WHAT IS FRACKING? FACTS ABOUT FRACKING

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Hydraulic fracturing, Also Known As Fracking, is a Well stimulation technique in which rock is fractured by a pressurized liquid. The process involves the high-pressure injection of ‘fracking fluid’ (primarily water, containing sand or other proppants suspended with the aid of thickening agents) into a wellbore to create cracks in the deep-rock formations through which natural gas, petroleum, and brine will flow more freely. When the hydraulic pressure is removed from the well, small grains of hydraulic fracturing proppants (either sand or aluminium oxide) hold the fractures open.

Hydraulic fracturing began as an experiment in 1947, and the first commercially successful application followed in 1950. Approximately 5million “frac jobs” had been performed worldwide on oil and gas wells. Such treatment is generally necessary to achieve adequate flow rates in shale gas, tight gas, tight oil, and coal seam gas wells. Some hydraulic fractures can form naturally in certain veins.

Drilling and hydraulic fracturing have made the United States a major crude oil exporter, but the leakage of methane, a powerful greenhouse gas, has dramatically increased. Increased oil and gas production from the decade-long fracking boom has led to lower prices for consumers, with near-record lows of the share of household income going to energy expenditures.

Hydraulic fracturing is highly controversial. Its proponents advocate the economic benefits of more extensively accessible hydrocarbons, as well as replacing coal with natural gas, which burns more cleanly and emits less carbon dioxide (CO2). Opponents of fracking argue that these are outweighed by the environmental impacts, which include groundwater and surface water contamination, noise and air pollution, and the triggering of earthquakes, along with the resulting hazards to public health and the environment.

Research has determined that human health is affected, including confirmation of chemical, physical, and psychosocial hazards such as pregnancy and birth outcomes, chronic rhinosinusitis, severe fatigue and asthma exacerbations. Groundwater contamination has been documented. Adherence to regulation and safety procedures is required to avoid further negative impacts.

There is considerable uncertainty about the scale of methane leakage associated with hydraulic fracturing, and even some evidence that leakage may cancel out the greenhouse gas emissions benefits of natural gas relative to other fossil fuels. For example, a report by Environmental Defense Fund (EDF) highlights this issue, focusing on the leakage rate in Pennsylvania during extensive testing and analysis was found to be approximately 10%, or over five times the reported figures. This leakage rate is considered representative of the hydraulic fracturing industry in the US generally.

Increases in seismic activity following hydraulic fracturing along dormant or previously unknown faults are sometimes caused by the deep-injection disposal of hydraulic fracturing flow back (a byproduct of hydraulically fractured wells), and produced formation brine (a byproduct of both fractured and nonfractured oil and gas wells). For these reasons, hydraulic fracturing is under international scrutiny, restricted in some countries, and banned altogether in others. The European Union is drafting regulations that would permit the controlled application of hydraulic fracturing.

GEOLOGY

MECHANICS

Fracturing rocks at great depth frequently becomes suppressed by pressure due to the weight of the overlying rock strata and the cementation of the formation. This suppression process is particularly significant in “tensile” (Mode 1) fractures which require the walls of the fracture to move against this pressure. Fracturing occurs when effective stress is overcome by the pressure of fluids within the rock.

The minimum principal stress becomes tensile and exceeds the tensile strength of the material. Fractures formed in this way are generally oriented in a plane perpendicular to the minimum principal stress, and for this reason, hydraulic fractures in well bores can be used to determine the orientation of stresses. In natural examples, such as dykes or vein-filled fractures, the orientations can be used to infer past states of stress.

VEINS

Most mineral vein systems are a result of repeated natural fracturing during periods of relatively high pore fluid pressure. The impact of high pore fluid pressure on the formation process of mineral vein systems is particularly evident in “crack-seal” veins, where the vein material is part of a series of discrete fracturing events and extra vein material is deposited on each occasion.

One example of long-term repeated natural fracturing is in the effects of seismic activity. Stress levels rise and fall episodically, and earthquakes can cause large volumes of connate water to be expelled from fluid-filled fractures. This process is referred to as “seismic pumping”.

DYKES

Minor intrusions in the upper part of the crust, such as dykes, propagate in the form of fluid-filled cracks. In such cases, the fluid is magma. In sedimentary rocks with significant water content, fluid at fracture tip will be steam.

PRECURSORS

Fracturing as a method to stimulate shallow, hard rock oil wells dates back to the 1860s. Dynamite or nitroglycerin detonations were used to increase oil and natural gas production from petroleum bearing formations. On 24 April 1865, US Civil War veteran Col. Edward A. L. Roberts received a patent for an “exploding torpedo”.

It was employed in Pennsylvania, New York, Kentucky, and West Virginia using liquid and also, later, solidified nitroglycerin. Later still the same method was applied to water and gas wells. Stimulation of wells with acid, instead of explosive fluids, was introduced in the 1930s. Due to acid etching, fractures would not close completely resulting in further productivity increase.

OIL AND GAS WELLS

The relationship between well performance and treatment pressures was studied by Floyd Farris of Stanolind Oil and Gas Corporation. This study was the basis of the first hydraulic fracturing experiment, conducted in 1947 at the Hugoton gas field in Grant County of southwestern Kansas by Stanolind. For the well treatment, 1,000 US gallons (3,800 l; 830 imp gal) of gelled gasoline (essentially napalm) and sand from the Arkansas River was injected into the gas-producing limestone formation at 2,400 feet (730 m). The experiment was not very successful as deliverability of the well did not change appreciably.

The process was further described by J.B. Clark of Stanolind in his paper published in 1948. A patent on this process was issued in 1949 and an exclusive license was granted to the Halliburton Oil Well Cementing Company. On 17 March 1949, Halliburton performed the first two commercial hydraulic fracturing treatments in Stephens County, Oklahoma, and Archer County, Texas. Since then, hydraulic fracturing has been used to stimulate approximately one million oil and gas wells in various geologic regimes with good success.

In contrast with large-scale hydraulic fracturing used in low-permeability formations, small hydraulic fracturing treatments are commonly used in high-permeability formations to remedy “skin damage”, a low-permeability zone that sometimes forms at the rock-borehole interface. In such cases, the fracturing may extend only a few feet from the borehole.

In the Soviet Union, the first hydraulic proppant fracturing was carried out in 1952. Other countries in Europe and Northern Africa subsequently employed hydraulic fracturing techniques including Norway, Poland, Czechoslovakia, Yugoslavia, Hungary, Austria, France, Italy, Bulgaria, Romania, Turkey, Tunisia, and Algeria.

MASSIVE FRACTURING

Massive hydraulic fracturing (also known as high-volume hydraulic fracturing) is a technique first applied by Pan American Petroleum in Stephens County, Oklahoma, USA in 1968. The definition of massive hydraulic fracturing varies, but generally refers to treatments injecting over 150 short tons, or approximately 300,000 pounds (136 metric tonnes), of proppant.

American geologists gradually became aware that there were huge volumes of gas-saturated sandstones with permeability too low (generally less than 0.1 millidarcys) to recover the gas economically. Starting in 1973, massive hydraulic fracturing was used in thousands of gas wells in the San Juan Basin, Denver Basin, the Piceance Basin and the Green River Basin, and in other hard rock formations of the western US.

Other tight sandstone wells in the US made economically viable by massive hydraulic fracturing were in the Clinton-Medina Sandstone (Ohio, Pennsylvania, and New York), and Cotton Valley Sandstone (Texas and Louisiana).

Massive hydraulic fracturing quickly spread in the late 1970s to western Canada, Rotliegend and Carboniferous gas-bearing sandstones in Germany, Netherlands (onshore and offshore gas fields), and the United Kingdom in the North Sea.

Horizontal oil or gas wells were unusual until the late 1980s. Then, operators in Texas began completing thousands of oil wells by drilling horizontally in the Austin Chalk and giving massive slickwater hydraulic fracturing treatments to the wellbores. Horizontal wells proved much more effective than vertical wells in producing oil from tight chalk; sedimentary beds are usually nearly horizontal, so horizontal wells have much larger contact areas with the target formation.

Hydraulic fracturing operations have grown exponentially since the mid-1990s when technologic advances and increases in the price of natural gas made this technique economically viable.

SHALES

Hydraulic fracturing of shales goes back at least to 1965, when some operators in the Big Sandy gas field of eastern Kentucky and southern West Virginia started hydraulically fracturing the Ohio Shale and Cleveland Shale, using relatively small fracs. The frac jobs generally increased production, especially from lower-yielding wells.

In 1976, the United States government started the Eastern Gas Shales Project, which included numerous public-private hydraulic fracturing demonstration projects. During the same period, the Gas Research Institute, a gas industry research consortium, received approval for research and funding from the Federal Energy Regulatory Commission.

In 1997, Nick Steinsberger, an engineer of Mitchell Energy (now part of Devon Energy), applied the slickwater fracturing technique, using more water and higher pump pressure than previous fracturing techniques, which was used in East Texas in the Barnett Shale of North Texas.

In 1998, the new technique proved to be successful when the first 90 days of gas production from the well called S.H. Griffin No. 3 exceeded the production of any of the company’s previous wells. This new completion technique made gas extraction widely economical in the Barnett Shale and was later applied to other shales, including the Eagle Ford and Bakken Shale. George P. Mitchell has been called the “father of fracking” because of his role in applying it in shales.

The first horizontal well in the Barnett Shale was drilled in 1991 but was not widely done in the Barnett until it was demonstrated that gas could be economically extracted from vertical wells in the Barnett.

PROCESS

According to the United States Environmental Protection Agency (EPA), hydraulic fracturing is a process to stimulate a natural gas, oil, or geothermal well to maximize extraction. The EPA defines the broader process to include acquisition of source water, well construction, well stimulation, and waste disposal.

METHOD

A hydraulic fracture is formed by pumping fracturing fluid into a wellbore at a rate sufficient to increase pressure at the target depth (determined by the location of the well casing perforations), to exceed that of the fracture gradient (pressure gradient) of the rock. The fracture gradient is defined as pressure increase per unit of depth relative to density and is usually measured in pounds per square inch, per square foot, or bars.

The rock cracks and the fracture fluid permeates the rock extending the crack further, and further, and so on. Fractures are localized as pressure drops off with the rate of frictional loss, which is relative to the distance from the well. Operators typically try to maintain “fracture width” or slow its decline following treatment, by introducing a proppant into the injected fluid – a material such as grains of sand, ceramic or other particulate, thus preventing the fractures from closing when injection is stopped and pressure removed.

Consideration of proppant strength and prevention of proppant failure becomes more important at greater depths where pressure and stresses on fractures are higher. The propped fracture is permeable enough to allow the flow of gas, oil, saltwater and hydraulic fracturing fluids to the well.

During the process, fracturing fluid leakoff (loss of fracturing fluid from the fracture channel into the surrounding permeable rock) occurs. If not controlled, it can exceed 70% of the injected volume. This may result in formation of matrix damage, adverse formation fluid interaction, and altered fracture geometry, thereby decreasing efficiency.

The location of one or more fractures along the length of the borehole is strictly controlled by various methods that create or seal holes in the side of the wellbore. Hydraulic fracturing is performed in cased wellbores, and the zones to be fractured are accessed by perforating the casing at those locations.

Hydraulic-fracturing equipment used in oil and natural gas fields usually consists of a slurry blender, one or more high-pressure, high-volume fracturing pumps (typically powerful triplex or quintuplex pumps) and a monitoring unit.

Associated equipment includes fracturing tanks, one or more units for storage and handling of proppant, high-pressure treating iron, a chemical additive unit (used to accurately monitor chemical addition), low-pressure flexible hoses, and many gauges and meters for flow rate, fluid density, and treating pressure.

Chemical additives are typically 0.5% of the total fluid volume. Fracturing equipment operates over a range of pressures and injection rates and can reach up to 100 megapascals (15,000 psi) and 265 litres per second (9.4 cu ft/s) (100 barrels per minute).

WELL TYPES

A distinction can be made between conventional, low-volume hydraulic fracturing, used to stimulate high-permeability reservoirs for a single well, and unconventional, high-volume hydraulic fracturing, used in the completion of tight gas and shale gas wells.

High-volume hydraulic fracturing usually requires higher pressures than low-volume fracturing; the higher pressures are needed to push out larger volumes of fluid and proppant that extend farther from the borehole.

Horizontal drilling involves wellbores with a terminal drillhole completed as a “lateral” that extends parallel with the rock layer containing the substance to be extracted. For example, laterals extend 1,500 to 5,000 feet (460 to 1,520 m) in the Barnett Shale basin in Texas and up to 10,000 feet (3,000 m) in the Bakken formation in North Dakota. In contrast, a vertical well only accesses the thickness of the rock layer, typically 50–300 feet (15–91 m). Horizontal drilling reduces surface disruptions as fewer wells are required to access the same volume of rock.

Drilling often plugs up the pore spaces at the wellbore wall, reducing permeability at and near the wellbore. This reduces flow into the borehole from the surrounding rock formation, and partially seals off the borehole from the surrounding rock. Low-volume hydraulic fracturing can be used to restore permeability.

FRACTURING FLUIDS

The main purposes of fracturing fluid are to extend fractures, add lubrication, change gel strength and to carry proppant into the formation. There are two methods of transporting proppant in the fluid – high-rate and high-viscosity. High-viscosity fracturing tends to cause large dominant fractures, while high-rate (slickwater) fracturing causes small spread-out micro-fractures. Water-soluble gelling agents (such as guar gum) increase viscosity and efficiently deliver proppant into the formation.

The fluid is typically a slurry of water, proppant, and chemical additives. Additionally, gels, foams, and compressed gases, including nitrogen, carbon dioxide and air can be injected. Typically, 90% of the fluid is water and 9.5% is sand with chemical additives accounting to about 0.5%. However, fracturing fluids have been developed using liquefied petroleum gas (LPG) and propane in which water is unnecessary.

The proppant is a granular material that prevents the created fractures from closing after the fracturing treatment. Types of proppant include silica sand, resin-coated sand, bauxite, and man-made ceramics. The choice of proppant depends on the type of permeability or grain strength needed.

In some formations, where the pressure is great enough to crush grains of natural silica sand, higher-strength proppants such as bauxite or ceramics may be used. The most commonly used proppant is silica sand, though proppants of uniform size and shape, such as a ceramic proppant, are believed to be more effective.

The fracturing fluid varies depending on fracturing type desired, and the conditions of specific wells being fractured, and water characteristics. The fluid can be gel, foam, or slickwater-based. Fluid choices are tradeoffs: more viscous fluids, such as gels, are better at keeping proppant in suspension; while less-viscous and lower-friction fluids, such as slickwater, allow fluid to be pumped at higher rates, to create fractures farther out from the wellbore. Important material properties of the fluid include viscosity, pH, various rheological factors, and others.

Water is mixed with sand and chemicals to create hydraulic fracturing fluid. Approximately 40,000 gallons of chemicals are used per fracturing. A typical fracture treatment uses between 3 and 12 additive chemicals. Although there may be unconventional fracturing fluids, typical chemical additives can include one or more of the following:

  • Acids—hydrochloric acid or acetic acid is used in the pre-fracturing stage for cleaning the perforations and initiating fissure in the near-wellbore rock.
  • Sodium chloride (salt)—delays the breakdown of gel polymer chains.
  • Polyacrylamide and other friction reducers decrease turbulence in fluid flow and pipe friction, thus allowing the pumps to pump at a higher rate without having greater pressure on the surface.
  • Ethylene glycol—prevents the formation of scale deposits in the pipe.
  • Borate salts—used for maintaining fluid viscosity during the temperature increase.
  • Sodium and potassium carbonates—used for maintaining the effectiveness of crosslinkers.
  • Anaerobic, Biocide, BIO—Glutaraldehyde used as a disinfectant of the water (bacteria elimination).
  • Guar gum and other water-soluble gelling agents—increases the viscosity of the fracturing fluid to deliver proppant into the formation more efficiently.
  • Citric acid—used for corrosion prevention.
  • Isopropanol—used to winterize the chemicals to ensure it doesn’t freeze.

The most common chemical used for hydraulic fracturing in the United States in 2005–2009 was methanol, while some other most widely used chemicals were isopropyl alcohol, 2-butoxyethanol, and ethylene glycol.

Typical fluid types are:

  • Conventional linear gels. These gels are cellulose derivative (carboxymethyl cellulose, hydroxyethyl cellulose, carboxymethyl hydroxyethyl cellulose, hydroxypropyl cellulose, hydroxyethyl methyl cellulose), guar or its derivatives (hydroxypropyl guar, carboxymethyl hydroxypropyl guar), mixed with other chemicals.
  • Borate-crosslinked fluids. These are guar-based fluids cross-linked with boron ions (from aqueous borax/boric acid solution). These gels have higher viscosity at pH 9 onwards and are used to carry proppant. After the fracturing job, the pH is reduced to 3–4 so that the cross-links are broken, and the gel is less viscous and can be pumped out.
  • Organometallic-crosslinked fluids – zirconium, chromium, antimony, titanium salts – are known to crosslink guar-based gels. The crosslinking mechanism is not reversible, so once the proppant is pumped down along with cross-linked gel, the fracturing part is done. The gels are broken down with appropriate breakers.
  • Aluminium phosphate-ester oil gels. Aluminium phosphate and ester oils are slurried to form a cross-linked gel. These are one of the first known gelling systems.

For slickwater fluids the use of sweeps is common. Sweeps are temporary reductions in the proppant concentration, which help ensure that the well is not overwhelmed with proppant. As the fracturing process proceeds, viscosity-reducing agents such as oxidizers and enzyme breakers are sometimes added to the fracturing fluid to deactivate the gelling agents and encourage flowback. Such oxidizers react with and break down the gel, reducing the fluid’s viscosity and ensuring that no proppant is pulled from the formation.

An enzyme acts as a catalyst for breaking down the gel. Sometimes pH modifiers are used to break down the crosslink at the end of a hydraulic fracturing job since many require a pH buffer system to stay viscous. At the end of the job, the well is commonly flushed with water under pressure (sometimes blended with a friction-reducing chemical.) Some (but not all) injected fluid is recovered.

This fluid is managed by several methods, including underground injection control, treatment, discharge, recycling, and temporary storage in pits or containers. New technology is continually developing to better handle waste-water and improve re-usability.

FRACTURE MONITORING

Measurements of the pressure and rate during the growth of a hydraulic fracture, with knowledge of fluid properties and proppant being injected into the well, provides the most common and simplest method of monitoring a hydraulic fracture treatment. This data along with knowledge of the underground geology can be used to model information such as length, width and conductivity of a propped fracture.

Injection of radioactive tracers along with the fracturing fluid is sometimes used to determine the injection profile and location of created fractures. Radiotracers are selected to have the readily detectable radiation, appropriate chemical properties, and a half-life and toxicity level that will minimize initial and residual contamination. Radioactive isotopes chemically bonded to glass (sand) and/or resin beads may also be injected to track fractures.

For example, plastic pellets coated with 10 GBq of Ag-110mm may be added to the proppant, or sand may be labelled with Ir-192 so that the proppant’s progress can be monitored. Radiotracers such as Tc-99m and I-131 are also used to measure flow rates. The Nuclear Regulatory Commission publishes guidelines which list a wide range of radioactive materials in solid, liquid and gaseous forms that may be used as tracers and limit the amount that may be used per injection and per well of each radionuclide.

A new technique in well-monitoring involves fibre-optic cables outside the casing. Using the fibre optics, temperatures can be measured every foot along the well – even while the wells are being fracked and pumped. By monitoring the temperature of the well, engineers can determine how much hydraulic fracturing fluid different parts of the well use as well as how much natural gas or oil they collect, during hydraulic fracturing operation and when the well is producing.

MICROSEISMIC MONITORING

For more advanced applications, microseismic monitoring is sometimes used to estimate the size and orientation of induced fractures. Microseismic activity is measured by placing an array of geophones in a nearby wellbore. By mapping the location of any small seismic events associated with the growing fracture, the approximate geometry of the fracture is inferred. Tiltmeter arrays deployed on the surface or down a well provide another technology for monitoring strain

Microseismic mapping is very similar geophysically to seismology. In earthquake seismology, seismometers scattered on or near the surface of the earth record S-waves and P-waves that are released during an earthquake event. This allows for motion along the fault plane to be estimated and its location in the Earth’s subsurface mapped.

Hydraulic fracturing, an increase in formation stress proportional to the net fracturing pressure, as well as an increase in pore pressure due to leakoff. Tensile stresses are generated ahead of the fracture’s tip, generating large amounts of shear stress. The increases in pore water pressure and in formation stress combine and affect weaknesses near the hydraulic fracture, like natural fractures, joints, and bedding planes.

Different methods have different location errors and advantages. Accuracy of microseismic event mapping is dependent on the signal-to-noise ratio and the distribution of sensors. Accuracy of events located by seismic inversion is improved by sensors placed in multiple azimuths from the monitored borehole. In a downhole array location, the accuracy of events is improved by being close to the monitored borehole (high signal-to-noise ratio).

Monitoring of microseismic events induced by reservoir simulation has become a key aspect in the evaluation of hydraulic fractures and their optimization. The main goal of hydraulic fracture monitoring is to completely characterize the induced fracture structure and distribution of conductivity within a formation.

Geomechanical analysis, such as understanding a formations material properties, in-situ conditions, and geometries, helps monitoring by providing a better definition of the environment in which the fracture network propagates. The next task is to know the location of proppant within the fracture and the distribution of fracture conductivity. This can be monitored using multiple types of techniques to finally develop a reservoir model than accurately predicts well performance.

HORIZONTAL COMPLETIONS

Since the early 2000s, advances in drilling and completion technology have made horizontal wellbores much more economical. Horizontal wellbores allow far greater exposure to a formation than conventional vertical wellbores. This is particularly useful in shale formations which do not have sufficient permeability to produce economically with a vertical well.

Such wells, when drilled onshore, are now usually hydraulically fractured in a number of stages, especially in North America. The type of wellbore completion is used to determine how many times a formation is fractured, and at what locations along the horizontal section.

In North America, shale reservoirs such as the Bakken, Barnett, Montney, Haynesville, Marcellus, and most recently the Eagle Ford, Niobrara and Utica shales are drilled horizontally through the producing interval(s), completed and fractured. The method by which the fractures are placed along the wellbore is most commonly achieved by one of two methods, known as “plug and perf” and “sliding sleeve”.

The wellbore for a plug-and-perf job is generally composed of standard steel casing, cemented or uncemented, set in the drilled hole. Once the drilling rig has been removed, a wireline truck is used to perforate near the bottom of the well, and then fracturing fluid is pumped.

Then the wireline truck sets a plug in the well to temporarily seal off that section so the next section of the wellbore can be treated. Another stage is pumped, and the process is repeated along the horizontal length of the wellbore.

The wellbore for the sliding sleeve technique is different in that the sliding sleeves are included at set spacings in the steel casing at the time it is set in place. The sliding sleeves are usually all closed at this time. When the well is due to be fractured, the bottom sliding sleeve is opened using one of several activation techniques and the first stage gets pumped. Once finished, the next sleeve is opened, concurrently isolating the previous stage, and the process repeats. For the sliding sleeve method, wireline is usually not required.

These completion techniques may allow for more than 30 stages to be pumped into the horizontal section of a single well if required, which is far more than would typically be pumped into a vertical well that had far fewer feet of producing zone exposed.

USES

Hydraulic fracturing is used to increase the rate at which fluids, such as petroleum, water, or natural gas can be recovered from subterranean natural reservoirs. Reservoirs are typically porous sandstones, limestones or dolomite rocks, but also include “unconventional reservoirs” such as shale rock or coal beds.

Hydraulic fracturing enables the extraction of natural gas and oil from rock formations deep below the earth’s surface (generally 2,000–6,000 m (5,000–20,000 ft)), which is greatly below typical groundwater reservoir levels. At such depth, there may be insufficient permeability or reservoir pressure to allow natural gas and oil to flow from the rock into the wellbore at high economic return. Thus, creating conductive fractures in the rock is instrumental in extraction from naturally impermeable shale reservoirs. Permeability is measured in the micro darcy to nanodarcy range.

Fractures are a conductive path connecting a larger volume of the reservoir to the well. So-called “super fracking,” creates cracks deeper in the rock formation to release more oil and gas, and increases efficiency. The yield for typical shale bores generally falls off after the first year or two, but the peak producing life of a well can be extended to several decades.

While the main industrial use of hydraulic fracturing is in stimulating production from oil and gas wells, hydraulic fracturing is also applied:

  • To stimulate groundwater wells
  • To precondition or induce rock cave-ins mining
  • As a means of enhancing waste remediation, usually hydrocarbon waste or spills
  • To dispose of waste by injection deep into the rock
  • To measure stress in the Earth
  • For electricity generation in enhanced geothermal systems
  • To increase injection rates for geologic sequestration of CO2

Since the late 1970s, hydraulic fracturing has been used, in some cases, to increase the yield of drinking water from wells in a number of countries, including the United States, Australia and South Africa.

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