**CALCULATION OF OPERATING**

**COLUMNS AND CALCULATION OF ITS CEMENTING**

Option number 7

**Initial data**

1. The purpose of the well is operational, for oil production.

2. Well profile – vertical.

3. Well depth, production string length *H* = 2700 m.

4. The diameter of the bit when drilling under the production string *D* _{D} = 190.5 mm.

5. Wellbore broadening factor a= 1.05.

6. Production string outer diameter *D ^{ }*

_{H}= 140 mm.

7. Depth of running the previous casing string *H* _{O} = 800 m.

8. The inner diameter of the previous column *D¢* _{in} = 219 mm.

9. Cementing of the production casing is carried out to a depth *h* = 0m.

10. The height of the cement glass in the production string *h* _{st} = 10 m.

11. The upper part of the column is cemented with lightweight cement slurry, the lower part – with normal density cement slurry. Depth of change of cement mortars *H* _{C} = 2400 m.

12. The time of thickening of cement mortars *T* _{NZ} = 140 min.

13. Depth of productive formations

2600-2650m., Рpl1 = 28.1 MPa, Рgrp = 41.5 MPa

14. Density of solutions:

– drilling ρ _{p} – 1240 kg / m ^{3} ;

– lightweight cement ρ _{ozr} = 1570 kg/m ^{3} ;

– cement mortar of normal density ρ _{tsr} = 1810 kg/m ^{3} ;

– displacement fluidρ _{pr} = 1240 kg/m ^{3} ;

– buffer liquid ρ _{bzh} = 1020 kg/m ^{3} ;

– oil at the beginning of operation ρ _{nn} = 850 kg/m ^{3} ;

– oil (selected fluid) at the end of operation ρ _{n} = 880 kg/m ^{3} ;

– liquid filling the pores of cement stone ρ _{gs} = 1100 kg/m ^{3} ;

– pressure testing liquid ρ _{cool} = 1020 kg/m ^{3} ;

– liquid in the column when testing it for tightness by lowering the level ρ _{f} = 1050 kg/m ^{3} ;

19. Depth of lowering the liquid level when testing the column for _{tightness НУГ} *=* 1300 m.

20. Depth of lowering the liquid level in the column at the end of operation *N* _{UK} = 1500 m.

**Calculation of the production casing**

Calculation of the column for excess external pressure

Calculation of the production string for excess external (collapsing) pressures is carried out for the following time points:

– at the end of the cementing process;

– with a decrease in the liquid level in the column when testing it for tightness in one step without a packer;

– at the end of the operation of the well.

Let us calculate __the excess external pressure at the end of casing string cementing__ for the characteristic depths.

– at the wellhead ( *Z* = 0):

*P* NIO _{u003d} *P* _{No} – *P* Bo _{u003d} 0

– at the shoe of the previous column ( *Z* = *H* _{O} ):

*Р* _{NI} u003d 10 ^{-6} *g* [ρ _{р} *h* + ρ _{ocr} ( *H* _{O} – *h* ) – ρ _{pr} *H* _{O} ] u003d 10 ^{-6} 10 [(1240 × 0 + 1570 (800 – 0) – 1240 × 800] u003d 2 .64 MPa

– at the depth of change of cement mortars ( *Z* = *H* _{C} ):

*Р* _{NI} u003d 10 ^{-6} *g* [ρ _{р} *h* + ρ _{otsr} ( *N* _{C} – *h* ) – ρ _{pr} *N* _{C} ] u003d 10 ^{-6} 10 [(1240 × 0 + 1570 (2400 – 0) – 1240 × 2400] u003d 7 .92 MPa

– at the production string shoe ( *Z* = *H* ):

*R* _{NI z} u003d 10 ^{-6} *g* [ρ _{r} *h* + ρ _{otsr} ( *N* _{C} – *h* ) + ρ _{tsr} ( *N* – *N* _{C} ) – ρ _{pr} *H* ] =

u003d 10 ^{-6} 10[ 1240 × 0 + 1570 (2400 -0) + 1810 (2700 – 2400) – 1240 × 2700] u003d 9.63 MPa

Based on the calculation data, we build a diagram of excess external pressures (Fig. 1, line I).

Calculate __the excess external pressure at the time of testing the production casing__ for tightness by lowering the level:

– at the wellhead ( *Z* = 0):

*P* NIO _{u003d} *P* _{No} – *P* Bo _{u003d} 0

– at the depth of the cement level ( *Z* = *h* ):

*R* _{NI} u003d 10 ^{-6} *g* ρ _{p} *h * u003d 10 ^{-6} × 10 × 1240 × 0 u003d 0 MPa

– at the shoe of the previous column ( *Z* = *H* _{O} ):

*R* _{NI} u003d 10 ^{-6} *g* ρ _{gs} *H* _{O} u003d 10 ^{-6} × 10 × 1100 × 800 u003d 8.8 MPa

– at the level of the productive layer. To do this, we first calculate the equivalent of the reservoir pressure gradient (a _{PL} ):

a _{PL1} = *R* _{PL1} / 0.01 *N* _{PL1} = 28.1 / 0.01 × 2625 = 1.07 < 1.1,

with a _{PL} < 1.1 *R* _{NI} is not taken into account

– at the depth of the liquid level in the column ( *Z* _{= НУГ} *)* :

*R* _{NI} u003d 10 ^{-6} *g* [ρ _{p} *h +* ρ _{gs} *(N* _{UG} *– h)* ] u003d 10 ^{-6} × 10 × [1240 × 0 + 1100 × 1300] u003d 14.3 MPa

– at the production string shoe ( *Z* = *H* ):

*R* _{NI} u003d 10 ^{-6} *g* [ρ _{p} *h +* ρ _{gs} *(H- h) –* ρ _{f} *(H- N* _{UG} *)* ] *=*

10 ^{-6} ×10×[1240×0+1100×(2700-0)-1050×(2700-1300)] = 15 MPa

Based on the calculation data, we build a diagram of excess external pressures at the time of testing the column for tightness by pressure reduction (Fig. 1, line II).

Calculate __the excess external pressure for the end of operation__

__wells:__

– at the wellhead ( *Z* = 0):

*P* NIO _{u003d} *P* _{No} – *P* Bo _{u003d} 0

– at the shoe of the previous column ( *Z* = *H* _{O} ):

*R* _{NI} u003d 10 ^{-6} *g* ρ _{gs} *H* _{O} u003d 10 ^{-6} × 10 × 1100 × 800 u003d 8.8 MPa

– at the depth of the liquid level in the column ( *Z* = *N* _{UK} ):

*R* _{NI} u003d 10 ^{-6} *g* ρ _{gs} *N* _{UK} u003d 10 ^{-6} × 10 × 1100 × 1500 u003d 16.5 MPa

– at the bottom of the well ( *Z* = *H* ):

*Р* _{NI} u003d 10 ^{-6} *g* [ρ _{gs} *N* – ρ _{w} ( *N* – *H* _{UK} )] u003d 10 ^{-6} • 10 [1100 × 2700 – 1050 (2700 – 1500)] u003d 17.1 MPa

Based on the calculation data, we build a diagram of excess external pressures at the end of the well operation (Fig. 1, line III).

It can be seen from the constructed diagrams that the maximum excess external pressure occurs at the end of the well operation.

For the zone of the production facility (formation interval ±50 m), we will take the coefficient of crushing strength equal to 1.15, for the rest of the string – 1.0. At the boundaries of the zone of the operational facility, from the diagram (Fig. 1, line III) we take the values of the excess external pressure:

– at a depth of 2550 m – 17.05 MPa;

– at a depth of 2700 m – 17.1 MPa.

The value of external overpressures that the casing string must withstand will be as follows:

– at a depth of 2550 m – 17.05 • 1.15 = 19.6 MPa;

– at a depth of 2700 m – 17.1 • 1.15 = 19.67 MPa.

On the diagram of excess external pressures at the end of the well operation (Fig. 1, line III) at the boundary of the zone of the production facility, we plot the obtained pressure values and connect them with straight lines. Thus, we have obtained a diagram of the pressures that the column must withstand, taking into account the normalized coefficients of safety factor for collapse. Using this diagram, you can graphically select the lengths of casing sections. For the layout of the column, we will accept sleeve pipes with a triangular thread of normal length, version “B” – NORMKB. A crushing pressure of 19.67 MPa is maintained by pipes NORMKB 139.7Kx7.0 (26.1 MPa). The maximum depth at which these pipes can be installed is 2700 m, up to the bottom of the well.

Production string layout

based on excess external pressure.

section number | Casing size | Wall thickness, mm | Steel strength group | Installation interval, m | Section length, m | Section weight, kN |

NORMCB 139.7 | 7.0 | To | 0-2700 | 639.9 |

Calculation of the column for tension (breaking)

The layout of the production string selected based on excess external pressure must be checked for axial tensile loads. To do this, sequentially (from bottom to top) for the top of each section, the coefficient of tensile strength (breaking away) is calculated.

For the first section:

*n* _{STR} = *Q* _{STR} /å *q _{i} × l _{i}* = 863/ 639.9= 1.35 > [

*n*

_{STR}] = 1.15

After the breakout calculation, the production string lineup remains the same.

Calculation of the column for excess internal pressure

Calculation of the column for excess internal pressure (rupture) is carried out for the moment of its testing by hydraulic pressure testing in one step without a packer.

The wellhead pressure during operation of an oil well will be:

*R* _{Y} u003d *R* _{PL} -10 ^{-6} *gρ* _{N} *N* _{PL} u003d 28.1 -10 ^{-6} 10 880 2625 u003d 5 MPa

Testing pressure must exceed the expected working pressure ( *Р* _{У} ), and must not be lower than the established minimum testing pressure for a given casing diameter ( *Р* _{OPR} _{min} ) /8/:

*R* _{ODA} ³ 1.1 *R* _{U} ³ 1.1 5 u003d 5.5 MPa;

*R* _{OPD} ³ *R* _{OPD} _{min} = 12.5 MPa

Based on these conditions, we accept *R* _{OPD} = 12.5 MPa

Calculate the internal overpressures for the characteristic points of the wellbore

– at the wellhead:

*R* VIO _{u003d} *R* _{Bo} – *R* _{No} u003d 12.5 – 0 u003d 12.5 MPa

– at the depth of the cement level ( *Z* = *h* ):

*R* _{VI} _{h} *u003d R* _{OPD} -10 ^{-6} g ( *ρ* _{p} – *ρ* _{f} )h u003d 12.5 – 10 ^{-6} 10 (1240 – 1050) 0 u003d 12.5 MPa

– at the shoe of the previous column ( *Z* = *H* _{O} ):

*R* VIN _{o} _{u003d} *R* _{B N o} – *R* _{N N o} u003d ( *R* _{ODA} +10 ^{-6} *gρ ozh* *N* _{O} ) -10 ^{-6} *gρ* _{gs} *N* _{O} u003d

u003d (12.5 + 10 ^{-6} 10 1020 800) -10 ^{-6} 10 1100 800 u003d 11.86 MPa

– at the depth of the productive formation (with *a* _{PL} < 1.1):

*R* _{VIN pl} u003d *R* _{OPD} -10 ^{-6} *g* [( *ρ* _{r} *– ρ* _{f} ) h+ (ρ _{gs} *–* ρ _{f} ) ( *N* _{PL} *–* h)]=

= 12.5-10 ^{-6} 10 [(1240 – 1050) 0 + (1100 -1050) (2625- 0)] = 11.18 MPa

Based on the obtained data, we construct a plot of excess internal pressures (Fig. 1, line IV).

Calculate the coefficients of safety for internal pressure for the top of each section of the selected layout. The values of internal overpressures ( *РVI* ) are _{taken} from the diagram (Fig. 1, line IV).

For the first section:

*n* _{VN} u003d *R* _{KR} / *R* _{VI} u003d 33.2 / 12.5 u003d 2.65u003e [ *n* _{VN} ] u003d 1.15

Thus, the section withstands excess internal pressure with the necessary margin of safety.

We finally accept the layout of the production string shown in the table

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