prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: How is electricity used in everyday life?

Read the following text and answer briefly.

Context 1: For other uses, see Electricity (disambiguation) 
"Electric" redirects here  For other uses, see Electric (disambiguation) 
Lightning is one of the most dramatic effects of electricity 
Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge  In early days, electricity was considered as being not related to magnetism  Later on, many experimental results and the development of Maxwell's equations indicated that both electricity and magnetism are from a single phenomenon: electromagnetism  Various common phenomena are related to electricity, including lightning, static electricity, electric heating, electric discharges and many others 
The presence of an electric charge, which can be either positive or negative, produces an electric field  The movement of electric charges is an electric current and produces a magnetic field 
When a charge is placed in a location with a non-zero electric field, a force will act on it  The magnitude of this force is given by Coulomb's law  Thus, if that charge were to move, the electric field would be doing work on the electric charge  Thus we can speak of electric potential at a certain point in space, which is equal to the work done by an external agent in carrying a unit of positive charge from an arbitrarily chosen reference point to that point without any acceleration and is typically measured in volts 
electronics which deals with electrical circuits that involve active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies 
Electrical phenomena have been studied since antiquity, though progress in theoretical understanding remained slow until the seventeenth and eighteenth centuries  Even then, practical applications for electricity were few, and it would not be until the late nineteenth century that electrical engineers were able to put it to industrial and residential use  The rapid expansion in electrical technology at this time transformed industry and society, becoming a driving force for the Second Industrial Revolution  Electricity's extraordinary versatility means it can be put to an almost limitless set of applications which include transport, heating, lighting, communications, and computation  Electrical power is now the backbone of modern industrial society 
Long before any knowledge of electricity existed, people were aware of shocks from electric fish  Ancient Egyptian texts dating from 2750 BCE referred to these fish as the "Thunderer of the Nile", and described them as the "protectors" of all other fish  Electric fish were again reported millennia later by ancient Greek, Roman and Arabic naturalists and physicians  Several ancient writers, such as Pliny the Elder and Scribonius Largus, attested to the numbing effect of electric shocks delivered by catfish and electric rays, and knew that such shocks could travel along conducting objects  Patients suffering from ailments such as gout or headache were directed to touch electric fish in the hope that the powerful jolt might cure them  Possibly the earliest and nearest approach to the discovery of the identity of lightning, and electricity from any other source, is to be attributed to the Arabs, who before the 15th century had the Arabic word for lightning ra‘ad (رعد) applied to the electric ray 
Ancient cultures around the Mediterranean knew that certain objects, such as rods of amber, could be rubbed with cat's fur to attract light objects like feathers  Thales of Miletus made a series of observations on static electricity around 600 BCE, from which he believed that friction rendered amber magnetic, in contrast to minerals such as magnetite, which needed no rubbing  Thales was incorrect in believing the attraction was due to a magnetic effect, but later science would prove a link between magnetism and electricity  According to a controversial theory, the Parthians may have had knowledge of electroplating, based on the 1936 discovery of the Baghdad Battery, which resembles a galvanic cell, though it is uncertain whether the artifact was electrical in nature 
Benjamin Franklin conducted extensive research on electricity in the 18th century, as documented by Joseph Priestley (1767) History and Present Status of Electricity, with whom Franklin carried on extended correspondence 
Electricity would remain little more than an intellectual curiosity for millennia until 1600, when the English scientist William Gilbert wrote De Magnete, in which he made a careful study of electricity and magnetism, distinguishing the lodestone effect from static electricity produced by rubbing amber  He coined the New Latin word electricus ("of amber" or "like amber", from ἤλεκτρον, elektron, the Greek word for "amber") to refer to the property of attracting small objects after being rubbed  This association gave rise to the English words "electric" and "electricity", which made their first appearance in print in Thomas Browne's Pseudodoxia Epidemica of 1646 
Further work was conducted in the 17th and early 18th centuries by Otto von Guericke, Robert Boyle, Stephen Gray and C  F  du Fay  Later in the 18th century, Benjamin Franklin conducted extensive research in electricity, selling his possessions to fund his work  In June 1752 he is reputed to have attached a metal key to the bottom of a dampened kite string and flown the kite in a storm-threatened sky  A succession of sparks jumping from the key to the back of his hand showed that lightning was indeed electrical in nature  He also explained the apparently paradoxical behavior of the Leyden jar as a device for storing large amounts of electrical charge in terms of electricity consisting of both positive and negative charges 
In 1791, Luigi Galvani published his discovery of bioelectromagnetics, demonstrating that electricity was the medium by which neurons passed signals to the muscles  Alessandro Volta's battery, or voltaic pile, of 1800, made from alternating layers of zinc and copper, provided scientists with a more reliable source of electrical energy than the electrostatic machines previously used  The recognition of electromagnetism, the unity of electric and magnetic phenomena, is due to Hans Christian Ørsted and André-Marie Ampère in 1819–1820  Michael Faraday invented the electric motor in 1821, and Georg Ohm mathematically analysed the electrical circuit in 1827  Electricity and magnetism (and light) were definitively linked by James Clerk Maxwell, in particular in his "On Physical Lines of Force" in 1861 and 1862 
While the early 19th century had seen rapid progress in electrical science, the late 19th century would see the greatest progress in electrical engineering  Through such people as Alexander Graham Bell, Ottó Bláthy, Thomas Edison, Galileo Ferraris, Oliver Heaviside, Ányos Jedlik, William Thomson, 1st Baron Kelvin, Charles Algernon Parsons, Werner von Siemens, Joseph Swan, Reginald Fessenden, Nikola Tesla and George Westinghouse, electricity turned from a scientific curiosity into an essential tool for modern life 
In 1887, Heinrich Hertz:843–44 discovered that electrodes illuminated with ultraviolet light create electric sparks more easily  In 1905, Albert Einstein published a paper that explained experimental data from the photoelectric effect as being the result of light energy being carried in discrete quantized packets, energising electrons  This discovery led to the quantum revolution  Einstein was awarded the Nobel Prize in Physics in 1921 for "his discovery of the law of the photoelectric effect"  The photoelectric effect is also employed in photocells such as can be found in solar panels and this is frequently used to make electricity commercially 
The first solid-state device was the "cat's-whisker detector" first used in the 1900s in radio receivers  A whisker-like wire is placed lightly in contact with a solid crystal (such as a germanium crystal) to detect a radio signal by the contact junction effect  In a solid-state component, the current is confined to solid elements and compounds engineered specifically to switch and amplify it  Current flow can be understood in two forms: as negatively charged electrons, and as positively charged electron deficiencies called holes  These charges and holes are understood in terms of quantum physics  The building material is most often a crystalline semiconductor 
The solid-state device came into its own with the invention of the transistor in 1947  Common solid-state devices include transistors, microprocessor chips, and RAM  A specialized type of RAM called flash RAM is used in USB flash drives and more recently, solid-state drives to replace mechanically rotating magnetic disc hard disk drives  Solid state devices became prevalent in the 1950s and the 1960s, during the transition from vacuum tubes to semiconductor diodes, transistors, integrated circuit (IC) and the light-emitting diode (LED) 
The presence of charge gives rise to an electrostatic force: charges exert a force on each other, an effect that was known, though not understood, in antiquity :457 A lightweight ball suspended from a string can be charged by touching it with a glass rod that has itself been charged by rubbing with a cloth  If a similar ball is charged by the same glass rod, it is found to repel the first: the charge acts to force the two balls apart  Two balls that are charged with a rubbed amber rod also repel each other  However, if one ball is charged by the glass rod, and the other by an amber rod, the two balls are found to attract each other  These phenomena were investigated in the late eighteenth century by Charles-Augustin de Coulomb, who deduced that charge manifests itself in two opposing forms  This discovery led to the well-known axiom: like-charged objects repel and opposite-charged objects attract 
The force acts on the charged particles themselves, hence charge has a tendency to spread itself as evenly as possible over a conducting surface  The magnitude of the electromagnetic force, whether attractive or repulsive, is given by Coulomb's law, which relates the force to the product of the charges and has an inverse-square relation to the distance between them :35 The electromagnetic force is very strong, second only in strength to the strong interaction, but unlike that force it operates over all distances  In comparison with the much weaker gravitational force, the electromagnetic force pushing two electrons apart is 1042 times that of the gravitational attraction pulling them together 
Study has shown that the origin of charge is from certain types of subatomic particles which have the property of electric charge  Electric charge gives rise to and interacts with the electromagnetic force, one of the four fundamental forces of nature  The most familiar carriers of electrical charge are the electron and proton  Experiment has shown charge to be a conserved quantity, that is, the net charge within an electrically isolated system will always remain constant regardless of any changes taking place within that system  Within the system, charge may be transferred between bodies, either by direct contact, or by passing along a conducting material, such as a wire :2–5 The informal term static electricity refers to the net presence (or 'imbalance') of charge on a body, usually caused when dissimilar materials are rubbed together, transferring charge from one to the other 
The charge on electrons and protons is opposite in sign, hence an amount of charge may be expressed as being either negative or positive  By convention, the charge carried by electrons is deemed negative, and that by protons positive, a custom that originated with the work of Benjamin Franklin  The amount of charge is usually given the symbol Q and expressed in coulombs; each electron carries the same charge of approximately −1 6022×10−19 coulomb  The proton has a charge that is equal and opposite, and thus +1 6022×10−19 coulomb  Charge is possessed not just by matter, but also by antimatter, each antiparticle bearing an equal and opposite charge to its corresponding particle 
The movement of electric charge is known as an electric current, the intensity of which is usually measured in amperes  Current can consist of any moving charged particles; most commonly these are electrons, but any charge in motion constitutes a current  Electric current can flow through some things, electrical conductors, but will not flow through an electrical insulator 
By historical convention, a positive current is defined as having the same direction of flow as any positive charge it contains, or to flow from the most positive part of a circuit to the most negative part  Current defined in this manner is called conventional current  The motion of negatively charged electrons around an electric circuit, one of the most familiar forms of current, is thus deemed positive in the opposite direction to that of the electrons  However, depending on the conditions, an electric current can consist of a flow of charged particles in either direction, or even in both directions at once  The positive-to-negative convention is widely used to simplify this situation 
The process by which electric current passes through a material is termed electrical conduction, and its nature varies with that of the charged particles and the material through which they are travelling  Examples of electric currents include metallic conduction, where electrons flow through a conductor such as metal, and electrolysis, where ions (charged atoms) flow through liquids, or through plasmas such as electrical sparks  While the particles themselves can move quite slowly, sometimes with an average drift velocity only fractions of a millimetre per second,:17 the electric field that drives them itself propagates at close to the speed of light, enabling electrical signals to pass rapidly along wires 
Current causes several observable effects, which historically were the means of recognising its presence  That water could be decomposed by the current from a voltaic pile was discovered by Nicholson and Carlisle in 1800, a process now known as electrolysis  Their work was greatly expanded upon by Michael Faraday in 1833  Current through a resistance causes localised heating, an effect James Prescott Joule studied mathematically in 1840 :23–24 One of the most important discoveries relating to current was made accidentally by Hans Christian Ørsted in 1820, when, while preparing a lecture, he witnessed the current in a wire disturbing the needle of a magnetic compass  He had discovered electromagnetism, a fundamental interaction between electricity and magnetics  The level of electromagnetic emissions generated by electric arcing is high enough to produce electromagnetic interference, which can be detrimental to the workings of adjacent equipment 
In engineering or household applications, current is often described as being either direct current (DC) or alternating current (AC)  These terms refer to how the current varies in time  Direct current, as produced by example from a battery and required by most electronic devices, is a unidirectional flow from the positive part of a circuit to the negative :11 If, as is most common, this flow is carried by electrons, they will be travelling in the opposite direction  Alternating current is any current that reverses direction repeatedly; almost always this takes the form of a sine wave :206–07 Alternating current thus pulses back and forth within a conductor without the charge moving any net distance over time  The time-averaged value of an alternating current is zero, but it delivers energy in first one direction, and then the reverse  Alternating current is affected by electrical properties that are not observed under steady state direct current, such as inductance and capacitance :223–25 These properties however can become important when circuitry is subjected to transients, such as when first energised 
The concept of the electric field was introduced by Michael Faraday  An electric field is created by a charged body in the space that surrounds it, and results in a force exerted on any other charges placed within the field  The electric field acts between two charges in a similar manner to the way that the gravitational field acts between two masses, and like it, extends towards infinity and shows an inverse square relationship with distance  However, there is an important difference  Gravity always acts in attraction, drawing two masses together, while the electric field can result in either attraction or repulsion  Since large bodies such as planets generally carry no net charge, the electric field at a distance is usually zero  Thus gravity is the dominant force at distance in the universe, despite being much weaker 
A hollow conducting body carries all its charge on its outer surface  The field is therefore zero at all places inside the body :88 This is the operating principal of the Faraday cage, a conducting metal shell which isolates its interior from outside electrical effects 
The principles of electrostatics are important when designing items of high-voltage equipment  There is a finite limit to the electric field strength that may be withstood by any medium  Beyond this point, electrical breakdown occurs and an electric arc causes flashover between the charged parts  Air, for example, tends to arc across small gaps at electric field strengths which exceed 30 kV per centimetre  Over larger gaps, its breakdown strength is weaker, perhaps 1 kV per centimetre  The most visible natural occurrence of this is lightning, caused when charge becomes separated in the clouds by rising columns of air, and raises the electric field in the air to greater than it can withstand  The voltage of a large lightning cloud may be as high as 100 MV and have discharge energies as great as 250 kWh 
A pair of AA cells  The + sign indicates the polarity of the potential difference between the battery terminals 
The concept of electric potential is closely linked to that of the electric field  A small charge placed within an electric field experiences a force, and to have brought that charge to that point against the force requires work  The electric potential at any point is defined as the energy required to bring a unit test charge from an infinite distance slowly to that point  It is usually measured in volts, and one volt is the potential for which one joule of work must be expended to bring a charge of one coulomb from infinity :494–98 This definition of potential, while formal, has little practical application, and a more useful concept is that of electric potential difference, and is the energy required to move a unit charge between two specified points  An electric field has the special property that it is conservative, which means that the path taken by the test charge is irrelevant: all paths between two specified points expend the same energy, and thus a unique value for potential difference may be stated :494–98 The volt is so strongly identified as the unit of choice for measurement and description of electric potential difference that the term voltage sees greater everyday usage 
For practical purposes, it is useful to define a common reference point to which potentials may be expressed and compared  While this could be at infinity, a much more useful reference is the Earth itself, which is assumed to be at the same potential everywhere  This reference point naturally takes the name earth or ground  Earth is assumed to be an infinite source of equal amounts of positive and negative charge, and is therefore electrically uncharged—and unchargeable 
Electric potential is a scalar quantity, that is, it has only magnitude and not direction  It may be viewed as analogous to height: just as a released object will fall through a difference in heights caused by a gravitational field, so a charge will 'fall' across the voltage caused by an electric field  As relief maps show contour lines marking points of equal height, a set of lines marking points of equal potential (known as equipotentials) may be drawn around an electrostatically charged object  The equipotentials cross all lines of force at right angles  They must also lie parallel to a conductor's surface, otherwise this would produce a force that will move the charge carriers to even the potential of the surface 
Ørsted's discovery in 1821 that a magnetic field existed around all sides of a wire carrying an electric current indicated that there was a direct relationship between electricity and magnetism  Moreover, the interaction seemed different from gravitational and electrostatic forces, the two forces of nature then known  The force on the compass needle did not direct it to or away from the current-carrying wire, but acted at right angles to it  Ørsted's slightly obscure words were that "the electric conflict acts in a revolving manner " The force also depended on the direction of the current, for if the flow was reversed, then the force did too 
Ørsted did not fully understand his discovery, but he observed the effect was reciprocal: a current exerts a force on a magnet, and a magnetic field exerts a force on a current  The phenomenon was further investigated by Ampère, who discovered that two parallel current-carrying wires exerted a force upon each other: two wires conducting currents in the same direction are attracted to each other, while wires containing currents in opposite directions are forced apart  The interaction is mediated by the magnetic field each current produces and forms the basis for the international definition of the ampere 
This relationship between magnetic fields and currents is extremely important, for it led to Michael Faraday's invention of the electric motor in 1821  Faraday's homopolar motor consisted of a permanent magnet sitting in a pool of mercury  A current was allowed through a wire suspended from a pivot above the magnet and dipped into the mercury  The magnet exerted a tangential force on the wire, making it circle around the magnet for as long as the current was maintained 
Experimentation by Faraday in 1831 revealed that a wire moving perpendicular to a magnetic field developed a potential difference between its ends  Further analysis of this process, known as electromagnetic induction, enabled him to state the principle, now known as Faraday's law of induction, that the potential difference induced in a closed circuit is proportional to the rate of change of magnetic flux through the loop  Exploitation of this discovery enabled him to invent the first electrical generator in 1831, in which he converted the mechanical energy of a rotating copper disc to electrical energy  Faraday's disc was inefficient and of no use as a practical generator, but it showed the possibility of generating electric power using magnetism, a possibility that would be taken up by those that followed on from his work 
Italian physicist Alessandro Volta showing his "battery" to French emperor Napoleon Bonaparte in the early 19th century 
The ability of chemical reactions to produce electricity, and conversely the ability of electricity to drive chemical reactions has a wide array of uses 
Electrochemistry has always been an important part of electricity  From the initial invention of the Voltaic pile, electrochemical cells have evolved into the many different types of batteries, electroplating and electrolysis cells  Aluminium is produced in vast quantities this way, and many portable devices are electrically powered using rechargeable cells 
A basic electric circuit  The voltage source V on the left drives a current I around the circuit, delivering electrical energy into the resistor R  From the resistor, the current returns to the source, completing the circuit 
An electric circuit is an interconnection of electric components such that electric charge is made to flow along a closed path (a circuit), usually to perform some useful task 
Electric power is the rate at which electric energy is transferred by an electric circuit  The SI unit of power is the watt, one joule per second 
Electricity generation is often done with electric generators, but can also be supplied by chemical sources such as electric batteries or by other means from a wide variety of sources of energy  Electric power is generally supplied to businesses and homes by the electric power industry  Electricity is usually sold by the kilowatt hour (3 6 MJ) which is the product of power in kilowatts multiplied by running time in hours  Electric utilities measure power using electricity meters, which keep a running total of the electric energy delivered to a customer  Unlike fossil fuels, electricity is a low entropy form of energy and can be converted into motion or many other forms of energy with high efficiency 
Electronics deals with electrical circuits that involve active electrical components such as vacuum tubes, transistors, diodes, optoelectronics, sensors and integrated circuits, and associated passive interconnection technologies  The nonlinear behaviour of active components and their ability to control electron flows makes amplification of weak signals possible and electronics is widely used in information processing, telecommunications, and signal processing  The ability of electronic devices to act as switches makes digital information processing possible  Interconnection technologies such as circuit boards, electronics packaging technology, and other varied forms of communication infrastructure complete circuit functionality and transform the mixed components into a regular working system 
Today, most electronic devices use semiconductor components to perform electron control  The study of semiconductor devices and related technology is considered a branch of solid state physics, whereas the design and construction of electronic circuits to solve practical problems come under electronics engineering 
Thus, the work of many researchers enabled the use of electronics to convert signals into high frequency oscillating currents, and via suitably shaped conductors, electricity permits the transmission and reception of these signals via radio waves over very long distances 
Early 20th-century alternator made in Budapest, Hungary, in the power generating hall of a hydroelectric station (photograph by Prokudin-Gorsky, 1905–1915) 
In the 6th century BC, the Greek philosopher Thales of Miletus experimented with amber rods and these experiments were the first studies into the production of electrical energy  While this method, now known as the triboelectric effect, can lift light objects and generate sparks, it is extremely inefficient  It was not until the invention of the voltaic pile in the eighteenth century that a viable source of electricity became available  The voltaic pile, and its modern descendant, the electrical battery, store energy chemically and make it available on demand in the form of electrical energy  The battery is a versatile and very common power source which is ideally suited to many applications, but its energy storage is finite, and once discharged it must be disposed of or recharged  For large electrical demands electrical energy must be generated and transmitted continuously over conductive transmission lines 
Electrical power is usually generated by electro-mechanical generators driven by steam produced from fossil fuel combustion, or the heat released from nuclear reactions; or from other sources such as kinetic energy extracted from wind or flowing water  The modern steam turbine invented by Sir Charles Parsons in 1884 today generates about 80 percent of the electric power in the world using a variety of heat sources  Such generators bear no resemblance to Faraday's homopolar disc generator of 1831, but they still rely on his electromagnetic principle that a conductor linking a changing magnetic field induces a potential difference across its ends  The invention in the late nineteenth century of the transformer meant that electrical power could be transmitted more efficiently at a higher voltage but lower current  Efficient electrical transmission meant in turn that electricity could be generated at centralised power stations, where it benefited from economies of scale, and then be despatched relatively long distances to where it was needed 
Since electrical energy cannot easily be stored in quantities large enough to meet demands on a national scale, at all times exactly as much must be produced as is required  This requires electricity utilities to make careful predictions of their electrical loads, and maintain constant co-ordination with their power stations  A certain amount of generation must always be held in reserve to cushion an electrical grid against inevitable disturbances and losses 
Electricity is a very convenient way to transfer energy, and it has been adapted to a huge, and growing, number of uses  The invention of a practical incandescent light bulb in the 1870s led to lighting becoming one of the first publicly available applications of electrical power  Although electrification brought with it its own dangers, replacing the naked flames of gas lighting greatly reduced fire hazards within homes and factories  Public utilities were set up in many cities targeting the burgeoning market for electrical lighting  In the late 20th century and in modern times, the trend has started to flow in the direction of deregulation in the electrical power sector 
The resistive Joule heating effect employed in filament light bulbs also sees more direct use in electric heating  While this is versatile and controllable, it can be seen as wasteful, since most electrical generation has already required the production of heat at a power station  A number of countries, such as Denmark, have issued legislation restricting or banning the use of resistive electric heating in new buildings  Electricity is however still a highly practical energy source for heating and refrigeration, with air conditioning/heat pumps representing a growing sector for electricity demand for heating and cooling, the effects of which electricity utilities are increasingly obliged to accommodate 
Electricity is used within telecommunications, and indeed the electrical telegraph, demonstrated commercially in 1837 by Cooke and Wheatstone, was one of its earliest applications  With the construction of first intercontinental, and then transatlantic, telegraph systems in the 1860s, electricity had enabled communications in minutes across the globe  Optical fibre and satellite communication have taken a share of the market for communications systems, but electricity can be expected to remain an essential part of the process 
The effects of electromagnetism are most visibly employed in the electric motor, which provides a clean and efficient means of motive power  A stationary motor such as a winch is easily provided with a supply of power, but a motor that moves with its application, such as an electric vehicle, is obliged to either carry along a power source such as a battery, or to collect current from a sliding contact such as a pantograph  Electrically powered vehicles are used in public transportation, such as electric buses and trains, and an increasing number of battery-powered electric cars in private ownership 
Electronic devices make use of the transistor, perhaps one of the most important inventions of the twentieth century, and a fundamental building block of all modern circuitry  A modern integrated circuit may contain several billion miniaturised transistors in a region only a few centimetres square 
A voltage applied to a human body causes an electric current through the tissues, and although the relationship is non-linear, the greater the voltage, the greater the current  The threshold for perception varies with the supply frequency and with the path of the current, but is about 0 1 mA to 1 mA for mains-frequency electricity, though a current as low as a microamp can be detected as an electrovibration effect under certain conditions  If the current is sufficiently high, it will cause muscle contraction, fibrillation of the heart, and tissue burns  The lack of any visible sign that a conductor is electrified makes electricity a particular hazard  The pain caused by an electric shock can be intense, leading electricity at times to be employed as a method of torture  Death caused by an electric shock is referred to as electrocution  Electrocution is still the means of judicial execution in some jurisdictions, though its use has become rarer in recent times 
Electricity is not a human invention, and may be observed in several forms in nature, a prominent manifestation of which is lightning  Many interactions familiar at the macroscopic level, such as touch, friction or chemical bonding, are due to interactions between electric fields on the atomic scale  The Earth's magnetic field is thought to arise from a natural dynamo of circulating currents in the planet's core  Certain crystals, such as quartz, or even sugar, generate a potential difference across their faces when subjected to external pressure  This phenomenon is known as piezoelectricity, from the Greek piezein (πιέζειν), meaning to press, and was discovered in 1880 by Pierre and Jacques Curie  The effect is reciprocal, and when a piezoelectric material is subjected to an electric field, a small change in physical dimensions takes place 
§Bioelectrogenesis in microbial life is a prominent phenomenon in soils and sediment ecology resulting from anaerobic respiration  The microbial fuel cell mimics this ubiquitous natural phenomenon 
Some organisms, such as sharks, are able to detect and respond to changes in electric fields, an ability known as electroreception, while others, termed electrogenic, are able to generate voltages themselves to serve as a predatory or defensive weapon  The order Gymnotiformes, of which the best known example is the electric eel, detect or stun their prey via high voltages generated from modified muscle cells called electrocytes  All animals transmit information along their cell membranes with voltage pulses called action potentials, whose functions include communication by the nervous system between neurons and muscles  An electric shock stimulates this system, and causes muscles to contract  Action potentials are also responsible for coordinating activities in certain plants 
In the 19th and early 20th century, electricity was not part of the everyday life of many people, even in the industrialised Western world  The popular culture of the time accordingly often depicted it as a mysterious, quasi-magical force that can slay the living, revive the dead or otherwise bend the laws of nature  This attitude began with the 1771 experiments of Luigi Galvani in which the legs of dead frogs were shown to twitch on application of animal electricity  "Revitalization" or resuscitation of apparently dead or drowned persons was reported in the medical literature shortly after Galvani's work  These results were known to Mary Shelley when she authored Frankenstein (1819), although she does not name the method of revitalization of the monster  The revitalization of monsters with electricity later became a stock theme in horror films 
As the public familiarity with electricity as the lifeblood of the Second Industrial Revolution grew, its wielders were more often cast in a positive light, such as the workers who "finger death at their gloves' end as they piece and repiece the living wires" in Rudyard Kipling's 1907 poem Sons of Martha  Electrically powered vehicles of every sort featured large in adventure stories such as those of Jules Verne and the Tom Swift books  The masters of electricity, whether fictional or real—including scientists such as Thomas Edison, Charles Steinmetz or Nikola Tesla—were popularly conceived of as having wizard-like powers 
With electricity ceasing to be a novelty and becoming a necessity of everyday life in the later half of the 20th century, it required particular attention by popular culture only when it stops flowing, an event that usually signals disaster  The people who keep it flowing, such as the nameless hero of Jimmy Webb’s song "Wichita Lineman" (1968), are still often cast as heroic, wizard-like figures 
Ampère's circuital law, connects the direction of an electric current and its associated magnetic currents 
^ Diogenes Laertius  R D  Hicks (ed )  "Lives of Eminent Philosophers, Book 1 Chapter 1 "  Perseus Digital Library  Tufts University  Retrieved 5 February 2017  Aristotle and Hippias affirm that, arguing from the magnet and from amber, he attributed a soul or life even to inanimate objects 
^ Aristotle  Daniel C  Stevenson (ed )  "De Animus (On the Soul) Book 1 Part 2 (B4 verso)"  The Internet Classics Archive  Translated by J A  Smith  Retrieved 5 February 2017  Thales, too, to judge from what is recorded about him, seems to have held soul to be a motive force, since he said that the magnet has a soul in it because it moves the iron 
^ a b c Guarnieri, M  (2014)  "Electricity in the age of Enlightenment"  IEEE Industrial Electronics Magazine  8 (3): 60–63  doi:10 1109/MIE 2014 2335431 
^ Srodes, James (2002), Franklin: The Essential Founding Father, Regnery Publishing, pp  92–94, ISBN 0-89526-163-4 It is uncertain if Franklin personally carried out this experiment, but it is popularly attributed to him 
^ a b Guarnieri, M  (2014)  "The Big Jump from the Legs of a Frog"  IEEE Industrial Electronics Magazine  8 (4): 59–61, 69  doi:10 1109/MIE 2014 2361237 
^ Hertz, Heinrich (1887)  "Ueber den Einfluss des ultravioletten Lichtes auf die electrische Entladung"  Annalen der Physik  267 (8): S  983–1000  Bibcode:1887AnP   267  983H  doi:10 1002/andp 18872670827 
^ "The Nobel Prize in Physics 1921"  Nobel Foundation  Retrieved 2013-03-16 
^ John Sydney Blakemore, Solid state physics, pp  1–3, Cambridge University Press, 1985 ISBN 0-521-31391-0 
^ Richard C  Jaeger, Travis N  Blalock, Microelectronic circuit design, pp  46–47, McGraw-Hill Professional, 2003 ISBN 0-07-250503-6 
^ "The repulsive force between two small spheres charged with the same type of electricity is inversely proportional to the square of the distance between the centres of the two spheres " Charles-Augustin de Coulomb, Histoire de l'Academie Royal des Sciences, Paris 1785 
^ Sewell, Tyson (1902), The Elements of Electrical Engineering, Lockwood, p  18   The Q originally stood for 'quantity of electricity', the term 'electricity' now more commonly expressed as 'charge' 
^ a b Berkson, William (1974), Fields of Force: The Development of a World View from Faraday to Einstein, Routledge, p  370, ISBN 0-7100-7626-6 Accounts differ as to whether this was before, during, or after a lecture 
^ "Lab Note #105 EMI Reduction – Unsuppressed vs  Suppressed"  Arc Suppression Technologies  April 2011  Retrieved March 7, 2012 
^ Almost all electric fields vary in space  An exception is the electric field surrounding a planar conductor of infinite extent, the field of which is uniform 
^ Paul J  Nahin (9 October 2002)  Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age  JHU Press  ISBN 978-0-8018-6909-9 
^ "The Bumpy Road to Energy Deregulation"  EnPowered  2016-03-28 
^ a b c d e f g h Van Riper, op cit , p  71 
Look up electricity in Wiktionary, the free dictionary 
Basic Concepts of Electricity chapter from Lessons In Electric Circuits Vol 1 DC book and series 
Context 3: Filip Fremo Minge – Ekofisk
Author: Filip Fremo Minge
Posted on 1  October 2019 12  October 2019
— Sunset over Ekofisk  Photo: Husmo Foto/Norwegian Petroleum Museum
The three are operated by ConocoPhillips on behalf of the Ekofisk licensees  The area also embraces former producers Albuskjell, Cod, Edda, Tor, West Ekofisk and Tommeliten G 
These fields all lie within production licence 018 apart from Tommeliten G, which was operated by Statoil from 1976 to 2003 
In all, 31 installations have been positioned in the Greater Ekofisk Area 
First Norwegian offshore field
Ekofisk began production on 15 June 1971, following its discovery in the autumn of 1969  Development of the field has occurred in several phases 
Its central facilities were installed during the early 1970s, with oil initially being buoy-loaded into tankers  From 1975, it has been piped to Teesside in the UK  The gas has been landed by pipeline at Emden in Germany from 1977 
ekofisk i et nøtteskall, engelsk
Jacked up six metres
The water depth in the Greater Ekofisk Area is 70-75 metres  However, declining pressure in the Ekofisk reservoir over the years has caused the seabed to subside 
Efforts began as early as 1985 to safeguard the installations against the effects of this development, and the steel platforms in the Ekofisk Complex were jacked up by six metres in 1987 
In addition, a protective breakwater was installed around the Ekofisk tank in 1989  The rate of seabed subsidence has declined sharply in recent years 
Waterflooding improves recovery
The Ekofisk 2/4 K water injection platform became operational in December 1987 as part of efforts to improve Ekofisk’s recovery factor – the share of petroleum in place actually produced 
Waterflooding capacity on the field to help maintain reservoir pressure was later expanded several times, and had reached just over 500 000 barrels per day by 2019 
Measured in barrels of oil equivalent, the recovery factor on Ekofisk has risen from an original estimate of 17 per cent to over 50 per cent 
Ekofisk I and II plus licence extension
The first phase of development and production on Ekofisk began with initial oil output from the converted Gulftide jack-up rig in 1971 and ended with the start-up of Ekofisk II in 1998 
Large parts of the Greater Ekofisk Area were restructured in the latter year, leading to plans for removing 15 installations – 14 steel platforms and the process facilities on the Ekofisk tank 
plattformer, historie, 2004, driftsenter åpnet,
Embla 2/7 D  Photo: ConocoPhillips/Norwegian Petroleum Museum
Designated Ekofisk I, these redundant structures include Ekofisk 2/4 A, 2/4 B, 2/4 FTP, 2/4 Q, 2/4 H, 2/4 R, 2/4 P and 2/4 T 
In addition come the Edda 2/7 C, Albuskjell 1/6 A, Albuskjell 2/4 F, Cod 7/11 A, West Ekofisk 2/4 D, Norpipe 36/22 A and Norpipe 37/4 A installations 
The concrete part of the tank – Ekofisk 2/4 T – will remain  Gulftide was removed as far back as 1974  Two platforms owned by other companies – Ekofisk 2/4 G and 2/4 S – have also gone 
A new plan for development and operation (PDO) of the field (Ekofisk II) was approved in 1994, at the same time as the Ekofisk licence was extended to 2028 
This creates a new Ekofisk Complex with two structures – the Ekofisk 2/4 X wellhead unit installed in the autumn of 1996 and the Ekofisk 2/4 J processing and transport platform in 1997 
Ekofisk II became operational in August 1998 and is intended to produce until 2028  Ekofisk, Eldfisk and Embla are tied back to the new complex, as was Tor until it shut down in December 2015 
Ekofisk West
historie, forsidebilde, 2003, ekofisk vekst godkjent i statsråd
Ekofisk Growth  Illustration: Ståle Ådland
In December 2002, soon after the Conoco-Phillips merger had been announced, the Ekofisk West project was presented to improve oil and gas recovery  Process capacity and reliability on Ekofisk were also to be enhanced 
This development primarily involved the construction and installation of a new platform, Ekofisk 2/4 M, with processing facilities and 24 new wells drilled over five years 
The latter could contribute to improved recovery both because there were more wells and because they would tap new locations in the reservoir  On stream in 2005, 2/4 M was linked to the Ekofisk Complex with a bridge 
Process capacity for produced water was also to be increased through upgrading on Ekofisk 2/4 J and Eldfisk 2/7 E  A third measure concerned laying a power cable from the Ekofisk Complex to 2/4 K in order to make electricity supplies more efficient 
New developments: Eldfisk II and Ekofisk South
Eldfisk 2/7 S løft
The deck of Eldfisk 2/7 S being mated with the steel jacket  Foto: Øyvind Sætre/ConocoPhillips
The plan for development and operation (PDO) of Eldfisk II, approved by the Storting (parliament) on 9 June 2011, includes a new wellhead, process and accommodation platform – Eldfisk 2/7 S 
In addition come 42 new wells as well as upgrades to existing platforms which extend their commercial life 
The PDO for Ekofisk South involves the construction of a new wellhead platform – Ekofisk 2/4 Z – as well as a new subsea water injection facility and 44 additional wells 
ConocoPhillips Norge, 2004 
Ministry of Petroleum and Energy, press release, “Vekstprosjekt på Ekofisk godkjent”, 6 June 2003 
https://www stortinget no/no/Saker-og-publikasjoner/Saker/Sak/?p=50343
https://www stortinget no/globalassets/pdf/innstillinger/stortinget/2010-2011/inns-201011-398 pdf
https://www regjeringen no/no/aktuelt/klart-for-40-nye-ar-pa-ekofisk-feltet/id642376/)
Published 1  October 2019 • Updated 12  October 2019
— Gassterminalen i Emden  Foto: Husmo Foto/Norsk Oljemuseum
Oil terminal in Teesside
Olje- og gassterminalene, engelsk,
Teesside terminal  Brian Henderson Thynne takes samples of refrigerated propane  Photo: Husmo Foto/Norwegian Petroleum Museum
The terminal at Teesside in north-east England receives oil and natural gas liquids (NGL) by pipeline from the Ekofisk field  It comprises stabilisation, NGL fractionation, storage tanks for crude oil and an export port 
After arriving through the Norpipe Oil line, crude and NGL are separated and the oil goes through a stabilisation process before reaching the 10 storage tanks, which each hold 750 000 barrels 
The NGLs go to the fractionation facility, with a daily capacity of 64 000 barrels, for separation into methane, ethane, propane, and normal and iso butane 
While the methane (natural gas) is used to fuel the plant, the other products (now known as liquefied petroleum gases – LPG) are made liquid by cooling and stored for export by sea 
One reason for the choice of Teesside as the landfall for the Ekofisk pipeline was the opportunity it offered to install deepwater quays 
The terminal has four of these, with those for crude oil able to handle tankers up to 150 000 deadweight tonnes  The LPG quays can accept carriers loading as much as 60 000 cubic metres 
Two of the crude oil quays lie on the main channel of the River Tees, while the others have been installed in dredged docks 
Gas terminal in Emden
Gas arriving at the Emden terminal from the Ekofisk Complex enters nine parallel treatment trains for cleaning, metering and onward distribution to the buyers 
The North Sea gas is very clean, and needs only limited treatment to remove small amounts of sulphur compounds using an absorption process  Impure molecules from the gas accumulate on the surface of small particles, which act as filter spheres 
Each of the nine trains comprises four process columns and a process oven  The gas enters the top of a column and leaves through the base after passing through the filter spheres 
That leaves the gas ready for sale, and it is piped to the fiscal metering station before entering the buyer receiving pipelines and distribution network 
Three separate commercial pipeline systems connect to the terminal, operated by Ruhrgas, BEB and Gastransport Services (previously Gasunie) respectively  They pipe the gas away on behalf of the gas buyers 
The Norsea Gas Terminal in Emden was officially opened in September 1977 by Norwegian industry minister Bjartmar Gjerde and Phillips executive Gordon Goerin 
Ranking as the first gas sales deal for the Norwegian continental shelf, the Ekofisk agreement paved the way for later contracts covering other fields off Norway 
Regularity at the Emden terminal has been very high, with its own equipment never causing shutdowns  Maintenance takes place when other parts of the system are off line 
The terminal has a daily capacity of about 2 1 million cubic feet of gas per day 
Gas transport restructured
Norpipe AS owned the gas pipeline from Ekofisk to Emden until the transport system for the Norwegian offshore sector was restructured at 1 January 2003 
Norsea Gas A/S furthermore served as the formal owner of the Emden facility, with Phillips Petroleum and then ConocoPhillips as operator for both pipeline and terminal 
olje- og gassterminalene,
Teesside gas terminal  Photo: Husmo Foto/Norwegian Petroleum Museum
Since 2007, Norway’s state-owned Gassco company has been responsible for technical operation of the facilities on behalf of their owners 
That included operator responsibility for the H7 and B11 booster platforms along the gas pipeline, which were shut down in 2007 and 2013 respectively and have since been removed 
The Gassled partnership is a project collaboration embracing 10 companies which collective own large parts of the gas infrastructure on the Norwegian continental shelf (NCS) 
A substantial proportion of Norway’s gas deliveries to Germany continues to arrive at the Emden terminal, including the volumes piped from Ekofisk 
Preliminary planning for a new terminal in the German port began in 2011, with Gassled taking the investment decision for this development in the autumn of 2012 
Construction work began in the following year, with the new facility being built on an unused part of the existing terminal site 
The new terminal has not expanded export capacity  But its functionality is well adapted to future processing needs for fields in the Greater Ekofisk Area and other parts of the NCS sending gas through the Norpipe system 
It was officially opened on 24 May 2016 by Elisabeth Aspaker, the Norwegian government minister for the EU and the European Economic Area  That closed a chapter in Ekofisk’s history 
Source: ConocoPhillips Norge
— Gas pipes at Ekofisk  Photo: Husmo Foto/Norwegian Petroleum Museum
In addition to ConocoPhillips’ own production from Ekofisk, these pipelines carry gas and oil from the company’s fields in the UK sector and from other fields on the Norwegian and British continental shelves 
The three fields in the Greater Ekofisk Area are also tied together by pipelines 
Oil pipeline to Teesside
rørledningene, engelsk,
Pipes and oil tanks at the Teesside plant  Photo: ConocoPhillips/Norwegian Petroleum Museum
The pipeline linking Ekofisk with the terminal for oil and natural gas liquids (NGL) at Teesside on the north-east English coast became operational in October 1975 
Pumps raise the pressure of the oil and NGL before they start their journey to land  Two pumping stations – 37/4 A and 36/22 A ­– originally stood along the pipeline to maintain this pressure, but have now been disconnected and removed 
The pipeline was installed with the ability to carry a million barrels per day  However, that much capacity has never been required 
In the UK sector, a 24-inch pipeline has been tied in with a Y connection to receive input from several British fields – including the J block developments operated by ConocoPhillips 
Output from the Greater Ekofisk Area is supplemented by crude from Valhall, Hod, Ula and Gyda heading for Teesside, optimising pipeline utilisation and thereby boosting value creation 
The pipeline is owned by Norpipe Oil AS and operated by ConocoPhillips 
Gas pipeline to Emden
Sandbags and gravel were used to cover Norpipe to Emden  Photo: Unknown/Norwegian Petroleum Museum
This pipeline became operational in September 1977  The starting pressure of around 132 bar is provided by compressors on the Ekofisk Complex 
The 443-kilometre distance to Emden was split into three equal sections, with platforms B11 and H7 located at the intermediate points to provide boosting if required 
However, additional compression was seldom needed on the final stage to Emden  H7 was shut down in 2007 and B11 in 2013, and both have since been removed 
These two booster platforms were located in the German sector of the North Sea, while the pipeline also crosses the Danish sector 
The pipeline has been trenched or covered with sand  Its final section passes the island of Juist before making landfall on the coast of East Friesland to the north of Emden 
Its daily capacity is roughly 59 4 million standard cubic metres (2 1 billion cubic feet)  In addition to gas from the Greater Ekofisk Area, it carries output from Valhall, Hod, Ula, Gyda and the Statpipe system (primarily Statfjord and Gullfaks) 
Posted on 24  June 2017 25  October 2019
Embla 2/7 D
This unmanned wellhead facility is remotely controlled from Eldfisk 2/7 S located 5 2 kilometres to the north, where oil and gas output from the platform is also processed 
Unmanned and remotely operated wellhead platform
On stream 12 May 1993
— Embla 2/7 D  Photo: ConocoPhillips
sokkelkart, illustrasjon, blokker, lisens, forsidebilde, engelsk,
Hand-colored map of the licenses of the first licensing round on the Norwegian continental shelf  Norwegian Continental Shelf Map, 1965 
The Phillips group was awarded block 2/7 as early as 1965, and the Embla reservoir lies in the southern part of this acreage  Drilling began there in 1974 to depths of 4 500-5 000 metres, but pressure and temperature in the wells were too high for testing with the available equipment 
The first production well was not drilled and tested until 1988, followed by a second in 1990



ground_truth: Electricity is used for transport, heating, lighting, communications, and computation.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the relationship between the maximum velocity and the amplitude of the blob or depletion?

Read the following text and answer briefly.

Context 2: \section{Model equations} \label{sec:equations}

In drift-fluid models the continuity equation
\begin{align}
 \frac{\partial n}{\partial t} + \nabla\cdot\left( n \vec u_E  \right) &= 0 \label{eq:generala} 
\end{align}
describes the dynamics of the electron density $n$  Here
$\vec u_E := (\hat{\vec b} \times \nabla \phi)/B$ gives the electric drift
velocity in a magnetic field $\vec B := B \hat{\vec b}$ and an electric
potential $\phi$  We neglect contributions of the diamagnetic drift~\cite{Kube2016} 




Equation~\eqref{eq:generala} is closed by invoking quasineutrality, i e  the divergence of the ion polarization, 
the electron diamagnetic and the gravitational drift currents must vanish
\begin{align}
  \nabla\cdot\left( \frac{n}{\Omega} \left( \frac{\partial}{\partial t} 
  + \vec u_E \cdot\nabla  \right)\frac{\nabla_\perp \phi}{B}  + n\vec u_d - n\vec u_g\right) &=0
    
 
 
  \label{eq:generalb}
\end{align}
Here we denote 
$\nabla_\perp\phi/B := - \hat{\vec b} \times \vec u_E$, 
the electron diamagnetic drift
$\vec u_d := - T_e(\hat{\vec b} \times\nabla n ) /enB$
with the electron temperature $T_e$,
the ion gravitational drift velocity  
$\vec u_g := m_i \hat{\vec b} \times \vec g /B$
with ion mass $m_i$, and the ion gyro-frequency
$\Omega := eB/m_i$ 

Combining Eq ~\eqref{eq:generalb} with Eq ~\eqref{eq:generala} yields
\begin{align}
 \frac{\partial \rho}{\partial t} + \nabla\cdot\left( \rho\vec u_E \right) + \nabla \cdot\left( n(\vec u_\psi + \vec u_d + \vec u_g) \right) &= 0\label{eq:vorticity}
\end{align}
with the polarization charge density 
$\rho = \nabla\cdot( n\nabla_\perp \phi / \Omega B)$ 
and
$\vec u_\psi := \hat{\vec b}\times \nabla\psi /B$ 
with 
$\psi:= m_i\vec u_E^2 /2e$ 
We exploit this form of Eq ~\eqref{eq:generalb} in our numerical simulations 

Equations~\eqref{eq:generala} and \eqref{eq:generalb} respectively \eqref{eq:vorticity} have several invariants 
First, in Eq ~\eqref{eq:generala} the relative particle number 
$M(t) := \int \mathrm{dA}\, (n-n_0)$ is conserved over time
$\d M(t)/\d t = 0$  
Furthermore, we integrate 
$( T_e(1+\ln n) -T_e \ln B)\partial_t n$
as well as
$-e\phi \partial_t\rho - (m_i\vec u_E^2/2+gm_ix - T_e\ln B)\partial_t n$ 
over the domain to get, disregarding boundary contributions,
\begin{align}
  \frac{\d}{\d t}\left[T_eS(t) + H(t) \right] = 0, \label{eq:energya}\\ 
    \frac{\d}{\d t} \left[ E(t) - G(t) - H(t)\right] =  0,
    \label{eq:energyb}
\end{align}
where we define 
the entropy
$S(t):=\int \mathrm{dA}\, [n\ln(n/n_0) - (n-n_0)]$,  
the kinetic energy 
$E(t):=m_i \int \mathrm{dA}\, n\vec u_E^2/2$ 
and the potential energies
$G(t) := m_i g\int \mathrm{dA}\, x(n-n_0)$
and
$H(t) := T_e\int \mathrm{dA}\, (n-n_0) \ln (B^{-1})$ 
Note that $n\ln( n/n_0) - n + n_0 \approx (n-n_0)^2/2$ for $|(n-n_0)/n_0| \ll 1$ and $S(t)$ thus reduces to the 
local entropy form in Reference~\cite{Kube2016}  

We now set up a gravitational field $\vec g = g\hat x$ and a constant homogeneous background
magnetic field $\vec B = B_0 \hat z$ in a Cartesian coordinate system 
Then the divergences of the electric and gravitational drift velocities $\nabla\cdot\vec u_E$ and $\nabla\cdot\vec u_g$
and the diamagnetic current $\nabla\cdot(n\vec u_d)$ vanish, which makes the 
flow incompressible  Furthermore, the magnetic potential energy vanishes $H(t) = 0$ 

In a second system we model the inhomogeneous magnetic field present in tokamaks as
$\vec B := B_0 (1+ x/R_0)^{-1}\hat z$ and neglect the gravitational drift $\vec u_g = 0$ 
Then, the potential energy $G(t) = 0$  
Note that 
$H(t) = m_i \ensuremath{C_\mathrm{s}}^2/R_0\int\mathrm{dA}\, x(n-n_0) +\mathcal O(R_0^{-2}) $
reduces to $G(t)$ with the effective gravity $g_\text{eff}:= \ensuremath{C_\mathrm{s}}^2/R_0$ with $\ensuremath{C_\mathrm{s}}^2 := T_e/m_i$  
For the rest of this letter we treat $g$ and $g_\text{eff}$ as well as $G(t)$ and $H(t)$ on the same footing 
The magnetic field inhomogeneity thus entails compressible flows, which is 
the only difference to the model describing dynamics in a homogeneous magnetic field introduced above  
Since both $S(t)\geq 0$ and $E(t)\geq 0$ we further derive from Eq ~\eqref{eq:energya} and Eq ~\eqref{eq:energyb} that the kinetic energy
is bounded by $E(t) \leq T_eS(t) + E(t) = T_e S(0)$; a feature absent from the gravitational system with 
incompressible flows, where $S(t) = S(0)$  

We now show that the invariants Eqs ~\eqref{eq:energya} and \eqref{eq:energyb} present restrictions on the velocity and
acceleration of plasma blobs  
First, we define the blobs' center of mass (COM) via $X(t):= \int\mathrm{dA}\, x(n-n_0)/M$ and 
its COM velocity as $V(t):=\d X(t)/\d t$  
The latter is proportional to the total radial particle flux~\cite{Garcia_Bian_Fundamensky_POP_2006, Held2016a} 
We assume
that $n>n_0$ and $(n-n_0)^2/2 \leq [ n\ln (n/n_0) - (n-n_0)]n $ to show for both systems 
\begin{align}
  (MV)^2 &= \left( \int \mathrm{dA}\, n{\phi_y}/{B} \right)^2
  = \left( \int \mathrm{dA}\, (n-n_0){\phi_y}/{B} \right)^2\nonumber\\
 
&\leq 2 \left( \int \mathrm{dA}\, \left[n\ln (n/n_0) -(n-n_0)\right]^{1/2}\sqrt{n}{\phi_y}/{B}\right)^2\nonumber\\
 
  &\leq 4 S(0) E(t)/m_i 
 
  \label{eq:inequality}
\end{align}
Here we use the Cauchy-Schwartz inequality and 
$\phi_y:=\partial\phi/\partial y$  
Note that although we derive the inequality Eq ~\eqref{eq:inequality} only for amplitudes $\triangle n >0$  we assume that the results also hold for depletions  This is justified by our numerical results later in this letter  
If we initialize our density field with a seeded blob of radius $\ell$ and amplitude $\triangle n$ as 
\begin{align}
  n(\vec x, 0) &= n_0 + \triangle n \exp\left( -\frac{\vec x^2}{2\ell^2} \right), \label{eq:inita}
 
 
\end{align}
and  
$\phi(\vec x, 0 ) = 0$,
we immediately have $M := M(0) = 2\pi \ell^2 \triangle n$, $E(0) = G(0) = 0$ and 
$S(0) = 2\pi \ell^2 f(\triangle n)$, where $f(\triangle n)$ captures the amplitude dependence of 
the integral for $S(0)$  

The acceleration for both incompressible and compressible flows can be estimated
by assuming a linear acceleration $V=A_0t$ and $X=A_0t^2/2$~\cite{Held2016a} and using 
$E(t) = G(t) = m_igMX(t)$ in Eq ~\eqref{eq:inequality}
\begin{align}
  \frac{A_0}{g} =  \mathcal Q\frac{2S(0)}{M} \approx \frac{\mathcal Q}{2} \frac{\triangle n }{n_0+2\triangle n/9} 
  \label{eq:acceleration}
\end{align}
Here, we use the Pad\'e approximation of order $(1/1)$ of $2S(0)/M $
and define a model parameter $\mathcal Q$ with $0<\mathcal Q\leq1$ to be determined by numerical simulations 
Note that the Pad\'e approximation is a better approximation than a simple 
truncated Taylor expansion especially for large relative amplitudes of order unity 
Eq ~\eqref{eq:acceleration} predicts that $A_0/g\sim \triangle n/n_0$ for small 
amplitudes $|\triangle n/n_0| < 1$ and $A_0 \sim g $ for very large amplitudes $\triangle n /n_0 \gg 1$, 
which confirms the predictions in~\cite{Pecseli2016} and reproduces the limits discussed in~\cite{Angus2014} 

As pointed out earlier for compressible flows Eq ~\eqref{eq:inequality} can be further estimated
\begin{align}
  (MV)^2  \leq 4 T_eS(0)^2/m_i  
  \label{}
\end{align}
We therefore have a restriction on the maximum COM velocity for compressible flows, which is absent for incompressible flows
\begin{align}
  \frac{\max |V|}{\ensuremath{C_\mathrm{s}}} = {\mathcal Q}\frac{2S(0)}{M} \approx \frac{\mathcal Q}{2} \frac{|\triangle n| }{n_0+2/9 \triangle n } \approx \frac{\mathcal Q}{2} \frac{|\triangle n|}{n_0} 
  \label{eq:linear}
\end{align}
For $|\triangle n /n_0|< 1$ Eq ~\eqref{eq:linear} reduces to the linear scaling derived in~\cite{Kube2016}  
Finally, a scale analysis of Eq ~\eqref{eq:vorticity} shows that~\cite{Ott1978, Garcia2005, Held2016a}
\begin{align}
  \frac{\max |V|}{\ensuremath{C_\mathrm{s}}} = \mathcal R \left( \frac{\ell}{R_0}\frac{|\triangle n|}{n_0} \right)^{1/2} 
  \label{eq:sqrt}
\end{align}
This equation predicts a square root dependence of the center of mass velocity 
on amplitude and size  





We now propose a simple phenomenological model that captures the essential dynamics
of blobs and depletions in the previously stated systems  More specifically 
the model reproduces the acceleration Eq ~\eqref{eq:acceleration} with and without
Boussinesq approximation, the square root scaling for the COM velocity 
Eq ~\eqref{eq:sqrt} for incompressible flows as well as the relation between the 
square root scaling Eq ~\eqref{eq:sqrt} and the linear scaling 
Eq ~\eqref{eq:linear} for compressible flows  
The basic idea is that the COM of blobs behaves like 
the one of an infinitely long plasma column immersed in an ambient plasma  
The dynamics of this column reduces to the one of a two-dimensional ball 
This idea is similar to the analytical ``top hat'' density solution for
blob dynamics recently studied in~\cite{Pecseli2016} 
The ball is subject to buoyancy as well as linear and nonlinear friction
\begin{align}
  M_{\text{i}} \frac{d V}{d t} = (M_{\text{g}} - M_\text{p}) g - c_1 V  - \mathrm{sgn}(V ) \frac{1}{2}c_2 V^2 
  \label{eq:ball}
\end{align}
The gravity $g$ has a positive sign in the coordinate system; sgn$(f)$ is the sign function  
The first term on the right hand side is the buoyancy, where 
$M_{\text{g}} := \pi \ell^2 (n_0 + \mathcal Q \triangle n/2)$ 
is the gravitational mass of the ball with radius $\ell$ and 
$M_\mathrm{p} := n_0 \pi \ell^2 $ 
is the mass of the displaced ambient plasma 
Note that if $\triangle n<0$ the ball represents a depletion and the buoyancy term has a negative sign, i e  the depletion will rise  
We introduce an inertial mass 
$M_{\text{i}} := \pi\ell^2 (n_0 +2\triangle n/9)$ 
different from the gravitational mass $M_{\text{g}}$ in order to 
recover the initial acceleration in Eq ~\eqref{eq:acceleration}  
We interpret the parameters $\mathcal Q$ and $2/9$ as geometrical factors 
that capture the difference of the actual blob form from the idealized
``top hat'' solution  
Also note that the Boussinesq approximation appears in the model as a neglect of inertia, $M_{\text{i}} = \pi\ell^2n_0$ 

The second term is the linear friction term with coefficient $c_1(\ell)$, which
depends on the size of the ball 
If we disregard the nonlinear friction, $c_2=0$, Eq ~\eqref{eq:ball} directly yields a 
maximum velocity $c_1V^*=\pi \ell^2 n g \mathcal Q\triangle n/2$ 
From our previous considerations $\max V/\ensuremath{C_\mathrm{s}}=\mathcal Q \triangle n /2n_0$, we thus identify 
\begin{align}
  c_1 = \pi\ell^2 n_0 g/\ensuremath{C_\mathrm{s}}  
  \label{}
\end{align}
The linear friction coefficient thus depends on the gravity and the size of the
ball  

The last term in \eqref{eq:ball} is the nonlinear friction  The sign of the force depends on whether
the ball rises or falls in the ambient plasma  
If we disregard linear friction $c_1=0$, we have the maximum velocity 
$V^*= \sigma(\triangle n)\sqrt{\pi \ell^2|\triangle n| g\mathcal Q/c_2}$, 
which must equal 
$\max V= \sigma(\triangle n) \mathcal R \sqrt{g \ell |\triangle n/n_0|}$ 
and thus
\begin{align}
  c_2 = {\mathcal Q\pi n_0\ell }/{\mathcal R^2} 
  \label{}
\end{align}
Inserting $c_1$ and $c_2$ into Eq ~\eqref{eq:ball}
we can derive the maximum absolute velocity in the form 
\begin{align}
  \frac{\max |V|}{\ensuremath{C_\mathrm{s}}} = 
        \left(\frac{\mathcal R^2}{\mathcal Q}\right) \frac{\ell}{R_0} \left( 
        \left({1+\left( \frac{\mathcal Q}{\mathcal R} \right)^{2} \frac{|\triangle n|/n_0 }{\ell/R_0}}\right)^{1/2}-1 \right)
  \label{eq:vmax_theo}
\end{align}
and thus have a concise expression for $\max |V|$ that captures both the linear
scaling \eqref{eq:linear} as well as the square root scaling \eqref{eq:sqrt} 
With Eq ~\eqref{eq:acceleration} and Eq ~\eqref{eq:sqrt} respectively Eq ~\eqref{eq:vmax_theo} we 
finally arrive at an analytical expression for the time at which the maximum velocity is reached via 
$t_{\max V} \sim \max V/A_0$  Its inverse $\gamma:=t_{\max V}^{-1}$ gives the
global interchange growth rate, for which an empirical expression was
presented in Reference~\cite{Held2016a} 


We use the open source library FELTOR 
to simulate 
Eqs ~\eqref{eq:generala} and \eqref{eq:vorticity} with and without 
drift compression 
For numerical stabilty we added small diffusive terms on the right hand 
sides of the equations 
The discontinuous Galerkin methods employ three polynomial coefficients and a minimum of $N_x=N_y=768$ grid cells  The box size is $50\ell$ in order to mitigate 
influences of the finite box size on the blob dynamics  
Moreover, we used the invariants in Eqs  \eqref{eq:energya} and \eqref{eq:energyb} as consistency tests to verify the code and repeated simulations 
also in a gyrofluid model  
No differences to the results presented here were found  
Initial perturbations on the particle density field are given by Eq ~\eqref{eq:inita},
where the perturbation amplitude $\triangle n/n_0$ was chosen between $10^{-3}$ and $20$ for blobs and $-10^0$ and $ -10^{-3}$ for depletions  
Due to computational reasons we show results only for $\triangle n/n_0\leq 20$  


For compressible flows we consider two different cases $\ell/R_0 = 10^{-2}$ and
$\ell /R_0 = 10^{-3}$  
 For incompressible flows Eq ~\eqref{eq:generala} and \eqref{eq:vorticity}
 can be normalized such that the blob radius is absent from the equations~\cite{Ott1978, Kube2012}  
 The simulations of incompressible flows can thus be used for both sizes  
The numerical code as well as input parameters and output data can be found 
in the supplemental dataset to this contribution~\cite{Data2017} 

\begin{figure}[htb]
    \includegraphics[width=\columnwidth]{com_blobs}
    \caption{
      The maximum radial COM velocities of blobs for compressible and incompressible flows are shown  
      The continuous lines show Eq ~\eqref{eq:vmax_theo} while the 
      dashed line shows the square root scaling Eq ~\eqref{eq:sqrt} with 
      $\mathcal Q = 0 32$ and $\mathcal R=0 85$ 
    }
    \label{fig:com_blobs}
\end{figure}
In Fig ~\ref{fig:com_blobs} we plot the maximum COM velocity for blobs 
with and without drift compression 
For incompressible flows blobs follow the square root scaling almost 
perfectly  Only at very large amplitudes velocities are slightly below
the predicted values  
For small amplitudes we observe that the compressible blobs follow
a linear scaling  When the amplitudes increase there is a transition to the
square root scaling at around $\triangle n/n_0 \simeq 0 5$ for 
$\ell/R_0=10^{-2}$ and $\triangle n/n_0 \simeq 0 05$ for $\ell/R_0=10^{-3}$, which is consistent with Eq ~\eqref{eq:vmax_theo} and Reference~\cite{Kube2016}  
In the transition regions the simulated velocities are slightly larger than the predicted ones from Eq ~\eqref{eq:vmax_theo} 
Beyond these amplitudes
the velocities of compressible and incompressible blobs align  

\begin{figure}[htb]
    \includegraphics[width=\columnwidth]{com_holes}
    \caption{
      The maximum radial COM velocities of depletions for compressible and incompressible flows are shown  
      The continuous lines show Eq ~\eqref{eq:vmax_theo} while the 
      dashed line shows the square root scaling Eq ~\eqref{eq:sqrt} with 
      $\mathcal Q = 0 32$ and $\mathcal R=0 85$ 
      Note that small amplitudes are on the right and amplitudes close to unity are on the left side 
  }
    \label{fig:com_depletions}
\end{figure}
In Fig ~\ref{fig:com_depletions} we show the maximum radial COM velocity 
for depletions instead of blobs 
For relative amplitudes below $|\triangle n|/n_0 \simeq 0 5$ (right of unity in the plot) the velocities
coincide with the corresponding blob velocities in Fig ~\ref{fig:com_blobs}  
 For amplitudes larger than $|\triangle n|/n_0\simeq 0 5$ the 
velocities follow the square root scaling 
We observe that for plasma depletions beyond $90$ percent the velocities 
in both systems reach a constant value that is very well predicted by the
square root scaling  

\begin{figure}[htb]
    \includegraphics[width=\columnwidth]{acc_blobs}
    \caption{
      Average acceleration of blobs for compressible and incompressible flows are shown 
      The continuous line shows the acceleration in Eq ~\eqref{eq:acceleration} 
      with $\mathcal Q=0 32$
      while the dashed line is a linear reference line, which corresponds to the Boussinesq approximation  
  }
    \label{fig:acc_blobs}
\end{figure}
In Fig ~\ref{fig:acc_blobs} we show the average acceleration of blobs 
for compressible and incompressible flows computed
by dividing the maximum velocity $\max V$ by the time  
to reach this velocity $t_{\max V}$  
We compare the simulation results
to the theoretical predictions Eq ~\eqref{eq:acceleration} of our model with and without inertia  
The results of the compressible and incompressible systems coincide and fit very
well to our theoretical values  
For amplitudes larger than unity the acceleration deviates significantly from the prediction with Boussinesq approximation 

\begin{figure}[htb]
    \includegraphics[width=\columnwidth]{acc_holes}
    \caption{
      Average acceleration of depletions for compressible and incompressible flows are shown 
      The continuous line shows the acceleration in Eq ~\eqref{eq:acceleration} 
      with $\mathcal Q=0 32$
      while the dashed line is a linear reference line, which corresponds to the Boussinesq approximation  
    }
    \label{fig:acc_depletions}
\end{figure}
In Fig ~\ref{fig:acc_depletions} we show the simulated acceleration of depletions in the
compressible and the incompressible systems  We compare the simulation results
to the theoretical predictions Eq ~\eqref{eq:acceleration} of our model with and without inertia 
Deviations from our theoretical prediction Eq ~\eqref{eq:acceleration} are visible for amplitudes smaller than $\triangle n/n_0 \simeq -0 5$ (left of unity in the plot)  The relative deviations are small at around $20$ percent  
As in Fig ~\ref{fig:com_depletions} the acceleration reaches a constant values
for plasma depletions of more than $90$ percent 
Comparing Fig ~\ref{fig:acc_depletions} to Fig ~\ref{fig:acc_blobs} the asymmetry between blobs and depletions becomes 
apparent  While the acceleration of blobs is reduced for large 
amplitudes compared to a linear dependence the acceleration 
of depletions is increased  In the language of our simple buoyancy 
model the inertia of depletions is reduced but increased for blobs  



In conclusion  
  we discuss the dynamics of seeded blobs and depletions in a 
  compressible and an incompressible system 
  With only two fit parameters our theoretical results reproduce the 
  numerical COM velocities and accelerations over five orders of magnitude 
  We derive the amplitude dependence of the acceleration of blobs and depletions from 
  the conservation laws of our systems in Eq ~\eqref{eq:acceleration}  
  From the same inequality a linear regime is derived in the compressible system for 
  ratios of amplitudes to sizes smaller than a critical value 
   In this regime 
  the blob and depletion velocity depends linearly on the initial amplitude and 
  is independent of size  The regime is absent from the system with incompressible flows 
  Our theoretical results are verified by numerical simulations for all 
  amplitudes that are relevant in magnetic fusion devices 
  Finally, we suggest a new empirical blob model that captures the detailed dynamics of more complicated models  
  The Boussinesq approximation is clarified as the absence of inertia and a thus altered acceleration of blobs and depletions 
  The maximum blob velocity is not altered by the Boussinesq approximation 

The authors were supported with financial subvention from the Research Council of Norway under grant
240510/F20  M W  and M H  were supported by the Austrian Science Fund (FWF) Y398   The computational
results presented have been achieved in part using the Vienna Scientific Cluster (VSC)  Part of this work was performed on the Abel Cluster, owned by the University of Oslo and the Norwegian metacenter
for High Performance Computing (NOTUR), and operated by the Department for Research Computing at USIT,
the University of Oslo IT-department 
This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 633053  The views and opinions expressed herein do not necessarily reflect those of the European Commission 
Context 3:  Both yielded very promising results, and the field came on stream in May 1993 
Embla comprises a sandstone reservoir at least 250 million years old  The other fields in the Greater Ekofisk Area comprise fine-grained carbonate rocks deposited about 70 million years ago 
The Embla reservoir has a temperature of 160°C compared with the 125°C normally found in the chalk formations 1 000 metres higher up, and its pressure is almost twice as high 
Fabricated by Heerema in the Netherlands, the Embla 2/7 D jacket (support structure) was installed by the M 7000 crane vessel  It stands 84 metres high and weighs 2 300 tonnes 
A 5 2-kilometre subsea umbilical from Eldfisk comprises three power cables for electricity supply and eight fibreoptic lines handling data transmission and telecommunication 
Eldfisk 2/7 S, embla,
Eldfisk 2/7 S  Photo: ConocoPhillips
The platform has six production wells and an average daily output of roughly 7 000 barrels of oil  All processing and metering took place on Eldfisk 2/7 FTP until 2015, and has now been switched to Eldfisk 2/7 S 
A 14-inch flowline linked 2/7 D with 2/7 FTP and runs today to 2/7 S  Produced at Wick in Scotland, this line was floated out to the field in one piece 
Topside equipment includes the wellhead area, helideck (built by Vindholmen Services in Arendal), crane, control room, workshop, test separator and glycol pump 
Normally unmanned, the platform is maintained as and when required and therefore incorporates a simplified accommodation module with lounge, mess, coffee room, galley, changing room, WC and 12 emergency beds 
More about platforms
Ekofisk 2/4 Z
This installation is a wellhead platform in the Ekofisk Complex 
Gulftide
This four-leg jack-up drilling rig was built in Glasgow during 1967 for Ocean Drilling & Exploration Co 
Posted on 1  September 2019 8  October 2019
— Gulftide with Ekofisk 2/4 A in the background  Photo: Aker Mek  Verksted/Norwegian Petroleum Museum
Gulftide was converted to cope with conditions on Ekofisk in the Åmøy Fjord near Stavanger  This jack-up drilling rig was equipped with process equipment and its derrick, helideck, hangar and legs were reinforced 
To win time, it was decided that the discovery well and three appraisals drilled on Ekofisk by Ocean Viking would be completed for production 
Principles for producing from Gulftide were relatively simple  Output flowed from the subsea wellheads to the platform, where it went through two-stage separation to remove gas and water 
With pressure also reduced, the gas was flared off and the oil sent on by flowlines to two loading buoys where shuttle tankers moored to take on cargo 
utbyggingen,
Tankskipet Donovania laster olje fra lastebøyen på Ekofisk  I bakgrunnen skimtes så vidt Gulftide  Foto: ConocoPhillips/Norsk Oljemuseum
Production could only continue while ships were loading  As soon as one tanker had been filled, the oil stream was diverted to the vessel waiting at the other loading buoy 
The problem with this approach was manifested when weather conditions ­– strong winds and/or high waves – forced the tankers to leave the buoys 
If that happened, production from the wellheads had to be suspended immediately  Given the prevailing weather on Ekofisk, that happened regularly  Output was halted for 20 per cent of the time during the first year 
https://ekofisk industriminne no/wp-content/uploads/sites/2/2019/09/Building-Ekofisk mp4
Gulftide was replaced as the temporary production installation in 1974 by the permanent Ekofisk 2/4 A (Alpha) and 2/4 B (Bravo) platforms for production, drilling and quarters 
In addition came the Ekofisk 2/4 C (Charlie) production, drilling and compression facility, the Ekofisk 2/4 FTP (field terminal platform) for production and risers, and Ekofisk 2/4 Q for accommodation 
Oil and gas were produced by 2/4 A, B and C through their own wells for processing in their separation plants and piping on the 2/4 FTP for a three-stage separation process 
At the same time, the tanker loading buoys were moved further from the platforms and the Ekofisk 2/4 T oil storage tank became operational 
This facility was extremely advantageous, because it allowed production to continue virtually regardless of whether bad weather prevented tankers from connecting to the buoys 
Ekofisktanken ble satt i drift i 1974  Foto: ConocoPhillips/Norsk Oljemuseum
The 2/4 FTP platform, where oil and gas from the three producing facilities was processed, had been planned to handle the level of output estimated for the main field 
Clear restrictions had been imposed by the Norwegian government on the amount of gas Phillips was allowed to flare  That also set a ceiling for oil production, since gas accompanies it up from the reservoir 
The solution was to install two powerful compression packages on 2/4 C in order to inject the gas under pressure back into the producing formation 
Accommodation facilities had to be provided on the two first platforms, 2/4 A and B  Where 2/4 C and FTP were concerned, however, they were tied together with bridges and to 2/4 Q 
Published 1  September 2019 • Updated 8  October 2019
Posted on 9  April 2019 25  October 2019
Jack-up drilling rig
Built 1967 in Glasgow for Ocean Drilling & Exploration Co 
Began test production on Ekofisk 15 June 1971
Produced on Ekofisk until 1974
— Gulftide at theEkofisk field  Photo: Terje Tveit/Norwegian Petroleum Museum
gulftide,
Gulftide  Photo: Unknown/Norwegian Petroleum Museum
A mere 17 months after the Ekofisk discovery was announced in December 1969, Gulftide was ready to come on stream as a temporary production platform 
Its official inauguration took place on 9 June, with initial test output commencing on 15 June  Full production began on 8 July 
The rig was chosen because it was available on the market  Established equipment for processing oil and gas was tailored to the limited space on board  Separate flowlines carried wellstreams from four subsea wells  Oil, gas and water were separated on board, with the gas flared and the oil piped to two buoys for loading into shuttle tankers 
Work on the process equipment was relatively simple  The problem was to tailor it to the rig  The subsea wellheads had to be reinforced to meet the demands posed by the North Sea, and a buoy loading system needed to be developed for waters where this technology had never been used before 
To gain time, it was decided that the three appraisal wells drilled by Ocean Viking to map the extent of the field – in addition to the discovery well – would be completed for production 
Første testflamme tent på Ekofisk  På Gulftide
1973, Teddy Broadhurst, gulftide,
arbeidsliv, hjelpearbeider
Gulftide, separator – på bildet kan man se at det er fire brønner 
arbeidsliv, gulftide, pionerkultur, arbeid, dekk, Norges første havbunnsbrønner, historie, 1971,
The producers would be topped with hydraulically controlled wellheads  Such equipment had been tried out on the seabed earlier, but on a limited scale and not in the deep and rough waters found on Ekofisk  This challenge was overcome by having the wellheads manufactured and then reinforced at the Phillips base in Dusavik outside Stavanger  Flowlines and control cables would also be laid from each well to Gulftide, with production comingled in a single riser to the topsides 
Weather conditions also represented a major problem when designing the loading buoys  Phillips itself had experience with such facilities, but the concept had only been used before in harbour-like conditions and waters no deeper than 27 metres  They were now to stand in 70 metres in the middle of the North Sea 
Gulftide was converted in the Åmøy Fjord outside Stavanger to cope with conditions on Ekofisk  The processing facilities were installed and reinforcements made to the derrick, helideck, hangar and leg structures 
Gulftide, Ekofisk 2/4 A, boretårn, flare, 1971, utbygging,
Gulftide with Ekofisk 2/4 A in the background  Photo: Aker Mek  Verksted/Norwegian Petroleum Museum
Planning began in late 1970, when Phillips received approval to begin laying the flowlines between wellheads and rig  Brown & Root won this contract, with the first oil pipelines on the Norwegian continental shelf laid by the Hugh W Gordon laybarge 
The production principle on Gulftide was relatively simple  Output flowed from the subsea wellheads to the rig, where it passed through two separation levels to be split into oil and gas while the huge pressure was reduced 
Gas was flared off and the oil was piped to one of the loading buoys where a shuttle tanker was moored  Production could only take place when a ship was present 
Offisiell åpning av norsk oljeproduksjon,
The Greek tanker, Theogennitor, unloads crude oil from loading buoys on the Ekofisk field  Gulftide in the background  Photo: ConocoPhillips/Norwegian Petroleum Museum
As soon as one tanker had become fully laden, the oil flow was switched to the other buoy where another ship was waiting to take on cargo 
The problem with this approach arose when weather conditions meant the tankers had to cast off from the buoys because of strong winds or high waves  The rig then had to shut down production from the wellheads immediately 
Given the weather conditions found on Ekofisk, output regularly had to cease  Production was suspended for 20 per cent of the first year for this reason 
Output began cautiously on 8 July 1971 from a single well  The second producer came on stream that September, the third was ready the following month and all four were producing by February 1972  They each flowed 10 000 barrels of oil per day 
Source: Kvendseth, Stig, Giant discovery, 1988 
Published 9  April 2019 • Updated 25  October 2019
Norpipe H-7
This platform served as a pumping/compressor station to maintain pressure in the 443-kilometre Norpipe gas pipeline from Ekofisk to Emden in Germany, which became operational in September 1977 
Kjappe fakta::
Compressor platform on Ekofisk-Emden gas pipeline
Installed 1976
Operational 1977
Shut down 29 October 2007
Removed 2013
— Norpipe GNSC-H7  Photo: Husmo Foto/Norwegian Petroleum Museum
Gas received initial compression to 132 bar at the Ekofisk Complex  The pipeline was divided into three equal lengths, with Norpipe GNSC B11 positioned at the end of the first third to maintain pressure as and when required 
From there, the gas then travelled the next third of the distance to the second and virtually identical compressor platform, H7 
This was also responsible for maintaining pressure, but additional compression was seldom required on this final leg of the journey to Emden 
Both platforms stood on the German continental shelf, but 48 kilometres of the pipeline also ran across the Danish North Sea sector 
The pipeline is trenched or covered with sand  On its final approach to the coast of East Friesland, it passes beneath the island of Juist before making landfall north of Emden 
Capacity in Norpipe is about 60 million standard cubic metres (scm) or 2 1 billion cubic feet per day  In addition to output from the Ekofisk-area fields, it carries gas from Valhall, Ula and the Statpipe system – primarily Statfjord and Gullfaks  Gas was also transported for a time from Hod and Gyda, but that has ceased 
fritid, Norpipe GNSC-H7,
Magnus Refsland and Werner Hein have pulled the crab trap (full of starfish) on the Norpipe H-7 platform  Photo: Husmo Foto/Norwegian Petroleum Museum
Built in 1976, the B11 platform had six decks  Its permanent staffing totalled 14 people, but various service personnel were also often on board  The regular crew included three in catering 
The 11 Phillips employees comprised the offshore installation manager, the nurse/radio operator, eight operators and a roustabout 
In addition to their direct function, the operators covered various other trades which meant the crew was self-sufficient in most circumstances 
Both platforms obtained a satellite antenna in 1986 which allowed them to received Norwegian TV, while the 24-bed accommodation were redecorated in 1981 and upgraded in the summer of 1990 
Work on the upgrading largely comprised converting all cabins to doubles with shower and WC  The galley and changing rooms were renewed and changing facilities for women provided 
A new module with a lounge for non-smokers, a smoking room, gym and pool room was also installed  During this work, the West Gamma accommodation rig was positioned alongside 
Upgrading equipment on the platform was also initiated in 1990  While the pipeline’s original daily capacity had been estimated at 2 100 million standard cubic feet, this was found to have declined after a number of years to 1 975 million 
To return to the original capacity, the compressors needed to be upgraded and power supply from the turbines increased  This was done both on the Ekofisk tank and on the H7 and B11 platforms  Gas coolers on the tank were replaced as well



ground_truth: The maximum velocity scales with the square root of the amplitude.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the water depth in the Greater Ekofisk Area?

Read the following text and answer briefly.

Context 3: 
Norpipe GNSC-H7, yrker, radiooperatør,
Radio operator Torleif Førland on the platform Norpipe H-7, with his amateur radio  Photo: Husmo Foto/Norwegian Petroleum Museum
The control systems were also upgraded in parallel  Control panels on turbines and compressors were replaced and metering instruments installed to conduct measurements in this equipment 
While the nearest neighbour to B11 was a Danish oil field, H7 stood in the middle of the shipping channel  M/S Hero broke down 15 nautical miles west of the latter platform at around 13 00 on 12 November 1977 
By 21 00, the ship was still adrift and heading directly for H7, and all 14 crew on the platform made ready to evacuate by helicopter – the waves were too high for the lifeboats  The wreck passed at 21 40 with a clearance of 400 metres 
German cargo carrier Reint collided with H7 on 30 September 1995, despite efforts by the standby ship to avert the threat  Production was halted as a safety measure, but the platform luckily suffered only minor damage  The collision was caused by inadequate watchkeeping on the ship’s bridge 
Operator responsibility for B11 and H7 was transferred at the beginning of 2003 to Norway’s state-owned Gassco company, which runs the Norwegian gas transport network 
This change had little significance for operation of the platforms, since the actual work was still carried out by ConocoPhillips as a technical service provider to Gassco 
H7 was shut down in 2007, and removal had been completed in 2013  In connection with preparations to remove the structure, operator responsibility was transferred to Statoil as the company in charge of the project on Gassco’s behalf 
Published 24  August 2016 • Updated 22  October 2019
Phillips inundates Sola with oil revenues
person by Kristin Øye Gjerde
Stavanger and neighbouring Sola were the first Norwegian local authorities to experience fantastic oil-related growth after the award of the first exploration licences in 1965 
— Phillips er i ferd med å etablere seg på Norscobasen nederst til høyre Ca 1972 Foto: Norsk fly og flyfoto/Norsk Oljemuseum
The Shell refinery at Risavika in Sola was completed two years later, while the Norsco base in Tananger became operational as early as 1966 
But things really took off once the Ekofisk field had been discovered in the autumn of 1969 and started trial production on 14 July 1971 
Operator Phillips Petroleum Company moved its offices from the Dusavik base outside Stavanger to Tananger in Sola, and Shell could finally start refining Norwegian rather than imported crude 
Sola’s population now rose steadily from 8 400 in 1965 to 15 000 two decades later, and jobs grew even faster – from about 2 000 in 1970 to almost 8 000 in 1985  That averages 10 per cent annually 
Phillips and Shell became cornerstone companies  A large part of their workforce, particularly in Phillips, worked offshore  In addition came newly established oil supply firms 
More jobs were also created in retail, public administration, education, health and social care, personal services and so forth 
Although traditional agriculture remained important for the local authority, the number of farmers gradually declined as a result of mechanisation [REMOVE]Fotnote: This article is based on the chapter “Elverket i Oljealderen” in I det regionale spenningsfelt  Sola Energi 1913-1999, Kristin Øye Gjerde 
Boreskipet Drillship ligger ved kai på Norscobasen i Tananger (1968)  Foto: NOM/Norsk Fly og Flyfoto
Boreskipet Drillship ligger ved kai på Norscobasen i Tananger (1968)  Foto: Norsk Fly og Flyfoto/Norsk Oljemuseum
The “agio tax”
The sharp rise in Sola’s revenues was attributable entirely to the oil industry, and it found itself in an enviable position during this period  Tax revenues rose even faster than population and jobs 
To give an indication, the local authority’s overall income from wealth and income taxes rose from NOK 9 3 million in 1966 to NOK 198 million in 1990  The biggest growth came in 1978-82, when it averaged 39 per cent a year [REMOVE]Fotnote: Sola local authority, plans 
The secret behind this sharp increase was the tax paid by the oil companies – primarily Phillips – on agio, or the percentage fee charged when exchanging one currency for another 
Under Norwegian law at the time, the companies paid tax on their interest income to the local authority where they had their head office  In making this rule, however, the government had failed to take account of the considerable sums involved 
As operator of the Greater Ekofisk Area, Phillips had placed capital to be used for new investment in banks around the world – particularly the UK 
These deposits yielded substantial interest payments, and tax was payable on converting this income into Norwegian kroner [REMOVE]Fotnote: Toralv Torstenbø, former chief executive officer in Sola local authority, interviewed by Kristin Øye Gjerde, 22 February 2001 
Sola council is said to have almost gone into shock the first time Phillips paid this agio tax  It suddenly had more money than it could spend 
During the 1970s and early 1980s, Sola’s municipal income always exceeded the budgeted amount  Large sums could be transferred every year to a capital fund 
Since the local authority was in a growth phase, additional funding was needed for the big developments it faced  While the rest of Norway experienced a slump in the late 1970s, Sola continued in top gear without a sign of unemployment 
Net income tax revenues came to NOK 55 5 million in 1978, while net spending was NOK 31 9 million  And these fantastic results went on improving 
By 1982, wealth and income taxes yielded NOK 203 4 million – compared with a budget of NOK 146 million, which was upgraded to NOK 190 million during the year 
According to Toralv Torstensbø, the financial controller, agio tax accounted for almost half this amount – in other words, as much as the tax paid by all other enterprises, private individuals and industry in Sola 
Its chief executive officer became a little overweening  In his comments on the 1982 budget, he declared that it would be “natural for Sola local authority to feel a strong regional responsibility and not to be too strict about the traditional division of costs between state, county and local authority ”
In line with this open-handed policy, Sola paid for both road projects and an upper secondary modern school which the county council was supposed to fund [REMOVE]Fotnote: Chief executive officer’s budget proposal for Sola local authority covering 1974-85 
Tightening up petroleum tax
This unexpected prosperity undoubtedly created some jealously in the neighbouring local authorities, and the media began to show an interest in the issue 
Local daily Stavanger Aftenblad interviewed Sola’s chief executive and controller in 1981, when its photographer took a shot which illustrated the boundless wealth – Torstensbø stood showering hundred-krone notes over his colleague 
This story was not only read by the paper’s regular subscribers  The following day, 150 copies were distributed to members of the Storting (parliament) 
That in turn prompted Centre Party representative Lars Velsand to make a passionate speech in which he described the position as a misuse of tax revenues 
He called on the government to intervene so that individual local authorities were unable to benefit in this way  Nor was he alone in finding it unreasonable that a small community like Sola should get so much money 
The result was an amendment to the Petroleum Tax Act on 11 June 1982, which specified that the proceeds from the agio tax should be transferred in future to central government 
Løfteskipet Uglen i aksjon ved Norscobasen i juli 1980  Foto: NOM/Norsk Fly og Flyfoto
Løfteskipet Uglen i aksjon ved Norscobasen i juli 1980  Foto: Norsk Fly og Flyfoto/Norsk Oljemuseum
Unfortunately, however, Sola had got used to consuming these revenues  It is easy to learn expensive habits, but not so straightforward to shrug them off again 
Matters had become a little unusual when the council’s executive board adopted the style of the oil company chiefs and took a helicopter outing during an ordinary budget meeting [REMOVE]Fotnote: Oskar Goa, former chief technical officer in Sola local authority, interviewed by Kristin Øye Gjerde, 23 October 2000 
However, most of the tax money benefitted the general public  Paying for Sola upper secondary school and new national and county highways is an example of this 
The council also invested on local authority school buildings and community facilities such as the big sports complex at Åsen, with an outdoor athletics ground and two modern indoor arenas  Dysjaland and Tananger also acquired new sports arenas 
A new cultural centre built in central Sola has a distinctive architecture in brick and glass, with a grassed roof to blend with the surrounding Jæren landscape  With two stages and a public library, this became the community’s main venue for events and so forth 
The local authority thereby built up a very good infrastructure  Power cables were laid in the same trenches as water and sewage pipes, a network of cycle lanes was built and street lighting installed 
On the downside, virtually all these investments boosted operating expenses  The council’s running costs rose by an annual average of 30 per cent in 1978-84, with the biggest growth in the last three years of the period 
So the calls by Storting representatives to transfer agio tax receipts from councils to central government represented a real threat to local politicians 
Sola joined forces with other local authorities in the same position, including Stavanger, Oslo and Bærum as well as Rogaland county council 
A delegation met the Storting’s standing committee on finance to present their case, and secured a commitment to accept a phased reduction in revenues over four years 
The local authorities would receive 80 per cent of agio tax receipts during the first year, then 60 per cent, 40 per cent and finally 20 per cent [REMOVE]Fotnote: Amendment to the Petroleum Tax Act adopted on 14 May 1982 
In reality, however, the run-down percentages were adjusted to extend over five years in annual steps of 80, 60, 20, 20 and 20 per cent  The total amount going to the local authorities was the same 
The arrangement was controversial to the last, and also uncertain because it had to be approved in each annual government budget 
Living within its means
After the tax change, Sola’s chief executive officer saw the writing on the wall  It seemed “to be unquestionable that [Sola] has seen its best days in purely financial terms and must return to setting tougher priorities for various assignments,” he asserted in connection with the budget process for 1983 [REMOVE]Fotnote: Chief executive officer’s budget proposal for Sola local authority, 1983 
It took the politicians a little longer to accept this reality, but they were forced to reduce investment and operating expenditures in the years which followed 
Cutting back on the new sports arenas and cultural centre was not very desirable  Nor was it pleasant to have to slow down  But savings had to be made, and long-terms spending plans were removed from the budget for possible reintroduction later 
A raft of measures were stripped from the budget in 1985, such as extensions to and modernisation of schools, sports arenas and swimming pools, a new somatic nursing home, housing for the intellectually disabled and sheltered housing  Grants for national and county roads were reduced [REMOVE]Fotnote: Chief executive officer’s budget proposal for Sola local authority, 1985 
Once the government’s compensation scheme had ended, Torstensbø – now chief executive officer – told Stavanger Aftenblad that he did not want to paint too gloomy a picture 
“But it’s clear that we must set much more moderate financial priorities than we’ve been used to  To sum up the position, we were previously flush with cash and poor in facilities  We’re now flush with facilities and poor in cash ”[REMOVE]Fotnote: Stavanger Aftenblad, ”Alt blir dyrere i det rike Sola”, 19 May 1987 
Sola kulturhus fotografert vinteren 2004
Rogaland county council also raised the question of whether it would be possible to establish a permanent arrangement which allowed local authorities and counties to benefit from some of the tax revenues paid by local oil companies 
The council pointed out that it was otherwise normal practice for Norwegian companies to pay taxes to the local communities they were based in 
This request was turned by Labour finance minister Gunnar Berge because the councils concerned still benefitted from bigger tax payments by oil company employees and on property [REMOVE]Fotnote: Stavanger Aftenblad, “Rogaland reiser skattekrav på ny”, 16 January 1988 
According to Torstensbø, this was only partly true  The big oil companies were not so significant for Sola’s income once the agio tax was excluded 
About NOK 2 million was received annually from Phillips, primarily in property tax  The most important taxpayers in the local authority were the roughly 90 companies at Aker Base  These were service providers such as Halliburton, Schlumberger and Baker Hughes 
At the same time, Sola acquired a steadily growing number of affluent residents and a growing share of its revenue came from income tax  Despite the cut-backs, it remained prosperous 
Published 29  July 2019 • Updated 29  July 2019
More about economy
Participants in Ekofisk
The question of who “owns” Ekofisk is not straightforward  In simple terms, however, the field and the rest of Norway’s continental shelf (NCS) belongs to the Norwegian state  This was determined on 14 June 1963, when the Storting (parliament) passed the Act Relating to Exploration for and Exploitation of Submarine Natural Resources  This permits licences to be awarded on certain terms 
Riding out the oil crisis
The greatest-ever oil bonanza, with oil prices hitting USD 130 per barrel, came to an abrupt end in 2014, when the cost of a barrel of crude slumped to less than USD 50 from June to December  And the bottom had still not been reached – this was only the start of a new oil crisis which lasted several years  What effect did this have on ConocoPhillips’ financial position off Norway?



ground_truth: The water depth in the Greater Ekofisk Area is 70-75 meters.