Analysis of vertical, Horizontal and deviated … American Journal of Oil and Chemical Technologies; ISSN (online): 2326-6589; ISSN (print): 2326-6570 Volume 1, Issue 8, October 2013

American Journal of Oil and Chemical Technologies; ISSN (online): 2326-6589; ISSN (print): 2326-6570

Volume 1, Issue 8, October 2013

10

Analysis of vertical, Horizontal and deviated wellbores stability

M.Aslannejad1, A. K. Manshad2, H.Jalilifar*3

1MSc student of Drilling Engineering, Persian Gulf University of Bushehr, Iran 2Assistant Prof. Petroleum, Persian Gulf University of Bushehr, Iran

3Associate Prof. Rock Mechanics, Shahid Bahonar University of Kerman, Iran

Corresponding Autthor Email: [email protected]

DOI: 10.142266/ajoct18-2 Abstract: Prediction and analysis of wellbore stability is considered as a critical and significant issue in drilling engineering. Loss of well due to instability prompts high expenditure and ceases drilling operation. Effective parameters on wellbore stability are in situ stress, pore pressure, rock strength, drilling mud pressure, and well path. Wellbore instability controlling, needs understanding of rock strength and in situ stresses. In general, in situ stresses and rock strength are uncontrollable; therefore wellbore instability can be prevented by properly adjusting the mud pressure and well path that are controllable factors. In this paper we use 3D analytical model of Al-Ajmi and Zimmerman [2005] to estimate the mud pressure required to avoid borehole collapse for a well located in Iran oil field. It is then compared with Flac outputs, in order to show the accuracy of results and investigate the wellbore stability in different states of vertical, horizontal and deviated. We concluded that using these two methods simultaneously can assist in the stability of wellbores effectively which result cost savings and minimizing time overruns on drilling projects. Keywords: wellbore stability, Failure criteria, FLAC, well path, drilling

1. Introduction Investigation of wellbore stability and advising a sensible plan before drilling, beget identification of problematic regions and improving of drilling operation. When a well is drilled, the rock surrounding the hole must take the load that was previously taken by the removed rock. As a result, the in situ stresses are significantly modified near the borehole wall. This leads to an increase in stress around the wall of the hole, that is to say, a stress concentration. The stress concentration can lead to failure of the borehole wall, depending on the rock strength [2]. The selection of a suitable failure criterion for wellbore stability analysis is difficult and controversial (Mclean and Addis, 1990) [2, 7]. It is therefore unclear to drilling engineer which failure criterion should be used. So far, the two most commonly used strength criteria in wellbore stability analysis are the Mohr–Coulomb criterion and the Drucker–Prager criterion. Researchers have found that these two strength criteria can give



11

very different minimum mud pressures. The Mohr–Coulomb criterion overestimates the minimum mud pressure because it neglects the strengthening effect of the intermediate principal stress while the Drucker–Prager criterion underestimates the minimum mud pressure because it exaggerates the intermediate principal stress effect [4]. Al-Ajmi and Zimmerman (2006) proposed the use of the Mogi–Coulomb criterion to predict brittle shear failure of rocks. This criterion was shown to accurately model laboratory failure data on a range of different rocks types. Using this Mogi–Coulomb criterion, they developed improved stability models for vertical, horizontal and deviated boreholes (Al_Ajmi and Zimmerman, 2009). L. Zhang and Ping Cao (2009) examined five failure criteria on various rock specimens in order to determine the best criterion for the wellbore stability analysis. Therefore, they concluded that the 3D Hoek–Brown and the Mogi–Coulomb criteria are appropriate for wellbore stability analysis. In this paper, we will use the Mohr-Coulomb and Mogi-Coulomb criteria to investigate minimum overbalance pressure as well as mud density for a well located in Iran oil field. 2. Effective parameters on wellbore stability Investigating failure criteria, it can be understood that wellbore stability depends on in situ stresses and rock strength. As alluded to above, stress alteration is the main reason of wellbore instability. In order to preclude the possibility of wellbore collapsing, drilling engineers should properly adjust mud pressure as well as the orientation of the wellbore with respect to the in situ stress. In general, the possible alteration of the borehole orientation is limited. It is therefore obvious that in most cases, wellbore instability can be prevented mainly by properly adjusting the mud pressure. Traditionally, the difference pressure between well and fluid formation, regardless of the rock strength and the field stresses, was about 100–200 psi. However, it cannot solely cover all the aspects of wellbore stability during drilling. [2] In Figure 1, A’-B’ shows the correct mud weight in which a layer is encountered, which has an increased lower mud threshold level, perhaps because it is higher in porosity, more fractured or gassy and its bulk modulus is lower than the layer above. In this case, the mud weight is increased at a higher value and the layer is drilled through. In contrast, A-B shows the worst case scenario in which the mud weight is just above the pore pressure gradient, meaning a kick will be experienced as soon as the lower bulk modulus layer is encountered. If the inappropriate mud weight is then increased above the minimum stress gradient, rapid mud loss and formation fracturing can occur, resulting potentially in the loss of the well with excessive formation damage. [10]



12

Figure 1. Schematic showing correct mud weight is a function of formation properties, which if not well understood can result in taking kicks and drilling-induced fractures. [10]

3. Rock mechanics properties and stress calculation

While rock strength is always an essential factor in cases of wellbore stability, the magnitude of the principal stresses and pore pressure are quite important. It is generally safe to assume that the vertical normal stress is equal to the weight of the overlaying rock, 0.027 MPa/m or 1.2 Psi/ft on average, that is,

(1) σ! = ρgh

where ρ is the average mass density of the overlying rock, g is the acceleration due to gravity, and h is the depth. [6] The poroelastic correlation is used to determine minimum and maximum horizontal stress (2) 𝜎! =

!!!!

𝜎! −!

!!!𝛼𝑃! + 𝛼𝑃! +

!!!!!

𝜀! +!"!!!!

𝜀!

(3) 𝜎! =!

!!!𝜎! −

!!!!

𝛼𝑃! + 𝛼𝑃! +!"!!!!

𝜀! +!

!!!!𝜀!

where σ! is minimum horizontal stress, σ! is maximum horizontal stress, σ! is vertical stress, ѵ is Poisson factor, α is Biot coefficient, P! is pore pressure, and ε!, ε! are strain in direction of minimum and maximum horizontal stress, respectively. [12]

4. Rock strength criteria

4.1. Mohr–Coulomb criterion



13

The Mohr-Coulomb failure criterion is widely used in rock mechanics due to its simplicity [3, 8]

(4) 𝜏 = 𝐶 + 𝜎!! 𝑡𝑎𝑛∅

Where τ is the shear stress σ!! is the effective normal stress, and c and ∅ are the cohesion and the internal friction angle of the rock, respectively. The Mohr–Coulomb criterion can also be expressed in terms of the maximum and minimum effective principal stresses, σ!! and σ!!

(5) 𝜎!! = 𝜎! + 𝑞𝜎!!

where 𝑞 is a parameter related to ∅, and σ! is the unconfined compressive strength of the rock. The parameters q and 𝜎! can be determined, respectively, by [4]

(6) 𝑞 = !!!"#∅!!!"#∅

, 𝜎! = !!"#$∅!!!"#∅

4.2. Mogi–Coulomb criterion

The Mogi–Coulomb criterion was proposed by Al-Ajmi and Zimmerman [2004] and is simply written as

(7) 𝜏!"# = 𝑎 + 𝑏𝜎!,!!

where σ!,!! and τ!"# are, respectively, the effective mean stress and the octahedral shear stress defined by

(8) 𝜎!,!! = !!!!!!!

!

(9) 𝜏!"# =!!

(𝜎!! − 𝜎!!)! + (𝜎!! − 𝜎!!)! + (𝜎!! − 𝜎!!)!

and a and b are material constants which are simply related to c and ∅ as follows:

(10) a = ! !!Ccos∅ , b = ! !

!sin∅

5. General and geomechanical information of Coopal oil field

The Coopal oil field is in the north of Khuzestan province and lies to the east of Ahvaz province. In situ stresses, geomechanical, and fluid flow information related to limestone reservoir in depth of 3791 m are listed in Table 1, 2. [11]



14

Table 1. In situ stress and geomechanical parameters for wellbore stability analysis in Coopal

oil field Overburden Stress (MPa)

Maximum Horizontal Stress (MPa)

Minimum Horizontal Stress (MPa)

Cohesion (MPa)

Friction Angle (degree)

Poisson’s ratio

Young’s modulus (GPa)

Density (gr/𝒄𝒎𝟑)

96.7 59.4 44.5 27 40 0.3 44 2.7

Table 2. Parameters of formation fluid flow

Pore pressure (MPa)

Permeability (md)

Porosity (%)

Oil density (gr/𝒄𝒎𝟑)

Fluid modulus (GPa)

31.1 3 8 0.692 0.63

In this part the optimum mud weight and well path are obtained using flac2D as well as analytical solution of The Mogi-Coulomb and Mohr-Coulomb criteria in order to preclude the possibility of wellbore instability.

6. Wellbore stability analysis with FLAC

To determine optimum mud weight, the analysis is initiated with mud weight higher than formation pore pressure, and in order to reach plastic state around the wellbore, various mud pressures should be examined. The investigation of wellbore stability in various mud pressures resulted in obtaining the onset of shear failure and plastic flow of rock into the borehole that listed in table 3.

Table3.pressure and mud weight at the onset of shear failure and plastic flow of rock

Formation Depth (m) Mud weight (pcf) Mud pressure (MPa) The onset of

plastic flow of rock

The onset of shear failure

The onset of plastic flow of rock

The onset of shear failure

Limestone 3791 53.4 40 31.82 23.8

As shown in figure 2, displacement around the wellbore is maximum value and reduces in parts far from the wellbore. The magnitude of maximum displacement in horizontal coordinate at the beginning of plastic flow is 7×10!! 𝑚 and this value for drilling parallel to the minimum horizontal stress is 7×10!! 𝑚 .



15

Figure 2. Displacement in horizontal co-ordinate at the beginning of plastic flow of wellbore (left), Horizontal displacement in drilling parallel to the minimum horizontal stress (Right)

It also shows that plastic zone around the horizontal borehole is more than the vertical one that represents drilling in vertical direction is more stable than horizontal one. The borehole drilling in the direction parallel to the maximum horizontal stress has more displacement than that the minimum horizontal stress; therefore drilling in this direction will increase the potential borehole instability.

Figure 4. Plastic zone drilling along with minimum horizontal stress



16

7. Wellbore stability analysis with Mogi-Coulomb and Mohr-Coulomb criteria

Regarding the limitation of FLAC in analyzing of deviated boreholes, it just investigates vertical and horizontal ones, whereas using analytical solution of the Mogi-Coulomb and Mohr-Coulomb criteria, boreholes with various inclinations (𝑖) and azimuths (∝) can be investigated. As illustrated in figure 4, the best drilling directions are vertical and deviated because lower mud pressure is required for wellbore stability in these directions. The predicted maximum inclination angle by the Mohr-Coulomb criterion is 40!, and by the Mogi-Coulomb criterion is 60! , that is, well drilling with inclination angles lower that predicted ones are safe and by increasing well inclination, the mud pressure should be increased. Figure 4 also shows that there is possibilities of plastic flow initiation if the pressure is lower than 32MPa, and by decreasing more, shear failure will probability happen because mud pressure decreasing leads to an increase in tangential stress and a decreasing in radial stress.



17

Figure 4. predicted mud pressure using the Mohr-Coulomb criterion (left), the Mogi-Coulomb criterion (Right)

Figure 4 also shows that the stability of the horizontal borehole (𝑖 = 90) is lower than the vertical one; therefore it needs higher mud pressure for being stable. Figure 5 shows the optimum mud weight for different drilling directions based on both the Mogi-Coulomb and the Mohr-Coulomb criteria. In practice, the minimum safe mud weight for drilling should be equal or more than that predicted by these two criteria, and drilling with mud weight lower than 53.3 pcf causes wellbore instability due to the onset of plastic flow of rock into the borehole.

Figure 5. predicted mud weight using the Mohr-Coulomb criterion (left), the Mogi-Coulomb criterion (Right)

The reason for difference between the Mohr-Coulomb and Mogi-Coulomb criteria in determination of well trajectory, mud pressure, and mud weight is that, the Mohr-Coulomb criterion involves only the maximum and minimum principal stresses, σ! and σ! , and therefore assumes that the intermediate stress σ! has no influence on rock strength so the predicted rock strength is lower than the real one, and then it needs more mud pressure to be stable, and due to this fact, the Mohr-Coulomb criterion is considered more conservative. Conversely, the Mogi-Coulomb criterion considers intermediate stress σ! so it predicts higher rock strength, and then the required mud weight for being stable is lower than that estimated by the Mohr-Coulomb criterion. Therefore, it represents field conditions more realistically than does the Mohr-Coulomb criterion.

8. Conclusions

Through this work, we can draw the following conclusions:

1. Wellbore stability analysis in different drilling directions showed that drilling in vertical direction is more stable than horizontal one and the well can be drilled with inclination angle lower than 60! in a direction parallel to the minimum in situ stress (i.e.σ!). 2. Plastic flow of rock into the borehole is initiated provided that mud pressure is lower than 32MPa and mud weight is lower than 53.3 pcf that causes wellbore instability. 4. Analytical solution of The Mogi-Coulomb and Mohr-Coulomb criteria can be used beside FLAC to examine wellbore stability more precisely.



19

5. The reason drilling direction is so important in this case study is that at the depth of interest there is a significant difference between the maximum and minimum horizontal principal stresses.

9.References

[1] Al‐Ajmi, Adel, M, R. Z,’’ Stability analysis of vertical borehole using the Mogi‐Coulomb failure criterion’’, International Journal of Rock Mechanics and Mining Sciences, 2006, 1200-1200. [2] Al-Ajmi, Adel M, Zimmerman, Robert W,’’ A new well path optimization model for increased mechanical borehole stability’’, Journal of Petroleum Science and Engineering 69, 2009, 53–62. [3] Fjaer E, Holt R.M, Horsrud P, Raaen A.M, and Risens R,’’ Petroleum Related Rock Mechanics’’, 53, 2nd Edition, Developments in Petroleum Science, Elsevier B.V 2008. [4] Zhang, Lianyang, Ping Cao, Radha, K.C, ’’Evaluation of rock strength criteria for wellbore stability analysis’’, Int. J. Rock Mech. Min. Sci, 2009, 1304-1316. [5] Al‐Ajmi, Adel, M, R. W, ’’Relation between the Mogi and the Coulomb failure criteria’’, International Journal of Rock Mechanics and Mining Sciences, 2004, 431‐439. [6] Goodman, Richard E, ‘’Introduction to rock mechanics’’, 2d Ed, John Wiley & sons, New York 1989. [7] McLean M, Addis M,’’ Wellbore stability: the effect of strength criteria on mud weight recommendations’’, SPE 20405, September 1990, 23–26. [8] Horsrud, P,’’ Estimating Mechanical Properties of Shale from Empirical Correlations ’’, SPE Drilling & Completion, June 2001, 68-73. [10] Rasouli, Vamegh and Brian, Evans,’’ Maximized production through deviated drilling and fraccing’’, Department of Petroleum Engineering, Curtin University of Technology, PESA News, December/January 2009/2010. [11] Koochaki, E, Gashtasbi k, ‘’Analysis of wellbore stability in Asmari formation of Coopal reservoir’’, sixth mine engineering conference, 427-434 [12] Wood Birch, Richard, "Options for Enhanced Well bore Stability", Schlumberger Oilfield services Caracas, Venezuela.

Documents

Analysis of vertical, Horizontal and deviated … American Journal of Oil and Chemical Technologies; ISSN (online): 2326-6589; ISSN (print): 2326-6570 Volume 1, Issue 8, October 2013