Kirsch Equation

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Chandong Chang - One of the best experts on this subject based on the ideXlab platform.

  • Heterogeneous in situ stress magnitudes due to the presence of weak natural discontinuities in granitic rocks
    Tectonophysics, 2015
    Co-Authors: Chandong Chang
    Abstract:

    Abstract Two field examples of hydraulic fracturing stress measurements are reported, in which the determined stress magnitudes exhibit severe variations with depth. The stress measurements were conducted in vertical boreholes drilled in granites in two different locations in South Korea. Several isolated intervals of intact rocks in the boreholes were vertically fractured by injecting water. The magnitudes of the minimum horizontal principal compressive stress (S hmin ) were determined from shut-in pressures. The magnitudes of the maximum horizontal principal compressive stress (S Hmax ) were estimated based on the Kirsch Equation using tensile strengths determined from hollow cylinder tests and Brazilian tests, in which pressurization-rate effects on tensile strength were taken into account. The stress states in both locations are in reverse-faulting stress regimes. The magnitudes of S Hmax are generally within a stress range defined by frictional limits of favorably oriented fractures having frictional coefficients of 0.6 and 1.0. However, S Hmax magnitudes do not increase linearly with depth, but rather scatter quite severely. It is noted that near the depths where the measured stresses are relatively low, natural discontinuities with wide apertures containing weak filling material exist, whereas near the depths of high stress, such wide discontinuities are scarce. Wide aperture discontinuities are predominantly oriented such that their slip tendency is high under the given stress conditions, meaning that if excessive shear stress is exerted, the weak discontinuities would slip to release the excessive stress. Such local processes would restrict S Hmax magnitudes within values that can only be sustained by the shear strengths of the discontinuities, leading to severe variations of S Hmax with depth. This result suggests that stress magnitudes are controlled quite locally by the frictional property of natural discontinuities, and that the stress state in granitic rock might be inherently heterogeneous because of the heterogeneous distribution of natural discontinuities having various frictional properties.

Karen Bybee - One of the best experts on this subject based on the ideXlab platform.

  • Mud Design To Prevent Circulation Losses
    Journal of Petroleum Technology, 2007
    Co-Authors: Karen Bybee
    Abstract:

    This article, written by Assistant Technology Editor Karen Bybee, contains highlights of paper SPE 105449, "Design of Well Barriers To Combat Circulation Losses," by Bernt S. Aadnoy, SPE, Mesfin Belayneh, SPE, and Miguel Arriado, U. of Stavanger, and Roar Flateboe, BP plc, prepared for the 2007 SPE/IADC Drilling Conference, Amsterdam, 20–22 February. The full-length paper summarizes a 10-year research program in borehole fracturing and mud design. Numerous experiments were conducted with oil- and water-based drilling fluids to understand better the mechanisms that lead to circulation losses. A new mechanistic model for fracturing is presented that is different from other recent models, and the model was verified with laboratory experiments. The model defines optimal barrier filtrate loss to place particles in the loss zone. Selected laboratory experiments are presented that demonstrate that borehole fracturing resistance can be improved significantly by changing mud composition. Introduction Recognizing that borehole-stability mechanisms are not understood fully, research carried out during the past 10 years has focused on the fundamental physics and chemistry. Fig. 1 shows a fracturing cell where specially prepared hollow concrete cores are fractured. The setup also allows for mud circulation to ensure that mud particles are well distributed inside the hole. The cell is rated to 69 MPa, and the axial load, confining pressure, and borehole pressure can be varied independently. Many oil- and water-based drilling fluids were tested as well as novel ideas such as changing rock wettability or creating other chemical barriers. Cores with circular, oval, and triangular holes were tested to study effects of hole geometry. Fig. 2 shows typical results from the fracturing experiments. The commonly used Kirsch Equation defines the theoretical fracture pressure in a nonpenetrating situation such as when using drilling muds. Only one of the three measured fracture pressures agrees with the theoretical model, and the other two are much larger. Several conclusions came out of this research.The theoretical Kirsch model underestimates the fracture pressure in general.There is significant variation in fracture pressure, depending on mud quality. This shows that the fracture pressure can be increased by designing a better mud. Several devices were constructed to study the mud and its filter cake. Fig. 3 shows a mud cell with six outlets to simulate fractures of various dimensions. The mud is circulated with a low-pressure pump to develop a filter cake across the slots. Then, a high-pressure pump increases the pressure until the mudcake breaks down. In this way, the stability and strength of the mudcake can be studied. Common muds and additives were used, and the observation was made that reducing the number of additives often results in a better mud. Nonpetroleum products also were studied to look for improvements.

H. Rezazadegan - One of the best experts on this subject based on the ideXlab platform.

  • Present-day stress of the central Persian Gulf: Implications for drilling and well performance
    Tectonophysics, 2013
    Co-Authors: Amir Hossein Haghi, Riyaz Kharrat, M.r. Asef, H. Rezazadegan
    Abstract:

    Abstract The present-day state of stress in the Persian Gulf is poorly understood but has significant impacts on well drilling and performance. The upper Permian to lower Triassic formation of Kangan/Dalan, Persian Gulf, exhibits a complex structural context in the neighborhood of the Oman Mountains and the Zagros orogenies. This formation is divided into four reservoir layers (K1 to K4) where three main lithologies (limestone, dolomite and anhydrite) are alternating. We conduct an analysis of the present-day stress and natural fractures at the wellbore using full-bore FMI logs, leak off test and density logs. For this purpose, borehole breakout and tensile fracture data are used to determine orientation of S H . Furthermore, density log, leak-off test and Kirsch Equation for tensile fracture formation in the wellbores are used to calculate the magnitude of S v , S h and S H , respectively. Vertical stress (S v ) gradient at 3100 m depth approximates 20 MPa/km (2.9 psi/m), indicating a bulk density of 2.04 g/cm 3 . A total of 131 drilling induced tensile fractures and 21 breakouts with an overall length of 262 m are observed in two wells, indicating a mean maximum horizontal stress (S H ) orientation of N53° (± 18.45°) for drilling-induced tensile fracture (DITF) data and N50° (± 10.79°) for breakout data. The mean orientation of S H rotates counterclockwise with depth from K2 (N70° ± 4.2°) to K4 (N40° ± 5.1°) reservoirs. Noticed correlation between these data and stress orientations from earthquake focal mechanism solution, first of all, indicates that the stresses are linked to the resistance forces generated by the Arabia–Eurasia collision at the Zagros orogeny and secondly confirms the reliability of focal mechanism solution data near continental collision zones. In the Kangan/Dalan Formation, the NW–SE main open fracture direction is found as a common regional direction which is sub-perpendicular to the present-day maximum horizontal stress. Minimum horizontal stress (S h ) gradient in reservoir sections is estimated to be equal to 17 MPa/km (2.5 psi/m). The concluded strike–slip stress regime (S H  > S v  > S h ) in the study area is consistent with the compressive regime in the Zagros thrust–fold belt. The present-day stress in the Kangan/Dalan Formation has implications for wellbore stability, lost circulation and well Inflow Performance Relationship (IPR). Wells are more unstable if deviated toward the S v direction, whereas well productivity and mud loss increase in wells deviated toward S H , which conveys the idea of a strike–slip faulting effect tends to keep the natural fractures open in that direction.

Bernt S. Aadnoy - One of the best experts on this subject based on the ideXlab platform.

  • A New Fracture Model That Includes Load History, Temperature, and Poisson's Effects
    SPE Drilling & Completion, 2009
    Co-Authors: Bernt S. Aadnoy, Mesfin Belayneh
    Abstract:

    Summary The fracture Equation used in the oil industry is derived from the Kirsch Equation for the hoop stress. Because of its simplicity, it is almost exclusively used for the prediction of fracture initiation pressures. However, it is not useful for analysis of load history. An analytic study was undertaken to model load history leading to the fracturing of the borehole. To use the model, initial conditions must be established, given by the virgin in-situ stress state and the pore pressure, followed by the load history and the temperature history. Imposing a volumetric strain balance, a new fracturing Equation is developed. Because the borehole is loaded in the radial direction, causing tension in the tangential direction, a Poisson's effect arises. In addition, the general solution includes effects of temperature history. Example cases will show the improvement with the new model. The first case compares the new load-history fracture model with the Kirsch solution. The Poisson's scaling factor in the new solution leads to a higher fracture pressure than the conventional solution. This may explain some of the discrepancy between models and field data. The second case investigates the thermal effects by comparing the fracture pressure for the drilling phase with a hot-production phase and a cold-water-injection phase. It is believed that by including the pressure and temperature load history, a better assessment of the fracture strength is obtained, leading to better predictions. Introduction Basis for the Model. Although the Kirsch solution for stresses in a circular hole was published more than 100 years ago, it was not untill 1980 that borehole mechanics started being applied to petroleum drilling. At that time, deviated wells were evolving, and because of the complexity, high inclination, and increasing length of these, borehole stability was identified as a critical factor. Bradley (1979) is considered the person that introduced application of classical mechanics into the petroleum industry by analyzing borehole fracturing and collapse in deviated boreholes. Later, Aadnoy and Chenevert (1987) presented the mathematical framework and elaborated on the applications. These early works still form the basis for modern wellbore-stability analyses. Continuing work, the past two decades have of course led to many contributions to the classical solutions. A full review will not be given here, but Fjaer et al. (1992) serves as a good general reference. More recently, Aadnoy and Belayneh (2004) have shown that the boundary condition given by the drilling fluid can be better represented as an elastoplastic barrier. The temperature effects are identified as having effect on the fracture pressure. Examples are given by Maury and Sauzay (1987) and Maury and Guenot (1995). A more recent paper by Gil et al. (2006) considers the temperature issues from a poroelastic and "stress-cage" perspective. The variable in the solution is the borehole pressure, which causes the borehole to be loaded in the radial direction. However, the solution used today does not include the full Poisson's effect (i.e., the effects in the tangential and axial direction of a radial loading). The objective of this paper is to include this effect. In the following, we will present the resulting expression for the new model, which is derived in the Appendix.

  • Design of Well Barriers To Combat Circulation Losses
    SPE Drilling & Completion, 2008
    Co-Authors: Bernt S. Aadnoy, Mesfin Belayneh, Miguel Angel Arriado Jorquera, Roar Flateboe
    Abstract:

    Summary The paper summarizes a 10-year research program at the University of Stavanger in borehole fracturing and mud design. Novel fracturing cells and mud cells were built to better understand the mechanisms that lead to circulation losses. Numerous experiments were conducted using both oil- and water-based drilling fluids. The paper presents a new mechanistic model for fracturing called "the elastoplastic-barrier model." It is different from other recent models, and it is verified with laboratory experiments. In simple terms, it defines optimal barrier filtrate loss to place particles in the loss zone, and the mechanical strength of the particles required to resist losses. Selected laboratory experiments are presented demonstrating that borehole fracturing resistance can be improved significantly by changing the mud composition. While testing commercial lost-circulation-material (LCM) products, it was found that some worked well, some were poor, and some worked only in synergy with others. On the basis of these findings, the composition of an optimal LCM pill will be presented. Nonpetroleum products also have been tested to search for improvements in mud design. One result is that calcium carbonate can be replaced with more-efficient materials. We also have shown that adding small amounts of carbon fiber has a positive effect. This research has been conducted in close cooperation with major mud companies and operators. A field case is presented from a shallow field. The mud was designed and tested during operation at the laboratory of the University of Stavanger. The result was a clear increase in fracture pressure, resulting in a successful operation. Experimental work A large industrial project, DEA-13 (Morita et al. 1990; Onyia 1994), was undertaken in the early 1990s to investigate lost-circulation problems with oil-based drilling fluids. Good understanding came out of this project. Publications by Morita et al. (1990) and Onyia (1994) give a good overview of these results. Many of the observations reported in DEA-13 have been seen during the work reported in this paper. There is one significant difference: Whereas DEA-13 focused on oil-based drilling fluids, the present work has been concerned mainly with water-based drilling fluids. At the University of Stavanger, experimental fracturing research has been carried out during the past 10 years. This work has resulted in several PhD theses and a number of master's theses. Recognizing that borehole-stability mechanisms are not understood fully, the research has had to focus on the fundamental physics and chemistry. Fig. 1 shows a fracturing cell where specially prepared, hollow concrete cores are fractured. The setup also allows for mud circulation to ensure that mud particles are well distributed inside the hole. The cell is rated to 69 MPa, and the axial load, the confining pressure, and the borehole pressure can be varied independently. Many oil- and water-based drilling fluids have been tested, along with other novel ideas such as changing rock wettability or creating other chemical barriers. Cores with circular, oval, and triangular holes have been tested to study the effects of hole geometry. Fig. 2 shows typical results from the fracturing experiments. The commonly used Kirsch Equation (Kirsch 1898) is used as a reference. The Kirsch Equation defines the theoretical fracture pressure with a nonpenetrating situation, such as when using drilling muds. From Fig. 2 it can be seen that only one of the measured fracture pressures agrees with the theoretical model; the two others are much larger. Several conclusions have come out of this research, including:The theoretical Kirsch model underestimates the fracture pressure in general.There is significant variation in fracture pressure, depending on the quality of the mud. This shows that the fracture pressure can be increased by designing a better mud. To study the mud and the filter cake, several devices have been constructed. Fig. 3 shows a mud cell provided with six outlets containing artificial fractures of various dimensions. The mud is circulated with a low-pressure pump to develop a filter cake across the slots. At this stage, a high-pressure pump increases the pressure until the mudcake breaks down. In this way, we can study the stability and the strength of the mudcake. We have used many common muds and additives and have observed that reducing the number of additives often gives a better mud. We also have studied nonpetroleum products to look for improvements. Some of this will be discussed later.

Roar Flateboe - One of the best experts on this subject based on the ideXlab platform.

  • Design of Well Barriers To Combat Circulation Losses
    SPE Drilling & Completion, 2008
    Co-Authors: Bernt S. Aadnoy, Mesfin Belayneh, Miguel Angel Arriado Jorquera, Roar Flateboe
    Abstract:

    Summary The paper summarizes a 10-year research program at the University of Stavanger in borehole fracturing and mud design. Novel fracturing cells and mud cells were built to better understand the mechanisms that lead to circulation losses. Numerous experiments were conducted using both oil- and water-based drilling fluids. The paper presents a new mechanistic model for fracturing called "the elastoplastic-barrier model." It is different from other recent models, and it is verified with laboratory experiments. In simple terms, it defines optimal barrier filtrate loss to place particles in the loss zone, and the mechanical strength of the particles required to resist losses. Selected laboratory experiments are presented demonstrating that borehole fracturing resistance can be improved significantly by changing the mud composition. While testing commercial lost-circulation-material (LCM) products, it was found that some worked well, some were poor, and some worked only in synergy with others. On the basis of these findings, the composition of an optimal LCM pill will be presented. Nonpetroleum products also have been tested to search for improvements in mud design. One result is that calcium carbonate can be replaced with more-efficient materials. We also have shown that adding small amounts of carbon fiber has a positive effect. This research has been conducted in close cooperation with major mud companies and operators. A field case is presented from a shallow field. The mud was designed and tested during operation at the laboratory of the University of Stavanger. The result was a clear increase in fracture pressure, resulting in a successful operation. Experimental work A large industrial project, DEA-13 (Morita et al. 1990; Onyia 1994), was undertaken in the early 1990s to investigate lost-circulation problems with oil-based drilling fluids. Good understanding came out of this project. Publications by Morita et al. (1990) and Onyia (1994) give a good overview of these results. Many of the observations reported in DEA-13 have been seen during the work reported in this paper. There is one significant difference: Whereas DEA-13 focused on oil-based drilling fluids, the present work has been concerned mainly with water-based drilling fluids. At the University of Stavanger, experimental fracturing research has been carried out during the past 10 years. This work has resulted in several PhD theses and a number of master's theses. Recognizing that borehole-stability mechanisms are not understood fully, the research has had to focus on the fundamental physics and chemistry. Fig. 1 shows a fracturing cell where specially prepared, hollow concrete cores are fractured. The setup also allows for mud circulation to ensure that mud particles are well distributed inside the hole. The cell is rated to 69 MPa, and the axial load, the confining pressure, and the borehole pressure can be varied independently. Many oil- and water-based drilling fluids have been tested, along with other novel ideas such as changing rock wettability or creating other chemical barriers. Cores with circular, oval, and triangular holes have been tested to study the effects of hole geometry. Fig. 2 shows typical results from the fracturing experiments. The commonly used Kirsch Equation (Kirsch 1898) is used as a reference. The Kirsch Equation defines the theoretical fracture pressure with a nonpenetrating situation, such as when using drilling muds. From Fig. 2 it can be seen that only one of the measured fracture pressures agrees with the theoretical model; the two others are much larger. Several conclusions have come out of this research, including:The theoretical Kirsch model underestimates the fracture pressure in general.There is significant variation in fracture pressure, depending on the quality of the mud. This shows that the fracture pressure can be increased by designing a better mud. To study the mud and the filter cake, several devices have been constructed. Fig. 3 shows a mud cell provided with six outlets containing artificial fractures of various dimensions. The mud is circulated with a low-pressure pump to develop a filter cake across the slots. At this stage, a high-pressure pump increases the pressure until the mudcake breaks down. In this way, we can study the stability and the strength of the mudcake. We have used many common muds and additives and have observed that reducing the number of additives often gives a better mud. We also have studied nonpetroleum products to look for improvements. Some of this will be discussed later.