If the conductor casing is not entirely cemented, e.g. for an offshore platform well, the uncemented portion will initially compress elastically. Any such compression will transfer some of the total load to the inner strings.
For a mudline suspension system, the casing strings are hung off at seabed. Only the surface to seabed tie-back section of each casing, together with the wellhead load and the tubing load, is supported by the conductor casing. This assumes a correctly designed tie-back system where overpull does not remove load from the mudline suspension system.
The distribution of applied loads between the conductor string and any inner strings must be known in order to check the ability of each string, but particularly the conductor string, to withstand those loads. The resulting wellhead movement must be known to ensure sufficient clearance when designing the wellhead area of the platform [15].
The load distribution between the strings can be calculated by considering the behaviour of the casings already in place as a set of parallel springs. Below, firstly, the platform wellhead behaviour is studied followed by the tie-back system from a mud line casing suspension.
a) Casing hangers at surface
Firstly, consider the behaviour of the conductor casing alone. See Figure G-21.
The incremental strain in the conductor string, resulting from an applied end load, W1, clue to the buoyant weight of the next string, is given by;
∆ε
01 =FIGURE G-21 : INCREMENTAL LOADING MODELLED AS COMBINATION OF PARALLEL SPRINGS
From Hooke's Law (Eq. App. 6-5);
where Aso is the conductor casing cross-sectional area.
Next consider the behaviour of the conductor casing together with the first inner string, as another string is landed, giving an additional load W2.
The additional incremental strain in the conductor string resulting from the additional applied end load W2 is given by
where ∆Z2 is the additional wellhead movement due to W2. The incremental strain in the first inner string is similarly given by
∆ε
12 =c1 2
Z
∆Z
where Zc1 is the uncemented length of that string.
From Hooke's Law again, for force equilibrium
Rearranging gives ;
( For the general case, therefore ;
where;
Wn = applied load due to next string or wellhead /BOP installation
∆
Zn = wellhead movement resulting from WnAsn = cross-sectional area of the nth string Zcn = top of cement for the nth string
The total wellhead movement will be given by;
∆
ΖΤΟΤ =∆
Ζ1+∆
Ζ2+∆
Ζn (G-50)The change in axial force generated in the ith string as a result of its final displacement is given by
where ∆Zi(TOT) is the total movement of that string. This change in force should be added to the initial force within that string.
From the above expression, it can be seen that the axial force generated in each string is proportional to the final vertical displacement and inversely proportional to the uncemented length. The displacement of the conductor string will be larger than any other string, the uncemented length shorter than for any other string and the cross-sectional area larger than for any string. Therefore, the compressive loads generated in the conductor casing will be considerably higher than in the other casings.
This method of predicting wellhead movement has been verified by comparison with actual data and found to be highly accurate. For deviated wells, having inclinations in the range 20-45 degrees, use of true vertical depths in the calculations again gave highly accurate results [15].
There are several general points that can be drawn from the above analysis. Firstly, the vertical movement observed at the wellhead is inversely proportional to the combined casing stiffnesses.
where the stiffness, K, of the ith string is given by;
Ki =
ci si
Z
EA (G-52)
The stiffness of a conductor casing is generally much larger than that of the other strings, as illustrated below:
As a result, it will be the stiffness of the conductor casing that dominates the response to the various loads applied. Since this stiffness varies linearly with the depth of the top of cement, wellhead movement is almost a linear function of the uncemented length of the conductor casing.
By monitoring the wellhead movement due to the landing of subsequent casings, the above calculations can be used to check the actual location of the top of cement. Remedial cementing action can then be taken, if necessary, before the later strings are landed.
Example
Consider the following example, which illustrates the step-wise procedure that should be adopted. The results of the calculations are summarised in Figure G-22.
FIGURE G-22 : RESULTS OF TYPICAL CALCULATION OF AXIAL WELLHEAD MOVEMENT
Consider a well where the following casing scheme will be used,
Assume that the 185/8 inch conductor casing has just been cemented in place and the support ring to enable the casing to hang from the marine conductor during cementing has been removed. The following sequence of operations will occur:
a) Installation of 21/ ¼ inch BOP
Wellhead movement due to this operation ∆ZBOP1 is (from Eq. G-49);
b) Landing 13 3/8 inch casing
Wellhead movement due to this operation
∆
Z1 is (from Eq. G-49);∆
Z1 =c) Removal of 21 1/4 inch BOP and installation of 13 3/8 inch BOP Wellhead movement due to this operation
∆
ZBOP2 is (from Eq. G-49);where;
d) Landing 9 5/8 inch casing
Wellhead movement due to this operation ∆Z3 is (from Eq. G-49)
where ;
W2 = 242,134 Ib (1,077,012 N)
Aso = 24.8 in² (0.0160 m²) Zco = 600 ft (183 m) As1 = 15.51 in² (0.0100 m²) Zc1 = 1500 ft(457 m) Thus, in field units;
In SI units
e) Landing production tubing
Wellhead movement due to this operation
∆
Z3 is (from Eq. G-49);where;
W3 = 179,832 lb (806,422 N)
Aso = 24.8 in² (0.0160 m²) Zco = 600 ft (183 m) As1 = 15.51 in² (0.0100 m²) Zc1 = 1500 ft (45 7 m) As2 = ll.45 in² (0.0074 m²) Zc2 = 6000 ft (1829 m) Thus, in field units
In SI units ;
Assuming that the Xmas tree will not be heavier than the 13 5/8 in BOP, this will be the maximum loading and the maximum displacement.
The total displacement is given by the sum of
∆
ZBOP1 = - 0.081 ft ( - 0.024 m )∆
Z1 = - 0.140 ft ( - 0.042 m )∆
ZBOP2 = +0.019 ft ( + 0.006 m)∆
Z2 = -0.156 ft ( - 0.047 m )∆
Z3 = -0.11 ft ( - 0.034 m )Thus ∆Ztot = -0.469 ft (-0.141 m)
The additional axial forces,
∆
Fa, generated in each of the casing strings is calculated using Eq. G-51 as follows;It can therefore be seen that in this instance 581,560 Ib (2,592,525 N) of compressional load is generated in the conductor casing equivalent to 87% of the total applied load (BOPs, casing and tubing). Around 12% of the load is carried by the 133/8 in casing, and the remaining 1% by the 95/8 in casing. Although there is a reduction in the tension, the total tension at the surface in the latter two strings stays positive.
b) Casing hangers at seabed
Firstly, consider the behaviour of the conductor casing alone. The incremental strain resulting from an applied load W1, due to the weight of the first tie-back string, is given by;
∆ε
01 =∆
Z1 is the wellhead movement due to W1 Zch is the distance from surface wellhead to casing hangers at mudline suspension system.From Hooke's law (Eq. App. 6-5);
∆ε
01 =where Aso is the conductor casing cross-sectional area.
Next consider the behaviour of the conductor casing together with the first tie-back string, as another tie-back string is landed, giving an additional load W2.
The additional incremental strain in the conductor, resulting from the applied end load W2 is given by;
where
∆
Z2 is the wellhead movement due to W2.The incremental strain in the first inner string, is similarly given by;
∆ε
12 =ch 2
Z
∆ Z
From Hooke's Law again, for force equilibrium,
Rearranging gives;
For the general case, therefore
∆
Zn =Wn = applied load due to next (tie-back) string or wellhead/BOP installation Zch = distance from wellhead to casing angers at mudline suspension system Asn = cross-sectional area of the nth string
∆Zn = wellhead movement resulting from Wn
The total wellhead movement will be given by
∆
ZTOT =∆
Z1+∆
Z2 + ...∆
Zn (G-53)The additional axial force generated in the ith string as a result of its final displacement is given by;
where
∆
Zi(TOT) is the total movement of that string.This additional force should be added to the initial force within the string.