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Abstract When a cool fluid such as water is injected into a hot reservoir, a growing region of cooled rock is established around the injection well. The rock matrix within the cooled region contracts, and a thermoelastic stress field is induced around the well. For typical waterflooding of a moderately deep reservoir, horizontal earth stresses may be reduced by several hundred psi. If the injection pressure is too high or if suspended solids in the water plug the formation face at the perforations, the formation will be fractured hydraulically. As the fracture grows, the flow system evolves from an essentially circular geometry in the plan view to one characterized more nearly as elliptical. This paper considers thermoelastic stresses that would result from cooled regions of fixed thickness and of elliptical cross section. The stresses for an infinitely thick reservoir have been deduced from information available in public literature. A numerical method has been developed to calculate thermoelastic stresses induced within elliptically shaped regions of finite thickness. Results of these two approaches were combined, and empirical equations were developed to give an approximate but convenient, explicit method for estimating induced stresses. An example problem is given that shows how this theory can be applied to calculate the fracture lengths, bottomhole pressures (BHP's), and elliptical shapes of the flood front as the injection process progresses. Introduction When fluids are injected into a well, such as during waterflooding or other secondary or tertiary recovery processes, the temperatures of the injected fluids are typically cooler than the in-situ reservoir temperatures. A region of cooled rock forms around each injection well, and this region grows as additional fluid is injected. Formation rock within the cooled region contracts, and this leads to a decrease in horizontal earth stress near the injection well. In Ref. 1, the magnitude of the reduction in horizontal earth stress was given for the case of a radially symmetrical cooled region. Another factor, which may occur simultaneously, is the plugging of formation rock by injected solids. There is extensive literature indicating that waters normally available for injection contain suspended solids. Laboratory tests demonstrate that these waters, when injected into formation rocks, can plug the face of the rock or severely limit injectivity. In field operations, injection often simply continues at a BHP that is high enough to initiate and extend hydraulic fractures." The injected fluid then can leak off readily through the large fracture face area. Because of the lowering of horizontal earth stresses that results from cold fluid injection, hydraulic fracturing pressures can be much lower than would be expected for an ordinary low-leakoff hydraulic fracturing treatment. For this reason, the well operator may not be aware that injected fluid is being distributed through an extensive hydraulic fracture. If injection conditions are such that a hydraulic fracture is created, then the flow system will evolve from an essentially circular geometry in the plan view to one characterized more nearly as elliptical. In this paper, thermoelastic stresses for cooled regions of fixed thickness and of elliptical cross section are determined, and a theory of hydraulic fracturing of injection wells is developed. Conditions under which secondary fractures (perpendicular to the primary, main fracture) will open also are discussed. Finally, an example problem is given to illustrate how this theory can be applied to calculate fracture lengths, BHP'S, and elliptical shapes of the flood front as the injection process progresses. Thermoelastic Stresses in Regions of Elliptical Cross Section If fluid of constant viscosity is injected into a line crack (representing a two-wing, vertical hydraulic fracture), the flood front will progress outward. so its outer boundary at any time can be described approximately as an ellipse that is confocal with the line crack. If the injected fluid is at a temperature different from the formation temperature, a region of changed rock temperature with fairly sharply defined boundaries will progress outward from the injection well but lag behind the flood front. The outer boundary of the region of changed temperature also will be elliptical in its plan view and confocal with the line crack (see Fig. 1). Stresses within the region of altered temperature, as well as stress in the surrounding rock, which remains at its initial temperature, will be changed because of the expansion or contraction of the rock within the region of altered temperature. The thermoelastic stresses within an infinitely tall cylinder of elliptical cross section can be determined from information available in the literature. 10 The interior thermoelastic stresses perpendicular and parallel to the major axes of the ellipse are given by Eqs. 1 and 2, respectively. SPEJ P. 78^
- North America > United States > California > Ventura Basin > West Montalvo Field (0.99)
- Europe > United Kingdom > North Sea > Central North Sea > Central Graben > Block 21/10 > Forties Field > Forties Formation (0.99)
Abstract Pressure and temperature gradients are created around wellbores during waterflooding or when fluids are injected in connection with any other secondary or tertiary recovery process. These gradients result in changes in earth stresses, which in turn cause hydraulic fracturing pressures to change. In this paper, analytical solutions have been used to determine the stresses resulting from radially symmetrical temperature and pressure changes around a wellbore. These stresses are required to predict the change in fracture extension pressure that is caused by the injection process. Exact, closed-form solutions are given for the stresses. These have been evaluated with a computer, and more convenient empirical formulas have been fitted to the calculated results. Solutions for discrete cylindrical or disk-shaped regions of changed temperature and pressure are shown. Also, the solutions can be adapted to annular elements of finite thickness that are convenient for incorporation to an r-z-type computer program. Such a program could then be used to compute the stresses resulting from temperature and pressure fields that vary gradually in the radial direction. This paper gives examples to illustrate the effect of injecting a large volume of liquid that is cooler than the in-situ reservoir, as is common when waterflooding. The cooling can have a large effect on lateral earth stresses, and for some conditions vertical hydraulic fracturing pressures can be significantly reduced. Introduction Thermal stresses can have a significant effect on engineering design because they can cause materials to fail. Many novel processes have been proposed for drilling and breaking rocks that make use of this fact. It is only recently, however, that the role of thermal stresses has been appreciated in the fracturing of geothermal and petroleum reservoirs. Several studies have been concerned with thermal stresses generated in geothermal wells. These studies indicate that thermal stresses open secondary fractures in the rock that substantially reduce the resistance to flow, thereby increasing the efficiency of the system. Other investigators have studied the effect that thermal stresses have on the results of in-situ earth stress measurements made by the hydraulic fracturing method. Another study predicted the thermal stresses resulting from hot-water injection into a cool reservoir. Others have proposed methods to exploit thermal stresses in the reservoir. It has been suggested that heating the reservoir will alter the in-situ earth stresses so that, in some circumstances, the horizontal stresses can be made to exceed the vertical stresses. If a fracture propagated under these conditions, the fracture would be horizontal, which is sometimes preferable to a vertical fracture. The purpose of this paper is to compute the earth stresses resulting from the injection of cool water into a warmer formation and then to deduce how the altered stresses will affect the hydraulic fracturing pressure. Initiation and propagation of hydraulic fractures are known to be controlled to a large degree by the magnitude of the earth stress that acts perpendicular to the plane of the fracture. It has been recognized for some time that the fluid pressure field in the surrounding reservoir rock will have an effect on the earth stress in the vicinity of a hydraulic fracture. During ordinary hydraulic fracturing operations, however, leakoff is controlled so that injected fluid volumes will be minimized. As a result, pressure and temperature changes in the rock surrounding the fracture do not ordinarily have a very significant effect on the fracturing operation. therefore, the primary concern has been the effect that temperature has on fracturing fluid rheology and leakoff behavior. There is another general problem of interest, where hydraulic fracturing occurs in connection with injection of large volumes of fluid, such as when waterflooding of when applying other secondary or tertiary recovery processes. For these cases, an extensive region of changed temperature or pressure can be created, and the effects on earth stresses and hydraulic fracturing processes are significant. The problem of calculating earth stress changes resulting from fluid injection is not trivial. the stress change at any position is not a point function, but rather it depends on the entire temperature and pressure fields. In this paper we review briefly the basic thermoelastic and poroelastic relationships for stress and strain. Because of an analogy between pressure and temperature effects, solutions for earth stress changes are valid for both pressure and temperature fields if the parameters are properly interpreted. SPEJ P. 129^
- North America > United States (0.46)
- Africa > Cameroon > Gulf of Guinea (0.24)
- Research Report (0.34)
- Overview (0.34)
- Energy > Oil & Gas > Upstream (1.00)
- Water & Waste Management > Water Management > Lifecycle > Disposal/Injection (0.34)
Abstract Discoveries of oil in Arctic regions have led to several engineering problems that are relatively new to the petroleum industry. An understanding of some of the new problems associated with construction of surface facilities as well as with the drilling and completion of wells requires an understanding of the mechanical properties of permafrost. permafrost. Synthetic permafrost samples have been prepared from quartz sand as well as from natural soils taken from Prudhoe Bay permafrost cores recovered from depths as great as 1,753 It. All samples have been recompacted and frozen under a condition of zero confining stress. Samples prepared in this way should exhibit behavior similar to that of shallow permafrost. Samples have been tested in uniaxial permafrost. Samples have been tested in uniaxial compression at constant strain rates as well as with constant axial stress. At constant temperature and low strain rates, the log of the maximum shear strength will plot as a straight line vs the log of the strain rate. For sand-ice samples at high strain rate, another mode of failure was evident that led to a maximum shear strength independent of strain rate. Under triaxial conditions, the maximum shear strength of sand-ice samples was generally increased with increasing stress level. In uniaxial tension, the tensile strength of sand-ice samples was found to be a function of temperature and strain rate. Elastic response of these samples was obscured by the more dominant flow behavior at low strain rates. Only at clearly high strain rates was an elastic response clearly discernible. Young's modulus measured after 10 to 15 percent plastic strain increases with increasing stress level. Introduction Within the last few years significant oil discoveries have been made in Arctic regions. There is much speculation that additional oil will be found in regions that are characterized by quite low ambient and soil temperatures. The drilling of wells and production of oil under these environmental conditions poses new problems not traditionally faced by the petroleum industry, but which presumably will be of increasing concern within the presumably will be of increasing concern within the next few years. One new engineering challenge is that of dealing with permafrost, soil which has been continuously frozen for a number of years. Already at Prudhoe Bay a number of wells have been drilled through about 2,000 ft of permafrost. As an example of permafrost influence, measurements have shown that, when thawed permafrost around a well refreezes, significant pressures can be generated. In order to understand this phenomenon, it will be necessary to understand the mechanical behavior of permafrost. In addition, surface facilities have been permafrost. In addition, surface facilities have been constructed where there is a thin, active region (which thaws during summer months) underlain by permafrost. An understanding of permafrost permafrost. An understanding of permafrost mechanical behavior will aid in the design of foundations for surface facilities. There are a number of variables that can influence the mechanical behavior of frozen soils such as minerology, percent of ice saturation, presence of excess ice, salt content, etc. In this paper we will describe a laboratory study of relatively fine-grained granular materials with pore spaces saturated with ice. The results presented here may not be applicable to frozen clays or gravels, where pore spaces are undersaturated or where a large amount of excess ice is present. Since permafrost is composed of ice and soil, its behavior will naturally reflect that of its constituents. The rate of yield or flow of ice is known to be a function of temperature, shear stress and strain, but is independent of hydrostatic pressure level. Soil, on the other hand, exhibits pressure level. Soil, on the other hand, exhibits yield behavior that is independent of temperature over the small range of permafrost temperatures of interest. For sandy soil, yield behavior is relatively independent of strain rate, but is significantly influenced by strain and stress level. Under stress, a dominant characteristic of shallow permafrost is that of yield or flow. Its rate of flow will be a function of all the variables mentioned above. Over-all deformation results from a combination of elastic and flow behavior. SPEJ P. 211
- Geology > Geological Subdiscipline > Geomechanics (0.88)
- Geology > Mineral > Silicate > Phyllosilicate (0.50)
Abstract Recent improvements in processes for recovering viscous reserves has renewed interest in the phenomenon of immiscible fingering. This paper phenomenon of immiscible fingering. This paper describes studies of immiscible fingering in linear Hele-Shaw and bead-packed models. immiscible fingers were readily initiated in all models. The fingers, however, were damped out before traveling very far in the uniform bead packs that contained connate water. The damping mechanism is believed due to the movement of the two phases in a direction transverse to the direction of gross flow. To study the transverse flow phenomenon under controlled conditions, oil and water were injected simultaneously and side by side in linear models. Transition zones were formed that grew broader as the distance from the inlet increased. The saturation distribution in the transition zones could be described mathematically by an "immiscible dispersion coefficient" and the well known error function solution of the dispersion equation. The immiscible dispersion coefficients were found to be proportional to the interstitial velocity and proportional to the product of the bead diameter proportional to the product of the bead diameter and packing inhomogeneity factor. Introduction In the literature of the petroleum industry, there is an obvious inconsistency in the descriptions of immiscible displacements occurring with unfavorable viscosity ratios. There is a vast literature that treats such displacements as being stable and capable of being described by relative permeability concepts such as those incorporated in the Buckley-Leverett approach. Furthermore, several experiments have been described that apparently confirm the validity of such an approach. On the other hand, there is also a considerable wealth of literature that argues that such displacements are unstable and will be characterized by immiscible fingers. Several mathematical studies have shown the inherently unstable nature of such displacements, and the appearance of fingers is confirmed by numerous experimental studies. In recent years, improvements in processes for recovering viscous reserves has renewed interest in the phenomenon of immiscible fingering. Consequently, we have recently pursued the question of immiscible fingering along the same conceptual lines used successfully in a study of miscible fingering. This has led to concepts about the mechanics of immiscible finger growth that have not previously been reported in the literature. This paper, which describes these studies, is divided into two main sections. The first section covers conceptual studies of immiscible displacements in linear, transparent models. It was found that immiscible fingers were readily initiated in the models, but the fingers were damped out before traveling very far in uniform bead packs containing connate water. The damping mechanism is believed due to movement of the two phases in a direction transverse to the direction of gross flow. Further studies of the transverse flow phenomenon are reported in the second section of the paper. Oil and water were injected simultaneously and side by side in linear models. Transition zones were formed that grew broader as the distance from the inlet increased. The saturation distribution in the transition zones could be described mathematically with an "immiscible dispersion coefficient" and the well known error function solution of the dispersion equation. This relationship is very similar to descriptions of transverse adding in miscible systems, and there is hope that a mathematical theory describing immiscible finger growth can ultimately be developed along the lines previously developed for miscible fingers. CONCEPTUAL EXPERIMENTS Exploratory or conceptual experiments of several types have been devised. SPEJ P. 39
- Reservoir Description and Dynamics > Reservoir Characterization (1.00)
- Reservoir Description and Dynamics > Formation Evaluation & Management (1.00)
- Reservoir Description and Dynamics > Improved and Enhanced Recovery > Waterflooding (0.94)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (0.89)
Abstract This paper explains the concept of a damaged region arising from high stress concentration at the leading edge of a hydraulically created fracture. Approximate stresses near the tip of the crack are calculated, and it is shown that a stable crack shape is possible for which all stresses are finite. A new energy balance is derived incorporating these thoughts, and it is shown that predicted fracturing pressures (using surface energies determined by cleavage) agree with experimental fracturing pressures determined in models. All calculations apply to the case of a nonpenetrating fluid. It is concluded from these studies that in some cases, particularly in small laboratory models, these phenomena significantly affect extension pressures and crack widths. Introduction One of the perplexing questions about hydraulic fracturing that has not been satisfactorily answered is, what pressure is necessary to extend a fracture? For many engineering problems involving failure, it is sufficient to calculate those loading conditions which would bring a stress or elastic strain within the material to a level that could not be tolerated. However, this approach is not useful when considering a sharp-edged crack; calculated stresses and elastic strains always reach infinitely large values near the tip of the crack if fluid pressure is applied all the way to the crack extremity. This difficulty has led to the concept of cohesiveness or absorption of surface energy, implying that behavior near the tip of the crack is not purely elastic. Additional note of the nonideal behavior of rocks will be made in this paper. Then, by simplifying and dealing with an average stress in an inelastic region, the approximate stress distribution around a hydraulic fracture will be calculated and the conditions under which a stable fracture can exist will be shown. A new energy balance equation is then derived incorporating the modified stress picture. Finally, predicted fracture extension pressures are compared with breakdown pressures obtained in laboratory models. This comparison shows that surface energies measured by the cleavage technique are consistent with those values manifested during fracture extension. PROBLEMS OF INDUCED STRESS It will be revealing to consider first the calculated stresses around a penny-shaped line crack, assuming that the rock behaves as a linear, elastic material. Fig. 1 shows the stress distribution in the plane of the crack as calculated with Sneddon's equation. If pressure p is applied uniformly within the crack, then infinitely large tensile stresses would be induced in the rock near the crack tip. Such stresses could not be sustained in a real material. Two approaches have been proposed to explain this dilemma. SPEJ P. 1ˆ
Abstract As fractures are propagated through rocks, energy is absorbed near the extending crack tip. Apparent surface energies for several rocks have been measured by cleavage under dynamic conditions. At nominal crack velocities from 0.5 to 500 in./min. measurements showed that fractures propagated in discrete jumps. Calculated surface energies and moduli were relatively insensitive to nominal rate of cleavage. In another set of experiments, rocks were cleaved under high confining stresses. The rocks were submerged in low leak-off fluids which formed a filter cake on the freshly cleaved surfaces (similar to the hydraulic fracturing process). Apparent surface energies were increased substantially as the surrounding fluid pressure was increased. Moduli in bending increased significantly upon application of the first 1,000 psi but were insensitive to stress level at greater pressures. INTRODUCTION For almost 20 years, hydraulic fracturing processes have been utilized effectively to stimulate oil and gas wells. During this period, some process improvements have resulted from studies of fracture orientation, mechanics of fracturing, areas generated, conductivities of cracks, etc. Yet many questions remain concerning the conditions and pressures needed during fracture propagation. In this paper we will report additional studies of the mechanics of fracture extension. It was shown previously that large rock samples could be cleaved under controlled conditions so as to measure the apparent surface energy (that amount of energy absorbed per unit area of new surface created). In this paper we consider the effects of two additional factors on surface energies, viz.:effect of cleavage rate and effect of confining stress level. THEORY Cleavage experiments were conducted on rock samples similar to that illustrated in Fig. 1. Blocks of rock several inches wide, 2- to 3-in. thick, and up to 3 ft in length were grooved longitudinally with shallow guide slots. A crack was initiated and allowed to extend along the web as the top of the rock specimen was pulled (or pushed) apart. Auxiliary equipment permits the measurement offorce applied at the top, separation at the top and crack length. (Further experimental details will be given in the next section.) The rock beams created by the crack are considered to' be cantilever beams. The deflection (or separation of the rock beams) at any point is calculated4,5 by the beam Eq. 1.
Abstract Values of rock surface energy (i. e. energy required to form a unit area of new surface) are useful for interpretation of drilling and fracturing phenomena. This paper describes the adaptation of a cleavage technique (splitting of large rocks under controlled conditions) for measuring surface energies. Values of surface energy obtained at room temperature and at low crack extension rates are reported for a variety of sandstones and limestones. Elastic moduli, tensile strengths and compressive strengths of the samples are also reported. The values of Young's moduli (measured in bending) are relatively low, probably because of the low stress levels imposed. Measured values of surface energy are generally higher than anticipated and probably reflect inelastic yielding near the extending tip of the crack. Introduction The technology of petroleum production includes many operations such as drilling and fracturing, which involve rock breakage. One of the fundamental properties of a rock needed to fully explain breaking and fracturing phenomena is the surface energy (i. e. the energy required to form a unit area of new surface).In this paper we describe an adaptation of the cleavage method (splitting of the rock under controlled conditions) to utilize large rock samples. Application of the theory of elastic cantilever beams and the Griffith concept of mechanical stability permits the calculation of surface energies from simple measurements. Values of surface energies obtained at room temperature on dry samples and at low, crack extension rates are reported for a variety of sandstones and limestones. Measured values of Young's Moduli, compressive strengths and tensile strengths are also reported for the rocks. THE EXPERIMENTAL METHOD Equipment designed to cleave large rock samples is shown on Fig. 1. This equipment consists essentially of two steel blocks cemented to a rock sample and forced apart with a steel rod. A ball joint and a pivot prevent bending stresses in the rod. A differential thread arrangement permits the rod to advance only 0.012 in./revolution of the driving nut. The axial force in the rod is measured with type FA-50–12 Baldwin Lima Hamilton strain gauges and a BLH type 20 strain gauge reader. Separation of the blocks is measured with a Starrett 656–617 dial gauge. The massive nature and design of the equipment minimize the amount of elastic energy stored in the steel parts as the stress in the rod is increased. This will permit the rock to split under controlled conditions as will become clear later. Fig. 2 shows a sketch of the rock sample during cleavage. Guide slots are cut longitudinally along the rock sample as suggested by Berry. An initiating slot is also cut across the top of the block to a depth of 1 to 2 in. During cleavage, elastic energy is stored in the flexed beams of rock of length C. If the length of steel rod L is held constant and the crack extends in length, then the elastic potential energy stored in the rock decreases. However, surface energy must be supplied as the crack extends in length. Griffith has proposed the following criteria for mechanical stability. The crack will extend as long as the potential energy available is greater than the surface energy required. However, the crack will stop extending when the change in potential energy with change in crack length is just equal to the change in surface energy with change in crack length. See Eq. 1. (1) U = potential elastic energy stored in the system S = surface energy of the system C = crack length L = length of steel rod The surface energy of the system is given by Eq. 2. The coefficient 2 is necessary since two new surfaces are being created. (2) SPEJ P. 307^
- Geology > Geological Subdiscipline > Geomechanics (0.69)
- Geology > Rock Type > Sedimentary Rock > Carbonate Rock > Limestone (0.46)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock > Sandstone (0.46)
Abstract Because of the influence of dispersion on miscible-displacement processes, diffusion and dispersion phenomena in porous rocks are of current interest in the oil industry. This paper reviews and summarizes a great deal of pertinent information from the literature.Porous media (both unconsolidated packs and consolidated rocks) can be visualized as a network of flow chambers, having random size and flow conductivity, connected together by openings of smaller size. In such a porous medium, the apparent diffusion coefficient D is less than the molecular diffusion coefficient Do, as measured in the absence of a porous medium. For packs of unconsolidated granular material the ratio D/Do is about 0.6 to 0..7. For all porous rocks, both cemented and unconsolidated, the ratio of diffusion coefficients can also be represented as where F is the formation electrical resistivity factor and is the porosity.If fluids are flowing through the porous medium, dispersion may be greater than that due to diffusion alone. At moderate flow rates the porous medium will create a slightly asymmetrical mix zone (trailing edge stretched out), with the longitudinal dispersion coefficient approximately proportional to the first power of average fluid velocity (if composition is nearly equalized in pore spaces by diffusion). If the velocity in interstices is large enough, there will be insufficient time for diffusion to equalize concentration within pore spaces. In this region, longitudinal dispersion increases more rapidly than fluid velocity.At low velocities in interstices, transverse dispersion is characterized by a region in which transverse diffusion dominates. If the fluid velocity gets high enough, there will be a transition into a region where there is stream splitting with mass transfer but with insufficient residence time to completely damp-out concentration variations within pore spaces.There are several variables that must be controlled to get consistent longitudinal and transverse dispersion results, viz.,edge effect in packed tubes, particle size distribution, particle shape, packing or permeability heterogeneities, viscosity ratios, gravity forces, amount of turbulence, and effect of an immobile phase. Introduction Diffusion and dispersion in porous rocks are of current interest to the oil industry. This interest arises because of the influence of dispersion on miscible-displacement processes.In a recovery process utilizing a zone of miscible fluid, there is the possibility of losing miscibility by dissipating the miscible fluid or by channeling or ‘fingering" through the miscible zone. Diffusion and dispersion are two of the mechanisms that may lead to mixing and dissipation of the slug. On the other hand, dispersion may tend to damp-out viscous fingers which may be channeling through the miscible slug. Hence, dispersion may be detrimental or beneficial (if it prevents fingering through the miscible zone). Therefore, it is doubly important that we understand these processes.In this paper we review, summarize and interpret a great deal of information from the literature. In particular, we will briefly discuss molecular diffusion in miscible fluids. Then we will discuss what differences to expect for diffusion in a porous rock. If there is movement of the fluid through the rock, then there may be an additional mixing or "dispersion". Furthermore, the dispersion longitudinally (in the direction of gross fluid movement) and transverse to the direction of fluid movement will not be equal. We will discuss both types of dispersion as well as several variables which can affect dispersion (viscosity differences, density differences, turbulence, heterogeneity of media, etc.). This group of variables has sometimes led to difficulty when comparing literature data. DIFFUSION OF MISCIBLE FLUIDS If two miscible fluids are in contact, with an initially sharp interface, they will slowly diffuse into one another. SPEJ P. 70^
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- Reservoir Description and Dynamics > Improved and Enhanced Recovery (1.00)
- Reservoir Description and Dynamics > Fluid Characterization > Fluid modeling, equations of state (1.00)
- Production and Well Operations > Well & Reservoir Surveillance and Monitoring > Production logging (1.00)