Bernt Sigve Aadnoy

Inversion technique to determine the in-situ stress field from fracturing data☆

Abstract Typically one assumes that the two horizontal in-situ stress are equal in borehole stability studies. This simplification has been necessary due to the lack of information. The new method presented here distinguishes between the in-situ stresses and estimates the magnitude and the direction of each of the two horizontal in-situ stresses. The input data used are the leak-off fracturing information. The new method uses stress transformation equations to take advantage of the directional characteristics of off-shore boreholes. By including the hole inclination and the azimuth, one can solve the two unequal horizontal in-situ stresses. The model results in finding the inverse of an overdetermined system of equations. A field study demonstrates the method.

Design of oil wells using analytical friction models

Abstract Recent wells have been drilled to more than 10 km from the platform, and companies are planning to extend these beyond 12 km. Well friction is one of the most important limiting factors in this process. Torque and drag prognoses are developed today on in-house simulators. Although this is a good tool for planning, improvements are made on a trial and error basis, and these simulators have limited availability. To provide more insight into the frictional aspect, a larger study was undertaken. Explicit analytical equations are derived to model drill string tension for hoisting or lowering of the drill string. The equations are developed for straight sections, build-up sections, drop-off sections and side bends. Both constant curvature models and a new modified catenary model are derived. The new catenary model is developed for arbitrary entry and exit inclinations. Equations to determine well friction in three-dimensional well profiles are also given. In addition, expressions for torque and drag are developed based on the tension equations. Equations for combined motion and drilling with a motor are also given. Using these equations, the total friction in a well is derived from the sum of the contributions from each hole section. Examples are provided to demonstrate the application for ordinary production wells, catenary wells, long-reach wells and horizontal wells. Optimization criteria are developed to design the well for minimum friction.

In-situ stress directions from borehole fracture traces

Abstract Logging tools are recently introduced which determine fracture traces on the borehole wall. ∗ These are valuable tools in geological reservoir analysis. Information about induced fracture traces from borehole fracturing can be used to estimate the directions of the in-situ stresses. This paper derives a model for that purpose. A few cases which can illustrate certain applications are also included. It is of particular interest to determine whether the induced fracture extends axially at an angle relative to the borehole axis. The main result of the model is to determine whether the principal in-situ stresses are oriented in a vertical plane, an horizontal plane, or at intermediate directions, as often expected in deeper geological structures.

In situ stress state from inversion of fracturing data from oil wells and borehole image logs

Abstract An analytical method is developed that shows that the in situ stress state is often not vertical/horizontal with depth, but often has a strike slip as expected from geological processes. The paper presents a theory for determining the in situ stress state from multiple fracturing data and induced fractures from image logs. A solution can be obtained with a minimum of two data sets. However, using an inversion technique, a solution can be obtained with any number of data sets, as the solution is over determined. The magnitude of the stresses is mainly determined from the fracturing data. Fracture information from image logs is mainly used to determine the geographic direction of the principal in situ stresses and also deviations from the horizontal/vertical direction.

Stresses around horizontal boreholes drilled in sedimentary rocks

Abstract The main purpose of this paper is to present the anisotropic stress equations that can used to analyze fracturing or collapse problems for horizontal boreholes, and to show how anisotropy in the elastic properties of the rock affects the stress field around a horizontal borehole. This paper gives the complete equations to determine stresses around boreholes in transverse isotropic, but linear elastic sedimentary rocks. The equations to determine the effective stresses are also given. It is shown that the stress fields and their direction is affected by the anisotropic material properties of the rock. Also shown is the deformation pattern of the borehole, which for anisotropic rocks is elliptical rather than cylindrical. Finally, a hydraulic fracturing example is given to show the effect of elastic anisotropy on the fracturing pressure.

A 3D Analytical Model for Wellbore Friction

This paper presents a new friction model for application in petroleum wells. Although very simple, it applies for all wellbore shapes such as straight sections, drop-off bends, buildup bends, side bends or a combination of these. The drillstring is modelled as a soft string. In high tension the string weight is negligible as compared to the tension. This leads to simplified equations where the friction caused by the weight is negligible. For this case the friction in a bend is formulated in terms of the 3D dogleg. The same model therefore applies for 2D and 3D wellbores. The entire well can be modelled by two sets of equations, one for straight wellbore sections and one for curved wellbores. The latter is based on the absolute directional change, or the dogleg of the wellbore. Three worked examples are given in the paper: a 2D well, a 3D well and combined hoisting and rotation in the 3D well. One main purpose of this paper is to provide a simple explicit tool to model and to study friction throughout the well by separating gravitational and tensional friction effects.

Effects of reservoir depletion on borehole stability

Abstract A simple model has been derived to estimate changes in critical borehole collapse and fracturing pressures when the pore pressure is depleted in the reservoir. The model estimates the increased rock matrix stress when the pore fluid is withdrawn. This change in matrix stress is furthermore used to estimate changes in borehole failure resistance.

Method for fracture-gradient prediction for vertical and inclined boreholes

A new method for the prediction of fracture gradients in deeper wells has been developed. The method is based on the principles of mechanics but uses a correlation method in the application of field data. The new, improved method (1) gives both leakoff and lost-circulation pressures; (2) works for vertical and inclined boreholes; and (3) identifies lithological effects. The results is given as a simple equation where only well depth, pore pressure, borehole angle, and lithology are needed to predict the fracture pressure. Because borehole inclination is included, the method can be used during both production and vertical-well drilling. The method was applied in a field study offshore Norway. The results show a remarkably good correlation with field observations.

Borehole stability of multilateral junctions

Abstract The oil industry has increased its emphasis on multilateral technology to improve production. This new technology, however, introduces a number of challenges. Junction failure is critical and has resulted in well failures because borehole stability must be maintained to drill and complete these wells successfully. Analytical models that take the junction geometry into account to assess the stability of lateral wellbore branches are presented. The junction is classified into the three following geometries: circular, oval and two adjacent boreholes. A principal conclusion is that any geometry that deviates from a circle leads to less stability. The stability window at the junction itself is smaller than the borehole above or below. Both fracturing and collapse at the multilateral junction are analyzed. A field case is discussed to demonstrate the application of the models.

Friction Analysis for Long-Reach Wells

Presently wells are drilled in the North Sea approaching a horizontal reach of 8 km. Plans for the near future is to extend these towards and beyond 12 km. Well friction is one of the most important limiting factors in this process. Torque and drag prognosis are today developed on in-house simulators. Although a good tool for planning, improvements are made on an trial and error basis, and, these simulators have limited availability. To provide more insight into the frictional aspect, a larger study was undertaken. Explicit analytical equations are derived to model drill string tension for hoisting or lowering of the drill string. The equations are developed for straight sections, build-up sections, drop-off sections and side bends. Both constant curvature models and a new modified catenary model are derived. The new catenary model is developed for arbitrary entry and exit inclinations. Equations to determine well friction in fully 3-dimensional well profiles are also given. Furthermore, based on the tension equations, expressions for torque and drag are developed. Equations for combined motion and drilling with motor are also given. Using these equations, the total friction in a well is given by the sum of the contributions from each hole section. A field study offshore Norway is included in the paper. Using the equations derived in the paper, the well path is chosen to minimize the torque on the rig, which is the limiting factor. The paper also summarize a number of guidelines for extended-reach well design, and shows the design of an ultra-reach well of more than 12 km reach.