Work on creating a well at local area provide for drilling and strengthening of the head. Upon completion, the company that carried out the order draws up a document for the well. The passport indicates the parameters of the structure, characteristics, measurements and calculations of the well.

Well calculation procedure

Company employees draw up an inspection report and a certificate of transfer for use.

The procedures are mandatory because they make it possible to obtain documentary evidence of the serviceability of the structure and the possibility of putting it into operation.

The documentation includes geological parameters and technological characteristics:

In order to check the correctness of the calculation, start a test pumping of water at high pump power. This allows for improved dynamics

In practice, the second formula is used for calculation accuracy. After obtaining the flow rate values, the average indicator is determined, which makes it possible to accurately determine the increase in productivity with an increase in dynamics by 1 m.

Calculation formula:

Dbeat= D2 – D1/H2 – H1

• Dsp – specific flow rate;
• D1, H1 - indicators of the first test;
• D2, H2 - indicators of the second test.

Only through calculations can the correctness of the research and drilling of the water intake be confirmed.

Design characteristics in practice

Familiarity with the methods for calculating a water intake well provokes the question - why does an ordinary water intake user need this knowledge? It is important to understand here that water yield is a single way of assessing the performance of a well in order to satisfy the residents’ need for water before signing the acceptance certificate.

To avoid problems in the future, proceed as follows:

1. The calculation is carried out taking into account the number of residents of the house. Average water consumption – 200 liters per person. This includes expenses for household needs and technical use. When calculating for a family of 4 people, we get the highest water consumption of 2.3 cubic meters/hour.
2. In the process of drawing up an agreement in the project, the value of water intake productivity is taken at a level of at least 2.5 - 3 m 3 / h.
3. After completing the work and calculating the well level, water is pumped out, dynamics are measured and water yield is determined at the highest flow rate of the home pump.

Problems may arise at the level of calculating the flow rate of a well during the process of control pumping with a pump owned by the performing company.

Moments that determine the speed of filling the well with water:

1. Volume of water layer;
2. The speed of its reduction;
3. Depth groundwater and changes in level depending on the season.

Wells with a water intake productivity of less than 20 m 3 /day are considered unproductive.

Reasons for low flow rates:

• features of the hydrogeological situation of the area;
• changes depending on the time of year;
• clogging of filters;
• blockages in the pipes that supply water upward or their defloration;
• natural wear and tear of the pump.

If problems are discovered after the well is put into operation, this indicates that there were errors at the parameter calculation stage. Therefore, this stage is one of the most important and should not be overlooked.

In order to increase the productivity of water intake, the depth of the well is increased in order to reveal an additional layer of water.

They also use water pumping methods empirically, apply chemical and mechanical influences on the water layers, or move the well to another location.

test

4. Calculation of anhydrous well flow rate, dependence of flow rate on the degree of formation opening, anisotropy parameter

In most gas-bearing formations, the vertical and horizontal permeabilities differ, and, as a rule, the vertical permeability k in is significantly less than the horizontal permeability k g. Low vertical permeability reduces the risk of water flooding of gas wells that have exposed anisotropic formations with bottom water during their operation. However, with low vertical permeability, the flow of gas from below into the area influenced by the imperfection of the well in terms of the degree of penetration is also difficult. The exact mathematical relationship between the anisotropy parameter and the amount of permissible drawdown when a well penetrates an anisotropic formation with bottom water has not been established. The use of methods for determining Qpr, developed for isotropic formations, leads to significant errors.

Solution algorithm:

1. Determine the critical parameters of the gas:

2. Determine the supercompressibility coefficient under reservoir conditions:

3. Determine the gas density under standard conditions and then under reservoir conditions:

4. Find the height of the formation water column required to create a pressure of 0.1 MPa:

5. Determine the coefficients a* and b*:

6. Determine the average radius:

7. Find coefficient D:

8. Determine the coefficients K o , Q * and the maximum water-free flow rate Q pr. without. depending on the degree of formation h and for two different meanings anisotropy parameter:

Initial data:

Table 1 - Initial data for calculating the anhydrous regime.

Table 4 - Calculation of anhydrous mode.

Analysis of the production capabilities of wells in the Ozernoye field equipped with ESP

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Study of the movement of liquid and gas in a porous medium

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Underground fluid mechanics

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Underground fluid mechanics

In case of flat-radial displacement of oil by water, the well flow rate is determined by the formula: (17) where: rn is the coordinate (radius) of the oil-water interface at time t...

Application of new technologies when carrying out repair and insulation work

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Fluid flow to the well with a partially isolated supply circuit

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This concept means the amount of water, oil or gas that a source can produce per conventional unit of time - in a word, its productivity. This indicator is measured in liters per minute, or in cubic meters per hour.

Calculation of flow rate is necessary both when constructing domestic water-bearing wells and in gas production and oil industry— each classification has a specific formula for calculations.

1 Why do you need to calculate the well flow rate?

If you know the flow rate of your well, you can easily select the optimal pump equipment, since the pump power must exactly match the productivity of the source. In addition, in case of any problems, a correctly completed well passport will greatly help the repair team to choose suitable way its restoration

Based on flow rates, wells are classified into three groups:

• Low-rate (less than 20 m³/day);
• Average flow rate (from 20 to 85 m³/day);
• High-flow rates (over 85 m³/day).

In the gas and oil industries, the operation of low-yield wells is unprofitable. Therefore, preliminary forecasting of their flow rate is a key factor that determines whether a new gas well will be drilled in the developed area.

To determine such a parameter in the gas industry there is a certain formula (which will be given below).

1.1 How to calculate the flow rate of an artesian well?

To perform calculations, you need to know two source parameters - static and dynamic water levels.

To do this, you will need a rope with a voluminous weight at the end (so that a splash can be clearly heard when it touches the water surface).

Indicators can be measured after one day after completion. It is necessary to wait a day after completion of drilling and flushing so that the amount of liquid in the well stabilizes. It is not recommended to take measurements earlier - the result may be inaccurate, since during the first day there is a constant increase in the maximum water level.

After the required time has elapsed, take a measurement. This must be done in depth - determine how long the part of the pipe in which there is no water is. If the well is made in accordance with all technological requirements, then the static water level in it will always be higher than the top point of the filter section.

The dynamic level is a variable indicator that will change depending on the operating conditions of the well. When water is withdrawn from a source, its quantity in the casing constantly decreases. In the case when the intensity of water intake does not exceed the productivity of the source, then after some time the water stabilizes at a certain level.

Based on this, the dynamic level of liquid in a well is an indicator of the height of the water column, which will remain with constant liquid intake at a given intensity. When using different powers, the dynamic water level in the well will be different.

Both of these indicators are measured in “meters from the surface”, that is, the lower the actual height of the water column in the siege column, the lower the dynamic level will be. In practice, calculating the dynamic water level helps to determine the maximum depth to which a submersible pump can be lowered.

Calculation of the dynamic water level is carried out in two stages - you need to perform medium and intensive water intake. Take measurements after the pump has worked continuously for one hour.

Having determined both factors, you can already obtain approximate information on the flow rate of the source - the smaller the difference between the static and dynamic levels, the greater the well flow rate. For a good artesian well, these indicators will be identical, but an average productivity source has a 1-2 meter difference.

Calculation of well flow can be done in several ways. The easiest way to calculate the flow rate is using the following formula: V*Hv/Hdin – Hstat.

Wherein:

• V – intensity of water extraction when measuring the dynamic level of the well;
• N din – dynamic level;
• N stat – static level;
• H in – height of the water column in the casing (the difference between the total height of the casing and the static liquid level)

How to determine the flow rate of a well in practice: let’s take as an example a well whose height is 50 meters, while the perforated filtration zone is located at a depth of 45 meters. The measurement showed a static water level of 30 meters deep. Based on this, we determine the height of the water column: 50-30 = 20 m.

To determine the dynamic indicator, assume that in one hour of operation the pump pumped two cubic meters of water from the source. After this, the measurements showed that the height of the water column in the well became 4 meters less (there was an increase in the dynamic level by 4 m)

That is, N din = 30+4=34 m.

In order to reduce possible calculation errors to a minimum, after the first measurement it is necessary to calculate the specific flow rate, with the help of which it will be possible to calculate the real indicator. To do this, after the first intake of liquid, it is necessary to give the source time to fill so that the level of the water column rises to a static level.

Then we take water at a higher intensity than the first time and measure the dynamic indicator again.

To demonstrate the calculation of specific flow rate, we use the following conditional indicators: V2 (pumping intensity) - 3 m³, if we assume that with a pumping intensity of 3 cubic meters per hour, Ndin is 38 meters, then 38-30 = 8 (h2 = 8).

The specific flow rate is calculated using the formula: Du = V 2 – V 1 / H 2 – H 1, where:

• V1 – intensity of the first water intake (lower);
• V2 – intensity of the second water intake (high);
• H1 – reduction of the water column when pumping at a lower intensity;
• H2 – decrease in the water column when pumping at higher intensity

We calculate the specific flow rate: D y = 0.25 cubic meters per hour.

The specific flow rate shows us that an increase in the dynamic water level by 1 meter entails an increase in the well flow rate by 0.25 m 3 /hour.

After the specific and ordinary indicators have been calculated, the real flow rate of the source can be determined using the formula:

Dr = (N filter – N stat) * Dn, where:

• H filter - depth top edge filter section of the casing;
• N stat – static indicator;
• Du – specific flow rate;

Based on previous calculations, we have: Dr = (45-30)*0.25 = 3.75 m 3 /hour - this is high level flow rate for (classification of high-yield sources starts from 85 m³/day, for our well it is 3.7*24=94 m³)

As you can see, the error preliminary calculation, in comparison with the final result, was about 60%.

2 Application of Dupuis formula

Classification of wells in the oil and gas industry requires calculating their flow rate using the Dupuis formula.

Dupuy's formula for a gas well is as follows:

To calculate oil production, there are three varieties of this formula, each of which is used for different types wells - since each classification has a number of features.

For an oil well with an unsteady inflow regime.

1

The technological operation of vertical hydraulic fracturing (HF) is often used in gas production fields to intensify the flow of fluid to the well. Wide practical use Hydraulic fracturing stimulates scientific and field research to study the patterns of gas filtration to wells with hydraulic fractures. The proposed article develops a new formula for calculating the flow rate of a gas production well after hydraulic fracturing, the calculations of which are much simpler than using the formulas. At the same time, the alternative formula proposed by the authors gives results that deviate from the results within no more than 3-5%, which allows us to recommend the alternative formula for practical use.

1. Geometric model of the near-wellbore zone and hydraulic fracture

Following the work of Kanevskaya R.D. and Katz R.M. We model a vertical hydraulic fracturing crack with finite thickness and conductivity in the form of an ellipse with semi-axes l and w (Fig. 1).

Rice. 1. Filtration area diagram:
1 - layer; 2 - crack; 3 - bottomhole formation zone.
a 2 - b 2 = l 2 - w 2 = f 2; f is the focal length of confocal ellipses;
r c - well radius. Fluid flow into the well is carried out only through a fracture

We model the boundary of the near-wellbore formation zone (BZZ) by an ellipse confocal to the elliptical fracture. The geometric dimensions and focal length f of these two confocal ellipses will be related by the equation

The permeabilities of the filler of the fracture 2, the bottomhole zone of the formation 3 and the uncontaminated (remote from the well) part of the formation ℓ will be denoted respectively as k 2 , k 3 and k 1 . Steady fluid filtration throughout the entire filtration region in Fig. 1, as in , we consider to obey the linear Darcy law. Along the elliptical boundaries of the fracture and the pressure zone, the pressure is assumed to be constant - these boundaries are taken as isobars when deriving the formula for the well flow rate.

To derive the formula for the flow rate of a well with a hydraulic fracture, we first calculate the filtration flows in each individual part of the filtration area in Fig. 1.

2. Calculation of fluid inflow into the well through a vertical hydraulic fracture

When calculating the fluid influx into a well from a vertical elliptical fracture, a point flow is placed at the origin of coordinates, the thickness of which determines the desired flow rate of the well with hydraulic fracturing. However, the well radius is ≈ 10-15 cm, and the maximum thickness (opening) of the crack is ≈ 1 cm. With such a ratio between the dimensions of the well radius and the crack thickness, it is problematic to model the flow to the well from a hydraulic fracturing crack using a point flow at the origin of coordinates, which, Apparently, this led the authors to a complex calculation algorithm.

To avoid computational difficulties associated with the use of point flow, in this work, at the stage of calculating the fluid inflow into the well from a hydraulic fracture, the latter is modeled in the form of two identical thin extended rectangles with dimensions ℓ′ (length) and 2w′ (width). The rectangles are directly adjacent to the well along different sides from it and their axis are located on one straight line passing through the center of the well. An elliptical fracture is identified with a rectangular one if, outside the circular contour of the well, they have equal lengths and areas cross sections. Based on this definition of the identity of two crack shapes, for geometric parameters cracks we obtain the following connection equations:

(2)

Let's consider the influx of fluid to the well through a hydraulic fracture rectangular shape. Steady plane-parallel filtration of a perfect gas, as is known, is described by solutions of the Laplace equation

(3)

relative to the function, where p is pressure. If a solution to equation (3) is found under appropriate boundary conditions, then the velocity field can be found from Darcy’s law using the formula

In the problem being solved, the computational domain is a rectangle on the sides of which the following boundary conditions are specified:

The solution to the boundary value problem (3)–(6) is constructed standard method Fourier and has the form

The undetermined coefficients A n in formula (7) are found from the last boundary condition (6). Using known formulas for the coefficients of the Fourier series, we obtain that

(9)

Substituting the coefficients A n from formulas (9) into (7) leads to to the following expression for function:

In formula (10) there is only one unknown quantity left - the filtration rate at the boundary x = 0 - at the inlet of the flow from the hydraulic fracture into the wellbore. To determine the unknown value v, we calculate the average value of the function Ф(x, y) at the boundary x = 0. Based on formula (10) for the average value

(11)

let's find that

(12)

On the other hand, at the boundary x = 0 the pressure must be equal to the bottomhole pressure and, therefore, the equality must be satisfied. Taking into account the last comment
from (12) for the unknown quantity we obtain next value:

(13)

Where .

Considering that the fluid influx into the well (calculated for atmospheric pressure and formation temperature) through a hydraulic fracture in a formation with thickness b′ is equal to , for the desired well flow rate Q we finally obtain the expression

(14)

3. Calculation of fluid inflow to a vertical elliptical hydraulic fracture from the confocal boundary of the reservoir zone

Let us now consider filtration in area 3 between the hydraulic fracture and the elliptical boundary of the bottomhole zone. At this stage of the study, we will take the shape of the crack in the form of an elongated ellipse with axes 2l (crack length) and 2w (parameter characterizing crack opening). The formula for the influx of perfect gas from the elliptical boundary of the BZZ to the elliptical boundary of the crack is well known and has the form:

(15)

4. Calculation of fluid inflow to the elliptical boundary of the reservoir zone from a circular supply circuit

Now let’s consider filtration in the 1st region between the elliptical boundary of the near-wellbore zone and a circular supply circuit with radius R. The formula for the fluid inflow to the elliptical boundary of the reservoir zone can be obtained using the EGDA method, based on formula (4)-(25) of the reference book for calculating electrical capacitances. Formula (4)-(25) in terms of the considered filtration problem based on EGDA will be written as follows:

(16)

where K(k) and K(k′) = K′(k) are complete elliptic integrals of the 1st kind with moduli k and respectively, and F(ψ; k) is an incomplete elliptic integral of the first kind. The module k and the argument ψ are calculated through the parameters of the PZP boundary equations and the radius R of the circular power circuit using the following formulas:

(17)

5. Derivation of a formula for calculating the flow rate of a gas production well with a vertical hydraulic fracture

Formulas (14), (15) and (16) give a system of three linear equations with three unknowns - the flow rate Q and the pressures P trsch and P PZP. Solving this system of equations by elimination method, to calculate the flow rate of a well with a vertical hydraulic fracture in the near-field zone, we obtain the following formula:

Comparing the ratio of the production rate of a well after hydraulic fracturing to the production rate of the same well without hydraulic fracturing, we obtain the following expression for the hydraulic fracturing efficiency coefficient:

Comparative calculations of the flow rates of wells with hydraulic fracturing using formulas (18) revealed that the maximum relative differences do not exceed 3-5%. At the same time, from a computational point of view, formula (18) is preferable for practice, since it has a simpler software implementation.

In practice, formulas (18) and (19) make it possible to calculate the predicted flow rate of a well where hydraulic fracturing is planned, and, ultimately, to assess the expected technical and economic efficiency of hydraulic fracturing.

BIBLIOGRAPHY

1. Technology for designing hydraulic fracturing as an element of the gas condensate field development system / O.P. Andreev [and others]. - M.: Gazprom Expo LLC, 2009. -
   183 p.
2. Cadet V.V., Selyakov V.I. Filtration of fluid in a medium containing an elliptical hydraulic fracture. Izv. universities Oil and gas. - 1988. - No. 5. - P. 54-60.
3. Kanevskaya R.D., Katz R.M. Analytical solutions to problems of fluid inflow to a well with a vertical hydraulic fracture and their use in numerical filtration models //
   Izv. RAS. MZHG. - 1996. - No. 6. - P. 59-80.
4. Well productivity. Guided by Hemant Mukherjee. - M.: 2001.
5. Basniev K.S., Dmitriev N.M., Rosenberg G.D. Oil and gas hydromechanics. - Moscow-Izhevsk: Institute of Computer Research, 2003. - 480 p.
6. Iossel Yu.Ya., Kochanov E.S., Strunsky M.G. Calculation of electrical capacitance. - L.: Energoizdat, 1981. - 288 p.

Bibliographic link

Gasumov R.A., Akhmedov K.S., Tolpaev V.A. CALCULATION OF THE PRODUCTION OF A GAS PRODUCTION WELL WITH A VERTICAL HYDRAULIC FRACTURE // Uspekhi modern natural science. – 2011. – No. 2. – P. 78-82;
URL: http://natural-sciences.ru/ru/article/view?id=15932 (access date: 02/01/2020). We bring to your attention magazines published by the publishing house "Academy of Natural Sciences"

MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION

higher vocational education

"Tyumen State Oil and Gas University"

Features of oil field development with horizontal wells

Guidelines

For independent work in the discipline “Features of field development with horizontal wells” for masters studying in the specialty 131000.68 “Oil and Gas Engineering”

Compiled by: S.I. Grachev, A.S. Samoilov, I.B. Kushnarev

Ministry of Education and Science of the Russian Federation

Federal state budget educational institution
higher professional education

"Tyumen State Oil and Gas University"

Institute of Geology and Oil and Gas Production

Department of Development and Operation of Oil and Gas Fields

Guidelines

In the discipline “Features of oil field development with horizontal wells”

for practical, laboratory classes and independent work for bachelors of direction 131000.62 “Oil and Gas Engineering” for all forms of education

Tyumen 2013

Approved by the editorial and publishing council

Tyumen State Oil and Gas University

The guidelines are intended for bachelors of the direction 131000.62 “Oil and Gas Engineering” for all forms of study. IN methodological guidelines The main tasks with examples of solutions in the discipline “Features of oil field development with horizontal wells” are given.

Compiled by: Associate Professor, Ph.D. Samoilov A.S.

Associate Professor, Ph.D. Fominykh O.V.

laboratory assistant Nevkin A.A.

© state educational institution of higher professional education

"Tyumen State Oil and Gas University" 2013

INTRODUCTION 2

Topic 1. Calculation of production rates of wells with horizontal termination and comparison of results. 7

Topic 2. Calculation of the flow rate of a horizontal well and an inclined well with a hydraulic fracturing fracture using the given formulas, comparing the results. 2

Topic 3. Calculation of the flow rate of a multilateral well. 17

Topic 4. Calculation of the optimal grid of horizontal wells and the comparative efficiency of their work with vertical ones. 21

Topic 5. Interpretation of the results of hydrodynamic studies of wells with horizontal completion in steady-state modes (according to the method of V.S. Evchenko). 2

Topic 6. Production rate of a horizontal well with hydraulic fractures located in an anisotropic, band-like formation. 34

Topic 7. Calculation of the maximum anhydrous drawdown of a well with a horizontal end…………………………………………………………………………………30

Topic 8. Modeling of unsteady fluid movement to a horizontal well using a two-zone scheme……………………………45

INTRODUCTION

With the large-scale introduction in the early 2000s and over the next decade into the Western Siberian field development system of horizontal wells (HS) and horizontal lateral trunks (HSS), accelerated production of oil reserves was achieved at quick payback investments without building new wells. The implementation was carried out promptly, not always in accordance with the adopted design decisions, or through transformation existing system development. However, without a systematic justification for the technology of horizontal opening and operation of objects, the design values ​​of the oil recovery factor (ORF) are not achieved.

IN last years horizontal opening technology is given much more attention when designing a development system; in some companies, the justification for the construction of each horizontal well is carried out in the form of a mini-project. What was influenced by the world financial crisis, when, in order to optimize production, the error and the share of uncertainty were minimized. New approaches have been applied to horizontal drilling technology, as evidenced by the operating results of GS and BGS built since 2009 (more than 350 wells have been built at Surgutneftegaz OJSC, more than 200 wells at Lukoil OJSC, and more than 100 wells at TNK-BP. , in OJSC NGK Slavneft there are more than 100 wells, in OJSC Gazprom Neft there are more than 70 wells, in OJSC NK Rosneft there are more than 50 wells, in OJSC NK RussNeft there are more than 20 wells).

It is known that it is not enough to determine only the basic parameters of the use of horizontal wells: length, profile, location of the trunk relative to the roof and base, limiting technological operating conditions. It is necessary to take into account the placement and parameters of the well pattern, formation patterns and regulation of their operating modes. It is necessary to create fundamentally new methods for monitoring and managing the production of oil reserves, especially for complex deposits, which will be based on a reliable study geological structure through the study of horizontal wells, the dependence of oil flow rate on the heterogeneity of the geological structure and hydraulic resistance along the length, creating uniformity in the production of oil reserves throughout the entire volume of the reservoir of the drained horizontal well, high-precision determination of the drainage zone, the possibility of carrying out and predicting the effectiveness of methods for increasing oil recovery, determining the main rock stresses, the efficiency of the flooding system directly depends on their accounting and mechanical methods impact on the formation (hydraulic fracturing).

The purpose of this guideline is to provide students with the knowledge used by modern science and production in well productivity management.

The methodological instructions for each problem by topic present a calculation algorithm and provide an example of a solution typical task, which significantly contributes to the successful completion of the task. However, its application is possible only after studying the theoretical foundations.

All calculations should be carried out within the framework of the International System of Units (SI).

Theoretical basis The disciplines are well presented in textbooks, the links of which are given.

Topic 1. Calculation of production rates of wells with horizontal termination and comparison of results

To determine the oil production rate in a single horizontal well in a uniformly anisotropic formation, the S.D formula is used. Joshi:

Where, Q g– oil flow rate of a horizontal well m 3 /sec; k h– horizontal permeability of the formation m2; h– oil-saturated thickness, m; ∆P– reservoir drawdown, Pa; μ n– oil viscosity Pa s; B 0– volumetric coefficient of oil; L– length of the horizontal section of the well, m; r c– wellbore radius in the productive formation, m; – semimajor axis of the drainage ellipse (Fig. 1.1), m:

, (1.2)

Where Rk– radius of the power circuit, m; – permeability anisotropy parameter, determined by the formula:

kv– vertical permeability of the formation, m2. The calculations assumed a vertical permeability of 0.3· k h, the averaged parameter of terrigenous sediments of Western Siberia, also for a reliable calculation the condition - , must be met.

Figure 1.1 - Inflow diagram to a horizontal wellbore in a circular formation

Borisov Yu.L. when describing an elliptic flow, he proposed another condition for determining Rk. The main radius of the ellipse (Fig. 1.2), which is the average value between the semi-axes, is used as this value:

(1.4)

Figure 1.2 - Scheme of inflow to a horizontal wellbore in a circular formation

General formula for the inflow to the gas station, obtained by Yu.P. Borisov, has the following form:

, (1.5)

Where J– filtration resistance, determined by the formula:

. (1.6)

Giger proposes to use formula (1.8), where for the filtration resistance J take expression

(1.7)

The general formula for the inflow to the gas station, obtained Giger is similar to the equations of previous authors:

. (1.8)

All symbols parameters are similar to those presented for the Joshi S.D. equation.

Task 1.1. For the geological and physical conditions of the PK 20 formation of the Yarainerskoye field, presented in Table 1.1, calculate the flow rate of a well with a horizontal end Q g using the presented methods, compare the results obtained, determine the optimal length of the horizontal section according to the graph of the dependence of the well flow rate on the length of the horizontal line for 10 values ​​(from the initial one) with a step of 50 meters for the solutions of the considered authors.

Table 1.1

Solution. The problem is being solved in the following order:

1. Let’s calculate the flow rate of the gas pipeline using the Joshi S.D. method. To do this, it is necessary to determine the anisotropy parameter from expression 1.3 and the semimajor axis of the drainage ellipse (expression 1.2):

Substituting the results obtained into expression 1.1 we get,

2. Let's calculate the flow rates of the gas pipeline using the method of Borisov Yu.P.

Filtration resistance determined by formula 1.6:

To determine the daily flow rate, we multiply the result by the number of seconds in a day (86,400).

3. Let's calculate the flow rates of the gas pipeline using the Giger method.

Filtration resistance J take expression (1.7)

We determine the flow rate of the gas pipeline:

To determine the daily flow rate, we multiply the result by the number of seconds in a day (86,400).

4. Let’s compare the results:

5. Let us calculate the well flow rates for 20 values ​​of the length of the horizontal section in increments of 50 meters using the presented methods and construct a graphical dependence:

L length of horizontal section	HS flow rate, m 3 /day (Joshi S.D.)	HS flow rate, m 3 /day (Borisova Yu.P.)	HS flow rate, m 3 /day (Giger)
	1360,612	1647,162	1011,10254
	1982,238	2287,564	1318,32873
	2338,347	2628,166	1466,90284
	2569,118	2839,562	1554,49788
	2730,82	2983,551	1612,26295
	2850,426	3087,939	1653,21864
	2942,48	3167,09	1683,77018
	3015,519	3229,168	1707,43528
	3074,884	3279,159	1726,30646
	3124,085	3320,28	1741,70642
	3165,528	3354,7	1754,51226
	3200,912	3383,933	1765,32852
	3231,477	3409,07	1774,58546
	3258,144	3430,915	1782,59759
	3281,613	3450,074	1789,60019
	3302,428	3467,016	1795,77275
	3321,015	3482,103	1801,2546
	3337,713	3495,624	1806,15552
	3352,797	3507,811	1810,56322
	3366,489	3518,853	1814,54859

Figure 1.3 – Dependence of changes in well flow rate on the length of the horizontal section

Conclusions: Based on the results of calculating the predicted flow rate of a horizontal well using the methods of Joshi S.D., Borisov Yu.P., Giger for the geological and physical conditions of the PK 20 formation of the Yarainerskoye field, the following follows:

- with a slight difference (in the shape of the inflow in the horizontal projection) of the analytical models of the operation of horizontal wells that penetrated a homogeneously anisotropic formation in the middle between the roof and the bottom, the difference in the calculated flow rates is quite large;

- for the conditions of the PK 20 formation of the Yaraynerskoye field, graphical dependences of the predicted well flow rate on the length of the horizontal section were constructed; according to the results of the analysis, it follows that the optimal options will be in the interval L 1=150 m. Q 1=2620 m 3 /day up to L 2=400 m. Q 2=3230 m 3 /day;

- the obtained values ​​are the first approximate results of the selection optimal length horizontal section of the well, further justification is based on clarifying the predicted flow rates using digital reservoir models and recalculating the economics, based on the calculation results of which the most rational option will be selected.

Options Task No. 1

Var.	No.	Field, formation	HS length, m	h nn, m	Kh, mD	Kv, mD	Viscosity, mPa*s	Rpl, MPa	Rzab, MPa	Well radius, m	Rk,m
	210G	Yaraynerskoe, PK20					1,12	17,5	14,0	0,1
	333G	Yaraynerskoe, AB3					1,16		6,0	0,1
	777G	Yaraynerskoye, AV7					1,16		11,0	0,1
	302G	Yaraynerskoe, AV10					1,16	21,8	13,0	0,1
	2046G	Yaraynerskoe, BV2					0,98	21,1	13,7	0,1
	4132G	Yaraynerskoe, BV4					0,98	23,1	16,0	0,1
	4100G	Yaraynerskoe, BV4-1					0,98	23,3	16,0	0,1
	611G	Yaraynerskoye, BV6					0,51		16,0	0,1
	8068G	Yaraynerskoe, BV8					0,41	24,3	5,8	0,1
		Yaraynerskoe, BV8					0,41	24,3	11,2	0,1
	215G	Yaraynerskoe, PK20					1,12	17,5	15,0	0,1
	334G	Yaraynerskoe, AB3					1,16		11,0	0,1
	615G	Yaraynerskoye, AV7					1,16		16,0	0,1
	212G	Yaraynerskoe, AV10					1,16	21,8	15,0	0,1
	2146G	Yaraynerskoe, BV2					0,98	21,1	17,8	0,1
	4025G	Yaraynerskoe, BV4					0,98	23,1	13,0	0,1
	513G	Yaraynerskoe, BV4-1					0,98	23,3	18,0	0,1
	670G	Yaraynerskoye, BV6					0,51		19,5	0,1
	554G	Yaraynerskoe, BV8					0,41	24,3	11,34	0,1
	877G	Yaraynerskoe, BV8					0,41	24,3	16,2	0,1
Continuation of Table 1.1
	322G	Yaraynerskoe, PK20					1,12	17,5	14,9	0,1
	554G	Yaraynerskoe, AB3					1,16		15,3	0,1
	789G	Yaraynerskoye, AV7					1,16		12,7	0,1
		Yaraynerskoe, AV10					1,16	21,8	9,8	0,1
	2475G	Yaraynerskoe, BV2					0,98	21,1	12,9	0,1
	4158G	Yaraynerskoe, BV4					0,98	23,1	13,8	0,1
		Yaraynerskoe, BV4-1					0,98	23,3	18,2	0,1
	688G	Yaraynerskoye, BV6					0,51		14,3	0,1
	8174G	Yaraynerskoe, BV8					0,41	24,3	18,6	0,1
	882G	Yaraynerskoe, BV8					0,41	24,3	15,2	0,1

Control questions.