YoungPetro - 3rd Issue - Spring 2012

spring / 2012

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Almost a year has passed since we brought the first is-sue of the YoungPetro into your hands. I have to admit it was not an easy year. We came across a lot of chal-lenges 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.

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Editor's Letter

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spring / 2012

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EditorsJakub JagielloAlexey KhrulenkoKrzysztof LekkiPatrycja SzczesiulRobert Skwara Bartłomiej StaszkiewiczLukasz ŚwirkLiliana TrzepizurDawid [email protected]

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6

The Concept of Universal Life-saver with Rotary-screw MoverMaxim S. Krasheninnikov

Gas Deviation Factor Through An Intelligent Method Called Artificial Neural Network

Mohammad Javad Kiani

East Meets West

Nodal Analysis Used To Offshore Well Operating Regime Optimization

Rareș Petre, Mihai Vasile

Viscosity of the electron gas in a conductorRadmir Ganiev

Flow Rate of Horizontal WellsRustam Bagautdinov

Keeping eyes on the horizonWojtek Stupka

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30

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55

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For online version of the magazine and news visit us at youngpetro.org

8

Abstract At the present time there is an active de-

velopment of oil and gas fields located offshore in the northern seas. Mineral re-sources are mined in severe natural and cli-matic conditions. These conditions compli-cate platforms’ accordance to high safety requirements to various industrial process-es. Moreover, according to the analysis of the accidents, there is a problem in provid-ing 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 ex-isting means of evacuation, and indicates so-lutions to some actual safety problems. This paper offers a versatile rescue tool with rota-ry-screw propeller, which can effectively over-come various environments. Features of ro-tary-screw mover allow to use technological and transport means in such areas where the usage of other movers is impossible or irra-tional. 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.

TheConceptofUniversalLife-saverwithRotary-screwMoverMaxim S. Krasheninnikov Anatoly P. Kulashov, Viktor A. Shapkin, Alla A. Koshurina

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]. Cur-rently 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 decreas-ing, 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 min-erals 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 innova-tions, as well as modern systems of regulation and organization of work.

* Nizhny Novgorod State Technical University

Þ Russia

Viktor Shapkin, Ph. D.

[email protected]

* University Þ Country Supervisor E-mail

MaximS.Krasheninnikov 9

spring / 2012

A good example of the introduction of mod-ern standards of safety was a system of self-regulation 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 ac-cidents in the oil and gas platforms will de-termine 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 technologi-cal 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 param-eters of the system «platform – anchoring devices – borehole machinery»;

Platform OwnerAccident

dateAccident location

Distance to shore

Platform personnel

People lost

Bohai-2 China Petroleum

Department25.11.1979

Bohai gulf between China and Korea

150 km 74 72

Alexander L. Kielland

Stavanger Drilling

27.03.1980The field Ekofisk in the

North Sea320 km 212 123

Ocean Ranger Mobil 15.02.1982 The North Atlantic 267 km 84 84

Piper AlphaOccidental Petroleum

06.07.1988120 miles northeast of

Aberdeen, England310 km 224 167

P-36 Petrobras 15.03.2001125 km to east coast

of Brazil125 km 175 11

Mumbai High North

Oil and Natural Gas Corporation

27.07.2005Mumbai coast, near the town of Maharashtra,

India150 km 384

362 injured 22 perished

Deepwater Horizon

Transocean (Switzerland)

20.04.2010 Mexican Gulf 84 km 12617 injured

11 perished

Table 1 – Some major accidents on the oil and gas platforms located on offshore area

10 TheConceptofUniversalLife-saverwithRotary-screwMover

3. Lack of emergency management systems that could impact on the state of technol-ogy systems and platforms as a whole in the event of loss of control standard con-trol 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 emer-gency crew to the platform.

Among the major threat occurrence cata-strophic consequences after accidents are:

1. Oil and gas emissions;

2. The sudden destruction of equipment and pipelines, as well as the supporting struc-tures of drilling rigs and platforms;

3. Leakage of hydrocarbons from the service-able 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 sys-tems and organization of work, special atten-tion must be given to ensuring the safety of platforms by technical means. We are talking about actual problem of timely, fast and effec-tive evacuation of the personnel platform in case of emergency.

It is known that the most promising water ar-eas 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

12

13

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and gas resources [3]. The main areas of hy-drocarbon resources concentration are the Barents Sea (3.8 billion tons), Kara Sea (4.7 billion tons), the East Siberian Sea (2.1 bil-lion tons) and the Sea of Okhotsk (2.1 billion tons) [3].

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 or-ganizations’ data allows us to formulate the set of operating conditions in a field for a ma-chine 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 oper-ation of drilling equipment icebergs posing a danger must to blow or take away to the side to avoid collision with the rigs.

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.

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 weath-er 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 cur-rents 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 inef-fective, because these rafts could not move in the arctic seas and ensure the necessary level of safety.

Fig. 3.1 – Aerial evacuation means


The use of lifeboats (Fig. 6) will be limited be-cause 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 pos-sible.

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 stabil-ity 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 float-ing machines vehicle with rotary-screw mov-er (rsm) occupies a special place. Features of rotary-screw mover allow to use technologi-cal and transport means in such areas where the usage of other movers is impossible or ir-rational. 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.

Fig. 3.2 – Aerial evacuation means


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The rotary-screw mover is used for different machines – road construction, agricultur-al, military, etc. For example, in Russia, this mover is used in heavy and powerful ma-chines for cutting the ice and in light cross-country 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 tow-ing vehicle for movement on a thick layer of silt on fish farms. In Japan, they produce life-saving and recreational vehicles with rotary-screw 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 cylin-der 0.15. The machine had a mass of 10.8 tons and a length of 7 m. The engineers of Mitsui

Fig. 4. – An example of an inflatable life raft for evacuation

Fig. 5 – Means of transporting people from the platform onto life rafts


Fig. 6.1 – Lifeboats

Fig. 6.2 – Lifeboats


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18

Fig. 7 – Output on the ice rotary-screw vehicle gpi-72

19

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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


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 wa-ter at 50 cm, where any other machine and ships cannot move, the machine breaks the ice thickness up to 43 cm.

Compared with the other types of ground movers the rotary-screw mover has many ad-vantages [4]:

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 ice-resistant stationary platforms.

But the creation of such vehicles for move-ment in difficult conditions (non-cohesive grounds, snow, ice, water and a combina-tion of these media) is impossible without re-search 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 param-eters:

È dimensions: length 9.5 m; width 4.6 m; height 3.06 m

È draught at full load 0.92 m

È gross weight 7.5 tons

È capacity 38 person (two person crew)

È rate of ice – up to 35 km/h; snow – up to 40 km/h; water – up to 5 km/h

È diameter of the cylinder screw mover 1.2 m

È length of screw mover 6.65 m

È height of the helical blade 0.2 m

È road 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 vi-sion. 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 dif-ferent 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 man-ufacture the Universal life-saver with rota-ry-screw mover.

Projecting according to the stages will allow creating life-saver with screw mover in ac-cordance 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 process-es and then goes their adjusting. This will help


spring / 2012

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


to achieve two goals: first to develop and ver-ify in practice the theory of motion of rotary-screw 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 mathe-matical model of motion rsv will be a «Ter-rain-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 pos-sible combinations;

3. Model which defines behavior of the ma-chine.

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 ab-solutely rigid in the early stages of the calcu-lation.

Model of the rotor will be the set of equa-tions of its surfaces.

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 sur-face 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-cyl-inder rotor (Fig. 7). This decomposition allows obtaining a very accurate description of the rotor surface.

In addition to the separation of one-and two-cylinder rotaries, this mover can have dif-ferent end caps (conical, spherical, parabolic shape, as well as their combinations), differ-ent blade sectional view (triangular, trapezoi-dal and sheet) and may contain up to 3-4 heli-cal 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 paramet-ric equations (for a Cartesian coordinate sys-tem) of the following form:

Fig. 12 – The result of the construction of the surface single-cylinder screws on the basis of the para-metric equations

Fig. 13 – The surface of one side of the helical blade


spring / 2012

X f r f P

Y f r f P

Z f hf P

= ×

= ×

= ×⋅

( ) cos[ ( )]

( ) sin[ ( )]

( )( )2 p

[ ]1

ƒ(r) – function of changing the distance from the axis of symmetry

ƒ – the specified range of the radiusƒ(h) – function changes the height of the being

constructed figureh – range of changes of heightƒ(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

In particular, the system of parametric equa-tions which describes the surface of one side of the helical blade (Fig. 13) looks like:

References1. 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 continen-tal 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.

X r h i

LP

jt t

Pi

Y r h iLP

jt

O B

b

= + × × × × −−× ×

= + × × × × −

( ) cos( )

( ) sin(

b 2

2

p p

p OO B

H b

tP

i

Z L L j

−× ×

= + ×

p ) [ ]2

r – radius of basic cylinderh – height of helical bladeLb – length of basic cylinderP – pitch of helical bladetO – thickness of helical blade at the basetB – thickness of helical blade at the vertexLH – 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 dif-ferent environments and make their asso-ciation with the model of the screw mover to describe the processes occurring in the contact zone of mover with a support base.


AbstactSince 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 experi-mental 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 toler-ance. 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 Devia-tion 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.

IntroductionIn 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 predic-tion of two phase flow pattern in a pipeline

was encountered, the presence of Z-Factor was felt. Hall and Yarborough (1973) present-ed an equation of state that accurately repre-sents the Starling-Katz Z-Factor chart. They proposed the following mathematical form:

Z=[0.06125tpprY ]exp[−1.2(1−t)2] [1]

ppr – pseudo reduced pressure t – reciprocal of the pseudo reduced tempera-

ture, i.e.Tpc /T Y – the reduced density that can be obtained

as the solution of the following equation:

F(Y)=X1+Y+Y2+Y3+Y4

(1−Y )3−(X2)Y

2+(X3)YX4 =0 [2]

X1 = −0.06125 ppr t exp [−1.2(1−t)2]X2 = 14.76 t−9.76 t2+4.58 t3

X3 = 90.7 t−242.2 t2 +42.4 t3

X4 = 2.18+2.82 t

GasDeviationFactorThroughAnIntelligentMethodCalledArtificialNeuralNetworkMohammad Javad Kiani

* Petroleum Department, Islamic Azad University, Masjed-Soleyman Branch, Khuzestan

Þ Iran

[email protected]

* University Þ Country E-mail

MohammadJavadKiani 25

spring / 2012

The computational procedure of solving equa-tion 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 relation-ship: Yk = 0.0125 ppr t exp [−1.2(1−t)2]

Step 2. Substitute this initial value in Equa-tion 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(Yk)ƒ`(Yk)

[3]

where f`(Yk) is obtained by evaluating the derivative of Eq. 2 at Yk, or:

ƒ`(Yk)=1+4Y+4Y2+4Y3+y4

(1−Y )4−2(X2)Y+(X3)(X4)Y

(X4−1)=0

[4]Step 4. Steps 2-3 are repeated n times, until

the error, i.e., abs(Yk−Yk+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 graph-ical method for a convenient approximation of the pseudo-critical pressure and pseudo-critical 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

26 GasDeviationFactorThroughAnIntelligentMethodCalledArtificialNeuralNetwork

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.

Neural Network ArchitectureConsidering the nature of our problem, a simple 3-layer Generalized Feed Forward Neu-ral 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 spontaneous-ly 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 functionΦn(x1,x2…xi) – activation function in the hidden

layer of n-unitsx1,x2,x3…xi – input unitswi – weight of the basis function

Network TrainingData points used in this paper are 75 sam-ples of 4 elements which have been obtained form 7 Southern Iranian Reservoirs and cop-ied into the MATLAB spreadsheet as two groups of input data and output data. Dur-ing 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 vali-dation. Remaining 15% are applied to test the trained network.

To check if desired trained network is ob-tained, 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 com-pared with targets and Mean Square Error (MSE) will be shown as a result. Unlike re-gression plot, MSE must be close to 0.0 and

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


spring / 2012

Fig. 3.1 – Comparison of Z-Factor Among Experimental, Artificial & calculating method; Unlike Correlated Z-Factor, ANN Z-Factor has Adapted on the Experimental Z-Factor

Fig. 3.2 – Comparison of Z-Factor Among Experimental, Artificial & calculating method; Unlike Correlated Z-Factor, ANN Z-Factor has Adapted on the Experimental Z-Factor

28 GasDeviationFactorThroughAnIntelligentMethodCalledArtificialNeuralNetwork

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) 0.95605

Z (Empirical) 0.683

Table 1 – Results of Z-Factor Estimation

ConclusionBy 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 avail-able in Table 2, is another reason that shows the accuracy of ANN.

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;

fY=((1+4*(Yk+Yk^2-Yk^3)+Yk^4)/

(1-Yk)^4)-2*X2*Yk+X3*X4*Yk^(X4-1);

Ykk=Yk-(FY/fY);

Error=abs(Yk-Ykk);

while Error>10^-5

Yk=Ykk;

FY=X1+((Yk+Yk^2+Yk^3+Yk^4)/

(1-Yk)^3)-X2*Yk^2+X3*Yk^X4;

fY=((1+4*(Yk+Yk^2-Yk^3)+Yk^4)/

(1-Yk)^4)-2*X2*Yk+X3*X4*Yk^(X4-1);

Ykk=Yk-(FY/fY);

Error=abs(Yk-Ykk);

end

Z=(0.06125*t*Ppr/Yk)*exp(-

1.2*(1-t)^2);

display (Z);

123456789

1011121314

15

1617181920

21

22232425

26

Snippet 1 – Applied Program in Calculation Z-Factor Through MTLAB Compiler

References1. Ahmad. T., Reservoir Engineering, Handbook, 2nd Edition, 2001.

2. Hajizade. Y., Intelligent prediction of reservoir fluid PVT data, Dissertation, Islamic Azad Uni-versity 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.


spring / 2012

With less than two months to go and prepa-rations going well on their way we am real-ly 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 meet-ing, which, by gathering specialist from the widely considered petroleum industry, will create a space for exchanging minds, knowl-edge 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 Stu-dent 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 poten-tial 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 gener-ation is very ambitious and diligent with leading their own research, gaining new knowledge and develop their interest in pe-troleum technologies. Finally – they have shown how big demand is for such meetings and how many benefits these meetings pro-vide for each of their attendees.

EastmeetsWest

2012

‘East meets West’ creates a full range of possibil-ities 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 ac-companied by very warm events highly support-ing 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 Con-gress 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 chal-lenges 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 Petro-leum Congress ‘East meets West’. Become a part of the ‘East meets West’ family and feel the tech-nical heart of the world, which will be pounding this year in Krakow.

Organizing Committee

spe.net.pl/emw

NodalAnalysisUsedToOffshoreWellOperatingRegimeOptimizationRareș Petre, Mihai Vasile

* Oil and Gas University of Ploiești

Þ Romania

Assoc. Prof. Dr. Eng. Mariea Marcu

[email protected]

[email protected]

* University Þ Country Supervisor E-mail

AbstractThis paper presents several issues on sub-

sea production systems, natural flowing as well as nodal analysis workflow. Nodal analysis consider several models such as:

ÈAnalysis is done (node is chosen) at per-foration interval;

ÈAnalysis is done at subsea X-tree point;

ÈUses of a subsea multiphase pump.

The study is performed using PIPESIM soft-ware, considering several working scenar-ios for sensitivity analysis , namely: static pressure variation as well as separator pres-sure variation, pipeline and riser inner di-ameters variation and the study on the in-fluence of upward two-phase flow theories on performances equipment curves. The optimal operating regime shall be selected following the simulation data analysis.

IntroductionThe hunger for reduction of capital invest-ment and the growing demand for increas-ing 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):

ÈSeparator for oil, gas and water

ÈDehydration installation

ÈCompressor

ÈWater pump

ÈOil pump

ÈWater treatment plant

All this equipment are necessary for a classi-cal separation system that is placed on a sat-ellite platform. This platform is fixed directly above the wellhead afterwards the gas and

Fig. 1 – Multiphase pumping system [1]

32 NodalAnalysisUsedToOffshoreWellOperatingRegimeOptimization

liquid are transported through separate flow-lines to the host platform (Fig. 3). If we install a multiphase pump (twin-screw or helico-ax-ial) to the subsea system so that it will be a full wellstream production through a flowline

(Fig. 4). Therefore is not necessary a satellite platform.

The following advantages are specific for the multiphase pumps [2]:

ÈReduced equipment, capital cost and com-plexity;

ÈElimination of separate oil/water and gas lines;

È Increased production rates;

ÈReduced wellhead back pressure;

ÈReduced weight and space requirements;

È Increased reservoir life;

Fig. 2 – Classical separation system [1]

Fig. 3 – Production system using satellite patform [3]

Fig. 4 – Production system using multipase pump [3]

RareșPetre,MihaiVasile 33

spring / 2012

Historically, multiphase pumps were catego-rized either as twin screw pumps or helico-axial pumps. Today, there are many types of multiphase pumps using diverse technologies and a more comprehensive classification is re-quired [1].

The helico-axial pumps and twin screw pumps are most used pumps in offshore production systems (Fig. 5).

Laboratory simulationsAny production system is composed of the following: reservoir, well and surface facili-ties.

To establish the optimal operating system all these elements must be analyzed and deter-mined 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

order to reach the desired production rate as economical as possible. For determinating the optimal flow of the offshore well, we consid-ered three models for the nodal analysis:

1. when the node point was at the perfora-tion interval (Fig. 6)

Fig. 5 – Classification of multiphase pumps [1] [4] [5]

Fig. 6 – First model with node at perforation interval


2. when the node point was at the subsea X-tree point (Fig. 7)

3. when the node point was in front of the multiphase pump (Fig. 8)

The objectives of the simulation with PIPES-IM software for these three models are:

È Influence of the upward two-phase flow theories on the equipment performance curves study;

È Influence of the inner diameter of the riser, respectively of the flowline and separator pressure on the equipment performances curves;

Fig. 7 – Second model with node at subsea X-tree point Fig. 8 – Third model with node in front of the multiphase pump

Fig. 9 – Flow Pattern in a vertical well [7]


spring / 2012

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


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


spring / 2012

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


Legend for all graphics

ÈMultiphase pumps in subsea production system assessment study;

ÈNodal 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 per-formance 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 sec-tional 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 de-creasing, more gas exit from solution. The gas bubbles coalesce and form slugs with the di-ameter 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 gradi-ent (Fig. 9.b) [6].

Fig. 12.2 – Nodal analysis in the helico-axial pump case and power limitation at 100 kW


spring / 2012

Churn Flow: This flow pattern occurs in up-ward 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 single-phase 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. There-fore, 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 design-ing 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:

ÈA separator pressure decreasing can ex-tends the well life even in the case of the lower reservoir pressure, but this pressure has technological limits.

ÈFlowline 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.

ÈRiser diameter influences the equipment performances curves only in the lower flow rates range

The third model (Fig. 8) is used to show the in-fluence of the multiphase pump in the subsea production system and to perform the nod-al 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 pres-sure for fluid flowing from the wellhead to the processing platform. The most important pa-rameter 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 be-tween 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 helico-axial 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).

ConclusionsFrom the parameters sensitivity study with riser inner diameter and flowline inner diam-eter 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 equip-ment performance curves and the nodal anal-ysis points also. If we can decrease this pres-sure, we can obtain a nodal analysis point at the lower reservoir pressures.


Using multiphase pumps in a subsea pro-duction 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-

sults that the last parameter is more impor-tant because it permits to have a nodal anal-ysis point at the lower reservoir pressure, which means the extension of the natural flowing well life.

References1. 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-Gath-ering System in West Texas, paper SPE 27995, University of Tulsa Centennial Petroleum Engi-neering 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 Uni-versity, 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 & Mecha-nistic 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

Want to take part in creating ?

Join us!youngpetro.org/[email protected]

For DC Ohm's equation is known:

Ι∆

Ι∆∆Ω

= ⇒ = ×UR

S Ur . . [ ]

2

I – amperage,∆U – voltage difference at the ends of the con-

ductor length ,R =R

S=×r ∆ ohmic resistance of the conductor,

rn – the resistivity of conductor material,S – area of conductor.

The potential for a Newtonian fluid in a po-rous medium is described by Darcy:

wk

gradPk P

= × = ×m m

∆∆

[ ]3

w – filtration rate,m – dynamic viscosity of the fluid,∆P – differential pressure over the length ,k – permeability of the porous medium.

ViscosityoftheelectrongasinaconductorRadmir Ganiev

* Ufa State Petroleum Technological University

Ph.D. T.O. Akbulatov

Þ Russia

[email protected]


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 spher-ical shape, conductor is similar to the ficti-tious ground, consisting of balls of the same size.

The balls may have different packaging, shown in Figure 3, such as tetragonal, when the cent-ers 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 equa-tion

Υ= ⋅a gradP [ ]1

Y – parameter that characterizes the flow of matter or energy

gradP – gradient strength values (pres-sure, voltage, temperature, con-centration)

RadmirGaniev 43

spring / 2012

Multiplying the equation (3) for the filtration area S get filtered fluid flow:

Q w Sk S

gradPk S P

= × =×× =

××

m m∆∆

[ ]4

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:

zM

V Na= =

× ×ρ ρµ

[ ]5

r – density of conductor material;V – volume conductor;Na – A v o g a d r o ' s n u m b e r

(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.

If the size of the ion is equal to D, the volume of all ions in a conductor:

V zD

ε

π= ×

× 3

66[ ]

The share of the space between the ions, the electron gas is employed, will be m:

m z D= − × ×1 0 52 73. [ ]

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 cur-rent I corresponds to the volumetric flow rate of the electron gas, which is given by (8)

Qm I

z=× × ×6 29 10

818.

[ ]

If the conductor has a resistance of R [W] and the area S, the length of the conductor:

∆Ω

=×R Sr

[ ]9

The volume of the conductor:

V SR S

cond = × =×

∆Ω

2

10r

[ ]

In this volume is X=z×Vnp electrons, under voltage difference ∆U. At the same time each electron will be a force (Fig. 4):f e

U= ×−

∆∆

[ ]11

e– – elementary electric charge

Fig. 1 – Fluids flow in porous media Fig. 2 – The motion of the electron gas between the ions

Fig. 3 – Fictitious model of soil

44 Viscosityoftheelectrongasinaconductor

The total force on all the X electrons from (12):

F f O O eU

= × = × ×−∼ ∼

∆∆

[ ]12

Consequently, the pressure drop in the elec-tron cloud, for X electrons:

PFS

f XS

e U XS

e U z V

Se U z R Snp

om

= =×=× ××

=

=× × ×

×=× × × ×

×

−

− −

∆∆

∆

∆∆∆

r

The permeability of the fictitious ground:

km Dc m

=×

× × −

3 2

236 114Ł

( )[ ]

c – Karman number (for packages with a ball = 5)

Substituting these values in equation (4),:

Q w Sk S

gradPk S P

= × =×× =

××

m m∆∆

[ ]15

Qm I

zm D e U z S R

c m

=× × ×

=

=× × × × × ×× × − × × ×

−

6 29 10

36 1

18

3 2 2

2 2

.

( )[Ł ∆

∆ Ωµ ρ

116]

Simplifying equation (16) we obtain the equa-tion (17):

QI

m D e U z Sc m

=× ×

=

=× × × × ×× × − × ×

−

6 29 101

36 117

18

2 2 2

2

.

( )[ ]Ł ∆

∆m

Hence, we find the m of the equation (16):

m=× × × × ×

× × − × × × ×

−m D e U z Sc m I

2 2 2

2 1836 1 6 29 1018Ł ∆

∆( ) .[ ]

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 ve-locity of the electron gas in a conductor

The volume of the ion:

VD

m

=×

=× ×

=

= ×

−

−

p p3 9 3

27 3

60 256 10

60 0089 10

( . )

.

The number of ions in 1 m³:

zV Na

=× ×

=× × ×

= ×ρµ

8 96 1 6 02 1063 546

8 5 1023

22. ..

.

The volume of the ion in 1 m³:

V zD

m

επ

= ××

= × × × =

= ×

−

−

322 27

5 3

63 5 10 0 0089 10

0 0756 10

. .

.

Hence the porosity of the conductor:

mV

=−=

− ×=

− −

−

11

10 0 7 1010

0 2446 6

6

..

Consequently, copper atoms are located in the tetragonal packing (Fig. 3).

The permeability of a fictitious soil is calcu-lated by formula (14):

k m=× ×× × −

= ×−

−0 3 0 256 1036 5 1 0 3

2 103 9 2

223 2. ( . )

( . )

Fig. 4 –Action of the electric force on the electron

RadmirGaniev 45

spring / 2012

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

I ACs

UR

U S= = = =

××

111

∆ ∆r

where RS

=×r , then

18 5 10

0 38 5 10

0 35 10 0 35 10

22

3

22

22 3 28 3

em cm

cm m

−

− −

=×

=×

=

= × = ×

..

.

. .

In 1 C contains 6.29×1018e– electrons then the total consumption of the electron cloud at a current 1 A:

Qm e

e=× × ×× ×

=

=× × ×

×=

=

−

−

−

6 29 108 5 10

0 3 6 29 10 108 5 10

0

18

22

18 6

22

..

. ..

.. /22 10 10 3× − m s

w= =×

= ×−

−−Q

Sm s

0 22 1010

0 22 1010

64.

. /

Given that S=10−6m2=1 mm2 we have:

RS

W m=×=

×= ⇒ =

r

0 01751

1 57.

V S m= ⋅ = ⋅ =− 57 10 576 3

then the number of electrons in V

z5722 2257 10 8 5 484 10= ⋅ ⋅ = ⋅. electrons

then ∆∆ ∆

PFS

z e US l

= =× ××

−

, because Fe=e–,

where EU

=

, then

∆P Pa=× × × ×× ×

= ×−

−

484 10 1 6 10 11 10 57

13 6 1022 19

69.

.

From ωµ

=××

k P∆∆

that should be

µω

=××

=× × ×

× ×=

= × ×

−

−

−

k P

Pa s

∆∆

2 10 13 6 100 22 10 57

2 2 10

23 9

4

10

..

.

Determine the flow regime of the electron cloud

For the model assuming an ideal soil charac-teristic dimension d equal to the effective di-ameter d of the particles have the following formula for the Reynolds number:

Re( . . )

.=×

× + ×

w d

mef

0 75 0 23 n

d – effective particle diameter,

νµρ

=el cloud.

rel. cloud. – the density of electron cloud.

rel cloudelz M

m V.

. .. .

.

=××=

× × ×× ×

=

=

−

−

8 5 10 9 1 100 3 0 0756 10

0 34

22 31

5

11 3kg m/ ;

νµρ

= =×

= × ×−

−

el cloud

Pa s.

..

. ;2 2 100 341

6 45 1010

10

Re( . . ). .

( . . .

.=×

× + ×=

=× × ×× +

− −

w d

mef

0 75 0 232 2 10 0 256 10

0 75 0 3 0 2

4 9

n

33 6 45 100 19 10

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 re-gime of the electron cloud.

The calculation of the electron gas in a sil-ver conductor

Background

rAr=10,5 g/cm3

Dion Ar=0.28 nm

M(Ar)=107.9 g/mole;


rom=0.016W×mm2/m

The calculation of viscosity and the velocity of the electron gas in a conductor

The volume of the ion:

VD

m

=×

=× ×

=

= ×

−

−

p p3 9 3

27 3

60 28 10

60 0115 10

( . )

.

The number of ions in 1 m³:

zV Na

=× ×

=× × ×

=

= ×

ρµ

10 5 1 6 02 10107 9

5 86 10

23

22

. ..

.

The volume of the ion in 1 m³:

V zD

m

επ

= ××

= × × × =

= ×

−

−

322 27

5 3

65 86 10 0 0115 10

0 0674 10

. .

.

Hence the porosity of the conductor:

mV

=−=− ×

=−

−

11

1 0 67 1010

0 3266

6

..

Consequently, copper atoms are located in the tetragonal packing (Fig. 3).

The permeability of a fictitious soil is calcu-lated by formula (14):

k m=× ×

× × −= ×

−−0 326 0 28 10

36 5 1 0 3263 3 10

3 9 2

223 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– cor-respond to ? pore space, where m =0.326, hence

I ACs

UR

U S= = = =

××

111

∆ ∆r

, where

RS

=×r

, then

15 86 10

0 3265 86 10

0 056 10 0 056 10

22

3

22

22 3

em cm

cm

−

− −

=×

=×

=

= × = ×

...

. . 228 3m

In 1C contains 6.29×1018 e– electrons then the total consumption of the electron cloud at a current 1 A:

15 86 10

0 3265 86 10

0 056 10 0 056 10

22

3

22

22 3

em cm

cm

−

− −

=×

=×

=

= × = ×

...

. . 228 3m

w= =×

= ×−

−−Q

Sm s

0 349 1010

0 349 1010

64.

. /

Given that S=10−6 m2=1 mm2 we have:

RS

W m=×=

×= ⇒ =

r

0,0161

1 62 5.

V S c= × = × =− 62 5 10 62 56 3. .

then the number of electrons in V

z5722 2262 5 10 5 86 366 10= × × = ×. . electrons

then ∆∆ ∆

PFS

z e US l

= =× ××

−

,

because Fe=e×E, where EU

=

, then

∆P Pa=× × × ×× ×

= ×−

−

363 10 1 6 10 11 10 62 5

9 29 1022 19

69.

..

From ωµ

=××

k P∆∆

that should be

µω

=××

=× × ×× ×

=

= × ×

−

−

−

k P

Pa

∆∆

3 3 10 9 29 100 349 10 62 5

1 4 10

23 9

4

10

. .. .

. ss

Determine the flow regime of the electron cloud

For the model assuming an ideal soil charac-teristic dimension d equal to the effective di-ameter d of the particles have the following formula for the Reynolds number:

Re( . . )

.=×

× + ×

w d

mef

0 75 0 23 n

d – effective particle diameter,

νµρ

=el cloud.

rel. cloud. – the density of electron cloud.

RadmirGaniev 47

spring / 2012

rel cloudelz M

m V.

. ..

=××=

× × ×× ×

=

=

−

−

5 86 10 9 1 100 326 10

0

22 31

50.0674.. / ;2427 3kg m

νµρ

= =×

=

= × ×

−

−

el cloud

Pa s.

..

. ;

1 4 100 2427

5 768 10

10

10

Re( . . )

. .( . . .

.=×

× + ×=

=× × ×

× +

− −

w d

mef

0 75 0 231 4 10 0 28 10

0 75 0 326 0

4 9

n

223 5 768 100 145 10

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 re-gime of the electron cloud.

Cu Ar Cu/Ar

r 0.0175 0.016 1.09

m 2.2×10−10 1.4×10−10 1.57

Table 1


14-15 April 2012

Kazakh National Technical University

EventsPresentation on the latest technologies of Oil & Gas Indus-

try 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

[email protected]

Þ www.kntu-spe.org

9th

Inte

rnat

iona

l You

th O

il &

Gas F

orum

49

summer / 2012

FlowRateofHorizontalWellsRustam Bagautdinov

* Ufa State Petroleum Technological University

Þ Russia

[email protected]


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:

ÈDaily well output is proportional to thick-ness and permeability of the stratum;

ÈThe difference between the vertical and horizontal permeabilities (vertical anisot-ropy factor of strata) is very little;

ÈThe wellbore wall contamination rate is estimated by a skin effect according to the formula

sk kk

lnRrw

=−× [ ]0 1

1

1 1

k0 – initial permeability of the stratumk1 – permeability of the contaminated zoneR1 – radius of the contaminated zonerw – radius of a well

Since the second half of the last century the majority of oil wells are drilled with f hori-zontal end (WHE). There are formulas offered by S.D.Joshi (2), U.P.Borisov (3), Aliev-Sher-emet’s (4) and others to carry out calculations dealed with daily outputs of WHE with exter-nal circular boundary profile

Qk h P

a a L=

× × × ×

×+ + ×

×

+ ×

×

2

0 250 5 2

0

2 2

π

µ

∆

lnL

hL

lnhr

,, ww

[ ]2

where

aL R

Lk= + +

2

0 5 0 25 24

0 5

, ,

,

Qk h P

c

=× × × ×

+ ×

[ ]2

42

30π

µπ

∆

lnRL

hL

lnhrw

Qk P

rh r

w

w

=×

+−

× +− − [ ]0

122

22

4∆ /

( )m

lnrh

r h rh

w w w

L – length of horizontal portion of a wellboreh – thickness of the stratum∆P = (Pk – Pw) – pressure differential between

the external circular boundary and a wellµ – viscosity of oil

50

Fig. 1 – Daily output ratio of anisotropy and isotropic strata

Fig. 2 – Strata’s anisotropy influence to daily out of WHE

RustamBagautdinov 51

spring / 2012

For vertical wells the rate of influence of ani-sotropy 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 be-cause of strata anisotropy factor. The rate of influence of anisotropy factor is estimated by a coefficient determined as b=kv/kh . For ter-rigenous formations kv < kh.

There are several methods to calculate daily output of WHE, one of them being the formu-la [5], that is depicted in journal «Building oil and gas wells in onshore and offshore» and is as following:

Qk h I P L

I R l k h lnlr

h

c d hd

w

=× × × × ×

× −( )+ × ××

[ ]4

22

5∆

m

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 permeabilitykh – horizontal permeabilityI – integral

Ik k

k cos k sind

arctghl

h

h

d

=×

× + ×

=×

∫0

2 2

2 2 2 2

2

a

a aa

a

v

v

kh, mD

kv, mD

rw,mµ,

Pa×sRk, m

ΔP, МPа

L, m

525 21-525 0,089 0,0276 350 3,6 150

Table 1 – Data initial

Let’s solve this integral with numerical meth-od. We shall separate expression into elemen-tary

∆ ∆

∆

∆

Ik k

k cos k sinh

h

=×

× + ×

==

= +

2 2

2 2 2 2

0

0 05

0 025

v

v a aa

aaa a a

,

,

∆ ∆

∆

∆

Ik k

k cos k sinh

h

=×

× + ×

==

= +

2 2

2 2 2 2

0

0 05

0 025

v

v a aa

aaa a a

,

,

When we sum:

b 1,5 2 5 10 15 20 25

I, m2 2,38E-13 2,27E-13 1,7E-13 1,2E-13 9,37E-14 7,77E-14 6,68E-14

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 Go-losov for extremely gallery

Qk h P L

Lh

lnhr

b

w

=× × × ×

× +×

[ ]2

22

6π

µ ππ

∆

Lb – distance from well axis to external boundary

It is interesting to expose the influence of dif-ferent factors upon daily output for WHE.

The influence of well radius. If we take the dai-ly 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.

For WHE with h=10 m and same Rb from (2) when rs=0,2 m we’ll get Q=1,01−1,04. There-fore the daily out of WHE less than daily out for vertical wells.

h, m

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.

52

The influence of strata vertical anisotropyIt’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).

Qk h P

lnRL

hL

lnhr

h

c

w

=× × × × ×

+××

2

42

π β

µβ

π

∆[77

2

0 250 5

2 2

]

,,

Qk k h P

a a L

V=× × × × × ×

×+ + ×

×

+

π β

µβ

h

lnL

∆

×××

××

=

hL

lnhrw

β

β

2

8 1

8 2

[ . ]

[ . ]kkh

V

The calculation with use these show the verti-cal anisotropy substantially influence to daily out of WHE with big thickness and little influ-ence with small thickness.

Fig. 2 – Strata’s anisotropy influence to daily out of WHE

The influence of contamination rateThe inflow for WHE with LP (where permea-bility k1 different than the other parts) may be find:

Qk L P Pb w=× × × −

××+

+

2

22

0

1

π

µπ

π

( )[

Lh

lnhR

sb

99]

s – 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

WHE h=5 h=20 m

1 1

0,95 0,83

0,91 0,72

Table 4 – Daily out’s dependence from skin-effect (Rb=500 m)

We can see that the influence of contamina-tion rate for WHE is less than that for a ver-tical well.

RustamBagautdinov 53

spring / 2012

The influence of length of WHEDaily output of WHE with LP isproportion-al to its length. For WHE with CP when the length of WHE increases as much as twice the daily output grows to 40-60% (RK=350 m).

Fig. 3 – Dependence of daily output from its length

The equation of curve may submit? Qcomparetive=Q150∙L

x

where parameter x<1

For h=5 m:

Èwhen L=150, Qcom/Q150=1 => x=0

Èwhen L=200 m, Qcom/Q200=1,14 => x= 0, 25

Èwhen L=400 m, Qcom/Q400=1,64 => x= 0,082

For h=40 m:

Èwhen L=150 m, Qcom/Q150=1 => x=0

Èwhen L=200 m, Qcom/Q200=1,19 => x=0,34

Èwhen L=400 m, Qcom/Q400=1,83 => x=0,1

The influence a form of external boundaryFor vertical wells daily out ratio between wells with LP and CP is

QQQ

LrRr

rel KKN

RKN

K

c

K

c

= =

×ln

ln[ ]

2

10

Rb = Lb=500 mrw = 0,1 mQcom = 1,08

For WHE it is as following

QQQ h

rel KKN

RKN

c

= =

× + ×

×

L lnRL

hL

lnhrw

42p

[222

11× +

×Lh

lnhr

b

wp]

[ ]

h =10 mQcom =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 anisotro-py greatly influence for strata with big thick-ness and less thin strata. The dependence dai-ly out from its length nonlinear.

References1. Akbulatov T.O., Salimgareev T.F., Salihov R.G. // Building oil and gas wells in onshore and off-

shore. – 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.

54

KeepingeyesonthehorizonWojtek Stupka

“Right now we are basically on the limits of what we can do, so what we need for tomor-row is to increase efficiency of every process we can - and that’s where you guys and the young-er generation comes in.”

With these words said by Phil Poettmann, chairman of SPE Moscow Section began ple-nary session of the International Scientific and Practical Conference “Oil and Gas Hori-zons”.

On the November 14-15 2011 for the third time Gubkin University SPE Student Chap-ter invited students from all over the world to present their research and discuss new chal-lenges in the Oil and Gas industry. Gladly for everyone this invitation met with exquisite response. Over hundred students represent-ing 19 universities from Russia, Kazakhstan, Belarus, Germany, Romania, Poland and even Japan and Mexico met to participate in stu-dent paper contest. This year the conference was divided into two segments, scientific part on day one and SPE themed second day. Dur-ing 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 frag-ile environments (Arctic area) or LNG distri-bution (Sakhalin project). After which stu-dent paper contest took place. In every of ten categories relating to all disciplines in petro-leum industry, from Geoscience to Econom-ics 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 ef-fort to make it interesting and from where everyone will gain valuable experience. From the SPE Student Chapters meeting where each university presented their history, organiza-tion structure and achievements. Through in-spiring 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.

55

summer / 2012

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 in-vite you to the “Oil and Gas Horizons 2012”. All the information you can find on www.gubkin-spe.org.

56

57

summer / 2012

SPE Leadership WorkshopS t u d e n t C h a p t e r s a p p r o a c h i n g p i v o t p o i n t

25th April 2012Krakow

youngpetro.org/workshops

58

Call for Papers - Summer Issue is waiting for Your paper!

Find more information at

YoungPetro.org/Papers

Thetopicsofthepapersshouldrefertothosepresentedinthelistbelow:

ÈDrillingEngineeringÈReservoirEngineeringÈFuelsandEnergyÈGeologyandGeophysicsÈEnvironmentalProtectionÈManagementandEconomics

Papers should be sent to: [email protected]

Submission Deadline:28 April 2012

Platinum sPonsor

AGH University of Science and Technology

SPE Student Chapter

spe.net.pl/emw

krakow25-27 iv 2012

Documents

YoungPetro - 3rd Issue - Spring 2012