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Hydraulic Fracturing

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Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*SPE J.*25 (05): 743–756.

Paper Number: SPE-10977-PA

Published: 01 October 1985

Abstract

This paper describes an approach to simulating the flow of water, oil, and gas in fully or partially fractured reservoirs with conventional black-oil models. This approach is based on the dual porosity concept and uses a conventional tridimensional, triphasic, black-oil model with minor modifications. The basic feature is an elementary volume of the fractured reservoir that is simulated by several model cells; the matrix is concentrated into one matrix cell and tee fractures into the adjacent fracture cells. Fracture cells offer a continuous path for fluid flows, while matrix cello are discontinuous ("checker board" display). The matrix-fracture flows are calculated directly by the model. Limitations and applications of this approximate approach are discussed and examples given. Introduction Fractured reservoir models were developed to simulate fluid flows in a system of continuous fractures of high permeability and low porosity that surround discontinuous, porous, oil-saturated matrix blocks of much lower permeability but higher porosity. The use of conventional models that permeability but higher porosity. The use of conventional models that actually simulate the fractures and matrix blocks is restricted to small systems composed of a limited number of matrix blocks. The common approach to simulating a full-field fractured reservoir is to consider a general flow within the fracture network and a local flow (exchange of fluids) between matrix blocks and fractures. This local flow is accounted for by the introduction of source or sink terms (transfer functions). In this formulation, the model is not directly predictive because the source term (transfer function) is, in fact, entered data and is derived from outside the model by one of the following approaches: analytical computation, empirical determination (laboratory experiments), or numerical simulation of one or several matrix blocks on a conventional model. To derive these transfer functions, imposing some boundary conditions is necessary. Unfortunately, it is generally impossible to foresee all the conditions that will arise in a, matrix block and its surrounding fractures during its field life. It would be helpful, therefore, to have a model that is able to compute directly the local flows according to changing conditions. However, to have low computing times, it is necessary to use an approximate formulation and, thus, to adjust some parameters to match results that are externally (and more accurately) derived in a few basis, well-defined conditions. By current investigative techniques, only a very general description of the matrix blocks and fissures can be obtained, so our knowledge of local flows is very approximate. This paper presents a modeling procedure that is an approximate but helpful approach to the simulation of fractured reservoirs and requires a few, simple modifications of conventional black-oil mathematical models. Review of the Literature Numerous papers related to single- and multiphase flow in fractured porous media have been published over the last three decades. On the basis of data from fractured limestone and sand-stone reservoirs, fractured reservoirs are pictured as stacks of matrix blocks separated by fractures (Figs. 1 and 2). The fractured reservoirs with oil-saturated matrices usually are referred to as "double porosity" systems. Primary porosity is associated with matrix blocks, while secondary porosity is associated with fractures. The porosity of the matrices is generally much greater than that of the fractures, but permeability within fractures may be 100 and even over 10,000 times higher permeability within fractures may be 100 and even over 10,000 times higher than within the matrices. The main difference between flow in a fractured medium and flow in a conventional porous system is that, in a fractured medium, the interconnected fracture network provides the main path for fluid flow through the reservoir, while local flows (exchanges of fluids) occur between the discontinuous matrix blocks and the surrounding fractures. Matrix oil flows into the fractures, and the fractures carry the oil to the wellbore. For single-phase flow, Barenblatt et al constructed a formula based on the dual porosity approach. They consider the reservoir as two overlying continua, the matrices and the fractures. SPEJ p. 743

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*SPE J.*25 (05): 729–742.

Paper Number: SPE-11599-PA

Published: 01 October 1985

Abstract

New analytical solutions for the response at a well intercepting a layered reservoir are derived. The well is assumed to produce at a constant rate or a constant pressure. We examine reservoir systems without pressure. We examine reservoir systems without interlayer communication and document the usefulness of these solutions, which enable us to obtain increased physical understanding of the performance of fractured physical understanding of the performance of fractured wells in layered reservoirs. The influence of vertical variations in fracture conductivity is also considered. Example-applications of the approximations derived here are also presented. Introduction We recently examined the response of vertically fractured wells in layered reservoirs. The conductivity of the fracture was assumed to be finite. The solutions presented in Refs. 1 and 2 were obtained by solving the partial differential equations and the associated conditions by standard finite-difference methods. During the course of that study, several analytical solutions were derived. Although approximate, the analytical solutions serve important functions. First, they provide information on the structure of the solution; thus they increase physical understanding. Second, they suggest procedures to correlate results obtained by finite-difference methods. (If the analytical solutions had been unavailable, it is doubtful that the correlations in Refs. 1 and 2 could have been obtained.) Third, they allow us to verify the accuracy of the finite-difference solutions when no solutions are available in the literature or when the solutions in the literature are not in agreement, which is important. We had difficulty validating our finite-difference model because solutions in the literature are not in agreement for all times of interest. To our knowledge, the analytical solutions presented here are not available in the literature. Comparisons with the numerical solutions are presented and the advantages of the analytical solutions are documented in this study. In addition to being used to examine fractured wells intercepting layered systems, the analytical solutions presented here also can be used to study cases where the presented here also can be used to study cases where the fracture extends above and/or below the productive interval and cases where the conductivity of the fracture is a function of depth. In this work we refer to a fracture with fracture height greater than the formation thickness as an "extended fracture." It is emphasized that the objective of this paper is to discuss the analytical aspects of the problems stated above. Practical considerations of these results are not germane to this paper. This aspect is discussed in more detail in Refs. 1 through 4. However, we show that the analytical solutions presented here lead to new methods of analysis that are not given in the literature. Example applications of the new methods of analysis are presented. Physical Model Physical Model The physical system discussed in this work is a multilayer, rectangular reservoir that is being drained by a hydraulically fractured well. The well is located at the center of the reservoir and the fracture. The fracture is parallel to two sides of the reservoir. Thus, the parallel to two sides of the reservoir. Thus, the reservoir-fracture system is symmetric about the well. For this reason, only a quarter of the physical system is modeled (Fig. 1). (For simplicity, only two layers are shown; all derivations given here are applicable to systems with more than two layers.) The top, bottom, and outer boundaries of the reservoir are assumed to be impermeable. Each layer of the reservoir is assumed to be a uniform and homogeneous porous medium. The properties of any given layer (porosity, compressibility, permeability, and thickness), however, may be different from that of another layer. There is no vertical communication between the layers, except by the vertical fracture. The fracture is considered to be a layered porous medium. This idealization is used to model variations in fracture conductivity with depth. Each layer of the fracture is assumed to be a homogeneous porous medium. The width and length of the fracture are independent of the vertical coordinate. The permeability of the fracture in a given layer is independent of the distance from the well. The most important feature of the mathematical model used in this study concerns the fracture height and the thickness of the layers in the fracture and reservoir. The model assumes that the fracture height, hf, can be equal to or greater than the formation thickness, h. More importantly, the thicknesses of the fracture layers are independent of the thicknesses of the layers in the reservoir. This feature of the model is in accordance with the conditions that should exist in practice. Fig. 2 depicts some of the conditions that can be simulated by this model. For convenience of notation, z=0 represents the top of the reservoir and the top of the fracture. SPEJ P. 729

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*SPE J.*25 (05): 623–628.

Paper Number: SPE-11794-PA

Published: 01 October 1985

Abstract

Reservoirs with bottomhole temperatures (BHT's) in excess of 250 deg. F [121 deg. C] and permeabilities of less than 1.0 md are commonly encountered in drilling and completing geothermal and deep gas wells. Successful stimulation of these wells often requires the use of massive hydraulic fracturing (MHF) treatments. Fracturing fluids chosen for these large treatments must possess shear and thermal stability at high BHT'S. The use of conventional fracturing fluids has been limited traditionally to wells with BHT's of 250 deg. F [121 deg. C] or less. Above 250 deg. F [121 deg. C], high polymer concentrations and/or large fluid volumes are required to maintain effective fluid viscosities in the fracture. However, high polymer concentrations lead to high friction pressures, high costs, and high gel residue levels. The large fluid volumes also increase significantly the cost of the treatment. Greater understanding of fracturing fluid properties has led to the development of a crosslinked fracturing fluid designed specifically for wells with BHT's above 250 deg F [121 deg C). The specialized chemistry of this fluid combines a high-ph hydroxypropyl guar gum (HPG) solution with a high-temperature gel stabilizer and a proprietary crosslinker. The fluid remains stable at 250 to proprietary crosslinker. The fluid remains stable at 250 to 350 deg. F [121 to 177 deg. C] for extended periods of time under shear. This paper describes the rheologial evaluations used in the systematic development of this fracturing fluid. In field applications, this fracturing fluid has been used to stimulate successfully wells with BHT's ranging from 250 to 540 deg. F [121 to 282 deg C). Case histories that include pretreatment and posttreatment production data are presented. Introduction Temperatures exceeding 250 deg F [121 deg C) and permeabilities less than 1.0 md are frequently encountered in permeabilities less than 1.0 md are frequently encountered in deep gas and geothermal wells. Successful economic completion of these wells requires that long, conductive fractures with optimal proppant distribution be created. Ultimately, the amount of production from these formations depends on the propped fracture length created. One successful stimulation technique used to create these long fractures is MHF. In these treatments, the fracturing fluids are often exposed to shear in the fracture for prolonged periods of time at high temperatures. Thus the fracturing fluids must exhibit extended shear and thermal stability at the high BHT'S. In addition, the fracturing fluid must not leak off rapidly into the formation, or the fracture may not be extended to the desired length. Many early treatments were limited by fracturing fluids that lost viscosity rapidly at high BHT's because of excessive thermal and/or shear degradation. Creation of a narrow fracture width, excessive fluid loss to the formation, and insufficient proppant transport resulted from the use of these low viscosity fluids. The solution to conventional fracturing fluid deficiencies was to develop a more efficient fracturing fluid (low polymer concentrations) with greater viscosity retention under shear at high temperatures, better fluid-loss control, and lower friction pressures. Generally, the components that make up crosslinked fracturing fluids include a polymer, buffer, gel stabilizer, and crosslinker. Each of these components is critical to the development of the desired fracturing fluid properties. The role of polymers in fracturing fluids is to properties. The role of polymers in fracturing fluids is to provide fracture width, to suspend proppants, to help provide fracture width, to suspend proppants, to help control fluid loss to the formation, and to reduce friction pressure in the tubular goods. Guar gum and cellulosic pressure in the tubular goods. Guar gum and cellulosic derivatives are the most common types of polymers used in fracturing fluids. The cellulosic derivatives are residue-free and thus help minimize fracturing fluid damage to the formation. However, the cellulosic derivatives are difficult to disperse because of their rapid rate of hydration. Guar gum and its derivatives are easily dispersed but produce some residue when broken. Buffers are used in conjunction with polymers so that the optimal pH for polymer hydration can be attained. When the optimal pH is reached, the maximal viscosity yield from the polymer is more likely to be obtained. The most common example of fracturing fluid buffers is a weak-acid/weak-base blend, whose ratios can be adjusted to that the desired ph is reached. However, some of these buffers dissolve slowly, particularly at cooler temperatures. Gel stabilizers are added to polymer solutions to inhibit chemical degradation. Examples of gel stabilizers used in fracturing fluids include methanol and various inorganic sulfur compounds. Other stabilizers are useful in inhibiting the chemical degradation process, but many interfere with the mechanism of crosslinking. The sulfur containing stabilizers possess an advantage over methanol, which is flammable, toxic, and expensive. SPEJ P. 623

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*SPE J.*25 (05): 629–636.

Paper Number: SPE-11900-PA

Published: 01 October 1985

Abstract

When filter-cake-building additives are used in fracturing fluids, the commonly applied static, 30-minute API filtration test is unsatisfactory, because in a dynamic situation (like fracturing) the formation of a thick filter cake will be inhibited by the shearing forces of the fracturing fluid. A dynamic, filter-cake-controlled, leakoff coefficient that is dependent on the shear rate and shear stress at the fracture face is, therefore, introduced. A test apparatus has been constructed in which the fluid leakoff is measured under conditions of temperature, rate of shear, duration of shear, and fluid-flow pattern as encountered under fracturing conditions. The effects of rock permeability, shear rate, and differential pressure on the permeability, shear rate, and differential pressure on the dynamic leakoff coefficient are presented for various, commonly used fracturing-fluid/fluid-loss-additive combinations. Introduction An important parameter in hydraulic fracturing design is the rate at which the fracturing fluid leaks into the formation. This parameter, known as fluid loss, not only determines the development of fracture length and width, but also governs the time required for a fracture to heal after the stimulation treatment has been terminated. The standard leakoff test is a static test, in which the effect of shear rate in the fracture on the viscosity of the fracturing fluid and on the filter-cake buildup is ignored. Dynamic vs. Static Tests The three stages in filter-cake buildup are spurt loss during initiation of the filter cake, buildup of filtercake thickness, during which time leakoff is proportional to the square root of time, and limitation of filter-cake growth by erosion. In the standard API leakoff test, 1 the fracturing fluid, with or without leakoff additives, is forced through a disk of core material under a pressure differential of 1000 psi [7 MPa), and the flow rate of the filtrate is determined. In such a static test, the third stage-erosion of the filter cake-is absent. In a dynamic situation there is an equilibrium whereby flow along the filter cake limits the filter-cake thickness, and the leakoff rate becomes constant. The duration of each of these stages depends on the type of fluid, the type of additive, the rock permeability, and the test conditions. The differences between dynamic and static filtration tests are shown in Fig. 1, where the cumulative filtrate volume (measured in some experiments with the dynamic fluid-loss apparatus described below) is expressed as a function of time (Fig. la) and as a function of the square root of time (Fig. ]b), The shear rate at the surface of the disk is either static (O s -1 ), or 109 s -1 or 611 s -1. The curves indicate that the dynamic filtration velocities are higher than those measured in a static test and increase rapidly with increasing shear rate. This is in agreement with the observations made by Hall, who used an axially transfixed cylindrical core sample along which fracturing fluid was pumped, while the filtrate was collected from a bore through the center. Fig. la shows how the lines were drawn to fit the data: Vc = Vsp + A t + Bt, .........................(1) where Vc = cumulative volume per unit area, t = filtration time, Vsp= spurt loss, A = static leakoff component, andB = dynamic leakoff component. In static leakoff theory, B =0 and then A =2Cw, twice the static leakoff coefficient.-3 Each of the terms in Eq. 1 represents one of the stages in the leakoff process-spurt loss, buildup of filter cake, and erosion of filter cake. Analysis of the experimental data shows that the spurt loss, Vsp, and the static leakoff component, A, are independent of the shear rate, but the dynamic component, B, varies strongly with the shear rate (see Table 1). This means that, the higher the shear rate, the more the leakoff process is controlled by the third stage. process is controlled by the third stage. One model commonly used is based solely on square-root-of-time behavior with a constant spurt loss. Fig. 1 shows that little accuracy is lost by describing the leakoff with a single square-root-of-time equation: Vc = VsP + m t,...........................(2) where the dynamic leakoff coefficient. Cw = 1/2m, depends heavily on shear. and the spurt loss remains the same as in Eq. 1 and independent of the shear rate Table 2 shows that the error in C, that arises as a result of measuring under static conditions can be more than 100%. SPEJ P. 629

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*SPE J.*25 (04): 491–501.

Paper Number: SPE-11625-PA

Published: 01 August 1985

Abstract

This paper gives a new formulation of fluid loss in hydraulic fracturing that is much more general than the classical theory while retaining its simplicity. The model allows many parameters to vary during filtration and can, therefore, simulate nonlinear effects. The model has been validated against laboratory data for Newtonian fluids and crosslinked gels. The results show that the finite length of the core, viscosity screenout, and shear sensitivity are important parameters that can be represented by the model. The standard analysis gives values of leakoff coefficients that will give incorrect, considerably higher leakoff when applied to field conditions. Introduction The estimate of fluid loss is an important part of a hydraulic fracturing treatment design. Although the control of fluid loss has improved with the use of modern fracturing fluids, the size of the generated fracture areas increases with the size of a job. Consequently, fluid loss can be important even in low-permeability reservoirs for large treatments. For design calculations, fluid loss has been treated in the past by use of the simplified theory proposed by Howard and Fast, which expresses the rate of filtration perpendicular to a fracture wall as a simple function of perpendicular to a fracture wall as a simple function of leakoff coefficients. The advantage of this approach, besides its simplicity, is that it can be directly (if not always correctly) related to experimental data on fluid filtration obtained in a laboratory. Apart from the correction of the derivation of the combined leakoff coefficient, very little has been done to improve the classical theory. With the recent development of a simulation approach to fracturing design, it has been recognized that fluid loss can be computed directly by solving the basic multiphase flow equations in porous media. Such an approach is more general and does not have many of the assumptions that limit the classical theory. However, the computational cost is much higher and the data required to describe the process are difficult to measure. This paper presents a generalization of the classical approach that includes the effect of several parameters that are variable in the field. The mathematical formulation includes the model of filter-cake behavior developed by the author and the results of the work of Blot et al., which improves the calculation of flow in the reservoir. The model is then formulated numerically, which allows us to introduce the effects of variable pressure, fluid viscosity, and different fluids contacting the wall in the filtration process, in accordance with real conditions during the treatment. Comparison with the experimental data of McDaniel et al. shows that the model is capable of exhibiting nonlinear behavior matching the laboratory data, which cannot be explained in terms of the previous simple theory. An important feature of the model is incorporation of the length of the core, which produces nonlinear behavior and can cause large errors in calculating the true value of the leakoff coefficient when the simple formulas are used. The new model retains the simplicity of the classical leakoff theory, although it is more comprehensive and potentially more accurate than the simulation-type potentially more accurate than the simulation-type leakoff calculations, because it is formulated in terms of measurable variables. Leak-off Models vs. Simulation The flow of fracturing fluid into the reservoir can be described, at least in principle, by the equations of multiphase flow in porous media. It would thus seem natural that an improved treatment of fluid loss would use numerical simulation of flow in the reservoir with the properties and pressure at the wall (behind the filter properties and pressure at the wall (behind the filter cake) as the boundary conditions. This approach, which we have taken in our current work, is indeed more general. It is not restricted by the assumption of one-dimensional (1D) flow, and it includes the effects of relative permeability and capillary pressure and handles changing conditions at the fracture face. However, the simulation approach also has problems. First, the process of fracture fluid filtration is more complicated than the reservoir multiphase flow. The properties of the invading fluid are greatly different from the properties of the invading fluid are greatly different from the reservoir fluid and are changing with time because of breakers, temperature changes, and mixing. The fluid can be miscible with one of the resident fluids. The proper formulation would require solution of three-phase proper formulation would require solution of three-phase flow (one phase being the fracture fluid) with relative permeability, capillary pressure, and viscosities permeability, capillary pressure, and viscosities changing with time. Even though such a formulation and solution is possible, the multiphase data are almost impossible to obtain because of the nonlinearity and instability of the gets. Consequently, one must make simplifying assumptions (e.g., the filtrate assumes the properties of the reservoir water). On the numerical level, an extremely fine grid would be required owing to usually very small penetration of the fracture fluid. SPEJ P. 491

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*SPE J.*25 (04): 482–490.

Paper Number: SPE-10259-PA

Published: 01 August 1985

Abstract

A test apparatus is designed to carry out dynamic and static fluid-loss tests of fracturing fluids. This test apparatus simulates the pressure difference, temperature, rate of shear, duration of shear, and fluid-flow pattern expected under fracture conditions. For a typical crosslinked fracturing fluid, experimental results indicate that fluid loss values can be a function of temperature, pressure differential, rate of shear, and degree of non-Newtonian behavior of the fracturing fluid. A mathematical development demonstrates that the fracturing-fluid coefficient and filter-cake coefficient can be obtained only if the individual pressure drops can be measured during a typical fluid-loss test. Introduction In a hydraulic fracturing treatment, the development of fracture length and width is strongly dependent on a number of key fluid and formation parameters. One of the most important of these parameters is the rate at which the fracturing fluid leaks, off into the created fracture faces. This parameter, identified as fluid loss, also influences the time required for the fracture to heal after the stimulation treatment has been terminated. This in turn will influence the final distribution of proppant in the fracture and will dictate when the well can be reopened and the cleanup process started. Historically, tests to measure fluid loss have been carried out primarily under what is characterized as static conditions. In such tests, the fracturing fluid is forced through filter paper or through a thin core wafer under a pressure gradient, and the flow rate at the effluent side is determined. Of course, the use of filter paper cannot account for reservoir formation permeability and porosity; therefore, the fluid-loss characteristics derived from such tests should be viewed as only gross approximations. The static core-wafer test on the other hand, reflects to some extent the interaction of the formation and fracturing-fluid properties. However, one important fluid property is altogether ignored in such static core-wafer tests. This is the effect of shear rate in the fracture on the rheology (viscosity) of fracturing fluid and subsequent effects of viscosity on the fluid loss through the formation rock. In the past, several attempts were made to overcome the drawbacks of static core-wafer tests by adopting dynamic fluid-loss tests. Although these dynamic tests were a definite improvement over the static versions, each had drawbacks or limitations that could influence test results. In some of the studies, the shearing area was annular rather than planar as encountered in the fracture. In other cases, the fluid being tested did not experience a representative shear rate for a sufficiently long period of time. An additional problem arose because most studies were performed at moderate differential pressures and temperatures. The final drawback in several of the studies was that the fluid flow and leakoff patterns did not realistically simulate those occurring in the field. In the first part of this paper, we emphasize the design of a dynamic fluid-loss test apparatus that possesses none of these drawbacks. In the second part of the paper, test results with this apparatus are presented for three different fluid systems. These systems are glycerol, a non-wall-building Newtonian fluid, a polymer gel solution that is slightly wall-building and non-Newtonian, and a crosslinked fracturing system that is highly non-Newtonian in nature and possesses the ability to build a wall (filter cake) on the fracture face (see Table 1). The fluids were subjected to both static and dynamic test procedures. In the third part of the paper, results of experiments carried out with crosslinked fracturing fluid for different core lengths, pressure differences, temperatures, and shear rates are compared and the significance of the difference of fluid loss is emphasized. Experimental Equipment and Procedure The major components of the experimental apparatus shown in Fig. 1 are a fluid-loss cell, circulation pump, heat exchanger, system pressurization accumulators, and a fluid-loss recording device. The construction material throughout most of the system is 316 stainless steel. The fluid loss is measured through a cylindrical core sample, 1.5 in. [3.81 cm] in diameter, mounted in the fluid-loss cell. Heat-shrink tubing is fitted around the circumference of the core and a confining pressure is maintained to prevent channeling. Fracturing fluid is circulated through a rectangular channel across one end of the core. SPEJ P. 482^

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*SPE J.*25 (03): 371–379.

Paper Number: SPE-10313-PA

Published: 01 June 1985

Abstract

This report discusses the philosophy, design, and implementation of small, precise, hydraulic fracture stimulations as applied in a micellar pilot in Salt Creek field, located in central Wyoming. Wellbore damage and relatively low permeability were resulting in low injection/withdrawal rates in the 1-acre [4046-M ] pilot in this field. Unchanged, these low rates would extend the pilot life by an unacceptable amount and also result in oil production rates too small for meaningful analysis. Accordingly, the decision was made to fracturestimulate the pilot wells on the basis of reservoir stimulation, which showed that the creation of very short (90 ft [29.5 m] tip-to-tip) fractures would not "harm" evaluation of the pilot's performance. Normal stimulation practices in this area would not give the control desired for this pilot situation to create a 90-ft-[29.5-m-] long fractures in a formation with a thickness of 100 ft [32.8 m]. The procedure that was developed consisted of measuring bottomhole treating pressure (BHTP) while pumping the pad, using these data to calculate the required sand-laden fluid volume, and then switching directly from pad to heavy sand concentration. A postappraisal of the treatments showed that BHTP measurement was necessary since the pressure varied from theoretical behavior for each well. After initial pressure increases that were predictable, a critical pressure was reached for each case and the value of this pressure (which governed slurry requirements) varied by 25 % from well to well. The effects of the treatments also were evaluated with postfracture pressure falloff tests (PFOT). The stimulations performed generally were successful (fracture design/pFOT lengths of 156/146, 90/100, 134/150, and 55/20), confirming that it is possible to create short, controlled hydraulic fractures by using the procedure outlined in this paper. Introduction The Salt Creek field is located in the Casper Arch section of central Wyoming and originally was discovered around 1900. Several productive formations are present in the field, but the major producer is the Second Wall Creek formation, which was the target for the micellar pilot. The Second Wall Creek is found at a depth of 2,200 ft [722 m], and current reservoir pressure in the pilot area is 580 psi [4 MPa]. The basic problem being experienced in the pilot was low injection/withdrawal rates caused by relatively low permeability, wellbore damage, and the requirement that wells be operated below formation parting pressure. These low rates were extending the pilot life by an unacceptable amount and would eventually result in oil production rates too low for meaningful interpretation. It was decided that hydraulic fracturing stimulation was the best solution, provided that short, controlled fractures could be created. Such a decision raises several questions. Theoretically, when a vertical hydraulic fracture is initiated, it will grow as a "penny-shaped" fracture until it encounters some barrier to vertical growth. Since the Second Wall Creek formation is on the order of 100 ft [32.8 m] thick, it would be seemingly difficult to limit fracture length to 90 ft [29.5 m]. Also, borehole televiewer and downhole television logs on offset openhole wells had shown the wells surveyed in the area to be "fractured," although these fractures were not Propped and, thus, not particularly conductive. Given this, the goal was respecified to create a propped fracture of the required length, without regard to the hydraulic length, and then to operate the wells below fracture closure pressure. It also was desired to create a propped fracture that calculated the required length from a standard PFOT analysis. In similar situations, the industry in the past has used a low-rate, low-viscosity, low-proppant-concentration approach to "dribble-in" a short fracture. However, it was felt this approach did not allow the control needed for this pilot application. Major disadvantages in the prior procedure included the following: inadequate knowledge and poor predictive capabilities concerning proppant settling made it difficult to design fracture length accurately; low-viscosity fluid probably would result in a "triangular"-shaped proppant distribution; and low sand concentration would result in nonuniform and inadequate fracture conductivity. Because of these disadvantages and the need to create precise-length fractures in the pilot area, a somewhat different approach was needed for these stimulations. The development of this fracturing procedure is presented in detail in the following discussions on "fracturing parameters." The basic idea was to pump a relatively large pad, thus ensuring adequate width, and then to switch directly to a heavy-concentration slurry. Since the fracturing fluid was a crosslinked polymer gel, the proppant would be perfectly suspended for the short pump times involved, thus ensuring vertically uniform conductivity . If fracture height could be determined, then the only major unknown determining propped length would be fracture width. Width is proportional to the net fracturing pressure (BHTP-fracture closure pressure), which is a function of the fluid properties. SPEJ P. 371^

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*SPE J.*25 (02): 157–170.

Paper Number: SPE-11634-PA

Published: 01 April 1985

Abstract

Lightweight, intermediate-strength proppants have been developed that are intermediate in cost between sand and bauxite. A wide variety of proppant materials is characterized and compared in a laboratory fracture conductivity study. Consistent sample preparation, test, and data reduction procedures were practiced, which allow a relative comparison of the conductivity of various proppants at intermediate and high stresses. Specific gravity, proppants at intermediate and high stresses. Specific gravity, corrosion resistance, and crush resistance of each proppant also were determined. proppant also were determined. Fracture conductivity was measured to a laminar flow of deaerated, deionized water over a closure stress range of 6.9 to 96.5 MPa [1,000 to 14,000 psi] in 6.9-MPa [1,000-psi] increments. Testing was performed at a constant 50 degrees C [122 degrees F] temperature. Results of the testing are compared with values from the literature and analyzed to determine proppant acceptability in the intermediate and high closure stress regions. Fracture strengths for porous and solid proppants agree well with calculated values. Several oxide ceramics were found to have acceptable conductivity at closure stresses to 96.5 MPa [14,000 psi]. Resin-coated proppants have lower conductivities than uncoated, intermediate-strength oxide proppants when similar size distributions are tested. Recommendations are made for obtaining valid conductivity data for use in proppant selection and economic analyses. proppant selection and economic analyses. Introduction Massive hydraulic fracturing (MHF) is used to increase the productivity of gas wells in low-permeability reservoirs by creating deeply penetrating fractures in the producing formation surrounding the well. Traditionally, producing formation surrounding the well. Traditionally, high-purity silica sand has been pumped into the created fracture to prop it open and maintain gas permeability after completing the stimulation. The relatively low cost, abundance, sphericity, and low specific gravity of high-quality sands (e.g., Jordan, St. Peters, and Brady formation silica sands) have made sand a good proppant for most hydraulic fracturing treatments. The closure stress on the proppants increases with depth, and even for selected high-quality sands the fracture conductivity has been found to deteriorate rapidly when closure stresses exceed approximately 48 MPa [7,000 psi]. Several higher-strength proppants have been developed to withstand the increased closure stress of deeper wells. Sintered bauxite, fused zirconia, and resin-coated sands have been the most successful higher-strength proppants introduced. These proppants have improved proppants introduced. These proppants have improved crush resistance and have been used successfully in MHF treatments. The higher cost of these materials as compared to sand has been the largest single factor inhibiting their widespread use. The higher specific gravity of bauxite and zirconia proppants not only increases the volume cost differential compared to sand but also enhances proppant settling. Lower-specific-gravity proppants not only are more cost effective but also have the potential to improve proppant transport. Novotny showed the effect of proppant diameter on settling velocity in non-Newtonian fluids and concluded that proppant settling may determine the success or failure of a hydraulic fracturing treatment. By using the same proppant settling equation as Novotny, the settling velocity of 20/40 mesh proppants is calculated for four different specific gravities and shown as a function of fluid shear rate in Fig. 1. The specific gravity of bauxite is 3.65 and sand is 2.65; therefore, bauxite is 37.7 % more dense than sand. The settling velocity for bauxite, as shown in Fig. 1, however, is approximately 65 % higher than sand. Work on proppants with specific gravities lower than bauxite was initiated to improve the transport characteristics of the proppant during placement. It has been demonstrated that vertical propagation of the fracture can be limited by reducing the fracturing fluid pressure. The viscosity range of existing fracturing pressure. The viscosity range of existing fracturing fluids makes minimizing fluid viscosity a much more effective method of controlling pressure than lowering the pumping rate. A potential advantage of decreasing the pumping rate. A potential advantage of decreasing the specific gravity of the proppant is that identical proppant transport to that currently achievable can take place in lower-viscosity fluids. (Alternatively, higher volumes of proppant can be pumped in a given amount of a proppant can be pumped in a given amount of a high-viscosity fracturing fluid.) Not only are low-viscosity fluids capable of allowing better fracture control, they are also less expensive. More importantly, it recently was shown that the conductivity of a created hydraulic fracture in the Wamsutter area is about one-tenth of that predicted by laboratory conductivity tests. P. 157

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*SPE J.*25 (02): 303–312.

Paper Number: SPE-11689-PA

Published: 01 April 1985

Abstract

Numerical studies of the effects of injection on the behavior of production wells completed in fractured two-phase geothermal reservoirs are presented. In these studies the multiple-interacting-continua (MINC) method is employed for the modeling of idealized fractured reservoirs. Simulations are carried out for a five-spot well pattern with various well spacings, fracture spacings, and pattern with various well spacings, fracture spacings, and injection fractions. The production rates from the wells are calculated using a deliverability model. The results of the studies show that injection into two-phase fractured reservoirs increases flow rates and decreases enthalpies of producing wells. These two effects offset each other so that injection tends to have small effects on the usable energy output of production wells in the short term. However, if a sufficiently large fraction of the produced fluids is injected, the fracture system may become liquid-filled and an increased steam rate is obtained. Our studies show that injection greatly increases the long-term energy output from wells because it helps extract heat from the reservoir rocks. If a high fraction of the produced fluids is injected, the ultimate energy recovery will increase many-fold. Introduction At present, reinjection of geothermal brines is employed or being considered at most high-temperature geothermal fields under development. At many geothermal fields, primarily those in the U.S. or Japan, reinjection is a primarily those in the U.S. or Japan, reinjection is a necessity because environmental considerations do not permit surface disposal of the brines (unacceptable permit surface disposal of the brines (unacceptable concentrations of toxic minerals). At other fields (e.g., The Geysers, CA) reinjection is used for reservoir management to help maintain reservoir pressures and to enhance energy recovery from the reservoir rocks. The effectiveness of injection in maintaining reservoir pressures has been illustrated at the Ahuachapan geothermal field in El Salvador. During the last decade various investigators have studied the effects of injection on pressures and overall energy recovery from geothermal fields. Theoretical studies have been carried out by Kasameyer and Schroeder, Lippmann et al., O'Sullivan wad Pruess, Schroeder et al., and Pruess, among others. Site-specific studies were reported by Morris and Campbell on East Mesa, CA; Schroeder et al. and Giovannoni et al. on Larderello, Italy; Bodvarsson et al. on Baca, NM; Tsang et al. on Cerro Prieto, Mexico; and Jonsson and Pruess et al. on Krafla, Iceland. These studies have given valuable insight into physical processes and reservoir response during injection. However, there is limited understanding of injection effects in fractured reservoirs, especially high-temperature, two-phase systems. Fundamental studies and quantitative results for the design of injection programs in such systems are greedy needed. The objectives of the present work are to investigate the effects of injection on the behavior of fractured two-phase reservoirs. Several questions will be addressed. How will injection affect flow rates and enthalpies of the production wans? Can injection increase the short-term usable energy output of well? What are the long-term effects of injection? How is the efficiency of injection dependent on factors such as well spacing and fracture spacing? Reliable answers to these questions should be valuable for field operators in the design of injection systems for two-phase fractured reservoirs. Approach In the present work we consider wells arranged in a five-spot pattern (Fig. 1). Because of symmetry we only need to model one-eighth of a basic element as shown in Fig. 1; however, our results always are presented for the full five spot. The "primary" (porous medium) mesh shown in Fig. 1 consists of 38 elements; some of the smaller ones close to the wells are not shown. The mesh has a single layer, so that gravity effects are neglected. The fractured reservoir calculations are carried out by the MINC method, which is a generalization of the double-porosity concept introduced by Barenblatt et al. and Warren and Root. The basic reservoir model consists of rectangular matrix blocks bounded by three sets of orthogonal infinite fractures of equal aperture b and spacing D (Fig. 2a. M the mathematical formulation the fractures with high transport and low storage capacity are combined into one continuum and the low-permeability, high storativity matrix blocks into another. The MINC method treats transient flow of fluid (steam and/or water) and heat between the two continua by means of numerical methods. Resolution of the pressure and temperature gradients at the matrix/fracture interface is achieved by partitioning of the matrix blocks into a series of interacting partitioning of the matrix blocks into a series of interacting continua. SPEJ P. 303

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*SPE J.*25 (01): 78–88.

Paper Number: SPE-11332-PA

Published: 01 February 1985

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^

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*SPE J.*25 (01): 46–54.

Paper Number: SPE-11648-PA

Published: 01 February 1985

Abstract

Measurements of width and pressure in a propagating hydraulic fracture have been made in tests conducted at the U.S. DOE's Nevada test site. This was accomplished by creating an "instrumented fracture" at a tunnel complex (at a depth of 1,400 ft [425 m]) where realistic insitu conditions prevail, particularly with respect to stress and geologic features such as natural fractures and material anisotropy. Analyses of these data show that the pressure drop along the fracture length is much larger than predicted by viscous theory, which currently is used in models, This apparently is caused by the tortuosity of the fracture path, multiple fracture strands, roughness, and sharp path, multiple fracture strands, roughness, and sharp turns (corners) in the flow path resulting from natural fractures and rock property variations. It suggests that fracture design models need to be updated to include a more realistic friction factor so that fracture lengths are not overestimated. Introduction Hydraulic fracturing, which has proved a valuable well-stimulation technique for low-permeability reservoirs, has been the subject of considerable study for nearly 30 years. Many theories have been advanced to model the process and aid in the design of the treatment. In process and aid in the design of the treatment. In general these theories differ mainly in the approach used to model the rock deformation (i.e., the width equation). The fluid mechanics model in all cases is based on A pressure drop that is derived theoretically for parallel pressure drop that is derived theoretically for parallel flow between smooth plates or in smooth pipes (at least for laminar flow, which prevails in the large majority of fracture treatments). Attempts to verify these models have been generally limited to laboratory studies, such as those of Blot et al., which are difficult to perform and may be impossible to scale if rock is used, postfracture well testing or production history matching analyses to deduce fracture length (e.g., those of Holditch and Lee ), analyses of fracturing pressure records by Nolte and Smith, 15 and wellbore width measurements by Smith. 16 The data from these studies are very limited and it is difficult to arrive at a consensus on the validity of the previously mentioned models. However, well testing and production history matching studies usually show that fracture lengths are overestimated considerably. This study is an initial attempt to measure pressure and width in propagating hydraulic fractures under conditions that avoid some of the size and scaling problems of laboratory tests and yet provide greater accessibility and instrumentation than field tests. These experiments were conducted at the U.S. DOE's Nevada test site, where hydraulic fractures were created and monitored from an existing tunnel complex. This initial experiment was conducted to determine whether it was feasible to measure important fracture parameters accurately and obtain significant information about fracture growth processes. Of particular importance was the pressure processes. Of particular importance was the pressure drop along the length of the propagating fracture. Background Hydraulic fractures are not the smooth parallel plates that they usually are modeled to be. Mineback experiments 17–20 have shown that there is considerable surface roughness and waviness, common en echelon fracturing and multiple stranding, and significant offsets when natural fractures are intersected. Natural fractures in core show many of these same characteristics, although the fracturing mechanism admittedly may be different. Laboratory experiments also show many of these same effects. Lamont and Jessen demonstrated the offset of hydraulic fractures at natural joints and showed the surface waviness and roughness of the fracture. Blot et al. 13 found that the roughness of the fracture surface depended on rock type and decreased with increasing confining stresses. Smith 16 measured fracture width at the wellbore with a TV camera and observed consider-able width variation or large-scale roughness. The effect of such variability of the fracture shape, path, and surface features must be an increase in pressure drop along the length of the fracture compared with that of the ideal case. This may have a significant influence on the resultant widths, lengths, and heights of the induced fracture. In the ideal case, the pressure drop for laminar flow usually is represented by a friction factor, (1) where NRe is the Reynolds number and C depends on the geometry. Huitt, Rothfus and Monrad, Rothfus et al. and Whan and Rothfus describe correlations for flow through parallel plates and tubes for both laminar and turbulent flow. For relatively smooth tubes C is 16 and for smooth parallel plates it is. Elliptic cross sections of zero ellipticity are calculated to have a C value of 2 pi 2. A generally held belief from all these studies is that in the laminar regime (NRe less than 2,000), flow through parallel plates is independent of roughness. parallel plates is independent of roughness. SPEJ P. 46

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*SPE J.*25 (01): 55–66.

Paper Number: SPE-11871-PA

Published: 01 February 1985

Abstract

In the first part of this paper, the title subject is studied by introducing two modified singular integrals. The problem is reduced to a set of singular integral equations; and problem is reduced to a set of singular integral equations; and it is solved numerically by employing the Lobatto-Chebyshev method. The stress intensity factor at the fracture tips of a hydraulically induced fracture in a layered medium is calculated in the second part of the paper. The effect of the fluid pressure and the in-situ stress gradient as well as the effect of the relative layer material properties on the magnitude of the stress intensity factors are properties on the magnitude of the stress intensity factors are studied numerically. It has been shown that the relative magnitude of the stress intensity factor at the fracture tips can he used to indicate the direction of fracture movement. Introduction Extensive analyses of bonded half-planes containing cracks have been conducted by many authors. In general, there are two approaches to this problem. In the first approach, the Mellin transform is applied to the field equations. This leads to a set of integral equations, which, in turn, are solved numerically. Erdogan and Biricikoglu, Cook and Erdogan, Ashbaugh, and Erdogan and Aksogan have used this method in their analyses of stresses in the bonded planes containing straight cracks. In the other approach, the same problem is studied by employing the complex potential function of Kolosov and Muskhelishvili. For a general discussion of this method, see Refs. 5 through 9. By using this method, the general problem of a half-plane containing a system of curvilinear problem of a half-plane containing a system of curvilinear cracks is solved by Ioakimidis and Theocaris. The associated boundary value problem is deduced to a system of complex singular integral equations, which then are solved numerically by applying the Lobatto-Chebyshev method. In this paper, the problem is studied by using a method very similar to that developed in Ref. 10, However, since we are studying the propagation of a hydraulically induced fracture in a layered rock medium, the loading condition of our problem is different from that previously cited. In our formulation, the cracks are subject to different distributions of internal loadings. As demonstrated later, although our method is, in principle, similar to that reported in Refs. 10 and 11, it differs in many ways. Our method is suitable for solving the problems of two cracks situated in two different half-planes and oriented at an arbitrary angle with respect to one another and studying the problems pertaining to the environment of hydraulic fracturing. It also should be mentioned here that the method used in this study is an extension of the method developed by Lu in his study of a plane problem of many cracks and the problem of a partially bonded plate. In our analysis of the problem, the plane of the fracture is assumed to be in a condition of plane strain. In view of the order of magnitude differences between the fracture length, height, and width of a hydraulically induced fracture, we believe that this assumption is acceptable except, perhaps, at a very early stage of fracturing. The general problem of two bonded half-planes containing many cracks of arbitrary shapes is considered first. The problem then is reduced to a case of two arbitrarily oriented straight cracks. The solution is carried out in full. Numerical values of the stress intensity factor at the fracture tips pertaining to the containment of a hydraulically induced fracture are presented and discussed at the end of the paper. Formulation of the Problem In the following derivations, we follow the notations in Ref. 15; for completeness and clarity, some obvious results are listed without further referencing. Throughout the paper, we use the superscripts phi (x) and psi (x) for x epsilon X (along the interface); the subscripts phi (s) and psi (s) for s epsilon L (along cracks); and zeta epsilon L+X; x, xi epsilon X; and s, L in integrals. Consider an elastic plane (under either plane stress or plane strain condition) made by bonding together two plane strain condition) made by bonding together two planes of different materials, where k +, G+ and k -, planes of different materials, where k +, G+ and k -, G - are the material constants for the upper (Z + ) and the lower (Z-) plane, respectively. Let there be p nonintersecting smooth cracks. Lj =ajbj (j=1..... p) on both these half-planes. Let the intensity (force/unit length) of the external load applied on the surface of crack Lj be Xj (s) + i Yj (s), where s is the complex coordinate of a point on Lj. SPEJ P. 55

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*SPE J.*25 (01): 39–45.

Paper Number: SPE-12030-PA

Published: 01 February 1985

Abstract

In this paper we describe the use of a novel technique, laser Doppler anemometry (LDA), to obtain information on fracturing fluid behavior. This technique permits measurement of fluid velocity at any point in a flow system. By scanning across the flow geometry, it is possible to obtain the velocity profile, which is related, possible to obtain the velocity profile, which is related, in turn, to the rheology of the fluid. At low shear rates, velocity profiles obtained for aqueous solutions of hydroxypropyl guar showed significant deviations from those calculated using known power law parameters. The investigation was extended by power law parameters. The investigation was extended by conducting a series of rheological experiments using rotational and capillary viscometers over a wide shear-rate range (10(–2) to 2 × 10(3) seconds (–1)) The data have been fitted to a three-parameter Ellis model, and the velocity profiles calculated from these data agree well with profiles calculated from these data agree well with experimental ones. The immediate results of this work are of interest in proppant transport modeling and correlate well with proppant transport modeling and correlate well with published data that show that apparent viscosities obtained published data that show that apparent viscosities obtained from proppant settling velocities are lower than those obtained from power law parameters. Introduction The role played by the rheology of fracturing fluids in the design of stimulation treatments does not need to be stressed. Friction pressure through pipes and/or annuli, fracture geometry, and proppant placement depend primarily on the rheological properties of treating fluids. primarily on the rheological properties of treating fluids. Fracturing fluids usually exhibit a non-Newtonian behavior. Under isothermal conditions, their rheological properties may be shear-dependent only, as in linear gels, properties may be shear-dependent only, as in linear gels, or much more complex (i.e., time/shear-dependent), as in the case of crosslinked gels. Several types of rheometers have been used to characterize the behavior of fracturing fluids: coaxial cylinder viscometers, cone and plate rheometers, and capillary viscometers. These traditional means of evaluating non-Newtonian rheology are subject to several drawbacks inherent in the measuring technique itself or in the type of fluid under study. For instance, coaxial cylinder and capillary viscometers do not allow for the direct computation of the shear rate that is applied to measured fluids. For a time-independent non-Newtonian fluid, a proper interpretation of the measurements must involve the determination of the first, or even higher order, derivative of the experimental curve Copyright 1985 Society of Petroleum Engineers (rotational speed/torque or flow-rate/pressure-drop curves). The time-dependent nature of some fluids complicates the problem, since, in these viscometers, fluid particles experience different shear rates and, therefore, particles experience different shear rates and, therefore, different shear histories. On the experimental side, difficulties may arise from the three-dimensional structure and from the correlative elasticity of crosslinked fluids-e.g., the Weissenberg effect in coaxial cylinder viscometers or the ejection of the fluid from cone and plate rheometers in steady rotation even at low speeds. Some of the limitations encountered in the rheological characterization of time-dependent fracturing fluids may be overcome with an improved experimental techniqueLDA. LDA is a direct and nondestructive technique for measuring particle velocities in a moving fluid. Therefore, it allows characterization of the flow kinematics. The technique was tested first on the simplest case of a time-independent fluid to evaluate its validity for fracturing rheological studies. In the following sections, after a description of the LDA technique and of the equipment, we illustrate the use of the LDA by the study of a noncrosslinked fluid that has been characterized using classical rheometrical methods. We stress the importance of the frequently forgotten Newtonian behavior of these linear gels at low shear rates. Implication of the results on the design of fracturing treatments also is discussed. The LDA Technique Principle LDA uses the Doppler shift of light scattered Principle. LDA uses the Doppler shift of light scattered by moving particles in a flow system to determine particle velocity and thus measure the fluid velocity at a given point. In dual-beam mode, the most common technique, two point. In dual-beam mode, the most common technique, two coherent laser beams of equal intensity intersect, and light scattered in any one direction is picked up by a photodetector (Fig. 1). The difference, fD, between the photodetector (Fig. 1). The difference, fD, between the two scattering frequencies, fsi and fs2 is independent of the scattering direction, es, and proportional to a velocity component, Vx, of the particles flowing through the beam intersection (Fig. 2). LDA has the great advantage of being a direct and nonperturbative velocimetry technique in that only light beams enter the flow through a transparent window. No flow calibration is required, and no probe (hot wire, turbine) is necessary inside the flow, thereby eliminating any disturbances. SPEJ P. 39

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*SPE J.*24 (05): 575–581.

Paper Number: SPE-10258-PA

Published: 01 October 1984

Abstract

The large increase in the use of crosslinked fracturing fluids in the past decade has led to the need for accurate evaluation of their flow properties. Traditional rotational viscometers are inadequate for studying the rheology of these crosslinked fracturing fluids, hereafter called "gels." A recently developed coiled-pipe viscometer is described, and gel response to various temperature and shear histories during preparation and testing is presented as determined by the pipe viscometer. If gel flow properties in the fracture are to be studied accurately with any viscometer, then preparation of the gel, thermal energy input, and mechanical energy input to the test sample should be controlled to duplicate the gel of the fracture. The pipe viscometer developed has the following attributes. Gel preparation is an integral part of the viscometer. Each element of the gel is subjected to the same degree of shear while mixing. The gel develops in-line as it moves to the test section of the viscometer. There are no stagnant periods. Heat transfer occurs from the walls of the conduit to the fluid in flow as in the fracture. Parallel flow sections are incorporated for scale-up information. Results are presented to elucidate the mechanism of gel formation and deterioration, gel stability at high temperatures, and the possible occurrence of slip flow in the fracture. The coiled-pipe viscometer shows potential to stimulate fluid preparation and flow in the fracturing process. Introduction Crosslinked fracturing fluids introduce complex flow behavior that has raised concerns about the efficacy of conventional study means developed for simpler non-Newtonian fluids. These particular fracturing fluids have characteristics that make their flow measurements more difficult than other non-Newtonian fluids. A basic water-soluble polymer, hydroxypropyl guar, (a guar gum derivative) is currently in general use. The guar gum molecule is a high-molecular-weight carbohydrate polymer or polysaccharide. Propylene oxide reacted with the guar yields the hydroxypropyl polymer used in the fracturing fluids. The modified guar gums can be gelled by transition metal ions. The crosslinked fracturing fluids used in this study included such polysaccharides reacted with an organic titanate chelate as a crosslinker. A few tests were made with the borate ion as crosslinker. In addition to pH. reactant types, and reactant concentrations, the extent of crosslinking-and thus, flow behavior-depends on shear and temperature levels during preparation for many crosslinked fracturing fluids. After the gel is formed in the initial preparation steps, its rheology depends on shear history. Then, not only is the rheology dependent on temperature in the Arrhenius sense, but thermal deterioration of the crosslinking bond significantly affects viscosity at temperatures common to the formations to be fractured. There are other complicating factors. A static gel realizes a more rigid structure than a gel in movement. Initial energy inputs-thermal and mechanical-affect the degree of crosslinking and thus flow behavior or proppant transport capability. Rotational viscometers, the traditional means of evaluating non-Newtonian rheology, are less effective when crosslinked gels are tested. Samples necessarily are prepared in batches and consequently this introduces a stagnant period in transfer to the viscometer-a time in which a gel structure is realized that would not occur in the fracture. There is further difficulty if some fluid remains unsheared in the bottom of the cup during the test. The batch preparation technique, common for rotational viscometer use, can affect the measured rheology. The energy input might vary, unequal shearing of portions of the batch might occur, and the shearing action might not be reproducible. Since the gel structure may degrade with shear, a series of tests on the same sample may give misleading results. The pipe viscometer reported in this paper has advantages over other pipe viscometers when used with crosslinked fluids. It overcomes deficiencies such as: fluids in traditional pipe viscometers are batch mixed before entering the viscometer; pipe lengths may be insufficient to detect stress-induced slip flow; shear is introduced to the samples other than from pipe walls; and capability might not exist to test such fluids at the high temperatures encountered in some reservoirs. A pipe viscometer was designed and constructed to overcome these deficiencies and perform specifically for testing crosslinked fracturing fluids. SPEJ P. 575^

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*SPE J.*24 (04): 375–381.

Paper Number: SPE-11024-PA

Published: 01 August 1984

Abstract

A technique has been developed to estimate the potential effects of directionally drilled wellbore orientation on pattern waterflood oil recovery in anisotropically fractured reservoirs. The technique attempts to quantify the tradeoff between drilling directional wells either more vertically or better aligned with the major fracture orientation in situations where simple vertical wells are not possible. Among the incentives to deplete some reservoirs with directionally drilled wells are the ability to access reserves located beneath large bodies of water from shore or island structures and the economy of centralized surface facilities. The orientation of these directionally drilled wells in anisotropically fractured oil reservoirs may have a significant impact on recovery efficiency. The described method involves combining the directional permeability characteristics of the reservoir caused by fractures, drilling accuracy, and the proposed wellbore orientation to estimate the volume of reservoir that may be affected by a nonvertical well. The distribution of fractures in the reservoir, average fracture length, and effective vertical permeability are noted as being major factors influencing the effect of directionally drilled wells on oil recovery. When applied to the Norman Wells oil field (N.W. Ter., Canada), it was possible to identify elongated target areas within which any directionally drilled well is expected to have similar oil recovery. Introduction Recent advances in drilling technology have made it possible to drill wellbores deviated from the normal vertical position, up to and including completely horizontal. This type of directional drilling will allow the depletion of oil reservoirs that are located beneath surface obstacles by drilling wells from remote surface locations. Access to many of the world's remaining petroleum reserves, in such offshore areas as the Canadian Beaufort Sea and the east coast, will have to be by drilling from conveniently located island or platform structures. The Norman Wells oil reservoir, of which approximately 60% lies beneath the MacKenzie River, is a current example of how directional drilling will make oil recovery possible. The proposed reservoir depletion program involves drilling wells from centralized surface facilities to program involves drilling wells from centralized surface facilities to implement a pattern waterflood oil-recovery scheme (Fig. 1). The wells will be deviated at as much as 700 to the vertical to reach the target locations from the centralized surface locations (Fig. 2). The reservoir rock is anisotropically fractured, and optimization of the wellbore orientation with respect to the fractures was recognized as an area of study with considerable potential for increasing oil recovery. Initial development planning indicated that wells should be as vertical as possible and aligned with the main fracture trend. This simple guideline resulted in many technically impossible wells and wells with poor anticipated oil recovery. The optimization procedure developed here subsequently was applied in the development planning of the Norman Wells reservoir and is believed to have helped maximize oil recovery while maintaining technically feasible and economically viable well designs. Background geological data and details of the proposed Norman Wells development plan are documented in Refs. 1 and 2. Theory Several analytical methods have been presented for determining the vertical and areal sweep efficiencies of pattern waterflood operations. These methods, or more sophisticated reservoir simulation techniques, may be employed to determine the recoverable reserves associated with the waterflooding of homogeneous reservoirs or reservoirs composed of discrete homogeneous units. The presence of fractures in an oil reservoir adds a new dimension to this problem because the flow characteristics of fractured rock systems are difficult to predict. SPEJ p. 375

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*SPE J.*24 (03): 249–255.

Paper Number: SPE-10962-PA

Published: 01 June 1984

Abstract

A flow loop was used to evaluate the stability of fracturing fluids at high temperatures. The design provides enough pressure to prevent vaporization of water-base systems up to 350F [177C]. Crosslinked polymer systems from four service companies were evaluated at 180 and 245F [82 and 118C]. The tests showed that crosslinked fracturing fluids degrade with temperature and shear, losing much of their viscosity and proppant-carrying capacity in a few hours. Thermal stability is a major factor in selecting gels for fracturing deep, high-temperature reservoirs. Introduction Job failures in deep, hot wells can be caused by "sand-outs." These sandouts, or "screenouts," can result from inadequate carrying capacity (reduced viscosity) or too high a fluid loss (dehydration) for the polymer loading of the fracturing fluid. This study investigates the reduction in viscosity of crosslinked fracturing fluids with time at temperatures and shear rates approximating downhole conditions. A flow loop was used to investigate the rheological properties of fracturing fluids as a function of time under shear at temperatures as high as 245F [118C]. The pipe loop configuration was chosen because our field experience indicated that rotational viscometers were too "kind" to fracturing systems. We experienced sandouts that should not have happened if the crosslinked fracturing systems used had the flow characteristics that rotational viscometry indicated they had. The flow loop configuration also avoids some of the problems inherent in rotational viscometers, such as fluid climbing the shaft and contamination of the sample. Flow loops have been used to condition and evaluate drilling fluids at high temperatures. However, some of these instruments were not designed to give quantitative results. Our instrument permits measurement of apparent viscosity at known shear rates, flow index, and consistency index, all at high temperatures. This paper describes the flow loop, test procedures used, and results obtained. The flow loop gives reproducible results at high temperatures and allows the evaluation of the rheological properties of fracturing fluids under flow conditions nearer those encountered in actual fracturing jobs than do rotational, high-temperature instruments. Previous Work Previous Work Very little information has been reported on temperature stability of crosslinked fracturing fluids, especially under shearing conditions. Elbel and Thomas discussed the use of viscosity stabilizers for high-temperature fracturing. Conway et al. subjected crosslinked fracturing fluids to shear and to high temperatures. Hsu and Conway described the development of more stable crosslinked gels for use in deep, hot formations. All these investigators used the Fann 50 viscometer for their work, although Conway et al. used a pump to shear the samples before testing. Flow Loop Description The flow loop was built to evaluate the flow properties of drilling fluids, fracturing fluids, heavy crudes, and waxy crudes. The current test system can operate up to 350F [177C] and 250 psi [1,724 kPa]. The flow loop schematic is shown in Fig. 1. The test fluid is poured into the mixing vessel (Pfaudler) and then flows through the pump. The capacity of the system--including the heat exchangers, the test section, and the mixing unit--is about 25 gal [0.095 m3]. A high-accuracy, oval gear flowmeter was used for flow rate measurement. The meter was used only intermittently because it is a high- shear device that was originally intended to handle oil-base systems. A low-shear magnetic flowmeter has been added to the loop. The magnetic flowmeter shears the test fluids much less than the gear meter and can thus be left on continuously when testing shear-sensitive fracturing fluids. A differential pressure transducer measures pressure drop over the 20-ft-long [6.1-m], 0.957-in.-ID [2.43-cm] test section. The system is heated with a hot oil heater. An in-line, variable-shear-rate cup and bob viscometer allows continuous measurement of apparent viscosity at test temperature and pressure. It also-permits the running of rheograms to measure the flow pressure. It also-permits the running of rheograms to measure the flow parameters of the test fluid at any time during a test. parameters of the test fluid at any time during a test. A remote indication panel provides displays of flow rate, pressure drop, temperatures, shear stress, and shear rate. These values also are recorded on paper and magnetic tapes. A detailed description of the equipment, including recent improvements, is given in the Appendix. The improvements include the magnetic flowmeter mentioned previously, an automated data collection and reduction system, and a smaller pump. SPEJ p. 249

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*SPE J.*24 (03): 256–268.

Paper Number: SPE-10377-PA

Published: 01 June 1984

Abstract

This paper describes fracturing experiments in dry blocks of various rock materials. The results have application to evaluation of hydraulic fracturing theories. The block dimensions were 3 in.×4 in.×12 in. [7.6 cm×10.2 cm×30.5 cm] with metal plates epoxied to the 3-in.×12-in. [7.6-cm×30.5-cm] faces. Remaining faces were coated with soft epoxy to provide an impermeable jacket. The blocks were loaded in a pressure cell with an upper movable piston bearing on the 3-in.×4-in. [7.6-cm×10.2-cm] faces. A servo-controlled press applied constant stress to these faces higher than a lateral confining stress applied by oil pressure. Fractures were initiated by injection of various fluids into a small notch located on a center plane parallel to the 4-in.×12-in. [10.2-cm×30.5-cm] faces. Fracture growth along the same plane was assured by the stress conditions. Use of these experiments to test theories of fracture propagation required measurement of three variables, fracture width b i , and propagation pressure p i at the notch entrance, and fracture length, L. b i was determined by a capacitance method, and p i was measured directly by a pressure transducer. L was measured by two methods - either ultrasonic signals or pressure pulses generated in miniature cavities. The ultrasonic method confirmed the existence of a Barenblatt liquid-free crack ahead of the liquid front whose relative length decreased with confining stress. The metal plates bonded to the 3-in.×4-in. [7.6-cm×10.2-cm] faces prevented slip at the top and bottom of the fracture, giving a three-dimensional (3D) crack of constant height. However, the b i , p i , and L data followed trends predicted by two-dimensional (2D) (plane strain) elastic theory reasonably well. Fracture closure measurements after shut-in showed an initial period of leakoff-controlled closure and a final period of creep-controlled closure. A p i slope change at the transition is identified with the instantaneous shut-in pressure (ISIP) in field records and is higher than the true confining stress. Introduction Methods of predicting crack dimensions during fracturing operations are essential to proper design of field treatments. Many fracture-propagation theories have been advanced. Contributions have been made by Barenblatt, 1 Khristianovitch and Zheltov, 4,5 Howard and Fast, 6 Perkins and Kern, 7 LeTirant and Dupuy, 8 Nordgren, 9 Geertsma and de Klerk, 10 Daneshy, 11 and Cleary 12,13 among others. However, practical methods of evaluating the theoretical work have been few. Mostly they have been. limited to indirect and generally inconclusive field evaluations. The Sandia mineback experiments 14–16 have provided more direct evaluations. However, even here important fracturing parameters are uncontrolled or unknown. This paper describes laboratory-scale hydraulic fracturing experiments that provide critical data for evaluating crack propagation theories. In these experiments we measured the fundamental variables of crack growth under controlled conditions with known fracturing parameters. Experimental Methods All fracturing experiments were carried out in dry blocks 3 in.×4 in.×12 in. [7.6 cm×10.2 cm×30.5 cm] in size. Mesa Verde sandstone and Carthage and Lueders limestone were used as sample materials. Scaling considerations were important. It was necessary to scale down injection rate and leakoff to be consistent with fracture dimensions. The scaling factor of importance was taken to be fluid efficiency, the ratio of crack volume to injected volume. This factor was controlled through appropriate combinations of sample permeability and fracturing fluid viscosity. As fracturing fluids we used thick grease, hydraulic oils of various viscosities, and gelled kerosene (Dowell's YFGO™). Fluid efficiencies ranged from 3 to 70%. Most experiments were conducted at efficiencies between 30 and 50 %, a range typical of most field treatments. Fig. 1 shows the experimental arrangement. Shaped aluminum plates were bonded with Hysol clear epoxy to the 3-in.×12-in. [7.6-cm×30.5-cm] faces of the sample block as shown. The remaining faces were coated with a thin layer of the same epoxy to provide an impermeable jacket for confining pressure. One of the aluminum plates contained an injection port communicating with a 1.4-in. [0.64-cm] borehole as illustrated. A pair of brass plates with faces 0.2 in.×0.5 in. [0.5 cm×1.3 cm] was epoxied into the borehole at its center. These plates, separated by a gap of 0.01 in. [0.025 cm] served as a parallel plate capacitor. They were connected to a capacitance bridge that detected changes in gap width through changes in capacitance. This provided a direct, continuous measurement of fracture width at the borehole.

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*SPE J.*24 (02): 141–152.

Paper Number: SPE-8939-PA

Published: 01 April 1984

Abstract

Computer-based numerical simulation can be used as a tool for analysis of fracturing treatments and prediction of postfracturing well performance. The physical problem studied involves fracture mechanics, fluid flow, and heat transfer both in the fracture and in the reservoir. The numerical model predicts fracture extension, length, and width; proppant transport and settlement; fracture closure; cleanup, and postfracturing performance under different producing conditions. The number of physical features that are customarily neglected in fracture designs have been incorporated in the present model. These include stress-sensitive reservoir properties, proper two-phase calculation of leakoff and cleanup, stress-dependent fracture permeability and temperature- and time-dependent fracturing fluid rheology. The utility and a priori predictive capability of the model is illustrated with two examples of fracturing jobs. The first example is a marginal gas well stimulated by a medium-size gelled-water fracturing job. The second example is a massive foam fracture in the Elmworth basin. In both cases, the simulator predicted results that are in good agreement with the observed productivity. Introduction Fracturing technology has been developing rapidly in recent years. Both the size and sophistication of field treatments have increased dramatically. The development of low-permeability gas reserves is especially dependent on successful and economical application of fracturing technology. The low-permeability gas sands often have permeability below 1 ud and discontinuous (lenticular) or dual porosity structure. A number of very large treatments have been performed with varied results. Compared with the rapid development of field technology, design and analysis of massive hydraulic fracturing (MHF) treatments have involved traditional methods based on correlations and crude approximations. Design methods used by service companies and industry concentrate on the prediction of fracture shape and proppant placement, and as such do not predict accurately deliverability after the fracturing job. Such methods cannot be used for design optimization, which must be based on accurate long-term production forecasts. In addition, the various aspects of the process are, of necessity, treated separately. Typically, fracture extension, leakoff, fracturing fluid heatup, and cleanup all are determined independently using simplifying assumptions about their mutual influence. The need for production-forecasting tools has been recognized by reservoir engineers who developed analytical and numerical techniques for predicting the deliverability of fractured wells. The most advanced approaches of this type involve conventional finite-difference reservoir simulation techniques and are used for optimization of treatment size. The common weakness of analyses of this type is that the fracture is treated as static and many of the variables controlling deliverability (such as fracture length, conductivity, propped length, and height) must be entered and are typically obtained by the design methods discussed previously. Also, the influence of the fracturing job on the reservoir (such as damage by the fluid) cannot be properly accounted for. The need for tools that would model the entire process in a more rigorous fashion is obvious. Most of the information on the fracturing operations in the field must be obtained indirectly, and production testing yields the basic and most important data. A meaningful tool for analysis of treatments must therefore correctly model the interaction between the fracturing operation and the postfracture behavior. This paper describes development and field application of a comprehensive simulator that treats in an integrated fashion all important aspects of the problem. The correctness of our approach has been confirmed by validation against field data, showing excellent agreement. Our model still simplifies treatment of fracture containment, and ongoing development is directed toward enhancements that will allow a priori optimization of treatments including containment. General Description of the Simulator Although the model is general and can be used in other applications, this paper addresses only those features of interest in fracturing treatments. The relevant geometry is shown in Fig. 1. The model simulates two-dimensional (2D), compressible, two-phase flow and heat transfer simultaneously with initiation and propagation of a vertical hydraulic fracture. Once the fracture exists, appropriate equations of two-phase flow and heat transfer in the fracture also are solved. SPEJ P. 141^

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*SPE J.*24 (02): 129–140.

Paper Number: SPE-10080-PA

Published: 01 April 1984

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^

Journal Articles

Publisher: Society of Petroleum Engineers (SPE)

*SPE J.*24 (01): 19–32.

Paper Number: SPE-9878-PA

Published: 01 February 1984

Abstract

Fracture geometry is an important concern in the design of a massive hydraulic fracture for improved natural gas recovery from low-permeability reservoirs. Determination of the extent of vertical fracture growth and containment in layered rock, a priori, requires an improved understanding of the parameters that may control fracture growth across layer interfaces. We have conducted laboratory hydraulic fracture experiments and elastic finite element studies that show that at least two distinct geologic conditions can inhibit or contain the vertical growth of hydraulic fractures in layered rock: a weak interfacial shear strength of the layers and an increase in the minimum horizontal compressive stress in the bounding layers. The second condition is more important and more likely to occur at depth. Differences in elastic properties within a layered rock mass may be important-not as a containment barrier perse, but in the manner in which variations in elastic properties affect the vertical distribution of the minimum horizontal stress magnitude. These results suggest that improved fracture treatment designs and an assessment of the potential success of stimulations in low-permeability reservoirs can be made by determining the in-situ stress st ate in the producing interval and bounding formations before stimulation. If the bounding formations have a higher minimum horizontal stress, then one can optimize the fracture treatment and maximize the ratio of productive formation fracture area to volume of fluid pumped by limiting bottomhole pressures to that of the bounding formation. Introduction In 1949, Clark introduced the concept of hydraulic fracturing to the petroleum industry. Since then, hydraulic fracture treatment to enhance oil and gas recovery in tight reservoir rocks has become standard practice. More recently, as a result of an increased need for better recovery techniques, massive hydraulic fracturing (MHF) has been used in low-permeability, gas-bearing sandstones in the Rock Mountain region and in Devonian shales of the Appalachian region, where it is uneconomical to retrieve gas in the conventional manner. Massive hydraulic fractures are designed to extend as much as 1000 m (3,281 ft) radially from the wellbore and generally require up to 1000 m3 (6,293 bbl) of fracture fluid. MHF has been developed by trial and error, and the results are uncertain in many situations. Some of these large-scale stimulation efforts have been successful, but others have been extremely disappointing failures. The reasons for these failures are not clear, but it seems likely that improved understanding of the fundamental mechanisms of hydraulic fracturing should suggest ways of improving the efficiency and reliability of the MHF stimulation technique or at least indicate where this technique can be applied successfully. Among the many technological problems encountered in MHF, one of the most important questions that must be answered properly to design a hydraulic fracture treatment for optimal gas recovery concerns the shape and overall geometry of the fracture. The question of fracture height and whether the hydraulic fracture will propagate into formations lying above and below the producing zone. When a fracture treatment is designed, the height of the fracture is the parameter about which the least is known, yet this influences all aspects of the design. A hydraulic fracture usually grows outward in a vertical plane and propagates above and below the packers as well as laterally away from the wellbore. Vertical propagation is undesirable whenever the fracturing is to be contained within a single stratigraphic interval. If the hydraulic fracture is not contained within the producing formation and propagates in both the vertical and lateral directions (an elliptical fracture), failure of the treatment can occur because the fracture fails to contact a sufficiently large area of the reservoir. Moreover, there is an effective loss of the expensive fracture fluid and proppant used to fracture the unproductive formations. An extreme example where the containment of a hydraulic fracture is essential is the case of developing a fracture in a gas-producing sandstone without fracturing through the underlying shale into another sandstone that is water-bearing. Therefore, it is of great economic importance to the gas industry to understand the parameters that can restrict the vertical propagation of massive hydraulic fractures. There are several parameters that are considered to have some effect on the vertical growth and possible containment of hydraulic fractures. SPEJ P. 19^