In the following example it is assumed that the formation is normally stressed, an average overburden gradient is present, and that the reservoirs are normally pressured:
σ
1 = 1.000 psi/ft [23.0.kPa/m]σ
2 =σ
3PPG = 0.465 psi/ft [l0.5 kPa/m]
(Note : In this example stress gradients ( ,σ "striped"), pressure gradients and formation strength gradients are used instead of stresses, pressures, and strength. It is further assumed that stresses, pore pressures and formation strength are relative to the same reference level. This assumption is realistic for onshore wells, with a free water level close to surface. For offshore wells actual downhole pressures should be used.)
The minimum horizontal stress must now be related to the overburden. If it is assumed that sedimentary rock in a tectonically relaxed area can be modelled as a horizontally constrained, elastic medium, the effective horizontal stress can be expressed as a formation of the effective vertical stress and Poisson's ratio (ν) with the following expression:
3
Poisson's ratio for sedimentary rocks is about 0.25. The minimum in-situ stress gradient (and FCG) .can then be estimated as follows:
σ3- PPG =
The Fracture Breakdown Gradient for a vertical well can now be estimated with Eq. App. 3-6:
FBG = 2σ3 - PPG
= 2 x 0.643 - 0.465 [ = 2 x 14.7 - 10.5]
= 0.822 psi/ft [ = 18.9 kPa/m]
The Formation Breakdown Gradient (FBG) for a deviated well can be estimated with Eq. App. 3-8:
FBG = 2σ3 - (σ1- σ3) x sin2 θz - PPG
= 2 x 0.643 - (1.0 - 0.643) sin2θz - 0.465 psi/ft [= 2 x 14.7 - (23.0 - 14.7) sin²θz - 10.5 kPa/m]
Substitution of different values for the hole angle θ leads to the values of formation breakdown gradient FBG, given in the table below:
It can be seen that with inclinations above 45°, the FBG drops to below the FCG. For these wells a fracture is initiated at the wellbore if the pressure exceeds the FBP, but is not propagated away from the wellbore provided the pressure remains below the minimum in-situ stress. For wells with inclinations above 45°, it is recommended not to exceed the FCP.
4.9.2 Appraisal well - example calculation
In this example it is planned to set casing in a moderately overpressured share section. From two previous wells, the pore pressure gradient in the shale is estimated to be 0.55 psi/ft [12.5 kPa/m].
Leak-off tests in these wells gave the following values of LOG. Hole deviation in the third well is Planned to be 45°. What are the estimated FCG and FBG at the casing shoe?
Well A: LOG = 0.90 psi/ft [20.5 kPa/m] (vertical hole) Well B: LOG = 0 85 psi/ft [19.0 kPa/m] (30° deviation)
We assume that Leak-off can be seen as an indication of impending formation breakdown, and that the FBG can be closely approximated by these values. We assume a normal overburden gradient of:
σ
1 = 1.00 psi/ft [23.0 kPa/m] Using Eq. App. 3-6 and Eq. App. 3-8 we can deriveσ
3: vertical well : 0.90 = 2σ
3- 0.55[ 20.5 = 2
σ
3- 12.5]deviated well : 0.85 = 2
σ
3- ( 1.00 -σ
3) sin² 30 - 0.55 [19.0 = 2σ
3- (23.0 -σ
3) sin² 30 - 12.5]it follows :
vertical well :
σ
3 = 0.725 psi/ft [σ
3 = 16.50 kPa/m]deviated well :
σ
3 = 0.733 psi/ft [σ
3= 16.56 kPa/m]and therefore :
0.725 ≤ FCG ≤ 0.733 psi/ft [16.50 ≤ FCG ≤ 16.56 kPa/m]
Substituting the values for
σ
3 back into Eq. App.3-8 for a 45° well gives the following range for the Fracture Breakdown Gradient:0.763 ≤ FBG ≤ 0.783 psi/ft [17.3 ≤ FBG ≤ 17.4 kPa/m]
For setting depth purposes, the lower value should be used for burst calculations, the higher value should be used.
4.9.3 Development well - example calculation
In this example a series of five production wells have been drilled from an off-shore platform.
Intermediate casing has been set in a hard shale. The pore pressure gradient in the first sand below the casing shoe has been determined with RFTs and is 0.600 psi/ft, [13.5 kPa/m]. From density logs the overburden is estimated to be 0.995 psi/ft, [22.5 kPa/m]. Leak-off tests have been carried out on each well in the first sand below the casing shoe, with the following results.
Four more wells at deviations up to 50° will be drilled from the same platform. What will be the formation strength at these angles?
We assume again that the Leak-off pressures give a good estimate of the FBG. Plotting the leak-off test results as in Figure App. 5-1 shows a fairly smooth trend and interpolation for casing shoe strengths in casing design would seem acceptable. Data of this nature can also be used to estimate the in-situ stresses, allowing extrapolation of the data with reasonable confidence.
The leak-off pressures lie on a fairly smooth curve, which indicates that the FBG is independent of hole azimuth. The simplification that σ2 = σ3 appears to be justified. If we substitute the values of the FBG in Eq. App. 3-8, we can estimate the minimum in-situ stress for each of the wells. In the table above we can see that the variation in the minimum in-situ stress is not too large. We therefore assume that we can take the average of the five measurements to make an estimate of the actual minimum in-situ stress. With Eq. App. 3-8 we can make an estimate of the FBG for the remaining wells e.g. at 45°
FBG = 2
σ
3 - (σ
1-σ
3) - sin²θz - PPG= 2 x 0.695 - (0.995 - 0.695) sin²θz - 0.600psi/ft [= 2 x 15.75 - (22.50 - 15.75) sin²θz - 13.5 kPa/m]
Note however, that the FCG in this case is
σ
3 = 0.695 psi/ft, [15.75 kpa/m]. This value may be used as the lower limit of the casing shoe strength for kick control purposes. The maximum mud gradient in circulation should also be checked against FCG.FIGURE APP. 5-1 : INTERPRETATION OF LEAK-OFF TEST DATA
5.0 Introduction
Once the casing scheme has been selected as described in Chapter D, the casing designer must design the individual strings, i.e. determine the wall thickness and material (grade) each one should be given to ensure that the string can withstand the loads that occur during drilling, installation and service (operation). The fundamental design criterion used here is that, for each load case considered,
L ≤ DF Cc,w,f
where L is the load for the load case in question, Cc,w,f is the load-hearing capacity of the proposed casing corrected for the effects of corrosion, wear and fatigue, and DF is the design factor to be applied to take strength and load variations into account.
The load cases to be taken into consideration in casing design are reviewed in Chapter F, while expressions for load determination are presented in Chapter G. Determination of the load-bearing capacity is considered in Chapter H, and the design factors currently recommended for use within the Group are reviewed in Chapter K. The influence of corrosion, wear and fatigue on load-bearing capacity is the subject of Chapter I.
Chapter J deals with the probability of buckling in the casing string and ways of preventing it, while Chapter L discusses ways of ensuring that the connections used in the casing string do not compromise its integrity. Appendices 6 to 9 present theories and definitions, and the derivation of a number of fundamental equations, used in casing design.
The design methods presented in Chapters F to K are illustrated with the aid of frequent short examples in the text, and a full-length example in Chapter M. In line with SIPM policy to support the use of SI units, all examples are in both field units and SI units.
A further important issue is the distinction between uniaxial and triaxial design. When the previous Casing Design Manual was published, uniaxial casing design methods were still used almost exclusively. As discussed in Chapter A, uniaxial design consists in comparing a uniaxial load (such as a pressure, an axial force or a torque) with a uniaxial load-bearing capacity.
Triaxial design methods compare the combined effect of radial, tangential and axial stresses in the casing wall with the material yield strength and represent a more realistic assessment of the ability of the casing to withstand a given load. The stresses can be analysed by using a combination of Hooke's law, the Lamé equations and the Von Mises yield criterion. However, triaxial casing design involves many more calculations than uniaxial design, and is only practical with the aid of suitable computer programs. Now that such programs are commercially available, SIPM recommends the use of triaxial casing design methods especially for the analysis of service loads. A casing design and analysis software package for use with in the Group will be implemented. The contents of the following chapters will support a manual verification of the output generated by this software.
6.0 Load cases