Design Of Hydraulic Fracture Treatments Research Articles

Fluid Loss from Hydraulically Induced Fractures

Dynamic fluid loss tests provide the best method for simulating the fluid loss process during hydraulic fracturing. Through the use of these tests and a reasonable theoretical model for the rate of fracture growth, fracture length can be predicted with acceptable accuracy. Introduction Successful design of hydraulic fracture treatments depends upon accurate knowledge of the fluid loss properties of the fracturing fluid. Howard and Fast properties of the fracturing fluid. Howard and Fast gave the first description of the fluid loss process and developed equations relating fracture area to fluid and formation properties and treating data. This development was based upon static filtration tests similar to the API mud filtration test. More recently, Hail and Dollarhide have shown that the static fluid loss test does not adequately represent conditions under which additives perform in a fracture treatment. They suggest using a dynamic fluid loss test to determine fluid loss parameters, and they develop an alternative form of the Howard and Fast equation for fracture area. In addition, they give data demonstrating some of the effects found in dynamic tests that are not present in static tests."Dynamic fluid loss" in this paper refers to fluid leakoff from a fracture when a high flow velocity along the fracture exists at the point where fluid leak-off occurs. This is the normal situation since hydraulic fracturing produces a long, narrow crack along which fluid flows at velocities up to several hundred feet per minute. High velocity is maintained far down the fracture even though volumetric flow rate decreases as the fracture becomes progressively more narrow. When additives are used, laboratory fluid loss data based on the older "static" test (no flow across the surface at which fluid leakoff occurs) are not representative and a "dynamic" fluid loss test should be run. In a dynamic fluid loss test, a high-velocity stream of fluid, which inhibits thick filter cake formation, moves past the rock surface at the same time fluid enters the core. As shown in Figs. 1 and 2 fluid loss during this test can be divided into three regimes: control by reservoir properties, control by reservoir properties and filter cake, and control by steady-state filter cake. Initially, pressure drop is totally dissipated across the core and fluid leakoff occurs as if no additive were present. Next, a filter cake begins to form and leakoff present. Next, a filter cake begins to form and leakoff velocity is lower because some pressure drop occurs across the cake. Finally, a steady state is reached at which the cake has a constant thickness and fluid leakoff velocity is constant. Flow velocity through the steady-state cake is dependent upon flow velocity across the rock surface, upon fluid and additive properties, and upon rock pore size. In this paper the properties, and upon rock pore size. In this paper the volume of fluid loss required to allow formation of a steady-state filter cake is termed the -spurt lose' (denoted Vsp), and the steady-state cake is described by the leakoff velocity, V(L). Filter cake thickness formed in a dynamic test is limited since particles outside the matrix are subjected to large shearing stresses. To illustrate the type of cake formed, Fig. 3A shows the face of a core exposed to a granular additive in oil and Fig. 3B shows one exposed to gelled water-silica flour (in these tests, additive contacted only a 0.75-in. strip across the core). These photographs show that cake formed by Use additive used in oil is almost entirely within the rock, since all rock characteristics observable outside the test zone are visible inside the test zone. JPT P. 882

A Computer Study of Horizontal Fracture Treatment Design

Abstract Published correlations for the principal aspects of hydraulic fracturingwere combined into a digital computer program to facilitate the study ofinterrelated variables. The computer program includes individual relationshipsfor fracture width during pumping, fracture area generated, propping agentembedment, flow capacities of propped fractures and transport of proppingagents in horizontal fractures. The effects of more than 20 treatment andformation parameters on the predicted results of hydraulic fracturingtreatments were studied. The effects of these parameters were determined forfracture width during injection,fracture width after the overburdencomes to rest on the propping agents, assumed not to be crushed,generatedand propped fracture area,location and concentration of propping agents inthe fracture when injection ceases,flow capacities of the various proppedsections of the fracture andexpected increase in the well productivity. The effects of propping agent, formation and fracturing fluid parameters onwell productivity are discussed. The parameters that were found to have themost pronounced effects on hydraulic fracturing treatments are injection rate, treatment volume, fracturing fluid coefficient, size and amount of proppingagent, spearhead volume, well damage radius and formation capacity. Introduction Many correlations have been published for predicting effects of variousparameters that are considered in the design of hydraulic fracturingtreatments. The Carter equation can be used to predict generated fractureradius as a function of fracture width, fracturing fluid leakoff and otherparameters. Fracture width can be determined by use of the Perkins and Kerncorrelation in which the fracture width is related to the fracture radius, fluid injection rate and certain formation and fracturing fluid parameters. Wahl and Lowe et al. have reported methods of predicting the location ofpropping agents in fractures when pumping ceases. The former study isapplicable to the case where the ratio of propping agent diameter to fracturewidth is less than 0.1. The latter is applicable when this ratio is greaterthan 0.1. These studies showed that the propping agent placement inhorizontal-radial fractures depends principally on how the individual particlesare transported in the fracture by the carrying fluid. Particle transport infractures is determined by local fluid velocity in the fracture, fluid andparticle properties, and the size of the particle relative to the fracturewidth. The distribution of propping agents, effective overburden pressure andformation rock strength control the propped fracture width by controlling theextent to which the propping agent particles embed into the fracture faces. From the distribution of propping agents and the propped fracture width, fracture flow capacities can be calculated for the various regions of thefracture. The flow capacities and the radial extent of these regions can becombined with reservoir information to predict the productivity increases forfractured wells. In all these studies, the effects of certain treatment and/orreservoir parameters on one facet of fracturing can be predicted only if otherfacets which the parameters affect are fixed. For instance, fracture width andradius are interrelated; that is, to calculate the value of one, the value ofthe other must be known. Also, some parameters influence more than one aspectof fracturing. For example, proppant transport is a function of both fracturewidth and fluid viscosity, but fracture width is itself a function of fluidviscosity. Since these calculations are complex and the parametersinterrelated, it is not possible to write an equation with which the over-alleffects of treatment parameters can be solved explicitly. For these reasons, the correlations for determining the effects of the parameters which are mostsignificant in hydraulic fracturing treatments have been incorporated into adigital computer program. Computer Program The program, which was written for an IBM 7094 computer, can be used topredict results of most of the combinations and values for the treatmentparameters that are ordinarily considered for fracturing treatments. Aspearhead of fracturing fluid and a propping agent-carrying fluid withdifferent fluid properties can be taken into account. Also, the total volumesand relative amounts of the spearhead and carrying fluids can be varied. Twodifferent propping agents (as used in tail-in operations) and a wide range offormation properties and injection rates are considered. The computer program(Fig. 12) consists of several sets of calculations. First, the final floodedfracture radius and average fracture width at the cessation of pumping arecalculated. This is done by simultaneous solution of the Perkins and Kernfracture width equation and the Carter equation for flooded fracture radius(equations used in the computer program appear in the Appendix). The next stepis to determine local fluid velocity in the fracture as a function of time andradius. Since it is, not possible to write this function in closed formexpression, a table of velocity values is generated by the program and storedfor subsequent use.

Relation of Formation Rock Strength to Propping Agent Strength in Hydraulic Fracturing

Abstract The introduction of new fracture propping agents that are brittle but much stronger than sand created the problem of what loading strength is required for a propping agent to be effective in a given formation. It is shown that the load at which the propping agent crushes should exceed the load at which total embedment in the fracture faces is possible. Simple laboratory tests to determine loading strength of the propping agent and embedment in the fracture faces, and use of these data in selecting a propping agent for a given formation, are discussed. Introduction One of the most important factors in the design of hydraulic fracturing treatments is the selection of a propping agent that can effectively provide the fracture flow capacity needed for stimulation of a well. Sand, once generally accepted as being synonymous with propping agent in hydraulic fracturing, is now recognized as having limited effectiveness in many formations because of its low resistance to crushing. Sand particles are brittle and have relatively low strength. Because of this property, sand particles are crushed in rocks that offer high resistance to the penetration of fracture faces by the proppant particles when the fracture attempts to close under the action of the overburden load. For rocks that offer a high resistance to penetration, deformable particles are more effective propping agents than sand. However, for this same type of rock, a propping agent that does not deform, yet does not crush, is often more effective. Thus, a rigid propping agent with sufficient strength to prevent crushing is desirable. A method for determining the strength required for a rigid propping agent to function effectively in given formations is discussed. BEHAVIOR OF RIGID PROPPANTS AND FRACTURE FACES RELATED STUDIES An early qualitative description of the reaction of propping sand in fractures was given by Hassebroek et al. In discussing fracturing in deep wells, the authors mentioned that even though propping sand entered the fractures, a high flow capacity did not result due to crushing or embedding of the propping sand. Dehlinger et al. in discussing the reaction of propping sand surmised that, because of the hardness of sand particles, deformation occurred in the fracture faces contacting the propping sand. In later studies," methods of determining the embedment of propping sand in fracture faces of soft rock and the critical load at which propping sand is crushed by the fracture faces in hard rock were discussed. In working with deformable proppants, Kern et al. considered proppant articles to be deformed into cylindrical disks by action of the overburden and then pressed slightly into the fracture faces by further action of the overburden. Rixie et al. reported on embedment pressure and presented a method of selecting a propping agent for use in given formations. The propping agents included sand, walnut shells and aluminum pellets. All these studies have contributed materially to a better understanding of propping agent behavior; however, the strength of brittle proppants (sand, glass and ceramics) required to result in embedment rather than crushing has not been discussed. This topic will be covered in the ensuing discussion. PROPPANT PARTICLE CRUSHING-EMBEDMENT For this discussion, a rigid propping agent is considered to be one that is brittle and fails under tensile stress when loaded to a critical value. In an earlier study it was shown that the Hertzian loading theory could be applied to a spherical brittle propping agent if the propping agent and fracture faces behaved elastically. At the failure of the proppant, the ratio of the load to the square of the diameter of the particle should be constant for a given material combination, or: (1) A partial derivation of this equation from proppant and formation properties is included in the Appendix. Should a rigid particle not be crushed as a load is applied, it embeds in the fracture faces. A study of particle embedment in fracture surfaces has been published. The embedment can be described by an equation based on Meyer's metal penetration hardness relationships: (2) In Eq. 2, B and m are constants that are characteristic of the rock; the significance of the other terms is shown in Fig. 1. JPT

Effects of Fracturing Fluid Velocity on Fluid-Loss Agent Performance

Abstract Conventional static tests of fluid-loss agents do not realistically simulate conditions in a fracturing treatment. The dynamic tests reported here show that fluid-loss volume is better represented as proportional to time, rather than as the square root of time. This leads to a different equation for fracture area. The leak-off rate increases with increasing shear rate at the fracture wall, by appears to approach a limiting value. Pressure effects are minor. Spurt loss ordinarily is not affected by the flow velocity in the fracture and is inversely proportional to concentration of agent. The filter cake, once it is well established, is resistant to damage by the flow of pain fracturing liquid (without fluid-loss agent). The latter two findings indicate that a treatment employing a high-concentration spearhead following by plain fluid can offer a more economical treatment under suitable conditions. Introduction The successful design of hydraulic fracturing treatments depends on accurate knowledge of the fluid-loss properties of the fracturing fluid. Howard and Fast, in giving the basic equation relating fracture area to fluid and treating parameters, described three mechanisms which might control the rate of fluid leak-off from the fracture. One mechanism usually is dominant in a given well treatment. For each mechanism, the leak-off velocity is inversely proportional to the square root of time, and the proportionality constant is designated as the fracturing- fluid coefficient. For the wall-building type of fluid-loss agent, the coefficient is determined by a filtration test in a pressure cell, usually with a rock wafer or core as the filter medium. In these static tests, the cumulative volume generally is proportional to the square root of time, after an initial spurt volume. The static-fluid-loss test is not representative of the conditions under which a fluid-loss agent performs in a fracturing treatment. The marked difference between the dynamic- and static-fluid-loss behavior of drilling fluids reported in the literature implies that dynamic testing is also needed with fracturing fluids. We have therefore undertaken a study of the dynamic-fluid-loss behavior of fracturing fluids. The testing apparatus has also afforded opportunity to evaluate the resistance of the filter cake to removal or damage by flowing fluid containing no fluid-loss agent, with and without sand. The results of these studies offer a means for more accurate evaluation of fluid-loss agent performance, and point the way to a "spearhead" fracturing technique which may offer mare economical treatment for some wells. EXPERIMENTAL METHODS The dynamic-fluid-loss testing method is applicable to any type of wall-building fracturing fluid. The present study aimed first at finding what phenomena are involved, and therefore has been limited in the number of materials tested. All of the results specifically reported herein are for kerosene containing a commercial solid fluid-loss agent, which is commonly used at 50 lb/1,000 gal of oil. Another agent in liquid form, used usually at 20 gal/1,000 gal oil, has shown all the same phenomena in dynamic tests, and generally the same level of fluid-loss control as the solid agent. The dynamic-fluid-loss core cell used in all tests is shown in Fig. 1. The fracture was simulated by the annulus between a 2.03 in. OD sandstone core and the surrounding pipe. Annulus widths of 0.234 and 0.117 in. were used, and the core was 3.5 in. long. The annular geometry provides a uniform fluid velocity and a well-defined shear rate over the entire filtering surface, and permits a large filter area (144 sq cm) in a reasonably compact cell. The leak-off fluid passed into a 0.5 in. diameter axial hole in the core. A hollow steel rod through this hole was threaded into a rounded "streamliner" upstream of the core, and into a mounting stud downstream. The streamliner and the stud had the same outside diameter as the core. In all tests except those where sand was circulated, the mounting stud had protruding rings which constricted the annulus, to minimize any tendency for channeling of the fluid to the side exit port. The ends of the core were sealed by Neoprene, steel and Teflon washers. The leak-off fluid was conducted from the hollow rod to an exit tube, through a metering valve (a fine-pitched needle valve) and a quick-opening toggle valve in series, and into graduated cylinders for volume measurement. Two separate circulating systems were used in the experimental program. The extensive initial testing was done at 50 to 150 psi. The fluid was circulated by a variable speed Moyno pump, and the flow rate was read by a rotameter flow meter. The filtration pressure was supplied by holding a back-pressure with a throttling valve. JPT P. 555ˆ

The Mechanics of Design and Interpretation of Hydraulic Fracture Treatments

Introduction Since formal introduction of hydraulic fracturing to the petroleum industry in 1948, the technique has increased in prominence each year until in many areas it is now the most popular method of well stimulation. In some areas it is the only technique which will effect commercial production; even some limestone formations which refuse to respond to multiple-stage acid treatments will, subsequent to hydraulic fracture treatments, make commercial wells. Many theories have been expounded to define conditions associated with hydraulic fracturing - some based on unrealistic prototypes and others on mathematical analyses substantiated as far as practical with laboratory experimentation. However, progress made has been mainly not the result of any mathematical or physical definition of the process, but industry's willingness to spend more for larger and higher rate treatments. Service companies have met the demands of the industry for treatments of greater magnitude until in some areas, treatments of from 100,000 to 200,000 gal injected at rates approaching 100 bbl/min are not only common but are performed with minimum difficulty. The cost of such treatments is of necessity great, and it is imperative that the manpower, equipment and materials be as effectively utilized as is technically possible. The purpose of this paper is not to clarify the turbid waters of fracturing theory, but to present the tools which we had used to make the technique more effective. Some equating will be necessary; however, development and discussion of theories will be largely confined to that necessary to justify the method of analysis. Basic Assumptions The following assumptions have been allowed as a basic definition of conditions:The pressure required to maintain fracture parting can be determined with fair reliability from either theoretical or empirical methods.The pressure required to maintain fracture parting is independent of fluid injection rate.For any one plane of parting, the functional variation in surface injection pressure with injection rate is the result of increased or decreased friction drop in conductor pipe and perforations.Functional variation in bottom-hole casing injection pressure with rate is the result of friction drop through perforations and is generally assumed, depending on number of perforations open, to be negligible for most wells below 3,000 ft in which ball sealers are not employed.