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We are the world’s largest oilfield services company1. Working globally—often in remote and challenging locations—we invent, 1. design, andlargest apply technology to helpcompany our customers find We areengineer, the world’s oilfield services 1. and produce oil and gas safely. Working globally—often in remote challenging locations—we invent, We are the world’s largest oilfieldand services company design, engineer, and apply technology to help our customers find invent, Working globally—often in remote and challenging locations—we 1. We are the world’s largest oilfield services and produce oil and safely. design, engineer, andgas apply technology to helpcompany our customers find 1. We are the world’s largest oilfield services company Working globally—often in remote and challenging locations—we and produce oil than and gas safely. We need more 5,000 begin dynamic careers in invent, Working globally—often in graduates remote andtochallenging locations—we invent, design, engineer, and apply technology to help our customers find the following domains: design, engineer, and apply technology to help our customers find and produce oil than and gas safely. We need more 5,000 graduates to begin dynamic careers in and produce oil and gas safely. n Engineering, Research and Operations the following domains: We need more than 5,000 graduates to begin dynamic careers in n Geoscience and Petrotechnical the following domains: n Engineering, Research and Operations n WeCommercial need moreand thanBusiness 5,000 graduates to begin dynamic careers in We need more Research than 5,000and graduates to begin dynamic careers in n Operations n Geoscience and Petrotechnical theEngineering, following domains: the following domains: n Geoscience and and Business Petrotechnical n Commercial n Engineering, Research and Operations Engineering,and Research and Operations n Commercial Business n Geoscience and Petrotechnical n Geoscience and Petrotechnical n Commercial and Business n Commercial and Business
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Almost a year has passed since we brought the first issue of the YoungPetro into your hands. I have to admit it was not an easy year. We came across a lot of challenges and obstacles but we have always tried to work hard on each of them. We had to fight with technical difficulties as well as our own weaknesses. Finally we have managed to overcome even the toughest ones. Despite all the problems we are glad that we have taken up the challenge and tried to make our dream come true. Someone once said that “an idea is the strongest force in the world” but even such strong force is completely powerless as long as it stays inside you. And that is why we encourage you to unleash your ideas. Our industry needs to go through a lot of changes to meet demands of the modern world. Rising energy needs compared with more and more stringent environmental requirements are making this nut even harder to crack. Consequently, during the last couple of years Oil and Gas industry has experienced the worsening of its public image but it is always easy to be a passive critic. That is a reason why you should be proud of yourself for choosing more difficult path and for using your ideas to create a real change in the industry.
chief@youngpetro.org
Editor's Letter
Thank you all for being with us throughout this year, because without you none of it would have ever happened. YoungPetro wishes you all many years filled with health, happiness and success.
Wojtek Stupka
spring / 2012
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Editor-in-Chief Wojtek Stupka chief@youngpetro.org Editors Jakub Jagiello Alexey Khrulenko Krzysztof Lekki Patrycja Szczesiul Robert Skwara Bartłomiej Staszkiewicz Lukasz Świrk Liliana Trzepizur Dawid Wojaczek editors@younpetro.org Art Director Marek Nogiec art@youngpetro.org Social Media Kacper Malinowski social@youngpetro.org Photo Arthur Perederiy photo@youngpetro.org
Published by An Official Publication of
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Anna Ropka - Chairman Magazine Partner
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The Concept of Universal Life-saver with 9 Rotary-screw Mover Maxim S. Krasheninnikov
Gas Deviation Factor Through An Intelligent 25 Method Called Artificial Neural Network Mohammad Javad Kiani
East Meets West 30 Nodal Analysis Used To Offshore Well 32 Operating Regime Optimization Rareș Petre, Mihai Vasile
Viscosity of the electron gas in a conductor 43 Radmir Ganiev
Flow Rate of Horizontal Wells 50 Rustam Bagautdinov
Keeping eyes on the horizon 55 Wojtek Stupka
spring / 2012
8 8ďťż
For online version of the magazine and news visit us at youngpetro.org
Maxim S. Krasheninnikov
9
̂̂The Concept of Universal Lifesaver with Rotary-screw Mover Maxim S. Krasheninnikov Anatoly P. Kulashov, Viktor A. Shapkin, Alla A. Koshurina
Abstract At the present time there is an active development of oil and gas fields located offshore in the northern seas. Mineral resources are mined in severe natural and climatic conditions. These conditions complicate platforms’ accordance to high safety requirements to various industrial processes. Moreover, according to the analysis of the accidents, there is a problem in providing fast reliable and efficient evacuation of the platform’s personnel. Present means of evacuation cannot work effectively under such difficult conditions. This paper shows the analysis of accidents that occurred on the platforms, reviews existing means of evacuation, and indicates solutions to some actual safety problems. This paper offers a versatile rescue tool with rotary-screw propeller, which can effectively overcome various environments. Features of rotary-screw mover allow to use technological and transport means in such areas where the usage of other movers is impossible or irrational. However, the creation of such devices is possible only with relevant research; such studies are conducted by Nizhny Novgorod State Technical University named after R.Y. Alekseev.
**Nizhny Novgorod State Technical University ÞÞRussia Viktor Shapkin, Ph. D. maks21118@mail.ru University Country Supervisor E-mail
The history of industrial development of oil fields in the offshore area began in 1947 when the American company "Kerr McGee" has built first in the world oil rig in the Gulf of Mexico, 16 kilometers from the coast at a depth of 6 feet and began drilling [1]. Currently about 35% petroleum and 32% of gas produced in the world occur in the offshore fields [6]. Since oil and gas reserves on the continental fields has been steadily decreasing, becomes more urgent question of oil and gas production is from offshore fields. Work on these platforms is more dangerous than on ground complexes. It is connected with more severe conditions in which minerals are extracted and damage of larger area in case of accident. In ensuring the safety of these facilities the most important role is played by technical and technological innovations, as well as modern systems of regulation and organization of work.
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The Concept of Universal Life-saver with Rotary-screw Mover
A good example of the introduction of modern standards of safety was a system of selfregulation oil and gas companies operating on the offshore. This system used in Norway, Holland, Britain and some other countries. Except the efficiency feature of the reforms was the tendency of companies to focus not on the total exclusion of accidents, but on the reduction of accidents with serious and significant consequences. Transition big oil companies to self-regulation has allowed for 5 years reduce the number of accidents with significant implications to 3 times [5]. But remaining probability of occurrence of major accidents calls for a reliable evacuation of personnel platforms. Review of major accidents in the oil and gas platforms will determine the prevailing risk factors that need
special attention when designing life-saving equipment. In the period from 1965 to 2011, i.e. over the past 46 years, on oil and gas platforms have been over 60 incidents in which at least 610 people perished and 93 people were seriously injured. Review and consideration of the character of most major accidents at oil and gas platforms, points to the following risk factors (hazards): 1. Weak control over the state technological systems and the state of the process, as well as the situation in the rooms and compartments of the platform; 2. Weak monitoring of the dynamic parameters of the system «platform – anchoring devices – borehole machinery»;
Platform
Owner
Accident date
Accident location
Distance to shore
Platform personnel
People lost
Bohai-2
China Petroleum Department
25.11.1979
Bohai gulf between China and Korea
150 km
74
72
Alexander L. Kielland
Stavanger Drilling
27.03.1980
The field Ekofisk in the North Sea
320 km
212
123
Ocean Ranger
Mobil
15.02.1982
The North Atlantic
267 km
84
84
Piper Alpha
Occidental Petroleum
06.07.1988
120 miles northeast of Aberdeen, England
310 km
224
167
P-36
Petrobras
15.03.2001
125 km to east coast of Brazil
125 km
175
11
Mumbai High North
Oil and Natural Gas Corporation
27.07.2005
Mumbai coast, near the town of Maharashtra, India
150 km
384
362 injured 22 perished
Deepwater Horizon
Transocean (Switzerland)
20.04.2010
Mexican Gulf
84 km
126
17 injured 11 perished
Table 1 – Some major accidents on the oil and gas platforms located on offshore area
Maxim S. Krasheninnikov
3. Lack of emergency management systems that could impact on the state of technology systems and platforms as a whole in the event of loss of control standard control system; 4. Dangerous and uncontrolled maneuvering boats in the vicinity of the platform; 5. The impact of wave and wind loads not taken into account in designing, leading to tensions exceeding the permissible values; 6. Loss of use of regular rescue facilities in emergency situations; 7. The lack of ships rescue squads in the area of a 15-minute distance to the platform. According to the statistics of emergencies, this is the time interval needed for emergency crew to the platform. Among the major threat occurrence catastrophic consequences after accidents are: 1. Oil and gas emissions;
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2. The sudden destruction of equipment and pipelines, as well as the supporting structures of drilling rigs and platforms; 3. Leakage of hydrocarbons from the serviceable equipment in combination with the wrong personnel actions; 4. Clash of the equipment, pipelines, and supporting structures of platforms with foreign objects such as ships or helicopters. These analysis results suggest that, along with the improvement of management systems and organization of work, special attention must be given to ensuring the safety of platforms by technical means. We are talking about actual problem of timely, fast and effective evacuation of the personnel platform in case of emergency. It is known that the most promising water areas on the possibility of creating oil and gas production facilities are the arctic seas, which accounts for more than 85% of potential oil
Fig. 1 – Arrangement of the Shtokman field
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Fig. 2 – Oil and gas platform in the ice cover
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The Concept of Universal Life-saver with Rotary-screw Mover
Fig. 3.1 – Aerial evacuation means and gas resources [3]. The main areas of hydrocarbon resources concentration are the Barents Sea (3.8 billion tons), Kara Sea (4.7 billion tons), the East Siberian Sea (2.1 billion tons) and the Sea of Okhotsk (2.1 billion tons) [3].
Requirements to platforms are determined by external conditions of their operation (Fig. 2). Meeting these requirements is instrumental to the optimality of designing, technical and environmental safety, and general decline the cost of field development.
Characteristics of the particular conditions of Russian oil and gas platforms may be shown on the example of the Shtokman field (Fig. 1) in the Barents Sea. Compilation of various organizations’ data allows us to formulate the set of operating conditions in a field for a machine to work. Distance to the continent 680 km; water depth 320-350 m; duration of the polar day, 102 days; low visibility due to fog, precipitation, blowing snow and low clouds; maximum wind speed 49 m/s; fluctuations in water level from +90 to -125 cm; maximum flow rate: 0.9 m/s – on the surface and 0.3 m/s – at the bottom; the maximum wave height 24 m; the maximum ice thickness 1.2 m. At operation of drilling equipment icebergs posing a danger must to blow or take away to the side to avoid collision with the rigs.
As seen from the Shtokman field conditions the distinguishing characteristic of Russian Arctic shelf is the presence of ice cover. Therefore widely used in the world lifesaving equipment doesn’t satisfy the Russian weather conditions. The use of aerial evacuation (Fig. 3) on oil and gas platforms in the offshore zone of the Arctic will be limited by the strong and gusty wind, and the emergence of powerful air currents rising up from the burning oil that may arise in the event of an accident. The usage of life rafts (Fig. 4), together with a special system of lowering, will also be ineffective, because these rafts could not move in the arctic seas and ensure the necessary level of safety.
Maxim S. Krasheninnikov
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Fig. 3.2 – Aerial evacuation means The use of lifeboats (Fig. 6) will be limited because of their functional limitation of motion in the water, as well as a high probability of freezing in case the boat stops. They need to bypass the ice fields, which is not always possible. Consequently, there is a need to develop lifesaving equipment, adapted to the northern seas.
Requirements for this lifesaving equipment have been formulated taking into account the external conditions of Russian oil and gas platforms. In general, lifesaving equipment for the Arctic must: 1. Operate under low temperatures, ice, gusty wind, storms and poor visibility 2. Owning a high nimblesness in different environments and amphibious qualities 3. Have a large reserve buoyancy and stability curve
4. Be able to overcome the stains of burning oil 5. To support the regime autonomous work to several days In this situation it is necessary to consider the usage of vehicles, movers of which have distinguishing characteristic: interaction with a supporting surface. Among the floating machines vehicle with rotary-screw mover (rsm) occupies a special place. Features of rotary-screw mover allow to use technological and transport means in such areas where the usage of other movers is impossible or irrational. The rotary-screw mover would allow movement in freezing water in the course of year and evacuate people in case of accidents in the arctic regions (Fig. 7). rsm combines the quality of hydraulic movers and onshore movers and can work effectively in the highly moistened soil, snow, ice, water and in the environment, which is a combination of these surfaces.
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The Concept of Universal Life-saver with Rotary-screw Mover
Fig. 4. – An example of an inflatable life raft for evacuation The rotary-screw mover is used for different machines – road construction, agricultural, military, etc. For example, in Russia, this mover is used in heavy and powerful machines for cutting the ice and in light crosscountry vehicle. In the United States – on military armored personnel carriers to move through the swamps and flooded fields. In Poland, this mover is used on a special towing vehicle for movement on a thick layer of silt on fish farms. In Japan, they produce lifesaving and recreational vehicles with rotaryscrew mover. In particular, the Japanese company Mitsui built a few rotary-screw vehicles (rsv), one of which is specially designed for the movement in Arctic ice off Alaska. Testing has shown that the machine on ice thickness of 30…50 cm reached the highest maximum traction ratio (the ratio of thrust to weight ratio) was equal to 45% at an inclination of the helical blade 30 degrees and at a ratio of height of the helical blade to diameter of base cylinder 0.15. The machine had a mass of 10.8 tons and a length of 7 m. The engineers of Mitsui
Fig. 5 – Means of transporting people from the platform onto life rafts
Maxim S. Krasheninnikov
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Fig. 6.1 – Lifeboats
Fig. 6.2 – Lifeboats
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Fig. 7 – Output on the ice rotary-screw vehicle gpi-72
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The Concept of Universal Life-saver with Rotary-screw Mover
Fig. 8 – Model of the universal life-saver with rotary-screw mover
Fig. 9 – Illustration of the operating conditions of the universal life-saver with rotary-screw mover
Maxim S. Krasheninnikov
21
give the following results: the machine can tow loads of 200 tons on water at a speed of 3 knots, on the ice – a speed of 25…40 knots, the machine can move in ice covered with water at 50 cm, where any other machine and ships cannot move, the machine breaks the ice thickness up to 43 cm.
ÈÈ capacity
Compared with the other types of ground movers the rotary-screw mover has many advantages [4]:
ÈÈ road
1. Ensures particularly high cross-country ability; 2. Shows a very low ground pressure; 3. Develops huge traction force; 4. Provides going out to ice and unequipped shore. Experience of using the rotary-screw mover on the amphibious transport and technological machines and ice-breaking machines indicates the perspective of a universal life-saver development to help the distressed vessel crews and staff of iceresistant stationary platforms. But the creation of such vehicles for movement in difficult conditions (non-cohesive grounds, snow, ice, water and a combination of these media) is impossible without research in relevant fields. In Fig. 8 and 9 shown the developed in NNSTU project of universal life-saver with rsm and conditions of use. The basic concept of universal life-saver was formulated after review of existing lifesaving devices and after determining the operating conditions in the Arctic shelf. Designed life-saver machine is a rotary-screw floating machine with the following parameters: ÈÈ dimensions:
length 9.5 m; width 4.6 m; height 3.06 m
ÈÈ draught ÈÈ gross
at full load 0.92 m
weight 7.5 tons
38 person (two person crew)
ÈÈ rate
of ice – up to 35 km/h; snow – up to 40 km/h; water – up to 5 km/h
ÈÈ diameter
of the cylinder screw mover 1.2 m
ÈÈ length
of screw mover 6.65 m
ÈÈ height
of the helical blade 0.2 m
clearance 0.54 m
The machine can move across the area of burning oil due to the hulls isolated by heat-resistant tiles. Such tiles are used on the hulls of space shuttles. The setting is determined by the systems of technical vision. Autonomous work for several days is achieved through the use of life support systems. But this project was completed more than 20 years ago and its result cannot be considered as the best possible technical solution. The process of creating a new improved model of the universal life-saver with rotary-screw mover will include the following steps: 1. Model of interaction of rsm with different grounds; 2. Correction the model of experiments; 3. Creation a model of rsv movement in different environments; 4. Tests of samples of rsv and correction models of motion; 5. Determination of optimal parameters of the rsv and rsm; 6. Create a prototype; 7. Analysis of the prototype. Design and manufacture the Universal life-saver with rotary-screw mover. Projecting according to the stages will allow creating life-saver with screw mover in accordance with safety requirements (Fig. 10, Fig. 11). As can be seen from the general sequence of design stages, firstly, goes the creating of a mathematical model of the different processes and then goes their adjusting. This will help
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The Concept of Universal Life-saver with Rotary-screw Mover
Fig. 10 – The general form of conceptual design the machine to the rescue personnel ice-resistant oil and gas platforms
Fig. 11 – The principal view the interior
Maxim S. Krasheninnikov
to achieve two goals: first to develop and verify in practice the theory of motion of rotaryscrew vehicles, and secondly receive, valuable information and recommendations necessary for the design of modern machines special purpose thanks to this theory. Received in the course of the project mathematical model of motion rsv will be a «Terrain-Vehicle» system [2], which is generally the unification of the following models: 1. Model of the rotary-screw mover; 2. Model of different terrains with their possible combinations; 3. Model which defines behavior of the machine. Here it is important to note that the rsm is made from materials that give high hardness that is why this mover can be considered absolutely rigid in the early stages of the calculation.
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It is advisable to divide the surface model by the following parts: the surface of the base of the cylinder, the of the screw blade, the surface of the tip of the rotor (with screw blade and without) the surface of the ends of the rotor, middle surface to describe the two-cylinder rotor (Fig. 7). This decomposition allows obtaining a very accurate description of the rotor surface. In addition to the separation of one-and twocylinder rotaries, this mover can have different end caps (conical, spherical, parabolic shape, as well as their combinations), different blade sectional view (triangular, trapezoidal and sheet) and may contain up to 3-4 helical blades. In general, the model of the rotary-screw mover, such as single-cylinder (Fig. 12), is a particular case of the helicoid equation. The surface is determined by a system of parametric equations (for a Cartesian coordinate system) of the following form:
Model of the rotor will be the set of equations of its surfaces.
Fig. 12 – The result of the construction of the surface single-cylinder screws on the basis of the parametric equations
Fig. 13 – The surface of one side of the helical blade
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The Concept of Universal Life-saver with Rotary-screw Mover
X = f ( r )×cos[ f ( P )] Y = f ( r )×sin[ f ( P )] [1] f ( P) Z = f ( h)× 2⋅ p
Lb tO − t B X = ( r + h×i )×cos( P ×2p × j − P ×p ×i ) Y = ( r + h×i )×sin( Lb ×2p × j − tO − t B ×p ×i ) [2] P P Z = LH + Lb × j
ƒ(r) – function of changing the distance from the axis of symmetry ƒ – the specified range of the radius ƒ(h) – function changes the height of the being constructed figure h – range of changes of height ƒ(P) – function that determines the shape of the figure in the plane perpendicular to the axis of symmetry i, j – the parameters of the equation, which are not shown in the formula of general form
r h Lb P tO tB LH
In particular, the system of parametric equations which describes the surface of one side of the helical blade (Fig. 13) looks like:
– radius of basic cylinder – height of helical blade – length of basic cylinder – pitch of helical blade – thickness of helical blade at the base – thickness of helical blade at the vertex – length of part of the screw head
At the moment created a mathematical model describing the shape of the screw mover which allows you to vary any desired parameter such as length and diameter of the base of the cylinder, the shape and size profile of the helix, the angle of winding and many others. Later will determine the choice of models used to describe the different environments and make their association with the model of the screw mover to describe the processes occurring in the contact zone of mover with a support base.
References 1. Around the World [electronic resource]: [official. site]. – Electronic data. Mode of access: http:// www.vokrugsveta.ru/vs/article/2938/, free 2. Bekker MG «Introduction to terrain-vehicle systems: Trans. from English» / Ed. Guskov VV. – Moscow. Mashinostroenie, 1973. – 520. 3. Bohatyryova EV «Methods of ensuring the safety of oil and gas platforms of the Arctic shelf: Dissertation of candidate of technical sciences» – Moscow, 2004. 4. Kulashov AP, Shapkin VA, Donato IO and others «Screw machine. Fundamentals of the theory of motion». Nizhny Novgorod: NNSTU, 2000. – 451. 5. Mokrousov SN «Security issues in the development of oil and gas resources on the continental shelf and on land of the Russian Federation» / / Journal-directory "Transport security and technology." – 2006. – No 1. 6. Osadchy A «Oil and Gas of the Russian Shelf: estimates and projections» / / Journal "Science and Life." – 2006. – No 7.
Mohammad Javad Kiani
25
̂̂Gas Deviation Factor Through An Intelligent Method Called Artificial Neural Network Mohammad Javad Kiani
Abstact Since oil is explored, numerous attempts have been led in order to determination reservoir properties, which are necessary in calculation of some other parameters. All of these correlations are based on experimental methods and oblige to be adapted with laboratory results. Dramatic errors and faults have been observed in developed correlations which sometimes unreliable results are ensued. Therefore some other sophisticated methods flourished to may could reduce errors by intense fault tolerance. One of these intelligent methods is Artificial Neural Network (ANN) which is developed according to the Body Neural Network. During this paper we try to train an ANN in order to estimation Gas Deviation Factor and finally we will illustrate that this method consequences are more reliable than results of Correlations. To serve this purpose we have applied Laboratory data points from 7 Southern Iranian Reservoirs.
**Petroleum Department, Islamic Azad University, Masjed-Soleyman Branch, Khuzestan ÞÞIran javad_petro11@yahoo.com University Country E-mail
was encountered, the presence of Z-Factor was felt. Hall and Yarborough (1973) presented an equation of state that accurately represents the Starling-Katz Z-Factor chart. They proposed the following mathematical form:
[
Z=
0.06125tppr Y
]
exp[−1.2(1−t)2] [1]
ppr – pseudo reduced pressure t – reciprocal of the pseudo reduced temperature, i.e.Tpc /T Y – the reduced density that can be obtained as the solution of the following equation: F(Y)=X1+ Y+Y +Y 3+Y −(X2)Y 2+(X3)Y X =0 [2] (1−Y) 2
3
4
4
Introduction In recent years many attempts have been done in order to develop different correlations for estimation Gas deviation Factor as one of the numerous oil properties. As the prediction of two phase flow pattern in a pipeline
X1 X2 X3 X4
= −0.06125 ppr t exp [−1.2(1−t)2] = 14.76 t−9.76 t2+4.58 t3 = 90.7 t−242.2 t2 +42.4 t3 = 2.18+2.82 t
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Gas Deviation Factor Through An Intelligent Method Called Artificial Neural Network
The computational procedure of solving equation 2 at any specific pseudo reduced pressure, ppr, and temperature, Tpr, is summarized in the following steps: Step 1. Make an initial guess of the unknown parameter, Yk, where k is an iteration counter. An appropriate initial guess of Y is given by the following relationship: Yk = 0.0125 ppr t exp [−1.2(1−t)2] Step 2. Substitute this initial value in Equation 2 and evaluate the nonlinear function. Unless the correct value of Y has been initially selected, Eq. 2 will have a nonzero value of F(Y): Step 3. A new improved estimate of Y, i.e., Yk+1, is calculated from the following expression:
Yk+1=Yk−
ƒ(Y k) [3] ƒ `(Y k)
where f`(Yk) is obtained by evaluating the derivative of Eq. 2 at Yk, or:
ƒ `(Y k)=
1+4Y+4Y 2+4Y 3+y4 −2(X2)Y+(X3)(X4)Y (X −1)=0 (1−Y)4 4
[4] Step 4. Steps 2-3 are repeated n times, until the error, i.e., abs(Y k−Y k+1), becomes smaller than a preset tolerance, 10−5. Step 5. The correct value of Y is then used to evaluate Eq. 1 for the compressibility factor. Hall and Yarborough pointed out that the method is not recommended for application if the pseudo-reduced temperature is less than one. pseudo-critical properties, i.e., ppc and Tpc, can be predicted solely from the specific gravity of the gas. Brown et al. (1948) presented a graphical method for a convenient approximation of the pseudo-critical pressure and pseudocritical temperature of gases when only the specific gravity of the gas is available. Case 1: Natural Gas Systems Tpc=168+325γg−12.5γg2 [5]
Fig. 1 – Neural Network Architecture
Mohammad Javad Kiani
27
ppc=677+15.0γg−37.5γg2 [6] Case 2: Gas-Condensate Systems Tpc = 187 + 330 γg − 71.5 γg2 [7] ppc = 706 − 51.7 γg − 11.1 γg2 [8] Tpc - pseudo-critical temperature, R° ppc - pseudo-critical pressure, psia γg - specific gravity of the gas mixture After serve the require of Correlated results it is the turn of training a network based on neural to have another consequences in order to achieve the best way for our purpose. So we are going to develop an ANN and ultimately will have comparison figures between results of ANN and Correlation.
Fig. 2 – Regression Plot of Z-Factor for Corresponding Trained Network, the experimental gathered data are on horizontal axes and the estimated data points by ANN are on vertical axes
Neural Network Architecture
Network Training
Considering the nature of our problem, a simple 3-layer Generalized Feed Forward Neural Network structure (Fig. 1) was selected for the Artificial Neural Network (ANN) model for analyzing the Gas Deviation Factor. The firs layer, input layer, consists of 3 processing elements (PE). The second layer is the Hidden layer and the number of PEs is spontaneously assigned according to the strength of the data. And finally the output layer consists of one element which is Z-Factor. The output layer is fully connected to all the units in the hidden layers as shown in Fig. 1. In this figure: F(x1…xn) – goal function Φn(x1,x2…xi) – activation function in the hidden layer of n-units x1,x2,x3…xi – input units wi – weight of the basis function
Data points used in this paper are 75 samples of 4 elements which have been obtained form 7 Southern Iranian Reservoirs and copied into the MATLAB spreadsheet as two groups of input data and output data. During the training network, we need to some data points to validate the trained network and finally some data points are required for network testing. Hence, 70% of samples are allocated for training, 15% assigned for validation. Remaining 15% are applied to test the trained network. To check if desired trained network is obtained, the regression plot most be drawn which can be seen in Fig. 2. Proximity of slope to 1.0 shows a stringent relationship between input and target data. It is bad consequence as slope moved down to 0.0. Ultimately, outputs will be gathered and compared with targets and Mean Square Error (MSE) will be shown as a result. Unlike regression plot, MSE must be close to 0.0 and
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Gas Deviation Factor Through An Intelligent Method Called Artificial Neural Network
Fig. 3.1 – Comparison of Z-Factor Among Experimental, Artificial & calculating method; Unlike Correlated Z-Factor, ANN ZFactor has Adapted on the Experimental Z-Factor
Fig. 3.2 – Comparison of Z-Factor Among Experimental, Artificial & calculating method; Unlike Correlated Z-Factor, ANN ZFactor has Adapted on the Experimental Z-Factor
Mohammad Javad Kiani
29
if rose, an incorrect result is inferred. MSE of trained network can be seen in table 1. Last part is made by comparison figures which have been led in order that show how accurate and reliable ANN is (Fig. 3). Samples
R
MSE
Training
53
9.60625e-1
5.00785e-4
Validation
11
9.19679e-1
6.73137e-4
Testing
11
9.51561e-1
2.46181e-4
Table 1 – Results of Z-Factor Estimation Total Regression Z (ann ) Z (Empirical)
0.95605 0.683
Table 1 – Results of Z-Factor Estimation
Conclusion By a glance on comparison figures it will be understood that Artificial Neural Network can estimate Z-Factor more accurate than correlations. The line of ANN outputs is more exactly adapted on laboratory gathered data points than results of correlation. There for it is expected to application of ANN rises in the future. Also as it can be seen from formulas, the way of arriving to answer of these correlations is lengthful and sometimes it is necessary to have long compiler wrote program, which is available in the next part, and also sometimes writing such programs is a bit confusing while it is easier to just train a network and use it in future. The regression of ANN and also Correlations via Experimental data points, which is available in Table 2, is another reason that shows the accuracy of ANN.
References 1. Ahmad. T., Reservoir Engineering, Handbook, 2nd Edition, 2001. 2. Hajizade. Y., Intelligent prediction of reservoir fluid PVT data, Dissertation, Islamic Azad University of Omidiye, November 2006. 3. Siruvuri. C., Haliburton Digital and Consulting Solutions; Nagarakanti. S. Nabors Industries; Samuel. R.; Haliburton Digital and Consulting Solutions; Stuck Pipe Prediction And Aviodance: A Convolutional Neural Network Approch; IADC/SPE 98375. 1 2 3 4 5 6 7 8 9 10 11 12 13 14
clc P=input ('pressure(psi):'); T=input ('Temperature(F):'); sp.gr=input ('Specific Gravity:'); Ppc=677+15*sp.gr-37.5*sp.gr^2; Tpc=168+325*sp.gr-12.5*sp.gr^2; t=Tpc/(T+460); Ppr=P/Ppc; X1=-0.06125*Ppr*t*exp(1.2*(1-t)^2); X2=14.76*t-9.76*t^2+4.58*t^3; X3=90.7*t-242.2*t^2+42.4*t^3; X4=2.18+2.82*t; Yk=0.0125*Ppr*t*exp(-1.2*(1-t)^2); FY=X1+((Yk+Yk^2+Yk^3+Yk^4)/ (1-Yk)^3)-X2*Yk^2+X3*Yk^X4;
15 fY=((1+4*(Yk+Yk^2-Yk^3)+Yk^4)/ (1-Yk)^4)-2*X2*Yk+X3*X4*Yk^(X4-1); 16 Ykk=Yk-(FY/fY); 17 Error=abs(Yk-Ykk); 18 while Error>10^-5 19 Yk=Ykk; 20 FY=X1+((Yk+Yk^2+Yk^3+Yk^4)/ (1-Yk)^3)-X2*Yk^2+X3*Yk^X4; 21 fY=((1+4*(Yk+Yk^2-Yk^3)+Yk^4)/ (1-Yk)^4)-2*X2*Yk+X3*X4*Yk^(X4-1); 22 Ykk=Yk-(FY/fY); 23 Error=abs(Yk-Ykk); 24 end 25 Z=(0.06125*t*Ppr/Yk)*exp(1.2*(1-t)^2); 26 display (Z);
Snippet 1 – Applied Program in Calculation Z-Factor Through MTLAB Compiler
spring / 2012
2012
East meets West
With less than two months to go and preparations going well on their way we am really pleasured to honestly claim, that the idea which was created and evaluated by just several minds, has managed to survive and now appears as a worldwide communication platform. From the very beginning the ‘East meets West’ meant to be a student event, which is organized by students, and also students were about to be the main benefiters. The challenge was to establish an annual meeting, which, by gathering specialist from the widely considered petroleum industry, will create a space for exchanging minds, knowledge and experiences among people even from the opposite side of the globe. But that’s not the end. It was equally important to create a relationship between SPE Student Chapters from the whole world, and then to establish a cooperation, which could lead to further development – both personal and professional. The first editions has shown great potential both at the side of organizers and the students attending the Congress. They have proven that a small group of students is able to bear a responsibility of organizing a big, international and professional event. They have also presented that the young generation is very ambitious and diligent with leading their own research, gaining new knowledge and develop their interest in petroleum technologies. Finally – they have shown how big demand is for such meetings and how many benefits these meetings provide for each of their attendees.
‘East meets West’ creates a full range of possibilities for students. First of all, it allows them to present the results of their extraordinary work during one of the biggest Student Paper Contests in Europe. Keeping in mind, that the overriding goal of each student is to join the industry, the leading companies are invited in each year for the Congress to present the offer of internships, trainings and jobs to the most talented young people in the world. Finally we need to remember about the social side of the Congress, which is accompanied by very warm events highly supporting creation of long lasting relationships between students and professionals. Moreover, we can see a slight, but very important influence of ‘East meets West’ on sometimes passive students, who once seeing or hearing about the advantages of the Congress, get mobilized and realize that hard work always pays off. Krakow International Student Petroleum Congress appears as a worthy continuer of the ‘East meets West’ tradition. From the 25th till the 27th of April eyes of the whole petroleum industry will be again turned to Krakow, where students and professionals, from the west to the east will gather in international discussion regarding challenges standing at a doorstep of our industry. The discussion is so important, because it reveals to the young generation the problems, which they will have to face in the following years and what is more – it reveals that these young people are the one, who will have take the responsibility for the future of our industry. Using the occasion that we have a chance to write these words – we would like to once again invite you to the Krakow International Student Petroleum Congress ‘East meets West’. Become a part of the ‘East meets West’ family and feel the technical heart of the world, which will be pounding this year in Krakow. Organizing Committee
spe.net.pl/emw
32
Nodal Analysis Used To Offshore Well Operating Regime Optimization
̂̂Nodal Analysis Used To Offshore Well Operating Regime Optimization Rareș Petre, Mihai Vasile
Abstract This paper presents several issues on subsea production systems, natural flowing as well as nodal analysis workflow. Nodal analysis consider several models such as: ÈÈAnalysis
is done (node is chosen) at perforation interval;
ÈÈAnalysis ÈÈUses
**Oil and Gas University of Ploiești ÞÞRomania Assoc. Prof. Dr. Eng. Mariea Marcu rares_petre@yahoo.com vasile_mihai88@yahoo.com University Country Supervisor E-mail
is done at subsea X-tree point;
of a subsea multiphase pump.
The study is performed using PIPESIM software, considering several working scenarios for sensitivity analysis , namely: static pressure variation as well as separator pressure variation, pipeline and riser inner diameters variation and the study on the influence of upward two-phase flow theories on performances equipment curves. The optimal operating regime shall be selected following the simulation data analysis.
Introduction The hunger for reduction of capital investment and the growing demand for increasing the production rate have influenced the development of technology in the last years for oil and gas production. One of the biggest achievements are the multiphase pumps (Fig. 1).
A classical separation system is composed of the following items (Fig. 2): ÈÈSeparator
for oil, gas and water
ÈÈDehydration
installation
ÈÈCompressor ÈÈWater ÈÈOil
pump
pump
ÈÈWater
treatment plant
All this equipment are necessary for a classical separation system that is placed on a satellite platform. This platform is fixed directly above the wellhead afterwards the gas and
Fig. 1 – Multiphase pumping system [1]
Rareș Petre, Mihai Vasile
33
(Fig. 4). Therefore is not necessary a satellite platform. The following advantages are specific for the multiphase pumps [2]: ÈÈReduced
equipment, capital cost and com-
plexity; ÈÈElimination
of separate oil/water and gas
lines; Fig. 2 – Classical separation system [1] liquid are transported through separate flowlines to the host platform (Fig. 3). If we install a multiphase pump (twin-screw or helico-axial) to the subsea system so that it will be a full wellstream production through a flowline
ÈÈIncreased
production rates;
ÈÈReduced
wellhead back pressure;
ÈÈReduced
weight and space requirements;
ÈÈIncreased
reservoir life;
Fig. 3 – Production system using satellite patform [3]
Fig. 4 – Production system using multipase pump [3]
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34
Nodal Analysis Used To Offshore Well Operating Regime Optimization
Fig. 5 – Classification of multiphase pumps [1] [4] [5] Historically, multiphase pumps were categorized either as twin screw pumps or helicoaxial pumps. Today, there are many types of multiphase pumps using diverse technologies and a more comprehensive classification is required [1].
order to reach the desired production rate as economical as possible. For determinating the optimal flow of the offshore well, we considered three models for the nodal analysis: 1. when the node point was at the perforation interval (Fig. 6)
The helico-axial pumps and twin screw pumps are most used pumps in offshore production systems (Fig. 5).
Laboratory simulations Any production system is composed of the following: reservoir, well and surface facilities. To establish the optimal operating system all these elements must be analyzed and determined to a correlation between them so as to achieve maximum productivity at minimal cost. It is know that the nodal analysis can analyze each component of the production system in
Fig. 6 – First model with node at perforation interval
Rareș Petre, Mihai Vasile
2. when the node point was at the subsea Xtree point (Fig. 7) 3. when the node point was in front of the multiphase pump (Fig. 8) The objectives of the simulation with PIPESIM software for these three models are:
Fig. 7 – Second model with node at subsea X-tree point
35
ÈÈInfluence
of the upward two-phase flow theories on the equipment performance curves study;
ÈÈInfluence
of the inner diameter of the riser, respectively of the flowline and separator pressure on the equipment performances curves;
Fig. 8 – Third model with node in front of the multiphase pump
Fig. 9 – Flow Pattern in a vertical well [7]
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36
Nodal Analysis Used To Offshore Well Operating Regime Optimization
Fig. 10.1 – The influence of the Beggs& Brill Original flow correlation theory on the equipment performance curves
Fig. 10.2 – The influence of the Govier, Aziz &Fogarasi flow correlation theory on the equipment performance curves
Rareș Petre, Mihai Vasile
37
Fig. 11.1 – Separator pressure influence on the performance equipment curves and nodal analysis points
Fig. 11.2 – Flowline inner diameter influence on the performance equipment curves and nodal analysis points
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38
Nodal Analysis Used To Offshore Well Operating Regime Optimization
Fig. 11.3 – Riser inner diameter influence on the performance equipment curves and nodal analysis points
Fig. 12.1 – Nodal analysis with speed variation and power limitation at 100 kW in the twin–screw pump case
Rareș Petre, Mihai Vasile
39
Fig. 12.2 – Nodal analysis in the helico-axial pump case and power limitation at 100 kW
Legend for all graphics ÈÈMultiphase
pumps in subsea production system assessment study;
ÈÈNodal
analysis with speed variation and power limitation at 100 kW in the twin – screw pump case.
In the following figures (Fig. 10.1, 10.2) the nodal analysis was applied for the first model (Fig. 6), to study the influences of the upward two-phase theories on the equipment performance curves. We use the the Beggs & Brill Original, respectively Govier, Aziz &Fogarasi flow correlation theories. The Beggs & Brill Original is one of the few correlations capable of handling “vertical flow” and “horizontal flow”. Govier, Aziz &Fogarasi is a correlation that was developed for upward two-phase flow in
wellbores. The model predicts the existence of four flow patterns: bubble flow, slug flow, churn flow and annular flow [6]. Bubble Flow: The entire tubing cross sectional area is filled with liquid and small free gas bubbles. The gas bubbles have different velocities, and except for their density, have little effect on the pressure gradient (Fig. 9.a) [6]. Slug Flow: As a results of the pressure decreasing, more gas exit from solution. The gas bubbles coalesce and form slugs with the diameter closed to tubing diameter. A gas slug is followed by a liquid slug. The gas velocity is greater than that of the liquid. Both the gas and liquid have effects on the pressure gradient (Fig. 9.b) [6].
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Nodal Analysis Used To Offshore Well Operating Regime Optimization
Churn Flow: This flow pattern occurs in upward flow only and is very chaotic in nature and changes from a continuous liquid phase to a gas phase occur. The gas bubbles may join and liquid may be entrained in the bubbles. Although the liquid effects are significant, the gas phase effects are predominant (Fig. 9.c) [6]. Annular Flow: The gas flows through the centre core of the pipe, while the liquid flow along the walls of the pipe as a film. Therefore, the system may be looked upon as a singlephase flow of gas through a tube of slightly reduced because of the liquid (Fig. 9.d)[6]. From these figures results that the upward two-phase flow theories have an important influences on the equipment performance curves, respectively on the nodal analysis points coordinates (Fig. 6 – 1st model). For the same input data, the results obtained with the both theories are different. Therefore, it is necessary to compare these results with the measurements pressure data inside of the tubing and flowline and to decide what two-phase theory is right to use in a designing process of a particular subsea production system. The second model (Fig. 7) is used to study the influence of the separator pressure and the inner diameter of the riser, respectively of the flowline on the equipment performance curves (Fig. 11.1, 11.2, 11.3). The results of this study are: ÈÈA
separator pressure decreasing can extends the well life even in the case of the lower reservoir pressure, but this pressure has technological limits.
ÈÈFlowline
diameter has some influence on the equipment performances curves in the cases of the bigger flow rates, because the friction gradient became important. In this case is necessary also to check if the severe slugging phenomenon is produced.
ÈÈRiser
diameter influences the equipment performances curves only in the lower flow rates range
The third model (Fig. 8) is used to show the influence of the multiphase pump in the subsea production system and to perform the nodal analysis taking account of the differential pressure on the pump, the speed variation and the power limitation at 100 kW in the twin –screw pump case (Fig. 12.1, 12.2). Multiphase pump implementation in a subsea production system extends the well life and permits the increasing of the well flow rate because the wellhead pressure can be low. The multiphase pump assures the necessary pressure for fluid flowing from the wellhead to the processing platform. The most important parameter of the multiphase pump regime is the differential pressure on the pump that must balance the pressures frictions drops along the pipeline and the elevation difference between the subsea wellhead and processing platform. The rotational speed variation is important in the lower flow rate range. Also, in the case of the power limitation, the helicoaxial pump type leads to a greater flow rate (86 m3/D in our case) than the twin-screw type pump (81 m3/D in our case).
Conclusions From the parameters sensitivity study with riser inner diameter and flowline inner diameter result, that the impact of flowline inner diameter is more important than riser inner diameter if flow rate increases. The multiphase flow theories influence the equipment performance curves and the nodal analysis points coordinates. Separator pressure influence the equipment performance curves and the nodal analysis points also. If we can decrease this pressure, we can obtain a nodal analysis point at the lower reservoir pressures.
Rareș Petre, Mihai Vasile
Using multiphase pumps in a subsea production system permits to obtain the nodal analysis points at lower reservoir pressures. From the sensitivity study with type pump (Twin screw, Helico-axial), speed (Twin screw) and differential pressure on the pumps, re-
41
sults that the last parameter is more important because it permits to have a nodal analysis point at the lower reservoir pressure, which means the extension of the natural flowing well life.
References 1. Saadawi, H.: An Overview of Multiphase Pumping Technology and its Potential Application for Oil Fields in the Gulf Region, paper 11720-MS, International Petroleum Technology Conference, 4-6 December 2007 Dubai, U.A.E; 2. Oxley, K.C., Shoup G.J.: A Multiphase Pump Application in a Low-Pressure Oilfield Fluid-Gathering System in West Texas, paper SPE 27995, University of Tulsa Centennial Petroleum Engineering Symposium, 29-31 August 1994, Tulsa, Oklahoma; 3. Shippen, M., Scott, S.: Multiphase Pumping as an Alternative to Conventional Separation, Pumping and Compression, 34th Annual PSIG meeting Portland, Oregon, October 25, 2002; 4. Heyl, B.: Multipahse Pumping, 24th International Pump Users Symposium, Texas A&M University, 2008; 5. Charron, Y., Pagnier, P.: Multiphase Flow Helico-Axial Turbine, Applications and Performance, paper SPE 88643, 11th Abu Dhabi international Petroleum Exhibition and Conference, 10-13 October 2004 Abu Dhabi, U.A.E.; 6. Yahaya, A., U., Al Gahtani, A.: A Comparative Study Between Empirical Correlations & Mechanistic Models of Vertical Multiphase Flow, paper SPE 136931, King Fahd University of Petroleum & Minerals, 04-07 April 2010 Al-Khobar, Saudi Arabia; 7. http://www.drbratland.com/PipeFlow2/chapter1.html.
spring / 2012
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Radmir Ganiev
43
̂̂Viscosity of the electron gas in a conductor Radmir Ganiev
Analogy method Experimentally determine the viscosity of the electron gas is unlikely. The movement of electric current in the conductor and the fluid flow in porous media have a lot in common. In terms of the geometry of the electron gas moving between the ions and the fluid moves between the particles of the porous medium. If we assume that the metal ions have a spherical shape, conductor is similar to the fictitious ground, consisting of balls of the same size. The balls may have different packaging, shown in Figure 3, such as tetragonal, when the centers of the balls are placed at the vertices of a tetrahedron, and porosity is then equal to m = 0.29. More loose packing is cubic, when the porosity m = 0.48 Between the flow of electric current and fluid flow there is a deeper analogy, because they are described by the same differential equation Υ = a ⋅ gradP [1] Y gradP
– parameter that characterizes the flow of matter or energy – gradient strength values (pressure, voltage, temperature, concentration)
**Ufa State Petroleum Technological University Ph.D. T.O. Akbulatov ÞÞRussia rustam-bagautdinov1@rambler.ru University Country E-mail
For DC Ohm's equation is known: Ι=
∆U S ∆U ⇒ Ι = . × . [2] R rΩ ∆
I – amperage, ∆U – voltage difference at the ends of the conductor length , R R = = r ×∆ ohmic resistance of the conductor, S rn – the resistivity of conductor material, S – area of conductor. The potential for a Newtonian fluid in a porous medium is described by Darcy: k k ∆P w = × gradP = × [3] m m ∆ w m ∆P k
– filtration rate, – dynamic viscosity of the fluid, – differential pressure over the length , – permeability of the porous medium.
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44
Viscosity of the electron gas in a conductor
Fig. 1 – Fluids flow in porous media
Fig. 2 – The motion of the electron gas between the ions
Multiplying the equation (3) for the filtration area S get filtered fluid flow:
If the size of the ion is equal to D, the volume of all ions in a conductor:
Q = w ×S =
k ×S k ×S ∆P × gradP = × [ 4] m m ∆
From equation (2) and (4) we have that the flow rate is analogous to the current, pressure drop is analogous to the voltage drop, and the parameter m/k is an analogue of the resistivity of the conductor. Try to reduce the equation (4) to the equation Om. If the mass of the metal atom is equal to −M and the density of the material of the conductor −r, in one cubic meter contains z atoms of the conductor: z=
ρ ρ ×V × Na = [5] M µ
r – density of conductor material; V – volume conductor; Na – Avogadro's number (Na=6.05×1023mole-1); m – molar mass of the metal atom. As is well known in the conductor atoms are not in a neutral state, but in the form of ions.
Vε = z×
π × D3 [6] 6
The share of the space between the ions, the electron gas is employed, will be m: m = 1 − 0.52× z× D3 [7] If the metal is monovalent, then in a cubic meter of the conductor is z-electron volume of the electron gas is equal to m×V, then one electron corresponds to m/z volume of the electron gas. Because in 1C=6.29×1018 electrons, then a current I corresponds to the volumetric flow rate of the electron gas, which is given by (8) Q=
m× I ×6.29×1018 [ 8] z
If the conductor has a resistance of R [W] and the area S, the length of the conductor: ∆ =
R ×S [9] rΩ
The volume of the conductor: Vcond = ∆ ×S =
R ×S 2 [10] rΩ
In this volume is X=z×Vnp electrons, under voltage difference ∆U. At the same time each electron will be a force (Fig. 4): ∆U f = e− × [11] ∆ Fig. 3 – Fictitious model of soil
e–
– elementary electric charge
Radmir Ganiev
45
The total force on all the X electrons from (12): ∆U [12] F = f ×O = O× e− × ∆� ∼
∼
Consequently, the pressure drop in the electron cloud, for X electrons: F f × X e− ×∆U × X = = = S S ∆ ×S e− ×∆U × z×Vnp e− ×∆U × z× R ×S = = ∆ ×S ∆ × rom P=
The permeability of the fictitious ground: k= c
m3 × DŁ2 [14] 36× c ×(1 − m)2 – Karman number (for packages with a ball = 5)
Substituting these values in equation (4),: Q = w ×S =
k ×S k ×S ∆P × gradP = × [15] m m ∆ 18
m× I ×6.29×10 = z m3 × DŁ2 × e− ×∆U × z×S 2 × R [16] = 36× c ×(1 − m)2 ×µ×∆ 2 × ρΩ
Q=
Simplifying equation (16) we obtain the equation (17): I ×6.29×1018 = 1 m2 × DŁ2 × e− ×∆U × z2 ×S [17] = 36× c ×(1 − m)2 ×m×∆
The calculation of viscosity for different types of conductors Calculation of the electron gas in a copper conductor
Background rcu=8,96 g/m³ Dion cu=0,256 nm; M(Cu)=63,548 g/mole; rom=0.0175W×mm2/m 2.1.1 The calculation of viscosity and the velocity of the electron gas in a conductor The volume of the ion: p × D3 p ×(0.256×10−9 )3 = = 6 6 = 0.0089×10−27 m3 V=
The number of ions in 1 m³: z=
ρ ×V × Na 8.96×1×6.02×1023 = = 8.5×1022 µ 63.546
Q=
The volume of the ion in 1 m³:
Hence, we find the m of the equation (16):
π × D3 = 3.5×1022 ×0.0089×10−27 = 6 = 0.0756×10−5 m3
m=
m2 × DŁ2 × e− ×∆U × z2 ×S [18] 36× c ×(1 − m)2 × I ×∆ ×6.29×1018
V ε = z×
Hence the porosity of the conductor: m=
1 − V 10−6 − 0.7×10−6 = = 0.244 1 10−6
Consequently, copper atoms are located in the tetragonal packing (Fig. 3). The permeability of a fictitious soil is calculated by formula (14): k=
0.33 ×(0.256×10−9 )2 = 2×10−23 m2 36×5×(1 − 0.3)2
Fig. 4 –Action of the electric force on the electron
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46
Viscosity of the electron gas in a conductor
In the conductor in 1 m³ is 8.5×1022Cu ions and it is equal to 8.5×1022e–, correspond to ? pore space, where m=0.3, hence
Determine the flow regime of the electron cloud
I =1 A=
1C ∆U ∆U ×S = = 1s R r×
where R = r × , then S 1 e− =
m 0.3cm3 = = 22 8.5×10 8.5×1022
For the model assuming an ideal soil characteristic dimension d equal to the effective diameter d of the particles have the following formula for the Reynolds number: Re =
= 0.35×10−22 cm3 = 0.35×10−28 m3 In 1 C contains 6.29×1018e– electrons then the total consumption of the electron cloud at a current 1 A: m×6.29×1018 × e− = 8.5×1022 × e− 0.3×6.29×1018 ×10−6 = = 8.5×1022 = 0.22×10−10 m3 / s
r × 0.0175× R= = = 1W ⇒ = 57m S 1 V = ⋅ S = 57 ⋅ 10−6 = 57m3 then the number of electrons in V 22
z57 = 57 ⋅ 10 ⋅ 8.5 = 484 ⋅ 10 electrons ∆F z× e− ×∆U = , because Fe=e–, S S ×l where E = U , then
then ∆P =
484×1022 ×1.6×10−19 ×1 = 13.6×109 Pa 1×10−6 ×57
From ω =
k ×∆P that should be µ×∆
k ×∆P 2×10−23 ×13.6×109 = = ω ×∆ 0.22×10−4 ×57 = 2.2×10−10 Pa× s µ=
µ ρel .cloud
z× M el 8.5×1022 ×9.1×10−31 = = m×V 0.3×0.0756×10−5 = 0.341kg / m3 ;
Given that S=10−6m2=1 mm2 we have:
∆P =
ν=
rel .cloud =
Q 0.22×10−10 = = 0.22×10−4 m / s S 10−6
22
– effective particle diameter,
rel. cloud. – the density of electron cloud.
Q=
w=
d
w × d ef . (0.75×m + 0.23)×n
ν=
µ ρel .cloud
Re =
=
2.2×10−10 = 6.45×10−10 Pa× s; 0.341
w × d ef .
= (0.75×m + 0.23)×n 2.2×10−4 ×0.256×10−9 = = (0.75×0.3 + 0.23)×6.45×10−10 = 0.19×10−3.
Using this formula and the experimental data, N. N. Pawlowski found that the critical Reynolds number is in the range 7.5<Rekr<9, at Re = 0.000194, we have a laminar flow regime of the electron cloud. The calculation of the electron gas in a silver conductor
Background rAr=10,5 g/cm3 Dion Ar=0.28 nm M(Ar)=107.9 g/mole;
Radmir Ganiev
rom=0.016W×mm2/m The calculation of viscosity and the velocity of the electron gas in a conductor
47
1 e− =
m 0.326cm3 = = 5.86×1022 5.86×1022
The volume of the ion:
= 0.056×10−22 cm3 = 0.056×10−28 m3
p × D3 p ×(0.28×10−9 )3 = = 6 6 −27 3 = 0.0115×10 m
w=
V=
The number of ions in 1 m³: ρ ×V × Na 10.5×1×6.02×1023 z= = = µ 107.9
Q 0.349×10−10 = = 0.349×10−4 m / s S 10−6
Given that S=10−6 m2=1 mm2 we have: R=
r × 0,016× = = 1W ⇒ = 62.5m S 1
= 5.86×1022
V = ×S = 62.5×10−6 = 62.5c 3
The volume of the ion in 1 m³:
then the number of electrons in V
V ε = z×
π × D3 = 5.86×1022 ×0.0115×10−27 = 6 = 0.0674×10−5 m3
z57 = 62.5×1022 ×5.86 = 366×1022 electrons ∆F z× e− ×∆U then ∆P = , = S S ×l
Hence the porosity of the conductor:
because Fe=e×E, where E =
m=
1 − V 1 − 0.67×10−6 = = 0.326 1 10−6
Consequently, copper atoms are located in the tetragonal packing (Fig. 3). The permeability of a fictitious soil is calculated by formula (14): k=
0.3263 ×(0.28×10−9 )2 = 3.3×10−23 m2 36×5×(1 − 0.326)2
In the conductor in 1 m³ is 5.86×1022 Ar ions and it is equal to 5.86×1022 e–, 5.86×1022 e– correspond to ? pore space, where m =0.326, hence 1C ∆U ∆U ×S , where I =1 A= = = 1s R r× r× , then S m 0.326cm3 1 e− = = = 22 5.86×10 5.86×1022 R=
= 0.056×10−22 cm3 = 0.056×10−28 m3 In 1C contains 6.29×1018 e– electrons then the total consumption of the electron cloud at a current 1 A:
U , then
363×1022 ×1.6×10−19 ×1 = 9.29×109 Pa 1×10−6 ×62.5 k ×∆P From ω = that should be µ×∆ ∆P =
k ×∆P 3.3×10−23 ×9.29×109 = = ω ×∆ 0.349×10−4 ×62.5 −10 = 1.4 ×10 Pa× s µ=
Determine the flow regime of the electron cloud For the model assuming an ideal soil characteristic dimension d equal to the effective diameter d of the particles have the following formula for the Reynolds number: Re = d ν=
w × d ef . (0.75×m + 0.23)×n
– effective particle diameter, µ ρel .cloud
rel. cloud. – the density of electron cloud.
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48
Viscosity of the electron gas in a conductor
z× M el 5.86×1022 ×9.1×10−31 = = m×V 0.326×0.0674×10−5 = 0.2427 kg / m3 ; rel .cloud =
ν=
µ ρel .cloud
=
1.4×10−10 = 0.2427
−10
= 5.768×10 Re =
Pa× s;
w × d ef .
=
(0.75×m + 0.23)×n 1.4×10−4 ×0.28×10−9 = = (0.75×0.326 + 0.23)×5.768×10−10 = 0.145×10−3.
Using this formula and the experimental data, N. N. Pawlowski found that the critical Reynolds number is in the range 7.5<Rekr<9, at Re=0.000145, we have a laminar flow regime of the electron cloud. Cu
Ar
Cu/Ar
r
0.0175
0.016
1.09
m
2.2×10
1.4×10
1.57
−10
−10
Table 1
49
9th International Youth Oil & Gas Forum
Kazakh National Technical University Events Presentation on the latest technologies of Oil & Gas Industry brought by leading companies’ representatives. Student Applied Petroleum Technology Paper Contest International intellectual contest «Oil Games» Exhibition Panel discussion Role game Trainings and seminars brought by the professionals for the students
kntu.conference2012@gmail.com www.kntu-spe.org
14-15 April 2012
summer / 2012
50
̂̂Flow Rate of Horizontal Wells Rustam Bagautdinov
Nowadays a great majority of oil wells are drilled directionally. Correlation between the calculated daily well output and factors influencing upon the latter for both linear (LP) and circular (CP) profiles and other forms of stratum external boundary is well known and it is as following:
**Ufa State Petroleum Technological University ÞÞRussia rustam-bagautdinov1@rambler.ru University Country E-mail
ÈÈDaily
well output is proportional to thickness and permeability of the stratum;
ÈÈThe
difference between the vertical and horizontal permeabilities (vertical anisotropy factor of strata) is very little;
ÈÈThe
wellbore wall contamination rate is estimated by a skin effect according to the formula
Q=
where R L a = 0, 5 + 0, 25 + 2 k L 2
4
s=
k0 − k1 R ×ln 1 [1] k1 rw
Q=
k0 k1 R1 r w
– initial permeability of the stratum – permeability of the contaminated zone – radius of the contaminated zone – radius of a well
Q=
Since the second half of the last century the majority of oil wells are drilled with f horizontal end (WHE). There are formulas offered by S.D.Joshi (2), U.P.Borisov (3), Aliev-Sheremet’s (4) and others to carry out calculations dealed with daily outputs of WHE with external circular boundary profile
2×π × k0 × h×∆P [2] a + a2 + 0, 25× L2 h h µ× ln + × ln 0, 5×L L 2× rw
0 ,5
2×π × k0 × h×∆P [3] 4R h h c + × ln µ ln L L 2πrw
k0 ×∆P / m [4] 2rw 2r r − ( h − rw ) 1+ × ln w + w h 2h h − 2rw
L – length of horizontal portion of a wellbore h – thickness of the stratum ΔP = (Pk – Pw) – pressure differential between the external circular boundary and a well µ – viscosity of oil
Rustam Bagautdinov
51
Fig. 1 – Daily output ratio of anisotropy and isotropic strata
Fig. 2 – Strata’s anisotropy influence to daily out of WHE
spring / 2012
52
kh2 × kv2 ∆a k × cos a + kh2 × sin2a
∆I =
2 v
2
∆a = 0, 05 For vertical wells the rate of influence of anisotropy factor of productive stratum is very little, but for WHE it is significantly higher. It is the fact that in oilfield practice daily output of WHE is less compared to expected one because of strata anisotropy factor. The rate of influence of anisotropy factor is estimated by a coefficient determined as b=kv/kh . For terrigenous formations kv < kh. There are several methods to calculate daily output of WHE, one of them being the formula [5], that is depicted in journal «Building oil and gas wells in onshore and offshore» and is as following:
Q=
4 × kh × h× I ×∆P × L [5] l d m 2× I (Rc − ld ) + kh × h× ln 2× rw
Rc
– radius of an external boundary, L – length of a horizontal portion of a well; h – thickness of a productive stratum; B0 – oil formation volume coefficient ∆P = Pk − Pw – pressure difference between limit boundary external kv – vertical permeability kh – horizontal permeability I – integral a
I=∫ 0
kh2 × kv2 da k × cos a + kh2 × sin2a 2 v
a = arctg kh, mD 525
rw,m
Rk, m
ΔP, МPа
L, m
21-525 0,089
0,0276
350
3,6
150
Table 1 – Data initial Let’s solve this integral with numerical method. We shall separate expression into elementary ∆I =
2 v 2 h
k ×k ∆a kv2 × cos 2a + k × sin2a
∆a = 0, 05 a0 = 0, 025 a = a + ∆a
When we sum: 1,5
2
5
10
15
20
25
2,38E-13
2,27E-13
1,7E-13
1,2E-13
9,37E-14
7,77E-14
6,68E-14
b I, m
2
Table 2 – Values of integral Because (Fig. 1) anisotropy strongly influent to strata with high thickness, faintly to strata with small thickness. For WHE with linear profile of external boundary we offer to use the formula of Golosov for extremely gallery Q=
Lb
2π × k × h×∆P× L [6 ] L h µ 2π × b + ln h 2π ×rw – distance from well axis to external boundary
It is interesting to expose the influence of different factors upon daily output for WHE. The influence of well radius. If we take the daily output for one for rs=0,1 m, vertical well’s the daily out with rs=0,2 m and Rb=500 m will be 1,08.
h, m
µ, Pa×s
2 h
a = a + ∆a
For WHE with h=10 m and same Rb from (2) when rs=0,2 m we’ll get Q=1,01−1,04. Therefore the daily out of WHE less than daily out for vertical wells.
2
h 2×ld
kv, mD
a0 = 0, 025
2,5
5
10
20
CP; (3)
1
1,6
3,8
7,0
LP; (5)
1
1,8
3,9
7,1
L=200 m, Rb=Lb=500 m Table 3 – The influence of strata thickness These accounts using (3) and (5) show (Fig. 1), that daily out of WHE nearly proportional to strata thickness.
Rustam Bagautdinov
53
Fig. 2 – Strata’s anisotropy influence to daily out of WHE
The influence of strata vertical anisotropy
The influence of contamination rate
It’s known that in terrigenous deposits the vertical permeability is usually less than that for horizontal one. Daily output for similar anisotropy strata offered by Griguletski (7) and Jochi (8).
The inflow for WHE with LP (where permeability k1 different than the other parts) may be find:
Q=
Q=
β=
2×π × kh ×β × h×∆P 4R h β ×h µ ln c + ×ln L 2πrw L
[7 7]
s
2×π × kh × kV ×β × h×∆P [8.1] a + a2 + 0, 25× L2 β × h β × h × ln µ× ln + L 0, 5×L 2× rw kh kV
Q=
[8.2]
The calculation with use these show the vertical anisotropy substantially influence to daily out of WHE with big thickness and little influence with small thickness.
2π × k0 × L×( Pb − Pw ) [9] 2π ×L h b + s + ln µ× 2πR 1 h – skin-effect factor that is delivered as well as for vertical wells (1).
Well’s type
s=0
s=10
s=20
Vertical
1
0,46
0,31
1 1
0,95 0,83
0,91 0,72
WHE h=5 h=20 m
Table 4 – Daily out’s dependence from skin-effect (Rb=500 m) We can see that the influence of contamination rate for WHE is less than that for a vertical well.
spring / 2012
54
The influence of length of WHE
The influence a form of external boundary
Daily output of WHE with LP isproportional to its length. For WHE with CP when the length of WHE increases as much as twice the daily output grows to 40-60% (R K=350 m).
For vertical wells daily out ratio between wells with LP and CP is
Fig. 3 – Dependence of daily output from its length The equation of curve may submit? Qcomparetive=Q150∙Lx where parameter x<1 For h=5 m: ÈÈwhen
L=150, Qcom/Q150=1 => x=0
ÈÈwhen
L=200 m, Qcom/Q200=1,14 => x= 0, 25
ÈÈwhen
L=400 m, Qcom/Q400=1,64 => x= 0,082
2× LK ln QKKN rc Q = = RK QRKN ln rc rel
Rb = Lb=500 m r w = 0,1 m Qcom = 1,08 For WHE it is as following
Q rel =
QKKN QRKN
For h=40 m: ÈÈwhen
L=150 m, Qcom/Q150=1 => x=0
ÈÈwhen
L=200 m, Qcom/Q200=1,19 => x=0,34
ÈÈwhen
L=400 m, Qcom/Q400=1,83 => x=0,1
[10]
4R h h L × ln c + × ln L L 2prw = [11] L h ] 2× b + ln h×[2 h 2p ×rw
h =10 m Qcom =0,7 That is f vertical well’s daily out with CP more than LP. But for WHE on the contrary. Well, the wellbore wall contamination and well radius less influence for WHE. For WHE with LP and CP we got that vertical anisotropy greatly influence for strata with big thickness and less thin strata. The dependence daily out from its length nonlinear.
References 1. Akbulatov T.O., Salimgareev T.F., Salihov R.G. // Building oil and gas wells in onshore and offshore. – M., 2004. – No9. – p. 8-10. 2. Akzamov F.A., Akbulatov T.O. etc. About several reasons low effectiveness of horizontal well. – M., 2009. – No6. – p.14-17. 3. Nikitin B.A., Griguletski V.G. Stationary oil tributary to horizontal well in isotropic strata. – 1992. – No8. – p. 10-12. 4. Joshi S.D. Fundamental of technologic horizontal wells //.–2003. – p.7-16.
55
̂̂Keeping eyes on the horizon Wojtek Stupka
“Right now we are basically on the limits of what we can do, so what we need for tomorrow is to increase efficiency of every process we can - and that’s where you guys and the younger generation comes in.” With these words said by Phil Poettmann, chairman of SPE Moscow Section began plenary session of the International Scientific and Practical Conference “Oil and Gas Horizons”. On the November 14-15 2011 for the third time Gubkin University SPE Student Chapter invited students from all over the world to present their research and discuss new challenges in the Oil and Gas industry. Gladly for everyone this invitation met with exquisite response. Over hundred students representing 19 universities from Russia, Kazakhstan, Belarus, Germany, Romania, Poland and even Japan and Mexico met to participate in student paper contest. This year the conference was divided into two segments, scientific part on day one and SPE themed second day. During the first day participants could witness “Horizons of Russian Oil and Gas Industry Development: Offshore Fields” the plenary session concerning the hottest topics of the
region such as operating in extreme and fragile environments (Arctic area) or LNG distribution (Sakhalin project). After which student paper contest took place. In every of ten categories relating to all disciplines in petroleum industry, from Geoscience to Economics and Management, jury awarded three best works. In addition to it judges decided to give 6 special jury prizes and Total Grand Prix prize which went to Ivan Deshenenkov - Ph.D. student from Gubkin University. Second day of the conference was focused on the SPE activities. Organizers put a lot of effort to make it interesting and from where everyone will gain valuable experience. From the SPE Student Chapters meeting where each university presented their history, organization structure and achievements. Through inspiring career speech given by Mike Mayorov – Country Sales Manager at Baker Hughes. To the round table for chapters boards, where representatives of the chapters discussed strategies and methods they are using to keep their organization strong.
summer / 2012
56
It was great pleasure for YoungPetro to be part of such great event. We wish Gubkin University SPE Student Chapter even bigger success in the next editions of the conference.
At the same moment we would like to invite you to the “Oil and Gas Horizons 2012”. All the information you can find on www.gubkin-spe.org.
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summer / 2012
58 ďťż
SPE Leadership Workshop Student Chapters approaching pivot point
25th April 2012 Krakow youngpetro.org/workshops
Call for Papers - Summer Issue is waiting for Your paper!
The topics of the papers should refer to those presented in the list below: ÈÈDrilling Engineering ÈÈReservoir Engineering ÈÈFuels and Energy ÈÈGeology and Geophysics ÈÈEnvironmental Protection ÈÈManagement and Economics
Papers should be sent to: papers@youngpetro.org
Find more information at YoungPetro.org/Papers
Submission Deadline: 28 April 2012
spe . net . pl / emw
krakow
25-27 iv 2012
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