PEH:Hydraulic Fracturing

Publication Information

Petroleum Engineering Handbook

Larry W. Lake, Editor-in-Chief

Volume IV - Production Operations Engineering

Joe Dunn Clegg, Editor

Copyright 2006, Society of Petroleum Engineers

Chapter 8 - Hydraulic Fracturing

By Stephen A. Holditch, Texas A&M University

Pgs. 323-366

ISBN 978-1-55563-118-5
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Introduction

The first hydraulic fracturing treatment was pumped in 1947 on a gas well operated by Pan American Petroleum Corp. in the Hugoton field. Kelpper Well No. 1, located in Grant County, Kansas, was a low-productivity well, even though it had been acidized. The well was chosen for the first hydraulic fracture stimulation treatment so that hydraulic fracturing could be compared directly with acidizing. Since that first treatment in 1947, hydraulic fracturing has become a common treatment for stimulating the productivity of oil and gas wells.

Hydraulic fracturing is the process of pumping a fluid into a wellbore at an injection rate that is too great for the formation to accept in a radial flow pattern. As the resistance to flow in the formation increases, the pressure in the wellbore increases to a value that exceeds the breakdown pressure of the formation open to the wellbore. Once the formation "breaks down," a fracture is formed, and the injected fluid begins moving down the fracture. In most formations, a single, vertical fracture is created that propagates in two directions from the wellbore. These fracture "wings" are 180° apart and normally are assumed to be identical in shape and size at any point in time; however, in actual cases, the fracture wing dimensions may not be identical. In naturally fractured or cleated formations, it is possible that multiple fractures can be created and propagated during a hydraulic fracture treatment.

Fluid that does not contain any propping agent (called the "pad") is injected to create a fracture that grows up, out, and down, and creates a fracture that is wide enough to accept a propping agent. The purpose of the propping agent is to prop open the fracture once the pumping operation ceases, the pressure in the fracture decreases, and the fracture closes. In deep reservoirs, man-made ceramic beads are used to hold open or "prop" the fracture. In shallow reservoirs, sand is normally used as the propping agent.

This chapter discusses the processes used to design and pump a hydraulic fracture treatment and provides an overview of the theories, design methods, and materials used in a hydraulic fracture treatment.

Introduction

Objectives of Hydraulic Fracturing

In general, hydraulic fracture treatments are used to increase the productivity index of a producing well or the injectivity index of an injection well. The productivity index defines the rate at which oil or gas can be produced at a given pressure differential between the reservoir and the wellbore. The injectivity index refers to the rate at which fluid can be injected into a well at a given pressure differential.

There are many applications for hydraulic fracturing. Hydraulic fracturing can increase the flow rate of oil and/or gas from low-permeability reservoirs, increase the flow rate of oil and/or gas from wells that have been damaged, connect the natural fractures and/or cleats in a formation to the wellbore, decrease the pressure drop around the well to minimize sand production, enhance gravel-packing sand placement, decrease the pressure drop around the well to minimize problems with asphaltine and/or paraffin deposition, increase the area of drainage or the amount of formation in contact with the wellbore, and connect the full vertical extent of a reservoir to a slanted or horizontal well. There could be other uses, but most of the treatments are pumped for these reasons.

A low-permeability reservoir is one that has a high resistance to fluid flow. In many formations, chemical and/or physical processes alter the reservoir rock over geologic time. Sometimes, these diagenetic processes restrict the openings in the rock and reduce the ability of fluids to flow through the rock. Low-permeability rocks are normally excellent candidates for stimulation by hydraulic fracturing.

Regardless of the permeability, a reservoir rock can be damaged when a well is drilled through the reservoir and when casing is set and cemented in place. Damage occurs because drilling and/or completion fluids leak into the reservoir and alter the pores and pore throats. When the pores are plugged, the permeability is reduced, and the fluid flow in this damaged portion of the reservoir may be substantially reduced. Damage can be especially severe in naturally fractured reservoirs. To stimulate damaged reservoirs, a short, conductive hydraulic fracture is often the desired solution.

In many cases, especially for low-permeability formations, damaged reservoirs, or horizontal wells in a layered reservoir, the well would be uneconomical unless a successful hydraulic fracture treatment is designed and pumped. The engineer in charge of the economic success of such a well must design the optimal fracture treatment and then go to the field to be certain the optimal treatment is pumped successfully.

Candidate Selection

The success or failure of a hydraulic fracture treatment often depends on the quality of the candidate well selected for the treatment. Choosing an excellent candidate for stimulation often ensures success, while choosing a poor candidate normally results in economic failure. To select the best candidate for stimulation, the design engineer must consider many variables. The most critical parameters for hydraulic fracturing are formation permeability, the in-situ stress distribution, reservoir fluid viscosity, skin factor, reservoir pressure, reservoir depth, and the condition of the wellbore. The skin factor refers to whether the reservoir is already stimulated or is damaged. If the skin factor is positive, the reservoir is damaged, and the well could be an excellent candidate for stimulation.

The best candidate wells for hydraulic fracturing treatments have a substantial volume of oil and gas in place and need to increase the productivity index. Such reservoirs have a thick pay zone, medium to high pressure, in-situ stress barriers to minimize vertical height growth, and either a low-permeability zone or a zone that has been damaged (high skin factor).

Reservoirs that are poor candidates for hydraulic fracturing are those with little oil or gas in place because of thin reservoirs, low reservoir pressure, or small areal extent. Reservoirs with extremely low permeability may not produce enough hydrocarbons to pay all the drilling and completion costs, even if successfully stimulated; thus, such reservoirs would not be good candidates for stimulation.

Developing Data Sets

For most petroleum engineers, developing a complete and accurate data set is often the most time-consuming part of fracture treatment design. The data required to run both the fracture design model and the reservoir simulation model can be divided into two groups: data that can be "controlled" by the engineer and data that must be measured or estimated, but cannot be controlled.

The primary data that can be controlled by the engineer are the well completion details, treatment volume, pad volume, injection rate, fracture fluid viscosity, fracture fluid density, fluid-loss additives, propping agent type, and propping agent volume. The data that must be measured or estimated are formation depth, formation permeability, in-situ stresses in the pay zone, in-situ stresses in the surrounding layers, formation modulus, reservoir pressure, formation porosity, formation compressibility, and reservoir thickness. There are three thicknesses that are important to the design engineer: the gross thickness of the reservoir, the net thickness of the oil- or gas-producing interval, and the permeable thickness that will accept fluid loss during the hydraulic fracture treatment.

The most critical data for the design of a fracture treatment (roughly in order of importance) are the in-situ stress profile, formation permeability, fluid-loss characteristics, total fluid volume pumped, propping agent type and amount, pad volume, fracture fluid viscosity, injection rate, and formation modulus. In hydraulic fracture treatment design, the two most important parameters are the in-situ stress profile and the permeability profile of the zone to be stimulated, plus the layers of rock above and below the target zone that will affect fracture height growth.

In new fields or reservoirs, most operating companies are normally willing to run logs, cut cores, and run well tests to determine important factors such as the in-situ stress and the permeability of the reservoir layers. With such data, along with fracture-treatment and production records, accurate data sets for a given reservoir normally can be compiled. These data sets can be used on subsequent wells to optimize the fracture treatment designs. It is normally not practical to cut cores and run well tests on every well. Thus, the data obtained from cores and well tests from a few wells must be correlated to log parameters, so the logs on subsequent wells can be used to compile accurate data sets.

To design a fracture treatment, most use pseudo-three-dimensional (P3D) models. To use a P3D model, the data must be entered by reservoir layer. Fig. 8.1 illustrates the important data profiles required by a P3D model. For the example in Fig. 8.1, the fracture treatment would be started in the sandstone reservoir. The fracture would typically grow up and down until a barrier is reached to prevent vertical fracture growth. In many cases, thick marine shale is a barrier to vertical fracture growth. In some cases, coal seams prevent fractures from growing vertically. Many coal seams are highly cleated, which means that they contain an abundance of small natural fractures. When the fracture fluid enters a highly cleated coal seam, there will be very high fluid leakoff into the coal cleats. In thick, highly cleated coal seams, the fracture is likely to be contained within the coal seam.

• 

  Fig. 8.1—Typical input data for a P3D model.

The data used to design a fracture treatment can be obtained from several sources, such as drilling records, completion records, well files, openhole geophysical logs, cores and core analyses, well tests, production data, geologic records, and other public records, such as publications. In addition, service companies provide data on their fluids, additives, and propping agents. Table 8.1 illustrates typical data needed to design a fracture treatment and possible sources for the data.

• 

  Table 8.1

Fracture Treatment Optimization

The goal of every fracture treatment design should be to attain the optimum fracture treatment for each and every well. In 1978, Holditch et al. discussed the optimization of both the propped fracture length and the drainage area (well spacing) for low-permeability gas reservoirs. Fig. 8.2 illustrates the method used to optimize the size of a fracture treatment, and clearly shows the following:

• 

  Fig. 8.2—Fracture treatment optimization process.

• As the propped length of a fracture increases, the cumulative production will increase, and the revenue from hydrocarbon sales will increase.
• As the fracture length increases, the incremental benefit (amount of revenue generated per foot of additional propped fracture length) decreases.
• As the treatment volume increases, the propped fracture length increases.
• As the fracture length increases, the incremental cost of each foot of fracture (cost/ft of additional propped fracture length) increases.
• When the incremental cost of the treatment is compared with the incremental benefit of increasing the treatment volume, an optimum propped fracture length can be found for every situation.

Additional economic calculations can be made to determine the optimum fracture treatment design. However, in all cases, the design must consider the effect of the fracture on flow rates and recovery, the cost of the treatment, and the investment guidelines of the company that owns and operates the well.

Field Considerations

After the optimum fracture treatment has been designed, it must be pumped into the well successfully. A successful field operation requires planning, coordination, and cooperation of all parties. Treatment supervision and the use of quality control measures will improve the successful application of hydraulic fracturing. Safety is always the primary concern in the field, and it begins with a thorough understanding by all parties of their duties. A safety meeting is always held to review the treatment procedure, establish a chain of command, ensure everyone knows his/her job responsibilities for the day, and establish a plan for emergencies.

The safety meeting also should be used to discuss the well completion details and the maximum allowable injection rate and pressures, as well as the maximum pressures to be held as backup in the annulus. All casing, tubing, wellheads, valves, and weak links, such as liner tops, should be tested thoroughly before starting the fracturing treatment. Mechanical failures during a treatment can be costly and dangerous. All mechanical problems should be discovered during testing and repaired before pumping the fracture treatment.

Before pumping the treatment, the engineer in charge should conduct a detailed inventory of all the equipment and materials on location. The inventory should be compared with the design and the prognosis. After the treatment has concluded, another inventory of all the materials left on location should be conducted. In most cases, the difference in the two inventories can be used to verify what was mixed and pumped into the wellbore and the hydrocarbon-bearing formation.

In addition to an inventory, samples of the base fracturing fluid (usually water) should be taken and analyzed. Typically, a water analysis is done on the base fluid to determine the minerals and type of bacteria present. The data from the water analysis can be used to select the additives needed to mix the viscous fracture fluid required to create a wide fracture and to transport the propping agent into the fracture. In addition, samples of the additives used during a treatment and the fracture fluid after all additives have been added should be taken and saved in case future analyses are required.

Fracture Mechanics

Fracture mechanics has been part of mining engineering and mechanical engineering for hundreds of years. In petroleum engineering, fracture mechanics theories have been used for only approximately 50 years. Much of what is used in hydraulic fracturing theory and design was developed by other engineering disciplines many years ago. However, certain aspects, such as poroelastic theory, are unique to porous, permeable underground formations. Three important parameters of fracture mechanics are in-situ stress, Poisson ’ s ration, and Young’ s modulus.

In-Situ Stresses

Underground formations are confined and under stress. Fig. 8.3 illustrates the local stress state at depth for an element of formation. The stresses can be divided into three principal stresses. In Fig. 8.3, σ₁ is the vertical stress, σ₂ is the minimum horizontal stress, and σ₃ is the maximum horizontal stress. These stresses are normally compressive, anisotropic, and nonhomogeneous, which means that the compressive stresses on the rock are not equal and vary in magnitude on the basis of direction. The magnitude and direction of the principal stresses are important because they control the pressure required to create and propagate a fracture, the shape and vertical extent of the fracture, the direction of the fracture, and the stresses trying to crush and/or embed the propping agent during production.

• 

  Fig. 8.3—The three principal compressive stresses.

A hydraulic fracture will propagate perpendicular to the minimum principal stress. For a vertical fracture, the minimum horizontal stress can be estimated with

....................(8.1)

where

σ_min = the minimum horizontal stress,

ν = Poisson ’ s ratio,

σ₁ = overburden stress,

α = Biot’ s constant,

p_p = reservoir fluid pressure or pore pressure, and

σ_ext = tectonic stress.

Poisson’ s ratio can be estimated from acoustic log data or from correlations based on lithology. Table 8.2 presents typical ranges for Poisson’ s ratio. The overburden stress can be computed with density log data. Normally, the value for overburden stress is approximately 1 psi/ft of depth. The reservoir pressure must be measured or estimated. Biot’

s constant is usually 1.0, but can be less than 1.0 on occasion.

• 

  Table 8.2

Poroelastic theory is often used to estimate the minimum horizontal stress.,, Eq. 8.1 combines poroelastic theory with a term that accounts for any tectonic forces that are acting on a formation. The first term on the right side of Eq. 8.1 is a linear elastic term that converts the effective vertical stress on the rock grains into an effective horizontal stress on the rock grains. The second term in Eq. 8.1 represents the stress generated by the fluid pressure in the pore space. The third term is the tectonic stress, which could be zero in tectonically relaxed areas, but can be important in tectonically active areas.

In tectonically active areas, the effects of tectonic activity must be included in the analyses of the total stresses. To measure the tectonic stresses, injection tests are conducted to measure the minimum horizontal stress. The measured stress is then compared with the stress calculated by the poroelastic equation to determine the value of the tectonic stress.

Basic Rock Mechanics

In addition to the in-situ or minimum horizontal stress, other rock mechanical properties are important when designing a hydraulic fracture. Poisson ’ s ratio is defined as "the ratio of lateral expansion to longitudinal contraction for a rock under a uniaxial stress condition." The value of Poisson’ s ratio is used in Eq. 8.1 to convert the effective vertical stress component into an effective horizontal stress component. The effective stress is defined as the total stress minus the pore pressure.

The theory used to compute fracture dimensions is based on linear elasticity. When applying this theory, the modulus of the formation is an important parameter. Young’ s modulus is defined as "the ratio of stress to strain for uniaxial stress." The modulus of a material is a measure of the stiffness of the material. If the modulus is large, the material is stiff. In hydraulic fracturing, a stiff rock results in more narrow fractures. If the modulus is low, the fractures are wider. The modulus of a rock is a function of the lithology, porosity, fluid type, and other variables. Table 8.2 illustrates typical ranges for modulus as a function of lithology.

Fracture Orientation

A hydraulic fracture will propagate perpendicular to the least principle stress (see Fig. 8.3). In some shallow formations, the least principal stress is the overburden stress; thus, the hydraulic fracture will be horizontal. Horizontal fractures have been documented. In reservoirs deeper than approximately 1,000 ft, the least principal stress will likely be horizontal; thus, the hydraulic fracture will be vertical. The azimuth orientation of the vertical fracture will depend on the azimuth of the minimum and maximum horizontal stresses. Lacy and Smith provided a detailed discussion of fracture azimuth in Lacy and Smith.

Injection Tests. The only reliable technique for measuring in-situ stress is by pumping fluid into a reservoir, creating a fracture, and measuring the pressure at which the fracture closes. The well tests used to measure the minimum principal stress are in-situ stress tests, step-rate/flowback tests, minifracture tests, and step-down tests. For most fracture treatments, minifracture tests and step-down tests are pumped ahead of the main fracture treatment. As such, accurate data are normally available to calibrate and interpret the pressures measured during a fracture treatment. In-situ stress tests and step-rate/flowback tests are not run on every well; however, it is common to run such tests in new fields or new reservoirs to help develop the correlations required to optimize fracture treatments for subsequent wells.

In-Situ Stress Tests. An in-situ stress test can be either an injection-falloff test or an injection-flowback test. The in-situ stress test is conducted with small volumes of fluid (a few barrels) and injected at a low injection rate (tens of gal/min), normally with straddle packers to minimize wellbore storage effects, into a small number of perforations (1 to 2 ft). The objective is to pump a thin fluid (water or nitrogen) at a rate just sufficient to create a small fracture. Once the fracture is open, the pumps are shut down, and the pressure is recorded and analyzed to determine when the fracture closes. Thus, the term "fracture-closure pressure" is synonymous with minimum in-situ stress and minimum horizontal stress. When the pressure in the fracture is greater than the fracture-closure pressure, the fracture is open. When the pressure in the fracture is less than the fracture-closure pressure, the fracture is closed. Fig. 8.4 illustrates a typical wellbore configuration for conducting an in-situ stress test. Fig. 8.5 shows typical data that are measured. Multiple tests are conducted to ensure repeatability. The data from any one of the injection-falloff tests can be analyzed to determine when the fracture closes. Fig. 8.6 illustrates how one such test can be analyzed to determine in-situ stress.

• 

  Fig. 8.4—Wellbore hardware required for an in-situ stress test.

• 

  Fig. 8.5—Typical data from an in-situ stress test.

• 

  Fig. 8.6—Closure pressure analysis.

Minifracture Tests. Minifracture tests are run to reconfirm the value of in-situ stress in the pay zone and to estimate the fluid-loss properties of the fracture fluid. A minifracture test is run with fluid similar to the fracture fluid that will be used in the main treatment. Several hundred barrels of fracturing fluid are pumped at fracturing rates. The purpose of the injection is to create a fracture that will be of similar height to the one created during the main fracture treatment. After the minifracture has been created, the pumps are shut down, and the pressure decline is monitored. The pressure decline can be used to estimate the fracture-closure pressure and the total fluid leakoff coefficient. Data from minifracture treatments can be used to alter the design of the main fracture treatment, if required.

Step-Down Tests. For any injection-falloff test to be conducted successfully, a clean connection between the wellbore and the created fracture is needed. The main objective of an in-situ stress test and the minifracture test is to determine the pressure in the fracture when the fracture is open and the pressure when the fracture is closed. If there is excess pressure drop near the wellbore because of poor connectivity between the wellbore and the fracture, the interpretation of in-situ stress test data can be difficult. In naturally fractured or highly cleated formations, multiple fractures that follow tortuous paths are often created during injection tests. When these tortuous paths are created, the pressure drop in the "near-wellbore" region can be very high, which complicates the analyses of the pressure falloff data. To determine the cause of near-wellbore pressure drop, step-down tests are run.

A step-down test is pumped just before the minifracture treatment. A step-down test is pumped at fracturing rates with linear fluids, the friction pressures of which are well known. The pressure at the bottom of the hole during the injection is a function of the net pressure in the fracture and the near-wellbore pressure drop. To measure the near-wellbore pressure drop, the net pressure in the fracture needs to be relatively constant during the step-down portion of the test. To do this, the step-down test is started by injecting into the well for 10 to 15 minutes. Experience has shown that, in most cases, the net pressure is relatively stable after approximately 10 to 15 minutes of injection. The injection rate is then "reduced in steps" to a rate of zero. The injection rate at each step should be held constant for approximately 1 minute so the stabilized injection pressure can be measured. The injection rate should be stepped from the maximum value to zero, in three to five steps, in less than 5 minutes. The objective of the step-down test is to measure the near-wellbore pressure drop as a function of injection rate. If the net pressure in the fracture is relatively stable, then the change in bottomhole injection pressure as the injection rate is reduced will be a function of the near-wellbore pressure drop.

The key to analyzing a step-down test is that the two main causes of near-wellbore pressure drop can be distinguished easily as the data are analyzed. When the pressure drop near the wellbore is caused by perforation friction, the near-wellbore pressure drop will be a function of the injection rate squared, as Eq. 8.2 shows.

....................(8.2)

If the near-wellbore pressure drop is caused by tortuosity, then the near-wellbore pressure drop will be a function of the injection rate raised to a power of one-half (0.5), as Eq. 8.3 shows.

....................(8.3)

A graph of the value of near-wellbore pressure drop vs. injection rate will provide a clear indication of what is causing the near-wellbore pressure drop. Fig. 8.7 illustrates that the graph of pressure drop vs. injection rate will be concave upward when the pressure drop is dominated by tortuosity and will be concave downward when the pressure drop is dominated by perforation friction.

• 

  Fig. 8.7—Effects of perforations and tortuosity on the near-wellbore pressure drop.

Net Pressure

The reason for computing values of in-situ stress and conducting stress tests, minifracture tests, and step-down tests is to compute the net pressure in the fracture. The net pressure is the difference between the actual pressure in the fracture and the minimum in-situ stress, σ_min.

....................(8.4)

The net pressure is generated by both tip effects and the pressure drop down the fracture caused by viscous fluid flow. Fig. 8.8 illustrates the net pressure profile down a typical fracture. In many formations, the pressure drop down the fracture is dominated by the pressure increases near the tip of the fracture as propagation occurs. The net pressure profile controls both the fracture height and fracture width distribution along the fracture length.

• 

  Fig. 8.8—Pressure profile in a propagating fracture.

The value of net pressure is important because the engineer needs to know for which value to design the main fracture treatment, to perform onsite analyses of the fracturing pressures, and to perform postfracture analyses of the fracturing pressures. One of the best methods to analyze a fracture treatment is to use a fracture propagation model to analyze the net pressures measured during a fracture treatment.

Fracture Propagation Models

The first fracture treatments were pumped just to see if a fracture could be created and if sand could be pumped into the fracture. In 1955, Howard and Fast published the first mathematical model that an engineer could use to design a fracture treatment. The Howard and Fast model assumed the fracture width was constant everywhere, allowing the engineer to compute fracture area on the basis of fracture fluid leakoff characteristics of the formation and the fracturing fluid.

Two-Dimensional Fracture Propagation Models

The Howard and Fast model was a 2D model. In the following years, other 2D models were published.,,, With a 2D model, the engineer fixes one of the dimensions, normally the fracture height, then calculates the width and length of the fracture. With experience and accurate data sets, 2D models can be used in certain formations with confidence, assuming the design engineer can estimate the created fracture height accurately.

Figs. 8.9 and 8.10 illustrate two of the most common 2D models used in fracture treatment design. The Perkins-Kern-Nordgren (PKN) geometry (Fig. 8.9) is normally used when the fracture length is much greater than the fracture height, while the Kristonovich-Geertsma-Daneshy (KGD) geometry (Fig. 8.10) is used if fracture height is more than the fracture length. In certain formations, either of these two models can be used successfully to design hydraulic fractures. The key is to use models (any model) to make decisions, rather than trying to calculate precise values for fracture dimensions. The design must always compare actual results with the predictions from model calculations. By "calibrating" the 2D model with field results, the 2D models can be used to make design changes and improve the success of stimulation treatments. If the correct fracture height value is used in a 2D model, the model will give reasonable estimates of created fracture length and width if other parameters, such as in-situ stress, Young ’

s modulus, formation permeability, and total leakoff coefficient, are also reasonably known and used.

• 

  Fig. 8.9—PKN geometry for a 2D fracture.

• 

  Fig. 8.10—KGD geometry for a 2D fracture.

To illustrate how certain variables affect fracture propagation, Eqs. 8.5 through 8.7 conform to the PKN fracture geometry assumptions. For fluid flow down an elliptical tube,

....................(8.5)

The PKN fracture mechanics equation is

....................(8.6)

and the PKN width equation is

....................(8.7)

Eq. 8.5 is the relationship used to compute the pressure distribution down the fracture for any given combination of injection rate, fracture fluid viscosity, fracture height, and fracture width. This equation, given certain physical dimensions and constraints, provides the pressure distribution in the fracture.

Eq. 8.6 provides the relationship between a given pressure distribution and what the dimensions of the fracture will be on the basis of rock mechanics theory. This equation, given a certain pressure distribution, provides the fracture width distribution. Eq. 8.5 and Eq. 8.6 are solved simultaneously to generate Eq. 8.7 . By reviewing Eq. 8.7 , one can observe that the fracture width will increase when the injection rate increases, the fracture fluid viscosity increases, the fracture length increases, or the formation modulus decreases. Similar equations have been derived by a number of authors. A complete discussion concerning the equations that describe the various 2D fracture models can be found in Geerstma and Geertsma and Haafkens.

Three-Dimensional Fracture Propagation Models. 2D models have been used for decades with reasonable success. Today, with high-powered computers available to most engineers, P3D models are used by most fracture design engineers. P3D models are better than 2D models for most situations because the P3D model computes the fracture height, width, and length distribution with the data for the pay zone and all the rock layers above and below the perforated interval.

Clifton provides a detailed explanation of how 3D fracture propagation theory is used to derive equations for programming 3D models, including P3D models. Figs. 8.11 and 8.12 illustrate typical results from a P3D model. P3D models give more realistic estimates of fracture geometry and dimensions, which can lead to better designs and better wells. P3D models are used to compute the shape of the hydraulic fracture as well as the dimensions. The key to any model, including 3D or P3D models, is to have a complete and accurate data set that describes the layers of the formation to be fracture treated, plus the layers of rock above and below the zone of interest. In most cases, the data set should contain information on 5 to 25 layers of rock that will or possibly could affect fracture growth. It is best to enter data on as many layers as feasible and let the model determine the fracture height growth as a function of where the fracture is started in the model. If the user only enters data on three to five layers, it is likely that the user is deciding the fracture shape rather than the model.

• 

  Fig. 8.11—Width and height from a P3D model.

• 

  Fig. 8.12—Length and height distribution from a P3D model.

Fracturing Fluids and Additives

To create the fracture, a fluid is pumped into the wellbore at a high rate to increase the pressure in the wellbore at the perforations to a value greater than the breakdown pressure of the formation. The breakdown pressure is generally believed to be the sum of the in-situ stress and the tensile strength of the rock. Once the formation is broken down and the fracture created, the fracture can be extended at a pressure called the fracture-propagation pressure. The fracture-propagation pressure is equal to the sum of the in-situ stress, plus the net pressure drop, plus the near-wellbore pressure drop. The net pressure drop is equal to the pressure drop down the fracture as the result of viscous fluid flow in the fracture, plus any pressure increase caused by tip effects. The near-wellbore pressure drop can be a combination of the pressure drop of the viscous fluid flowing through the perforations and/or the pressure drop resulting from tortuosity between the wellbore and the propagating fracture. Thus, the fracturing-fluid properties are very important in the creation and propagation of the fracture.

Properties of a Fracturing Fluid

The ideal fracturing fluid should be compatible with the formation rock and fluid, generate enough pressure drop down the fracture to create a wide fracture, be able to transport the propping agent in the fracture, break back to a low-viscosity fluid for cleanup after the treatment, and be cost-effective. The family of fracture fluids available consist of water-based fluids, oil-based fluids, acid-based fluids, and foam fluids. Table 8.3 lists the types of fracturing fluids that are available and the general use of each type of fluid. For most reservoirs, water-based fluids with appropriate additives will be best. In some cases, foam generated with N₂ or CO₂ can be used to stimulate shallow, low-pressure zones successfully. When water is used as the base fluid, the water should be tested for quality. Table 8.4 presents generally accepted levels of water quality for use in hydraulic fracturing.

• 

  Table 8.3

• 

  Table 8.4

The viscosity of the fracture fluid is important. The fluid should be viscous enough (normally 50 to 1000 cp) to create a wide fracture (normally 0.2 to 1.0 in.) and transport the propping agent into the fracture (normally hundreds to thousands of feet). The density of the fluid is also important. Water-based fluids have densities near 8.4 ppg. Oil-base fluid densities will be 70 to 80% of the densities of water-based fluids. Foam-fluid densities can be substantially less than those of water-based fluids. The fluid density affects the surface injection pressure and the ability of the fluid to flow back after the treatment. In low-pressure reservoirs, low-density fluids, like foam, can be used to assist in the fluid cleanup.

A fundamental principle used in all fracture models is that "the fracture volume is equal to the total volume of fluid injected minus the volume of fluid that leaks off into the reservoir. The fluid efficiency is the percentage of fluid that is still in the fracture at any point in time, when compared with the total volume injected at the same point in time. The concept of fluid loss was used by Howard and Fast to determine fracture area. If too much fluid leaks off, the fluid has a low efficiency (10 to 20%), and the created fracture volume will be only a small fraction of the total volume injected. However, if the fluid efficiency is too high (80 to 90%), the fracture will not close rapidly after the treatment. Ideally, a fluid efficiency of 40 to 60% will provide an optimum balance between creating the fracture and having the fracture close down after the treatment.

In most low-permeability reservoirs, fracture-fluid loss and efficiency are controlled by the formation permeability. In high-permeability formations, a fluid-loss additive is often added to the fracture fluid to reduce leakoff and improve fluid efficiency. In naturally fractured or highly cleated formations, the leakoff can be extremely high, with efficiencies down in the range of 10 to 20%, or less. To fracture treat naturally fractured formations, the treatment often must be pumped at high injection rates with fluid-loss additives.

Fracture-Fluid Additives

Typical additives for a fracture fluid have been described in detail by Ely. Typical additives for a water-based polymer fluid are briefly described next. Table 8.5 presents additional information on additives.

• 

  Table 8.5

Polymers are used to viscosify the fluid. Crosslinkers are used to change the viscous fluid to a pseudoplastic fluid. Biocides are used to kill bacteria in the mix water. Buffers are used to control the pH of the fracture fluid. Surfactants are used to lower the surface tension. Fluid-loss additives are used to minimize fluid leakoff into the formation. Stabilizers are used to keep the fluid viscous at high temperature. Breakers are used to break the polymers and crosslink sites at low temperature.

The operator of an oil or gas well normally does not own the equipment, fluids, or additives required to pump a fracture treatment. The operator hires a service company to mix and pump the fracture treatment. Each service company has its own research department for developing fracture fluids and additives. Each service company obtains its additives from various suppliers. As such, there are no "rules" one can use to select the specific additives for a fracture fluid without first consulting with the service company that will mix and pump the fluid into the well. Many times, pilot tests of the fracture fluids must be conducted to be certain all the additives will work properly at the temperature in the reservoir and for the duration of the treatment.

Propping Agents and Fracture Conductivity

Propping agents are required to "prop open" the fracture once the pumps are shut down and the fracture begins to close. The ideal propping agent is strong, resistant to crushing, resistant to corrosion, has a low density, and is readily available at low cost. The products that best meet these desired traits are silica sand, resin-coated sand (RCS), and ceramic proppants.

Types of Propping Agents

Silica sand is obtained from sand mining. There are several sources in the United States and a few outside the United States. The sand must be tested to be sure it has the necessary compressive strength to be used in any specific situation. Generally, sand is used to prop open fractures in shallow formations. Sand is much less expensive per pound than RCS or ceramic proppants.

RCS is stronger than sand and is used where more compressive strength is required to minimize proppant crushing. Some resins can be used to form a consolidated pack in the fracture, which will help to eliminate proppant flow back into the wellbore. RCS is more expensive than sand, but it has an effective density that is less than sand.

Ceramic proppants consist of sintered bauxite, intermediate-strength proppant (ISP), and lightweight proppant (LWP). The strength of a ceramic proppant is proportional to its density. Also, the higher-strength proppants, like sintered bauxite, cost more than ISP and LWP. Ceramic proppants are used to stimulate deep ( > 8,000 ft) wells where large values of in-situ stresses will apply large forces on the propping agent.

Factors Affecting Fracture Conductivity

The fracture conductivity is the product of propped fracture width and the permeability of the propping agent, as Fig. 8.13 illustrates. The permeability of all the commonly used propping agents (sand, RCS, and the ceramic proppants) will be 100 to 200 +

darcies when no stress has been applied to the propping agent. However, the conductivity of the fracture will be reduced during the life of the well because of increasing stress on the propping agents, stress corrosion affecting the proppant strength, proppant crushing, proppant embedment into the formation, and damage resulting from gel residue or fluid-loss additives.

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  Fig. 8.13—Definition of fracture conductivity.

The effective stress on the propping agent is the difference between the in-situ stress and the flowing pressure in the fracture, as Fig. 8.14 illustrates. As the well is produced, the effective stress on the propping agent will normally increase because the value of the flowing bottomhole pressure will be decreasing. However, as Eq. 8.1 shows, the in-situ stress will decrease with time as the reservoir pressure declines. This phenomenon of decreasing in-situ stress as the reservoir pressure declines was proven conclusively by Salz. Fig. 8.15 illustrates the differences in fracture conductivity as effective stress increases on the propping agent for a variety of commonly used propping agents. The data in Fig. 8.15 clearly show that for shallow wells, where the effective stress is less than 6,000 psi, sand can be used to create high-conductivity fractures. As the effective stress increases to larger and larger values, then the higher-strength, more-expensive propping agents must be used to create a high conductivity fracture.

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  Fig. 8.14—Effective stress on the propping agent.

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  Fig. 8.15—Effect of stress on fracture conductivity from common propping agents.

When choosing a propping agent, a proppant that will maintain enough conductivity after all crushing and embedment occurs must be chosen. The effects of non-Darcy flow, multiphase flow, and gel residue damage should also be considered.

Proppant Transport

To create a hydraulic fracture, fluid is injected at high rate and pressure into a wellbore and into a formation that is open to the wellbore. Viscous fluid flow within the fracture and tip effects create the net pressure required to generate the created width profile and the created fracture height. The volume of fluid pumped will affect the created fracture length. However, without pumping a propping agent into the fracture, the created fracture will close once the pumping operation ceases. The flow of oil and gas from the formation into the fracture is dependent on the propped fracture dimensions. The really important characteristics of a fracture are the propped width, height, and length distributions; therefore, proppant transport considerations are very important in designing a hydraulic fracture treatment. Fig. 8.16 illustrates the difference between the created fracture dimensions and the propped fracture dimensions.

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  Fig. 8.16—Difference between created and propped fracture dimensions.

The first fluid pumped into a well during a fracture treatment is called the "prepad." The prepad is used to fill the casing and tubing, test the system for pressure, and break down the formation. Next, the pad fluid, which is the viscous fracturing fluid used during the treatment, is pumped. No propping agent has been added to the pad. The purpose of the pad is to create a tall, wide fracture that will accept the propping agent. Following the pad, the fluid containing propping agent, which is called the slurry, is pumped. The slurry moves into the fracture, transporting the propping agent. The particles move up, out, and down the fracture with the slurry. The particles also can settle in the fracture as a result of gravitational forces.

Daneshy provided a thorough summary of proppant transport issues. The effects of gravity on proppant settling can be computed by beginning with Stokes

’ law. Eq. 8.8 is Stokes’ law for a single spherical particle of diameter d_p and density ρ_p settling in a Newtonian fluid with a density of ρ_f and a viscosity of μ.

....................(8.8)

Eq. 8.8 shows that the settling velocity will increase as the diameter and density of the propping agent increase and as the density and viscosity of the fracturing fluid decrease. To minimize proppant settling, propping agents that are smaller in diameter and/or less dense, as well as a more viscous fluid, can be used.

However, Stokes’ law must be modified with the use of non-Newtonian fluids and to account for the other particles in suspension in the slurry during the pumping operation. Daneshy provides a complete discussion on the factors that affect proppant transport and how Stokes’

law has been modified to account for many important factors. For example, at low proppant concentrations (1 to 3 ppg), the viscosity of the slurry is relatively unchanged. At high proppant concentrations (8 to 14 ppg), the slurry viscosity can be 3 to 10 times more than the viscosity of the clean fluid. Such factors must be recognized and included in any fracture-propagation design model.

There are other factors that must be included when trying to compute the propped fracture dimensions. The type of fracture fluid will affect proppant transport. Linear fracture fluid will not transport proppants as well as fluids with structure, such as crosslinked fluids or viscoelastic surfactant fluids. Geologic realities also must be considered. For example, no fracture is exactly vertical, and the walls of a fracture are rarely smooth. If there are turns and ledges along the fracture walls, these geologic features tend to reduce proppant settling when compared with the theoretical equations for transport in smooth-wall, parallel-plate systems. Smith et al. discussed other issues and presented several case histories in which fracture-treatment data were analyzed to determine the propped fracture dimensions. Smith stated that fracture height growth during and after pumping operations, fluid loss in layered formations, and slurry viscosity all affect the propped fracture dimensions.

Fracture Treatment Design

Data Requirements

The most important data for designing a fracture treatment are the in-situ stress profile, formation permeability, fluid-loss characteristics, total fluid volume pumped, propping agent type and amount, pad volume, fracture-fluid viscosity, injection rate, and formation modulus. It is very important to quantify the in-situ stress profile and the permeability profile of the zone to be stimulated, plus the layers of rock above and below the target zone that will influence fracture height growth.

There is a structured method that should be followed to design, optimize, execute, evaluate, and reoptimize the fracture treatments in any reservoir. The first step is always the construction of a complete and accurate data set. Table 8.1 lists the sources for the data required to run fracture propagation and reservoir models. The design engineer must be capable of analyzing logs, cores, production data, and well-test data and be capable of digging through well files to obtain all the information needed to design and evaluate the well that is to be hydraulically fracture treated.

Design Procedures. To design the optimum treatment, the effect of fracture length and fracture conductivity on the productivity and the ultimate recovery from the well must be determined. As in all engineering problems, sensitivity runs need to be made to evaluate uncertainties, such as estimates of formation permeability and drainage area. The production data obtained from the reservoir model should be used in an economics model to determine the optimum fracture length and conductivity. Then a fracture treatment must be designed with a fracture propagation model to achieve the desired length and conductivity at minimum cost. The most important concept is to design a fracture with the appropriate data and models that will result in the optimum economic benefit to the well operator, as Fig. 8.2 shows.

A hydraulic fracture propagation model should be run to determine what needs to be mixed and pumped into the well to achieve the optimum values of propped fracture length and fracture conductivity. The base data set should be used to make a base case run. The engineer then determines which variables are the most uncertain. The values of in-situ stress, Young ’

s modulus, permeability, and fluid-loss coefficient often are not known with certainty and must be estimated. The design should acknowledge these uncertainties and make sensitivity runs with the fracture-propagation model to determine the effect of these uncertainties on the design process. As databases are developed, the number and magnitude of the uncertainties will diminish.

In effect, the design engineer should fracture treat the well many times on his or her computer. Sensitivity runs lead to a better design and educate the design engineer on how certain variables affect the values of both the created and propped fracture dimensions.

Fracturing Fluid Selection. The selection of the fracture fluid for the treatment is a critical decision. Economides et al. developed a flow chart that can be used to select the category of fracture fluid on the basis of factors such as reservoir temperature, reservoir pressure, the expected value of fracture half-length, and water sensitivity. Fig. 8.17 presents the fluid-selection flow chart for a gas well. The information in Fig. 8.17 is compatible with the information in Table 8.3.

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  Fig. 8.17—Process for selecting a fracture fluid.

To use Fig. 8.17, one must follow a path that depends on formation temperature, reservoir pressure, and an intangible variable called water sensitivity. For a low-temperature, high-pressure reservoir, the desired fracture conductivity and the desired fracture length must be considered. Economides et al. suggest that Fig. 8.17 can also be used to select a fluid to fracture treat an oil reservoir that is not water sensitive.

The definition of what comprises a water-sensitive reservoir and what causes the damage is not always clear. Most reservoirs contain water, and most oil reservoirs can be waterflooded successfully. Thus, most fracture treatments should be pumped with suitable water-base fracture fluids. Acid-base fluids can be used in carbonates; however, many deep carbonate reservoirs have been stimulated successfully with water-base fluids containing propping agents. Oil-base fluids should be used only in oil reservoirs when water-base fluids have proved conclusively to not work. Pumping oil-base fluids is more dangerous than pumping water-base fluids, and special care should be taken in the field.

Propping-Agent Selection. Fig. 8.18 presents a flow chart created by Economides and Nolte for selecting propping agents. To use Fig. 8.18, the maximum effective stress on the propping agent must be determined. The effective stress is defined in Fig. 8.14. The maximum effective stress depends on the minimum value of flowing bottomhole pressure expected during the life of the well. If the maximum effective stress is less than 6,000 psi, then Fig. 8.18 recommends that sand be used as the propping agent. If the maximum effective stress is between 6,000 and 12,000 psi, then either RCS or intermediate-strength proppant should be used, depending on the temperature. For cases in which the maximum effective stress is greater than 12,000 psi, high-strength bauxite should be used as the propping agent.

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  Fig. 8.18—Proppant selection based on closure pressure (after Economides and Nolte).

Fig. 8.18 should be used only as a guide, because there will be exceptions. For example, even if the maximum effective stress is less than 6,000 psi, the designer may choose to use RCS or other additives to "lock" the proppant in place when proppant flowback becomes an issue. In high-flow-rate gas wells, non-Darcy pressure drops can lead to the use of ceramic proppants to maximize fracture conductivity.

For fracture treatments in countries that do not mine sand for fracturing, the largest cost of the proppant is often the shipping charges. If the propping agent must be imported, intermediate-strength proppants may be selected, even for relatively shallow wells, because the cost differential between the intermediate strength proppants and sand is not much of a factor.

To confirm exactly which type of propping agent should be used during a specific fracture treatment, the designer should factor in the estimated values of formation permeability and optimum fracture half-length. Cinco-Ley published an equation that can be used to determine the optimum fracture conductivity. The dimensionless fracture conductivity is defined as

....................(8.9)

To minimize the pressure drop down the fracture, the value of C_fD should be approximately 10 or greater. The required fracture conductivity can be computed as

....................(8.10)

where k = the formation permeability (md) and L_f = the fracture half-length (ft). For example, if the formation permeability is 25 md and the optimum fracture half-length is 50 ft, then the optimum fracture conductivity would be 3,927 md-ft. The treatment must be designed to create a fracture wide enough, and pump proppants at concentrations high enough, to achieve the conductivity required to optimize the treatment. However, in many low-permeability reservoirs, the dimensionless fracture conductivity, C_fD , must be 50 to 100 for the fracture fluid to clean up after the treatment. As such, the "optimum" value of C_fD = 10 is considered a minimum value, and C_fD should be even larger than 10 when fracture fluid cleanup issues are a problem. In high-permeability formations, C_fD values of 10 or greater are often not feasible.

Some tend to compromise fracture length and conductivity in an often unsuccessful attempt to prevent damage to the formation around the fracture. Holditch showed that substantial damage to the formation around the fracture can be tolerated as long as the optimum fracture length and conductivity are achieved. However, damage to the fracture or the propping agents can be very detrimental to the productivity of the fractured well. Ideally, the optimum fracture length and conductivity can be created while minimizing damage to the formation. If the opposite occurs—that is, the formation is not damaged, but the fracture is not long enough or conductive enough—then the well performance usually will be disappointing.

Evaluating Risks in the Design

The well operator always should evaluate risks such as mechanical risks, product price risks, and geologic risks. Uncertainties in the data can be evaluated by making sensitivity runs with both reservoir models and fracture propagation models. One of the main risks in hydraulic fracturing is that the entire treatment will be pumped and/or paid for (i.e., the money is spent), but, for whatever reason, the well does not produce at the desired flow rates nor achieve the expected cumulative recovery. In some cases, mechanical problems with the well or the surface equipment cause the treatment to fail. Other times, the reservoir does not respond as expected.

To evaluate the risk of mechanical or reservoir problems, 100% of the costs and only a fraction of the revenue can be used in the economic analyses. For example, one in every five fracture treatments in a certain formation is not successful; therefore, 80% of the expected revenue and 100% of the expected costs can be used to determine the optimum fracture length. Fig. 8.19 illustrates how such an analysis can alter the desired fracture length.

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  Fig. 8.19—Optimizing the fracture design considering risks.

Finally, after the optimum, risk-adjusted fracture treatment has been designed, it is extremely important to be certain the optimum design is pumped correctly into the well. For this to occur, the operator and the service company should work together to provide quality control before, during, and after the treatment is pumped. The best engineers spend sufficient time in the office designing the treatment correctly, and then go to the field to help supervise the field operations or provide on-site advice to the supervisor.

Acid Fracturing

Designing an acid-fracturing treatment is similar to designing a fracturing treatment with a propping agent. Williams, Gidley, and Schechter presents a thorough explanation of the fundamentals concerning acid fracturing. The main difference between acid fracturing and proppant fracturing is the way fracture conductivity is created. In proppant fracturing, a propping agent is used to prop open the fracture after the treatment is completed. In acid fracturing, acid is used to "etch" channels in the rock that comprise the walls of the fracture. Thus, the rock has to be partially soluble in acid so that channels can be etched in the fracture walls. As such, the application of acid fracturing is confined to carbonate reservoirs and should never be used to stimulate sandstone, shale, or coal-seam reservoirs. Long etched fractures are difficult to obtain because of high leakoff and rapid acid reaction with the formation.

Acid-Fracturing Candidate Selection

In general, acid fracturing is best applied in shallow, low-temperature carbonate reservoirs. The best candidates are shallow, in which the reservoir temperature is less than 200°F and the maximum effective stress on the fracture will be less than 5,000 psi. Low temperature reduces the reaction rate between the acid and the formation, which allows the acid to penetrate deeper into the fracture before becoming spent. Because limestone reservoirs are ductile, a low effective stress on the fracture is required to maintain adequate fracture conductivity over the life of the well. In deep limestone reservoirs, in which problems exist with high bottomhole temperature and high effective stress on the fracture, water-based fluids with propping agents can be used successfully to stimulate the formation. In deep dolomite reservoirs that are less ductile than limestones, acid fracturing may work satisfactorily; however, proppant fracturing with water-based fluids may work also.

Acid-fracture fluids with propping agents are not recommended. When the acid reacts with the carbonate formation, fines are always released. If a propping agent is used with acid, the fines plug up the propping agent, resulting in very low fracture conductivity. When deciding to stimulate many carbonate reservoirs, the costs and benefits of an acid-fracture treatment should be compared with a treatment that uses water-based fluids carrying a propping agent. It should not be assumed that acid fracturing works best because the formation is a carbonate.

There could be a few applications in which acid fracturing could be the preferred treatment in a deep, high-temperature carbonate reservoir. For example, if a high-permeability carbonate reservoir is damaged as a result of drilling operations or non-Darcy flow effects, then a stimulation treatment can be applied to improve the productivity index. In such cases, injecting acid at fracturing rates can improve the permeability near the wellbore, which will reduce the pressure drop caused by skin and/or non-Darcy flow.

In other cases, especially in deep dolomites that contain an abundance of natural fractures, acid fracturing may work better than proppant fracturing. In such reservoirs, it is common that multiple fractures are opened when pumping begins. With multiple fractures, no single fracture ever gains enough width to accept large concentrations of propping agent. Near-wellbore screenouts often occur as the proppant concentration is increased to more than 2 to 3 ppg. In such cases, acid fracturing may work better than proppant fracturing.

Other considerations when selecting acid-fracturing candidates are cost and safety. In deep, hot reservoirs, the cost of an acid-fracturing treatment can exceed the costs of a proppant-fracture treatment. In hot reservoirs, expensive chemicals are required to inhibit the acid-reaction rate with the steel tubular goods and to retard the reaction rate with the formation. Acid must be handled with extreme care in the field. When pumping large volumes of high-strength acid, at high injection rates and at high pressures, safety should be the top concern of everyone in the field.

Acid Fluids Used in Fracturing

The most commonly used fluid in acid fracturing is 15% hydrochloric acid (HCl). To obtain more acid penetration and more etching, 28% HCl is sometimes used as the primary acid fluid. On occasion, formic acid (HCOOH) or acetic acid (CH₃COOH) is used because these acids are easier to inhibit under high-temperature conditions. However, acetic and formic acid cost more than HCl. Hydrofluoric acid (HF) should never be used during an acid fracturing treatment in a carbonate reservoir.

Typically, a gelled water or crosslinked gel fluid is used as the pad fluid to fill the wellbore and break down the formation. The water-based pad is then pumped to create the desired fracture height, width, and length for the hydraulic fracture. Once the desired values of created fracture dimensions are achieved, the acid is pumped and fingers down the fracture to etch the walls of the fracture to create fracture conductivity. The acid is normally gelled, crosslinked, or emulsified to maintain fracture width and minimize fluid leakoff. Because the acid is reactive with the formation, fluid loss is a primary consideration in the fluid design. Large amounts of fluid-loss additives are generally added to the acid fluid to minimize fluid leakoff. Fluid-loss control is most important in high permeability and/or naturally fractured carbonate formations; thus, long etched fractures are difficult to obtain.

Acid-Fracture Design Considerations

In addition to Williams, Gidley, and Schechter, two papers, provide the technology commonly used today to design acid fracture treatments. There are several unique considerations to be understood when designing acid fracture treatments. Of primary concern is acid-penetration distance down the fracture. The pad fluid is used to create the desired fracture dimensions. Then the acid is pumped down the fracture to etch the fracture walls, which creates fracture conductivity. When the acid contacts the walls of the fracture, the reaction between the acid and the carbonate is almost instantaneous, especially if the temperature of the acid is 200°F or greater. As such, the treatment must be designed to create a wide fracture, with minimal leakoff, with viscous fluids. Fig. 8.20 illustrates why the design engineer should be striving to create a wide fracture. If a wide fracture is created with a viscous acid and minimal fluid loss, then a boundary layer of spent acid products will reduce the rate at which the live acid contacts the formation at the walls of the fracture. However, as the flow in the fracture becomes more turbulent and less laminar, the live acid will contact the walls of the fracture more easily, and the acid will not penetrate very far into the fracture before becoming spent.

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  Fig. 8.20—Acid-flow behavior in the fracture.

Factors such as fracture width, injection rate, acid viscosity, and reservoir temperature all affect acid penetration. Figs. 8.21 and 8.22 illustrate how fracture width and formation temperature affect acid penetration in the fracture, respectively. In Fig. 8.21, as the fracture width increases, the distance that unspent acid will reach in the fracture also increases. The distance increases because, in a wide fracture, there is less turbulence. This results in less mixing as the live acid moves down the fracture; therefore, the viscous and leakoff properties of the fracture fluid should be controlled to maximize fracture width. Fig 8.22 contains information concerning the effects of reservoir temperature, acid strength, and formation lithology. It is clear that the use of higher-strength acid increases the penetration distance in the fracture before the acid spending. Also, as temperature increases, the acid penetration distance decreases. As the temperature increases, the reaction rates between the acid and the formation increase substantially. In fact, the reaction rate doubles every time the temperature increases 18°F. Fig. 8.22 also shows that dolomite is less reactive with HCl than limestone; therefore, acid fracturing may work slightly better in reservoirs that are more highly dolomitized.

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  Fig. 8.21—Effect of fracture width on acid-penetration distance.

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  Fig. 8.22—Effect of temperature, lithology, and acid concentration on acid-penetration distance.

The problem with acid fracturing that prevents its successful application in many reservoirs involves sustaining fracture conductivity over time. When the acid etches the fracture walls, the resulting fracture conductivity can be several orders of magnitude more conductive than similar treatments that use water-based fluids and propping agents. Fig. 8.23 presents data concerning fracture conductivity as a function of effective stress on the fracture and rock embedment strength. The embedment strength is easily measured and can be correlated with the compressive strength of the rock. As the compressive strength increases, the rock embedment strength increases. The data in Fig. 8.23 show that, when the embedment strength is less than 100,000 psi, large fracture conductivities, on the order of 10 to 50,000 md-ft, can be created during an acid-fracture treatment, as long as the effective stress on the fracture is 1,000 psi or less. However, once the effective stress on the fracture exceeds 5,000 psi, the fracture conductivity decreases substantially. As such, in deep limestone reservoirs in which the maximum effective stress on the fracture is much greater than 5,000 psi, an acid fracture will not stay open as the well is produced. In such cases, water-based fluids carrying propping agents should be considered as an alternative to acid fracturing.

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  Fig. 8.23—Fracture conductivity in a carbonate reservoir as a function of effective stress on the fracture and embedment strength.

Fracturing High-Permeability Formations

Smith and Hannah documented the evolution of hydraulic fracturing in high-permeability reservoirs since the 1950s. The first fracture treatments in the 1950s were pumped in moderate- to high-permeability formations. Those treatments were designed to remove formation damage that usually occurred during the drilling and completion operations. Low-permeability reservoirs were fracture treated in the 1950s and 1960s, but, at low oil and gas prices, low-permeability reservoirs were generally not economic, even after a successful fracture treatment.

The values of high, moderate, and low permeability need to be defined on the basis of both the formation permeability and the reservoir fluid viscosity, or the k/μ ratio, where k is the formation permeability in md, and μ is the formation fluid viscosity in cp. For a gas well, the average viscosity of the gas is assumed to be approximately 0.02 cp. For a typical gas well, a low-permeability formation might be where k < 0.1 md, a medium-permeability reservoir might be 10> k> 1 md, and a high-permeability reservoir might be 25 md> k. If the formation contains oil with a fluid viscosity of 2 cp, then all the permeability values must be multiplied by a factor of 100 to determine what is a low-, moderate-, and high-permeability formation. This example illustrates that the definition of "high permeability" also depends on the value of the reservoir-fluid viscosity. In heavy-oil plays, in which the reservoir fluid viscosity is several thousand centipoises, then formations with several Darcies permeability would be considered a low-permeability reservoir. From this point forward, we assume that the formation fluid is either gas or light oil; thus, a formation with a permeability of several hundred millidarcies or more will be considered high permeability.

Candidate Selection Criteria for High-Permeability Formations

The main reasons for fracture treating high-permeability formations are to improve both the reservoir and wellbore communication, to bypass formation damage, to reduce the drawdown around the wellbore, to increase the back stress on the formation, to control sand production, to reduce fines migration, to reduce asphaltene deposition, and to reduce water coning. As mentioned, the early fracture treatments were pumped to break through damage near the wellbore and increase the productivity index of the formation. Today, fracture treatments in high-permeability wells are pumped to bypass damage, but other reasons have become just as important. For example, many treatments are pumped for sand-control purposes. By creating a short, highly conductive fracture connecting the reservoir to the wellbore, the productivity index is increased; thus, more oil and gas can be produced with a lower drawdown. As the drawdown is reduced, the tendency of a poorly consolidated reservoir to produce sand is also reduced. The reduction in drawdown also helps to deter fines migration, asphaltene deposition, and water coning in certain formations.

Design Considerations for High-Permeability Formations

Most fracture treatments in high-permeability formations are designed to achieve a tip screenout. A tip screenout design is one in which the pad volume is designed carefully so that the pad leaks off during the treatment, causing the propping agent to bridge at the tip of the fracture near the end of the job. At this point, the fracture quits growing in length, but pumping continues. As pumping continues, the pressure in the fracture increases, which leads to increasing width and, sometimes, increasing height. The fracture continues to inflate and is packed with the propping agent. The purpose of a tip-screenout design is to create a short, extremely wide fracture that is completely packed with the propping agent.

Smith and Hannah documented that Amoco successfully combined hydraulic fracturing and gravel packing in the Hackberry field south of Lake Charles, Louisiana, in 1984. Hannah et al. described a combination fracture treatment and gravel pack in an offshore field in 1994. Since the early 1990s, "frac-pack" treatments have become standard for many producing areas worldwide. Frac-pack treatments tend to reduce the skin factors from very high numbers (10 to 50) to essentially a skin of zero. In other words, the damage to the formation surrounding the wellbore during the drilling and completion of the well is negated by the frac-pack operations. In many cases, the productivity index is increased by a factor of three or more by the frac-pack treatments.

Park provided information concerning the design criteria for tip screenout treatments that are part of a frac-pack operation. In general, the designed fracture lengths for a frac-pack treatment are from 10 to 50 ft. The treatments are designed to create as wide a propped fracture as possible; thus, treatments are designed for proppant concentrations as high as 17 to 20 lbm/ft² . Many unconsolidated or poorly consolidated sands have values of Young ’

s modulus that range from 90,000 to 200,000 psi, which theoretically can result in created fracture widths of 3 in. and propped fracture widths of 2 in. As the value of modulus increases, the rock becomes stiffer, the created fractures become narrower, and the amount of propping agent that can be placed in the fracture decreases. Tip screenout treatments can be designed with almost any fracture-treatment-design model. Just like any design, the engineer must have data that describe the reservoir and the treatment conditions accurately. Some fracture design models have special features to optimize the size of the pad volume, the leakoff characteristics of the fluid, and other variables that affect tip screenout designs.

Early frac-pack treatments were pumped with the equipment, fluids, and gravel commonly used in gravel-packing operations. For example, the fluid most commonly used was hydroxyethyl cellulose gel because it is clean and should not significantly damage the reservoir. Also, 40- to 60-mesh gravel was used as the propping agent. As the technology has evolved, other fluids such as hydroxypropyl guar crosslinked with borates and viscoelastic surfactant fluids have been used successfully to pump a frac-pack treatment. Because fracture conductivity is so important, the use of 20- to 40-mesh proppants is now common.

In summary, fracture treatment technology was first developed in the 1950s to break through damage in high-permeability reservoirs. In the 1960s, gelled water fluids were used successfully to fracture treat both low- and high-permeability oil and gas wells. The technology evolved in the 1970 and 1980s; the industry was pumping massive hydraulic fracture treatments in microdarcy reservoirs. Massive treatments in tight reservoirs are still being pumped today and will become even more important in the future. However, in the 1990s, because of the tip screenout design process and frac-pack operations, stimulation of high-permeability reservoirs is once again an important aspect of hydraulic fracturing to reduce the effects of formation damage and to enhance gravel packing.

Fracture Diagnostics

Fracture diagnostics involves analyzing the data before, during, and after a hydraulic fracture treatment to determine the shape and dimensions of both the created and propped fracture. Fracture diagnostic techniques are divided into several groups.

Direct Far-Field Techniques

Direct far-field methods consists of tiltmeter-fracture-mapping and microseismic-fracture-mapping techniques. These techniques require sophisticated instrumentation embedded in boreholes surrounding the well to be fracture treated. When a hydraulic fracture is created, the expansion of the fracture causes the earth around the fracture to deform. Tiltmeters can be used to measure the deformation and to compute the approximate direction and size of the created fracture. Surface tiltmeters are placed in shallow holes surrounding the well. Downhole tiltmeters are placed in vertical wells at depths near the zone to be fracture treated. As with surface tiltmeters, downhole tiltmeter data are analyzed to determine the orientation and dimensions of the created fracture.

Microseismic fracture mapping relies on a downhole receiver array of accelerometers or geophones to locate microseisms or microearthquakes that are triggered by shear slippage in natural fractures surrounding the hydraulic fracture. Fig. 8.24 illustrates the principle of microseismic fracture mapping. In essence, noise is created in a zone surrounding the hydraulic fracture. With sensitive arrays of instruments, the noise can be monitored, recorded, analyzed, and mapped.

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  Fig. 8.24—Principle of microseismic fracture mapping.

Although direct far-field techniques can be used to map hydraulic fractures, the technology is still under development. When the technology is used in a field, the data and knowledge gained are often used on subsequent wells to spread out the costs. Knowing the fracture orientation is useful in planning field development and in optimizing future fracture treatments.

Direct Near-Wellbore Techniques

Direct near-wellbore techniques are run in the well that is being fracture treated to locate or image the portion of fracture that is very near (within inches of) the wellbore. Direct near-wellbore techniques consist of tracer, temperature, production, borehole image, downhole video, and caliper logs. If a hydraulic fracture intersects the wellbore, these direct near-wellbore techniques can be of some benefit in locating the hydraulic fracture.

However, these near-wellbore techniques are not unique and cannot supply information on the size or shape of the fracture once the fracture is two to three wellbore diameters in distance from the wellbore. In naturally fractured reservoirs, in which multiple fractures are likely to exist, the reliability of direct near-wellbore techniques are even more speculative. As such, direct near-wellbore techniques are used only to find where the hydraulic fracture exited the wellbore and to map the fracture that is essentially connected directly to the wellbore.

Indirect Fracture Techniques

Indirect fracture techniques consist of hydraulic fracture modeling of net pressures, pressure-transient-test analyses, and production-data analyses. Because the fracture-treatment data and the post-fracture production data are normally available on every well, the indirect fracture diagnostic techniques are the most widely used methods to determine the shape and dimensions of both the created and the propped hydraulic fracture.

The fracture-treatment data can be analyzed with a P3D fracture propagation model to determine the shape and dimensions of the created fracture. The P3D model is used to history match the fracturing data, such as injection rates and injection pressures. Data, such as the in-situ stress and permeability in key layers of rock, can be varied (within reason) to achieve a history match of the field data.

Post-fracture production and pressure data can be analyzed with a 3D reservoir simulator to estimate the shape and dimensions of the propped fracture. Values of formation permeability, fracture length, and fracture conductivity can be varied in the reservoir model to achieve a history match of the field data.

The main limitations of these indirect techniques are that the solutions may not be unique and may require as much fixed data as possible. For example, if the engineer has determined the formation permeability from a well test or production test before the fracture treatment, so that the value of formation permeability is known and can be fixed in the models, the solution concerning values of fracture length become more unique. Most of the information in the literature concerning post-fracture analyses of hydraulic fractures has been derived with these indirect fracture diagnostic techniques.

Limitations of Fracture Diagnostic Techniques. Warpinski discussed many of these same fracture diagnostic techniques. Table 8.6 lists certain diagnostic techniques and their limitations. Fracture diagnostic techniques do work and can provide important data when entering a new area or a new formation. In most cases, however, fracture diagnostics is expensive, which limits its widespread use in industry. In the future, if costs are reduced, fracture diagnostics may become more widely applied.

• 

  Table 8.6

Net-Pressure Analysis

Net pressure is defined as the pressure in the fracture minus the in-situ stress. Nolte and Smith published a classic paper that can be used to interpret net-pressure behavior in the field or after the treatment to determine estimates of fracture growth patterns. Their analysis method uses the PKN theory, which assumes that as long as the fracture height is contained, the net pressure will increase with time according to

....................(8.11)

where 1/8 < e < 1/5 and slope e = 1/5 for low leakoff and 1/8 for high leakoff.

When Nolte and Smith began analyzing bottomhole pressure data collected during fracture treatments, they found that the PKN theory held for certain situations, but other fracture propagation modes were observed. Fig. 8.25 summarizes their findings. In Fig. 8.25, Mode I conforms to Eq. 8.11; however, three other modes were identified by analyzing field data.

• 

  Fig. 8.25—Interpretation of fracturing pressures.

Mode II conforms to either stable height growth or increased fluid loss. Mode II fracturing is not unusual, nor is it cause for concern. Lateral fracture growth during Mode II is less than Mode I, but the fracture is still being propagated and can be filled with proppant.

When the slope of the graph of log(p_n) vs. log(Δt) increases to a unit slope (Mode III), then the fracture has stopped propagating in length, and the fracture is being inflated as the net pressure increases. This is the desired behavior if a tip screenout treatment has been designed. During Mode III, it is still possible to pack the fracture with proppant; however, the pressure has to be monitored closely to be certain the maximum allowable surface injection pressure is not exceeded. Mode IV occurs when the fracture height is increasing rapidly. Normally, rapid height growth is not desirable, and the fracture treatment should be flushed and terminated if Mode IV is reached during the treatment.

The pressures analyzed in a "net pressure graph," such as Fig. 8.25, are bottomhole pressures and should be corrected for near-wellbore pressure drops. Fig 8.26 shows the pressures in the entire system. During every fracture treatment, the surface pressure can be measured. On certain wells, the bottomhole treating pressure (BHTP), which is the pressure inside the wellbore at the perforations, can be measured. If the BHTP is not measured directly, then that value must be computed with the surface pressure and the estimates of pipe friction and hydrostatic head. The hydrostatic head can be estimated accurately, even when propping agents are being added, because a densitometer is used to measure the density of the slurry as it is pumped. Problems may occur in trying to estimate the pipe friction when using crosslinked polymer fluids containing propping agents. Significant errors can occur in the pipe friction estimates when high proppant concentrations (

>

4 ppg) are being pumped.

• 

  Fig. 8.26—Wellbore and near-wellbore hydraulics.

If the BHTP is computed or measured successfully, the near-wellbore pressure drop must be subtracted to determine the pressure in the fracture near the wellbore, p_f. The pressure in the fracture near the wellbore is the value that must be known and analyzed to determine the width, height, and length of the fracture with either net pressure theory or P3D fracture propagation models. The near-wellbore pressure drop is composed of two parts: the perforation friction and tortuosity. By running a step-down test before the main fracture treatment, the near-wellbore pressure drop often can be estimated accurately. One problem is that the perforation friction and the tortuosity pressure drop can change during the treatment as the propping agent is introduced. The propping agent can erode perforations or plug some of the pathways that are causing the tortuosity pressure drops. At the end of the treatment, the pressure data need to be analyzed as the pumps are shut down to determine if the near-wellbore pressure drop has changed during the treatment.

Post-Fracture Well Behavior

There are many factors that the engineer must consider when analyzing the behavior of a well after it has been fracture treated. The engineer should analyze the productivity index of the well both before and after the fracture treatment. Other factors of importance are ultimate oil and gas recovery and calculations to determine the propped fracture length, the fracture conductivity, and the drainage area of the well. Post-fracture treatment analyses of the fracture treatment data, the production data, and the pressure data can be very complicated and time consuming. However, without adequate post-fracture evaluation, it will be impossible to continue the fracture treatment optimization process on subsequent wells.

Productivity Index Increase

Many of the early treatments in the 1950s were designed to increase the productivity index of damaged wells. These treatments were normally pumped to break through damage in moderate- to high-permeability wells. The productivity index of an oil well is

....................(8.12)

For a gas well,

....................(8.13)

where and are evaluated at the average pressure of

....................(8.14)

J is the productivity index in terms of barrels per psi per day or mcf-cp per psi squared per day. Viscosity and compressibility are included in the equation describing the productivity index of a gas well, because they are pressure dependent. McGuire and Sikora published a procedure (Fig. 8.27) that was the first tool a fracture-treatment design engineer could use to determine the fracture length and fracture conductivity required to achieve a certain fold of increase in the productivity index. The McGuire and Sikora graph can be used to draw the following conclusions:

• 

  Fig. 8.27—McGuire and Sikora graph.

• For high-permeability reservoirs, fracture conductivity is more important than fracture length.
• For low-permeability reservoirs, fracture length is more important than fracture conductivity.
• For a given fracture length, there is an optimum value of conductivity ratio.
• Most fracture treatments in undamaged formations should result in stimulation ratios of 2 to 14.

These conclusions have allowed engineers to design successful fracture treatments for more than 40 years.

At approximately the same time as the classic McGuire and Sikora paper was published, Prats published another classic paper. Assuming J is the productivity index for a fractured well at steady-state flow, and J_o is the productivity index of the same well under radial flow conditions, Prats found that

....................(8.15)

for a well containing an infinite conductivity fracture whose fracture half-length is L_f . Prats explained that a well with a fracture half-length of 100 ft will produce as if the well had been drilled with a 100-ft diameter drill bit. In other words, the hydraulic fracture, if conductive enough, acts to extend the wellbore and stimulate flow rate from the well. If the dimensionless fracture conductivity, C_fD (Eq. 8.9), is equal to 10 or greater, the hydraulic fracture will essentially act as if it is an infinitely conductive fracture.

Ultimate Recovery for Fractured Wells

Hydraulic fracturing should always increase the productivity index of a well; and, under certain circumstances, the hydraulic fracture can increase the ultimate recovery. Figs. 8.28 and 8.29 illustrate the differences that sometimes occur between low-permeability and high-permeability reservoirs. In Fig. 8.28, when a high-permeability well is fracture treated, the drainage volume and the recovery efficiency in the reservoir are not significantly altered. The fracture treatment increases the flow rate, increases the decline rate, and decreases the producing life of the well. The ultimate recovery is not changed. The same reserves are recovered in a shorter period of time, which reduces overall operating costs. Accelerating the recovery of a fixed volume of reserves is often beneficial. If the well is located in the Arctic or offshore in deep water, where operating costs are very high, then recovering the reserves sooner is very advantageous.

• 

  Fig. 8.28—Production behavior in a high-permeability formation.

• 

  Fig. 8.29—Production behavior in a low-permeability formation.

Fig. 8.29 illustrates the normal situation in low-permeability reservoirs. Without a fracture treatment, most low-permeability wells will flow at low rates and recover only modest volumes of oil and gas before reaching their economic limit. By definition, a low-permeability well will not be economic unless a successful fracture treatment is both designed and pumped into the formation. When the stimulation treatment is successful, the flow rate will increase, the ultimate recovery will increase, and the producing life will be extended. In fact, many low-permeability wells will produce for 40 or more years, given adequate product prices and minimal operating costs. It is usually very easy to justify fracture treatments in low-permeability wells when the fracture treatment substantially increases the ultimate recovery.

Post-Fracture Well-Test Analyses

Post-fracture well-test analyses are used to compute estimates of the propped fracture length, fracture conductivity, and drainage area of the formation. It is important to keep good records of the flow rates of oil, gas, and water, as well as the flowing pressures after the fracture treatment. If possible, a pressure-buildup test should be run after the well cleanup following the fracture treatment. Lee presented a complete discussion on how to analyze production and pressure data after a fracture treatment to estimate fracture properties.

Nomenclature

a	=	constant (solved for)
A	=	area, L2, acres
B	=	Borate crosslinker
c	=	acid concentration
co	=	original acid concentration
Cf	=	fracture conductivity, md-ft
CfD	=	dimensionless fracture conductivity
dp	=	proppant diameter, L
dpf	=	perforation diameter, L, in.
g	=	gravitational constant
G	=	Shear modulus, m/L3
h	=	fracture height, L
hg	=	gross height, L
hi	=	fracture height, L
hn	=	net pay, L
H	=	fracture height, L
i	=	injection rate, L3/t
ipf	=	specific injection rate, bbl/min-perforation
J	=	productivity index, STB/D/psi
Jo	=	productivity index of unfractured well, STB/D/psi
Js	=	productivity index of stimulated well, STB/D/psi
k	=	formation permeability, L2, md
kf	=	fracture permeability, L2, md
L	=	fracture half-length, L, ft
Lf	=	fracture half-length, L, ft
n	=	number for perforations
pe	=	pressure at the extremity of the reservoir, psi
Pf	=	pipe friction
pf	=	actual pressure in the fracture, m/Lt2
ph	=	hydrostatic head
pn	=	net pressure, m/Lt2
p′n	=	critical net pressure, m/Lt2
pp	=	pore pressure (reservoir pressure), m/Lt2
ppfr	=	perforation friction, psi
ps	=	surface pressure, m/Lt</sup>2</sup>
pt	=	pressure drop because of tortuosity
pwf	=	flowing bottomhole pressure, m/Lt2
Pe	=	stress on proppant
Ppf	=	perforation friction
qg	=	gas flow rate, Mcf/D
qo	=	oil flow rate, STB/D
Q	=	injection rate, L3/t
re	=	drainage radius, ft
rw	=	wellbore radius, ft
S1–6	=	in-situ stresses in layers 1–6, m/L2
t	=	time, t
T	=	temperature, T, °F
u	=	viscosity, cp
	=	average gas viscosity, cp
ν	=	Poisson’ s ratio
	=	velocity in the fracture, L/t
vt	=	terminal settling velocity, ft/min
vx	=	velocity down the fracture
w	=	fracture width, L
	=	average fracture width, L
ww	=	fracture width at the wellbore, L
x	=	distance, L
z	=	gas compressibility factor
α	=	Biot’ s constant
α	=	discharge coefficient, usually 0.9 (in Eq. 8.2 )
Δt	=	change in time, t
Δpτ	=	pressure drop near perforations wellbore because of tortuosity, m/Lt2
∂ Δp	=	change in net pressure in the fracture, m/Lt2
∂x	=	incremental distance down the fracture, L
μ	=	fluid viscosity, m/Lt
ρ	=	fracturing-fluid density, m/L3
ρp	=	proppant density, m/L3
ρmin	=	minimum in-situ stress, m/L2
ρf	=	fluid density, m/L3
σc	=	closure stress on the fracture
σext	=	tectonic stress, m/Lt2
σmin	=	minimum horizontal stress (in-situ stress), m/Lt2
σob	=	overburden stress, m/Lt2
σ1	=	vertical (overburden) stress, m/Lt2
σ2	=	minimum horizontal stress, m/Lt2
σ3	=	maximum horizontal stress, m/Lt2

References

SI Metric Conversion Factors

bbl	×	1.589 873	E – 01	=	m3
cp	×	1.0*	E – 03	=	Pa•s
°F		(°F – 32)/1.8		=	°C
ft	×	3.048*	E – 01	=	m
ft2	×	9.290 304*	E – 02	=	m2
in.	×	2.54*	E+ 00	=	cm
lbm	×	4.535 924	E – 01	=	kg
psi	×	6.894 757	E+ 00	=	kPa

*

Conversion factor is exact.