fracture dimensions and determine the best treating materials and engineering design. Geomechanics can be also important to Health, Safety and Environment (HSE) considerations. One of the important examples is cuttings injection design. It requires substantial understanding of a geomechanical environment before a good injection simulation can be performed with a computer software program. Only with the integration of the geomechanics and injection simulation, can a safe disposal domain be designed. Even during the injection process, geomechanical understanding is necessary to explain pressure anomalies and allow us to make smart operational decisions. Aside from drilling, geomechanics can be extended to completion and production optimization for sand control, stimulation, etc. In a word, geomechanics has been playing an increasingly important role in drilling and other petroleum engineering aspects as well. Data Requirements For different drilling applications, different sets of geomechancs parameters may be needed. However, in general they fall into the following categories: • Wellbore geometry • Rock mechanical properties • Stress and pressure • Wellbore fluids • Fluid and rock interaction Wellbore geometry accounts for the hole size, deviation, azimuth, length of an openhole interval, etc. Rock mechanical properties may at least include Young’s modulus and Poisson’s ratio. Rock strength, permeability, and other properties may also be needed depending on the interest of investigation. Stress magnitudes and orientation are very important for the wellbore stability that is a key design criterion for drilling. Formation pressure and fracture gradients define an initial mud weight window. Furthermore, wellbore stability should be considered for this window. If this window is not wide enough, wellbore strengthening may be applied to widen the mud weight window. Wellbore fluids provide information about the chemistry, rheology and particulate type and concentration. These are all important for understanding wellbore behaviors. Rig daily operations provide information about fluid and rock interaction. This can also be obtained through pressure tests such as leak-off tests (LOT). Data Collection These data are generally obtained through analysis of the AADE-08-DF-HO-04 following documentations: • Well diagrams • Formation Pressure, Mud weight, Frac Gradient Profile Plots • Drilling, Mud and Mud Logging reports • Logs ƒ Full Wave Sonic (Compressional & Shear)/other sonic logs ƒ Density/Neutron/GR/Caliper/Borehole image logs ƒ Formation pressure tests ƒ Other logs • Region information ƒ Basin study report/Seismic map/Fault map • Other information ƒ Core test report, cuttings analysis report ƒ Well testing, hydraulic fracturing report or water injection report ƒ LOT/Extended LOT Due to the wide range of data source, such analysis normally requires extended knowledge and experience in order to extract the valuable information out of the documentations. Data Analysis Rock mechanical properties can be obtained through lab tests. However, rock samples are normally not readily available because coring, sample preservation, HTHP testing, etc. can be complicated and costly procedures. A more common methodology is a so called log-based analysis. Results from lab tests can then be used as calibrations. Table 1 summarizes methods for obtaining various parameters for drilling related geomechanics analysis. Data quality control is always a necessary step for generating correct results. Case History To demonstrate the data analysis process, here we include an actual case history for cuttings injection simulation. This simulation was done for performance analysis of a cuttings injection project that has been going on for several years. Due to confidentiality, critical information has been removed for this publication. A geomechanical model must be constructed to provide a base structure for cuttings injection simulations. It is critical that the model reflect the best understood reality as closely as is practical, so that the simulated operational parameters result in output that represents real world performance. This is necessary in order to ensure the safe and efficient disposal of the drilling wastes. Geomechanical modeling incorporates pore pressure and effective stress values in developing an understanding of the total active stresses. It is critical to understand the permeability, Young’s modulus, etc. in order clarify total active stresses. Due to the fact that limited direct data are normally available for potential cuttings injection disposal AADE-08-DF-HO-04 Geomechanics Modeling for Better Drilling Performance zones, more expertise is required to understand and describe the geomechanical environment for these operations than for typical hydraulic fracturing design. In hydraulic fracturing, pore pressure is normally known with well testing methods or production records. However, for cuttings injection it is quite likely that pressure and stresses will have to be determined simultaneously by solving the related correlation equations using the limited known data points for total stresses at given depths. Stress Environment: The Big Picture One of the first tasks in developing the geomechanical model was determination of the stress environment in the disposal zone. The pertinent acquired log data were reviewed for quality control as a first step in the process. No log quality issues were identified. Stepping further back in reviewing the stress in the area, the stress environment was better understood in light of plate tectonics in the area. It was found that the area of interest is in a unique strike/slip environment. Due to colliding movement of the two continental plates, severe stress anisotropy should be expected. The world stress map indicates strike-slip and thrust faulting regimes with the strike in the nearly N-W direction. The compression stress component, therefore, is maximized in the NW direction. This understanding is essential for selecting a good approach to determine the stress environment. Details and figures are omitted here to protect the confidential information. Determining the Lithology The lithology was determined utilizing the provided logs. During a log-based analysis, differentiation was achieved primarily with the gamma ray log and translated into shale volumes by making use of the mud logs, as well as the other logs provided. The formations of interests were determined to be claystone and sandstone. Determining the Closure Pressure The closure pressure was analyzed with the SQRT Time Plot, G-Function Plot, GdP/dG Plot. This is demonstrated with the LOT #1 data. Figure 1 represents the plots of LOT #1 and LOT #2. Figure 2 is the analysis plot with the SQRT method. Figure 3 is the analysis plot with the G-Function method. Figure 4 is the analysis plot with the Gdp/dG method. Table 2 summarizes the pressure decline analysis (PDA) for the LOT #1 on closure pressure at the depth of 7907 ft (2410 m) with the three methods. These results are very close to one another with an average of 15.9 ppg, which is the same as determined directly from the LOT raw data plot. Many times, these results don’t agree with each other and one has to be cautious to select the correct result. With the same method, some other pressure decline data from cuttings slurry injection were analyzed and the summary of some the data are listed in Table 3. 3 In Table 3, there are two data sets with significant variance from the others. The first one is the determination of a 15.87 ppg equivalency from LOT#1. This is a significantly lower value than the average. It is possibly due to the strong stress anisotropy which creates a low tangential stress area at and near the wellbore. This effect would not be seen again after the fracture has grown into the far field area. Apparently in this case, the fracture initiation pressure is smaller than the far field minimum horizontal stress. The second notable variance is the 18.98 ppg result for Injection#2. This might have been caused by solids accumulation inside the fracture that might possibly increase the stress at closure. Cleaning the solid deposit or creating a new fracture would reduce the closure pressure back to what is close to the far field stress – minimum horizontal stress. Subsequent batches showed reduced pressures and the variance that has occurred during the life of the injection project point to some significant transient dynamics of solids placement and movement in the disposal zone. After eliminating the two data sets in question, an average of 0.94 psi/ft or 18.12 ppg equivalent minimum horizontal stress was determined for the depths of injection. Determining Permeability Determination of the permeability from the available data remains approximate. Leak-off tests were first performed on the originally targeted claystone formation at the base of the injection zone. Due to the limited nature of the pressure decline data available, a pressure decline analysis method developed by Soliman14 was applied to the test data to determine the permeability. This method can also be used to obtain a formation pressure estimate. It requires identification of the flow regime with a –tdP/dt versus t plot, from which a constant for calculating permeability can be defined with (PiPw)tn versus t. The pore pressure can also be determined at the same time. A summary of this technique is given in appendix. Figure 5 indicates the results from two LOT tests performed at 7907 ft with a brine fluid of 9.1 ppg. Utilizing Soliman’s method, a claystone permeability of 0.14 md was determined from LOT #1, as shown in Figure 6. The bleedback volume from the LOT #1 test was 1.2 bbl after 40 minutes of shut-in. A total of 6.5 barrels were injected at a rate of 0.3 bpm. This volume of fluid loss indicates a relative larger permeability than normally expected in claystone formations. This permeability should be the average of the matrix and natural fractures if they exist. However, due to the short such-in time, the interpreted permeability can be higher than the reality. The interpreted value can be used as an upper bound for the claystone formation permeability for the cuttings injection simulation. Neither the SP log, nor resistivity logs show good indications of permeability of any formations. It is believed that the sandstone formations may have relatively low permeability. Determining the Pressure The pressure decline analyses were performed on the test 4 H. Wang, M. Soliman, Z. Shan, B. Towler and injection data in order to better understand the nature of in situ pressure before and during the injection operations. Analysis was demonstrated with data acquired from LOT #1. The analysis plots are displayed in Figure 7 and Figure 8. A summary of a selection of the test results can be found in the Table 4. These results were either obtained by the Horner or Soliman’s methods. These analyses were performed to determine pressure in the claystone formations. While the provided resistivity logs and density logs reveal no indication of significant abnormally pressured zones, analyses do indicate pressures consistently higher than a normal pressure gradient of 0.45 psi/ft. However, this is inconsistent with a review of the mud weights used in drilling the well to provide an estimate of pore pressure in the sandstone. (Refer to the Track “PS ppg” on the log analysis, Figure 9). The low mud weights used indicate a normal pressure gradient in the sandstone formation, which would tend to indicate higher permeability and formation extent, which would have allowed equilibration of pressure over geologic time. A typically very low permeability claystone might be expected to be sufficiently non-transmissive such that pressure would not be dissipated, however, the permeability of the claystone has been previously estimated to be approximately 0.14 md. With that permeability, the pressure gradients in the claystone and sandstone formations should be basically identical. Based on the findings, it is believed that the pore pressure gradient is approximately normal and a 0.455 psi/ft pressure gradient was assumed in both sandstone and claystone formations at the depths of interests. Analyses show a gradual increase in pressure with increasing injection time, indicating the additive effects of continued waste injection. Therefore, the early data best represents the far initial reservoir pressure. For a large body of the fluid injection, an increasingly longer shut-in time should be expected to obtain and estimate of the original formation pressure, especially when the formation permeability is relatively low. AADE-08-DF-HO-04 ⎡ ⎛ v p ⎞2 ⎤ ρv × ⎢3⎜⎜ ⎟⎟ − 4⎥ ⎢⎣ ⎝ vs ⎠ ⎥⎦ E= 2 ⎛ vp ⎞ ⎜⎜ ⎟⎟ − 1 ⎝ vs ⎠ 2 s and ⎛ vp ⎞ ⎜⎜ ⎟⎟ − 2 ⎝ vs ⎠ ν= ⎡⎛ v p ⎞ 2 ⎤ 2 ⎢⎜⎜ ⎟⎟ − 1⎥ ⎢⎣⎝ v s ⎠ ⎥⎦ 2 where, νp – compressional velocity νs – shear velocity ρ - density from density log Conversion to static values was performed by taking porosity into consideration. The analysis indicates that the Young’s Modulus is about 1.5 and 2.0 million psi for claystone and sandstone respectively and Poisson’s Ratio is about 0.3 for both claystone and sandstone. Refer to Track “Mechanical Properties” in Figure 9. Simulation Results With the geomechanical model created, a multiple batch simulation was performed to see whether the result will match with recorded data. Figure 10 shows the result of a 7400 min multiple batch injection simulation. It is the bottomhole injection over time. The recorded data for the same period of time is displayed in Figure 11. It can be seen that they match very well. Figure 12 shows the multiple fractures generated from the simulator for this 7400 min multiple batch injection period. Determining the Minimum Horizontal Stress There are different methods for interpreting horizontal stresses. But, many of them have limitations and they all need calibration with some other data source, such as pressure tests. The method used herein is an “effective stress” method, which assumes that there is a correlation between the vertical stress and horizontal stress in shale. The method requires the knowledge of the overburden stress. The vertical stress was assumed to be 1.0 psi/ft, where the density log was not available for depths shallower than 1000 meters. The interpreted stresses are calibrated to the LOT results. Refer to Track “PS ppg” in Figure 9 for minimum horizontal stress designated as Shm_ppg. Conclusions and Summary • Geomechanics modeling can provide the basis for improving drilling performance in various aspects. • Data categories are summarized and data documentations are listed for data collection. • Data analysis for geomechanics modeling requires a wide range of knowledge and experience in order to extract and integrate the data into the model. • A general process was demonstrated with an actual case history for cuttings injection performance analysis. • The case study indicates that the new method for pore pressure and permeability analysis was easy to use. Determining Young’s Modulus and Poisson’s Ratio Young’s Modulus and Poisson’s Ratio were derived using a synthetic sonic log based on the following equations: Acknowledgments The authors would like to thank Halliburton for granting permission to publish the paper. AADE-08-DF-HO-04 Geomechanics Modeling for Better Drilling Performance Nomenclature CEC – Cation Exchange Capacity ELOT – Extended Leak-Off Test EMW – Equivalent Mud Weight GR – Gamma Ray HSE – Health Safety Environment HTHP – High Temperature High Pressure ISIP – Instantaneous Shut-In Pressure LOT – Leak-Off Test NPT – Non-Productive Time PDA – Pressure Decline Analysis ROP – Rate of Penetration SP – Spontaneous Potential SQRT – Square Root TVD – True Vertical Depth E – Young’s Modulus, psi K – Permeability, md KIC – Fracture Toughness, psi-inch0.5 Pc – Closure Pressure, psi Pi – Initial Reservoir Pressure, psi Po – Pore Pressure, psi Pw – Surface Injection Pressure, psi SH – Maximum Horizontal Stress, psi Sh – Minimum Horizontal Stress, psi Sv – Vertical Stress, psi ν – Poisson’s Ratio νp – compressional velocity, ft/s νs – shear velocity, ft/s ρ – density, slug/ft3 References 1. 2. 3. 4. 5. 6. Caicedo, H.U., Calhoun, W.M., Ewy, R.T., SPE/IADC 92576, “Unique ROP Predictor Using Bit-specific Coefficient of Sliding Friction and Mechanical Efficiency as a Function of Confined Compressive Strength Impacts Drilling Performance,” presented at the SPE/IADC Drilling Conference held in Amsterdam, The Netherlands, 23-25 February 2005. J.C. Rojas, D. E. Clark, J. Zhang, “Stressed Shale Drilling Strategy – Water Activity Design Improves Drilling Performance,” SPE 102498, presented at the 2006 SPE Annual Technical Conference and Exhibition held in San Antonio, Texas, U.S.A., 24-27 September 2006 F.K. Mody and A.H. Hale, “Borehole-Stability Model To Couple the Mechanics and Chemistry of Drilling-Fluid/Shale Interactions,” JPT, November 1993, pp 1093 Aston, M. S., Alberty, M. R., de Jong, H. J. and Armagost, K.: “Drilling Fluids for Wellbore Strengthening,” SPE/IADC 87130 presented at the 2004 IADC/SPE Drilling Conference, Dallas, Texas, 2-4 March 2004. Alberty, M. W. and McLean, M. R.: “A Physical Model for Stress Cages”, SPE 90493 presented at 2004 SPE Annual Technical Conference and Exhibition, Houston, Texas, 26-29 September 2004. Sweatman, R. E., Kessler, C.W. and Hillier, J.M.: “New Solutions to Remedy Lost Circulation, Crossflows, and Underground Blowouts,” SPE/IADC 37671 presented the 1997 SPE/IADC Drilling Conference held in Amsterdam, The Netherlands, 4-6 March 1997. 7. 8. 9. 10. 11. 12. 13. 14. 5 Wang, H., Sweatman, R., Engelman, B., Deeg, W., Whitfill, D. Soliman, M. Y., and Towler, B. F.: “The Key to Successfully Applying Today’s Lost Circulation Solutions,” SPE 95895, presented at the 2005 SPE Annual Technical Conference and Exhibition, Dallas, Texas, 9-12 October 2005. Wang, H., Towler, B.F. and Mohamed, S.Y.: “Fractured Wellbore Stress Analysis – Can Sealing Micro-cracks Really Strengthen a Wellbore?” paper SPE/IADC 104947 presented at 2007 SPE/IADC Drilling Conference, Amsterdam, The Netherlands, 20-22 February 2007. Wang, H., Towler, B.F. and Mohamed, S.Y.: “Near Wellbore Stress Analysis and Wellbore Strengthening for Drilling Depleted Formations.” SPE 102719 presented at the 2007 SPE Rocky Mountain Oil & Gas Technology Symposium, Denver, Colorado, U.S.A., 16–18 April 2007. Wang, H., Soliman, M.Y., Towler, B. F., “Investigation of Factors for Strengthening a Wellbore by Propping Fractures,” IADC/SPE 112629, presented at the 2008 IADC/SPE Drilling Conference held in Orlando, Florida, U.S.A., 4–6 March 2008. Whitfill, D., Wang, H., Jamison, D. E., and Angove-Rogers, A.: “Preventing Lost Circulation Requires Planning Ahead,” SPE 108647 presented at the 2007 International Oil Conference and Exhibition in Veracruz, Mexico, 27-30 June, 2007. Whitfill, D., Jamison, D. E., Wang, H., and Thaemlitz, C.: “New Design Models and Materials Provide Engineered Solutions to Lost Circulation,” SPE 101693 presented at the 2006 Russian Oil and Gas Technical Conference and Exhibition, Moscow, Russia, 3-6 October, 2006. Wang, H., Soliman, M.Y., Whitfill, D. L., Towler, B.F., “Case Histories Show Wellbore Strengthening as a Cost-Effective Option for Drilling with Narrow Mud Weight Windows,” AADE-08-DF-HO-17, presented at the 2008 AADE Fluids Conference and Exhibition held at the Wyndham Greenspoint Hotel, Houston, Texas, April 8-9, 2008. Soliman, M.Y., Craig, D., Bartko, K., Rahim, Z., Ansah, J., Adams, D., “New Method for Determination of Formation Permeability, Reservoir Pressure, and Fracture Properties from a MiniFrac Test,” ARMA/USRMS 05-658, presented at Alaska Rocks 2005, The 40th U.S. Symposium on Rock Mechanics (USRMS): Rock Mechanics for Energy, Mineral and Infrastructure Development in the Northern Regions, held in Anchorage, Alaska, June 25-29, 2005. Appendix The early development of fracture diagnostic techniques aimed at the determination of fracture closure pressure and leakoff coefficient. Later development concentrated on the transient analysis of the before-closure data leading to the calculation of reservoir properties such as initial pressure and permeability. More recent techniques have been presented to analyze the after-closure data. These analysis techniques rely heavily on the conventional well-testing technology. One particular technique is used in this paper to determine the parametric properties of the formations being fractured during slurry injection. After-Closure Analysis One major weakness in some of the before-closure analysis techniques is strong dependence on an assumed fracture-propagation model. In addition the change of model 6 H. Wang, M. Soliman, Z. Shan, B. Towler dimension; fracture length and width makes a unique analysis very difficult to achieve. Analysis of after-closure data would to some extent eliminate this problem. Several models for after-closure analysis have been developed. In this paper we used a technique that we found easy to apply and which provided reliable analysis. The technique we have used is grounded in well test analysis technology. If we consider the MiniFrac test (or a fracturing treatment for that matter) as a pump-in/shut-in test with analogy to the standard injection falloff test, we may use classical testing techniques to analyze the falloff data. Strictly speaking, the MiniFrac test is not a conventional well test because of the propagation of the fracture during the pumping period. However, the pumping period of a MiniFrac test is usually short, and specialized well-testing techniques may be applied to the falloff period with a fairly high degree of accuracy. In other words, the effect of fracture propagation during the pumping period on the fall-off period may be small enough that ignoring it will not result in significant error in the calculation. Because the falloff period is usually much longer than the pumping period an existing well test analysis technique may be used to analyze the falloff data, beyond the closure time, for reservoir pressure and reservoir permeability. It is possible to identify one of several flow regimes depending on the reservoir, fracture and perforation schemes. These flow regimes may be linear, pseudo-radial, bilinear and spherical flow regimes. The simplest and most common is the pseudoradial flow regime. This flow regime will be reviewed next. Pseudo-radial Flow Regime Equation 1 describes the behavior of the pressure data during the after-closure period when the created fracture is fairly short and the fracture has no, or little, residual conductivity. These conditions lead to pseudo radial flow condition. Equation 2 is a rewrite of equation 1 in field units. The constant 1694.4 is (141.2 (2 × 24 )) resulting from using time in hr and the injected volume in barrel per day. Equation 3 is the log-log form of equation 2, while equation 4 is the derivative form of equation 2. In all these equations, the time, t, is the total time of the test measured from the start of the test, meaning that it includes both the injection and shut-in times. 1 t Dinj pD = .............................................................. (1) 2 tD 1694.4Vμ 1 ................................................. (2) p fo -pi = kh t ( ) ⎛ 1694.4Vμ ⎞ log p fo -pi = log ⎜ ⎟ − log (t ) ...................... (3) kh ⎠ ⎝ ⎛ ∂ p fo ⎞ 1694.4Vμ ⎤ ⎟ = log ⎡⎢ log⎜⎜ t ⎥ - log(t ) ................... (4) ⎟ ⎣ kh ⎦ ⎝ ∂t ⎠ (p AADE-08-DF-HO-04 ) Equation 3 indicates that if a pseudo-radial flow regime dominates the reservoir, plotting the pressure drop fo -p i versus total time on a log-log graph will eventually yield a straight line whose slope is -1. Equation 4 also indicates that a plot of the derivative function versus time would also yield a straight with slope of -1. The slope of the straight line of the derivative plot is only a function of observed pressure, test time and the flow regime. Thus the slope of the straight line is indicative of the pseudo-radial flow regime. Because of its independence of initial reservoir pressure and reservoir properties, it is an ideal technique to determine the prevailing flow regime. Once the flow regime is determined to be pseudo-radial using the derivative plot, a plot of pressure versus the reciprocal of time, as per equation 2, would yield a straight line. The intercept of the straight line is the initial reservoir pressure while the slope of the straight line is a function of formation permeability. Formation permeability may also be calculated from Eqs. 2-4; however, it is recommended that equation 3 be used for that purpose. It can be seen that the presented analysis technique is a function of the total injected volume. However it is still recommended that the injection rate is kept fairly constant during the test. Other Flow Regimes Three other flow regimes may be observed, linear, bilinear, and spherical. Equations 5-7 are the corresponding form of equation 1 respectively. V p fo -pi = 31.05 4h ⎛ μ ⎜ ⎜ φ ct kL2f ⎝ ⎞ ⎟ ⎟ ⎠ (5) V 0.75⎛ 1 ⎞ ⎟ p fo-pi = 264.6 ( μ) ⎜⎜ ⎟ h ⎝ φ ct k ⎠ 0.25 (6) p fo -pi = 2.9434 × 10 Vch (φ ct ) 4 0 .5 ⎛ 1 ⎞ ⎟ ⎜ ⎜ t p +Δt ⎟ ⎠ ⎝ 0 .5 ⎛ 1 ⎞ ⎟ ⎜ k f wf ⎜⎝ tinj + Δ t ⎟⎠ 0.75 1 μ⎞ ⎜ ⎟ ⎝k⎠ 0.5 ⎛ 1.5 ⎛ 1 ⎞ ⎟ ⎜ ⎜ t inj +Δt ⎟ ⎠ ⎝ 1.5 (7) The identification and analysis of the various flow regimes follows the logic discussed in the pseudo radial flow section with the exception that observed slope would be -0.5, -0.75, or -1.5 depending on the flow regime occurring in the formation. The exponent of time in the Cartesian plot will also depend on the identified flow regime. Which of these flow regimes dominates the after closure period depends on reservoir properties, fracture length, residual fracture conductivity, and the geometry of the fracture well intersection. AADE-08-DF-HO-04 Geomechanics Modeling for Better Drilling Performance Tables Table 1 Summary for Methods to Obtain the Rock Mechanical Properties and in-situ Stresses. Critical Parameters Methods Possible Data Sources Calculate from shear and compressional sonic Full waveform Sonic log, dipole Sonic log Young’s Modulus (E) slowness and bulk density or monopole Sonic log and Bulk Density Ratio of stress to strain Uni-axial core tests Calculate from shear and compressional sonic Full waveform Sonic log, dipole Sonic log Poisson’s Ratio ( ) slowness or monopole Sonic log Ratio of lateral strain to longitudinal strain Uni-axial core tests Shale: Empirical relationship with sonic porosity Seismic interpretation for interval transition or resistivity. Using NCT (Normal Compaction velocity Trend) to infer pore pressure (Eaton’s, Ratio, Sonic, density, resistivity, Dc exponent, Equivalent depth or other empirical methods) Gamma Ray, Temperature logs Pore pressure (Po) Permeable zones: Formation Tester Lithological stratigraphy for lithological Measurement. Analysis on Compartmentization, horizons, faults, diapers etc. fault seal, Centroid effect, Buoyancy etc. Formation testers. Background gas, connection gas, trip gas, Infer from operations well kicks and mud-weight Direct measurements LOT, ELOT Pore pressure, Vertical stress and Minimum horizontal Stress prediction Pseudo-Poisson’s ratio, Empirical effective stress stress correlations (Sh) Water injection, hydraulic fracturing data, Infer from operations Mini-Frac Analysis, lost circulation data Vertical stress Bulk density log, Water depth, Water table Integrate from bulk density log (Sv) depth Maximum horizontal Sonic log interpretation; Full waveform Sonic log Analysis on borehole breakout related to Breakout image or multi-arms caliper log, stress wellbore pressure (SH) wellbore pressure history Fracture Toughness Fracture toughness lab tests Direct test on rock or core samples (KIC) Table 2: Summary of Pressure Decline Analysis for LOT #1 LOT #1 Closure Pressure Analysis Method Fluid Weight, ppg Depth, ft P, psi SQRT Time 9.1 7907 2755 G-Function 9.1 7907 2735 GdP/dG 9.1 7907 2782 Pc, psi Pc, ppg 6497 15.80 6477 15.75 6524 15.87 Table 3: Summary of Closure Pressures Based Pressure Decline Analysis Operation Fluid Weight, ppg Top Perf Depth, ft Pc_surf, psi Pc, psi Pc, ppg Pc, psi/ft LOT#1 9.1 7907 2782 6524 15.87 0.83 LOT#2 9.1 7907 3708 7450 18.12 0.94 P_Test 9.1 7623 3482 7089 17.88 0.93 Injection#1 10 7623 3337 7301 18.42 0.96 Injection#2 10.4 7623 3402 7525 18.98 0.99 Injection#3 9.2 7623 3404 7051 17.79 0.92 Injection#4 8.8 7623 3600 7088 17.88 0.93 7 8 H. Wang, M. Soliman, Z. Shan, B. Towler AADE-08-DF-HO-04 Table 4: Formation Pressure of Claystone Formations Determined with PDA Operation Fluid column Weight, ppg LOT#1 9.1 P_Test 9.1 Injection#1 10 Injection#2 10.4 Injection#3 9.2 Injection#4 8.8 Top Perf Depth, ft Pi_surf, psi 7907 720 7623 850 7623 1490 7623 2768 7623 2630 7623 3223 Figures Figure 1: Results of LOT #1 and #2 for the Depth of 7907 ft Pi, ppg Pi, psi/ft 10.85 0.56 11.24 0.58 13.76 0.72 17.38 0.90 15.83 0.82 16.93 0.88 AADE-08-DF-HO-04 Geomechanics Modeling for Better Drilling Performance 9 LOT #1 Analysis dP/d[sqrt(dt)] PsRad 2000 2500 Blessed Pc 2755.351 Tc 6.905 EFFc 0.358523 Isip 4081.926 dPs 1326.575 1500 1 2 3 sqrt(dt) Less Smoothing 4 5 6 More Smoothing Figure 2: SQRT Time plot for LOT#1 LOT #1 Analysis dP/d[G] Early Tp 3500 Late PsRad 2500 Pressure, psi(psi) 3000 Isip 2000 9.250 Isip 4081.926 Delta P* 1169.869 Delta Ps 1346.613 Eff 0.379 Pc 2735.313 Tc 7.237 Effc 0.368 1500 Pressure, psi(psi) 3000 3500 Isip 1 2 G(dt) Less Smoothing 3 More Smoothing Figure 3: G-Function plot for LOT #1 10 H. Wang, M. Soliman, Z. Shan, B. Towler AADE-08-DF-HO-04 LOT #1 Analysis 4000 PsRad Isip Vertical 1000 800 600 400 200 1000 2 G(dt) Less Smoothing 3 More Smoothing Figure 4: Gdp/dG plot for LOT #1 1st LOT 100000 -tdpw/dt 10000 1000 k = 0.14 md y = nx + b n = -1.5 Spherical flow b = 585 = n*c = -1.5c c = -390 100 10 1.00 10.00 100.00 time, hrs Figure 5: LOT Analysis - The slope of -1.5 indicates a Spherical Flow Regime 1000.00 G dP/dG 3000 2500 2000 Pressure, psi(psi) Horizontal 1 0.10 1200 3500 Pivoting 1500 9.250 Isip 4081.926 Delta Ps 1299.926 Pc 2782.000 Gc 1.063 Tc 6.947 Effc 0.360 1400 dP/d[G] Tp AADE-08-DF-HO-04 Geomechanics Modeling for Better Drilling Performance 11 (pi-pw)t^1.5 vs. t 0 -50 -100 Test formation lithology: Claystone Test Brine Density: 9.1 ppg Test Depth: 7907 ft Pi: 720 psi (surface pressure) Pi: 4462 psi (at bottom) Pi gradient: 10.85 ppg or 0.564 psi/ft LOT1 = 15.9 ppg -200 -250 -300 c = -390 -350 -400 -450 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 t, hrs Figure 6: Permeability Calculation - K=0.14 md determined from the horizontal line of C=-390 Inj. Period injection well 8.40 2000 3000 4000 5000 (minutes) Pressure, psi(psi) (pi-pw)t^1.5 -150 2.0 5.0 10 20 50 (tp+dt)/dt 100 200 P* 718.792 Figure 7: An Example of Horner’s Plot for Formation Pressure Analysis with PDA 500 1.00 12 H. Wang, M. Soliman, Z. Shan, B. Towler AADE-08-DF-HO-04 pw vs. (1/t)^1.5 4,500 4,000 3,500 pw, psi 3,000 2,500 Test Brine Density: 9.1 ppg Test Depth: 7907 ft Spherical flow regime 2,000 1,500 1,000 Pi = 720 psi surface pressure 500 0 0 5 10 15 20 25 30 35 40 (1/t)^1.5, 1/hr Figure 8: An Example of Soliman’s Method for Formation Pressure with PDA 45 50 AADE-08-DF-HO-04 Geomechanics Modeling for Better Drilling Performance 13 Figure 9: Log Based Analysis for Geomechanical Modeling 10000 7500 5000 Bottom Hole Injection Pressure (psi) K=10, Cw 0.002 27Aug - 01Sept 2003 1250 2500 3750 Time (min) 5000 Figure 10: Simulation Results for a Multiple Batch Injection 6250 14 H. Wang, M. Soliman, Z. Shan, B. Towler AADE-08-DF-HO-04 Bottomhole Injection Pressure from 27Aug2003 to 01Sept2003 Bottomhole Injection Pressure, psi 12500 10000 7500 5000 2500 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 Data Points over Time Figure 11: Recorded Pressure for a Multiple Batch Injection Figure 12: Simulated Multiple Fractures Created with the Injection