Summary

This paper summarizes the theory of using a practically oriented simulator to assess the mechanical stability of a wellbore in a triaxial, linearly elastic stress field. The model can be used to determine the range of mechanically stable well inclinations in a given formation and to produce mud-weight programs tailored to efficient and safe drilling, even in difficult conditions. In the Nelson discovery in Block 22/11 of the North Sea, the model was used to evaluate mechanical instability experienced during drilling of deviated appraisal wells through overpressured Oligocene shale. Simulation results showed that, within a range of drilling-mud densities, wells of any orientation can be drilled through the shale. However, practical considerations of formation heterogeneity, swab and surge pressures, and possible chemical interaction dictate that inclined wells beyond about 65° should not be attempted until more field data are acquired to enhance confidence in the use of the model in Block 22/11.

Introduction

Wellbore stability has always been fundamentally important in oil and gas recovery. Wellbore stability recently has become an area of intense study because of the need to drill highly inclined and horizontal wells. This need, which stems mainly from economic considerations (improved efficiency, reduced field development costs, development of marginal fields, etc.), has been encouraged by tremendous improvements in deviated-drilling technology. Assessments to date have shown that horizontal wells can increase production by as much as 300% compared with corresponding vertical wells, and increases in the ultimate hydrocarbon recovery are suggested.1,2

Wellbore instabilities are induced mechanically or chemically. Chemical problems arise from the interaction between the wellbore fluid and the formation and are beyond the scope of this paper. The principal mechanical problems are breakouts (or cave-ins), which result from insufficient fluid pressure in the wellbore, and tensile fracturing, which results from excessive wellbore fluid pressure. The threshold mud pressures for the onset of these two mechanisms depend on the in-situ effective stresses, the response of the formation material to a triaxial, stress field, and the field conditions.

This paper summarizes a model for assessing the mechanical stability of wells that is based on classic rock-mechanics analysis and discusses its application to the Nelson field, Block 22/11. The model consists of a 3D elastic analysis of the effective in-situ stresses around a borehole in an isotropic formation, combined with the Hoek and Brown3 triaxial failure criterion. The well-established 3D elastic analysis has been incorporated in many other models.4,5 This model is unique because the failure criteria are derived from, or constrained by using, field data.

Theoretical Considerations

The mechanical stability of a wellbore can be quantified adequately with knowledge of the in-situ stress field and the material properties of the formation. The in-situ stresses in the formation are totally described by the three principal stresses, and the usual assumption made in geotechnical engineering is that these stresses are in the vertical and horizontal directions. It is also assumed that the vertical principal stress, sV, increases with depth and can be computed as the weight of the overlying vertical column of material. These assumptions, particularly true in areas of little or no tectonic activity and low topographic relief, have been validated by a collation of stress data from various countries.6

The minimum horizontal principal stress, sHmin is routinely determined in typical oilfield leakoff tests and fracturing operations. Experience has shown that a wide variability in the interpretation of leakoff test data exists, so caution must be exercised in the use of sHmin values derived in this manner.

Owing to the uncertainties associated with the determination of the maximum horizontal principal stress, sHmax very few published values exist.7 The usual method for determining sHmax involves the use of hydrofracture stress-measurement theory8,9 and depends on the knowledge of sHmin and formation pore pressure, pp. The theory relates formation breakdown (fracturing) pressure, pc, and the uniaxial tensile strength, st, of the formation by Equation 1

where K, the poroelastic constant, has the approximate range 1 K 2, depending on formation permeability and compressibility.

K = 2 is applicable to permeable formations where pc penetrates the pore spaces of the surrounding formation, and K=1 (very low permeability) recognizes the presence of pp in the surrounding pore space.

When tests are performed during or soon after drilling, it can be, argued that K=1 is applicable because the formation of mudcake virtually precludes permeation of wellbore fluid into the formation. Hence, Eq. 1 reduces to Equation 2

For any wellbore pressure, pb,

where pbc. Thus, the true value of sHmax is approached as pb increases, and the expression enables a least upper bound to be established for sHmax using the drilling-mud weights and wellbore pressures during leakoff and formation-integrity tests. The lower bound for sHmax is given by the sHmin trend with depth.

The direction of sHmax is determined either from the fracture orientation at the wellbore after a fracturing operation1 or from analysis of wellbore breakouts.11 Seismological records in the area also provide estimates of stress direction.

Induced Stresses Around a Wellbore.

Given the in-situ stress magnitudes and direction, the formation properties, and the orientation of a wellbore, the induced stress field around the wellbore can be theoretically calculated under assumptions of linear elasticity and isotropic formation. Furthermore, knowledge of the in-situ fluid pressure allows the effective stresses around the wellbore to be derived. The equations are well known and presented elsewhere.4,5,12

Tensile Failure.

The well-known minimum-principal-stress failure criterion is adopted for tensile failure.5,10 Failure is assumed to occur at the borehole wall when the local minimum principal stress in the borehole plane is reduced sufficiently to overcome the rock tensile strength.

Induced Stresses Around a Wellbore.

Given the in-situ stress magnitudes and direction, the formation properties, and the orientation of a wellbore, the induced stress field around the wellbore can be theoretically calculated under assumptions of linear elasticity and isotropic formation. Furthermore, knowledge of the in-situ fluid pressure allows the effective stresses around the wellbore to be derived. The equations are well known and presented elsewhere.4,5,12

Tensile Failure.

The well-known minimum-principal-stress failure criterion is adopted for tensile failure.5,10 Failure is assumed to occur at the borehole wall when the local minimum principal stress in the borehole plane is reduced sufficiently to overcome the rock tensile strength.

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