Abstract:
A borehole technique for in-situ determination of principal stresses operating in a plane normal to the borehole includes using a downhole jack to independently initiate three spaced apart fractures in a subterranean formation, measuring the breakdown pressure required to initiate the fractures and then using the measured breakdown pressures in two-dimensional axial transformation equations to compute the maximum and minimum stresses that are active in the normal plane. The technique is useful while drilling the borehole by lowering a jack having three platens that can be independently activated to bear against the borehole wall along three radii which are offset from each other about the borehole axis. In use each platen is extended in turn to bear against the borehole wall until a fracture is initiated.

Description:
This invention relates generally to measuring a stress condition in a borehole and more particularly to measurements including fracturing of a subterranean formation traversed by the borehole. The invention further relates to a downhole tool for fracturing of the subterranean formation. 
     BACKGROUND OF THE INVENTION 
     Formations in the earth are characterized by stress conditions which vary with depth and whose principal directions are generally vertical and horizontal. In the horizontal plane at any point, the horizontal stress reaches a maximum in one direction and a minimum at right angles to the maximum condition. Information concerning these maximum and minimum horizontal stress conditions is of substantial value in a variety of disciplines such as underground transportation systems, foundations of major structures, cavities for storage of liquids, gases or solids, and in prediction of earthquakes. Further, this information is essential in petroleum exploration and production, e.g. while drilling a well or borehole the information is useful for blowout prevention, in a completed well it is useful for evaluating hydraulic fracture treatment, and also in determining many critically important aspects of reservoir behavior, such as bulk and pore volume compressibility, permeability, direction of fluid flow, and reservoir compaction/surface subsidence. 
     Currently, the technique of hydrofracturing is often used to measure the least principal stress in the plane normal to the borehole axis, i.e., the normal plane. In hydrofracturing, the least principal stress in a normal plane is measured with a borehole injection test. While these injection tests are an accurate means of determining in-situ stresses and can be carried out at great depths, they are expensive, time consuming in that they require interruption of drilling to set borehole packers, and further, these tests are difficult to interpret. 
     In injection tests small volumes of fluid are pumped into small sections of the borehole, which are isolated by inflatable packers, with just enough pressure to create a small fracture. After each fracture of the formation, the pressure decline is measured as fluid leaks off. As long as the fracture is open, this pressure falloff should represent linear flow, and a plot of pressure falloff vs. the square root of time should be a straight line. Once the fracture closes, the pressure falloff is no longer linear and the slope of the pressure falloff vs. time plot will change. The point where this slope change occurs is interpreted to be the in-situ closure stress, which equals the minimum horizontal stress, for that depth. 
     The use of inflatable packers to isolate a test interval in a borehole is not only time consuming but can present another problem as these packers may cause unwanted fracturing of the formation. This unwanted fracturing would mean that the results of the fracturing tests are incorrect. 
     Accordingly, it is an object of this invention to improve fracturing of a selected location in a subterranean formation traversed by a borehole. 
     It is a more specific object of this invention to accomplish formation fracturing through a borehole which is filled with a fluid. 
     It is another more specific object to operate a downhole tool for formation fracturing without interrupting drilling operations. 
     It is yet another object to allow accurate calculation of principal horizontal stresses existing in the formation surrounding a vertical borehole. 
     It is yet another object to allow accurate calculation of principal stresses existing in the plane of the formation normal to an inclined borehole. 
     SUMMARY OF THE INVENTION 
     According to this invention, the foregoing and other objects and advantages are attained by determining in-situ the maximum and minimum principal stresses in a plane normal to a borehole penetrating a subterranean formation. The stress determinations are based on three actual measurements of breakdown pressure applied sequentially to the borehole wall along three radii which are offset from each other about the axis of the borehole at an angle of about 60 degrees. Sufficient pressure is selectively applied to the wall by a downhole jack to initiate three independent fractures in the formation with the fractures spaced apart according to the three offset radii. Standard equations for two-dimensional axial transformation are then applied using the three breakdown pressure measurements to obtain the magnitude and direction of the maximum and minimum principal stresses operating in a plane normal to the borehole axis. 
     In another aspect of this invention there is provided a downhole jack comprising a set of three individually expandable platens which are formed as 180 degree sections of a cylinder, with three of the cylinder sections arranged in a vertical stack to form the downhole tool. The included angle between the midpoint radius of adjacent platens is aligned on the downhole tool to be about 60 degrees. 
     In a preferred embodiment, pressure measurements are made while carrying on drilling operations by disposing a drill collar including the downhole jack and instrumentation for pressure measurement approximate to the drill bit. The drilling fluid pressure (i.e., mud pressure) is increased until it is slightly lower than the fluid pressure required to hydrofracture the borehole. In this pressure condition, an incremental increase in pressure is required to provide a breakdown pressure which will fracture the borehole, and this incremental pressure is supplied by the downhole jack. After the fracture has been created and the breakdown pressure recorded, the fracture is allowed to close. The bottom hole pressure is monitored to determine the pressure at which the induced fracture closes in a manner similar to the closure stress determined in the injection tests described above. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Other features and intended advantages of the present invention will be more readily apparent by reference to the following detailed description in connection with the accompanying drawings, in which: 
     FIG. 1 is a schematic illustration of a wellbore including pressure measuring instruments and the downhole jack for fracturing the formation. 
     FIG. 2 is a cross-sectional illustration of a typical deviated borehole showing subterranean stresses. 
     FIG. 3 is a schematic illustration of one end of the borehole jack according to this invention. 
     FIG. 4 is a schematic illustration of the side of the borehole jack shown in FIG. 3. 
     FIG. 5 is a graphic representation of downhole pressure showing fracturing of the formation according to this invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     This invention is directed to method and apparatus for determining the stress at a desired location in a borehole, and is applicable to vertically drilled boreholes and boreholes inclined at an angle up to about 25° from the vertical. In accordance with this invention the sum of the pressure exerted by a platen plus the pressure of the drill fluid provide a breakdown pressure which is required to fail the borehole wall. The breakdown pressure is directly related to the tangential stresses operating on the borehole wall at the fracture location. The tangential stresses measured at the three fracture locations are used to determine the maximum and minimum principal stresses operating in the normal plane, through the standard equations for two-dimensional axial transformation. 
     FIG. 1 illustrates schematically an apparatus located in a wellbore useful in performing the method of the present invention. A drill string 10 is suspended within borehole 30 in a formation 50. The drill string 10 includes a drill bit 20 attached to the end thereof for penetrating the earth 50 to produce the borehole 30. Disposed within the drill string 10 and preferably approximate the drill bit 20 are a plurality of drill collars 22 including a downhole jack and instrumentation for measuring pressure of the drill fluid, and the pressure exerted on the borehole walls by the platens of the downhole jack. Those skilled in the art are familiar with many drill collars and devices for use in making measurement while drilling (MWD) determinations which are conveniently incorporated within the drill string 10 as one or more drill collars 22. The data obtained by the measuring instruments included within drill collars 22 is conveniently stored for later manipulation within a computer 26 located on the surface. Those skilled in the art will appreciate that the data is transmitted to the surface by any conventional telemetry system for storage and manipulation in the computer 26. 
     FIG. 2 illustrates a section of a typically deviated borehole 40 passing through a plurality of rock formations. The stresses operating in the borehole illustrated at 40 of FIG. 2 include the vertical overburden stress designated as σ ob  at 48 and the minimum horizontal stress for typical rock formations 52, 54, 56, and 58 designated as σ min . The maximum horizontal stress, which as previously stated operates at right angles to the minimum condition, is not illustrated. Those skilled in art familiar with formation stress conditions will recognize the magnitude of the minimum stress for the different formations relative to the overburden 48 such as a low minimum stress for sandy material at 52 and 58 e.g. σ min  =(0.2-0.5)σ ob , and intermediate and high minimum stresses for other rock compositions such as shale and limestone illustrated at 54 and 56 where σ min  =(0.5-0.7)σ ob  for intermediate material, and σ min  ˜σ ob  for a high minimum stress. 
     Referring now to FIG. 3 there is illustrated the downhole jack 62 of the present invention which generally comprises three expandable platens 64, 66 and 68 with corresponding pistons 70, 72 and 74. As illustrated, platen 64 is in an extended position. The pistons are controllably extendable for moving the platens to contact and bear against a borehole wall. The pistons may be operated by hydraulic pressure or electric power which is provided through the drill string 10 as is well known to those skilled in the art. 
     FIG. 3 shows the radial arrangement of the piston 70, 72 and 74 such that each piston is angularly offset from the others about the axis of the jack 62 by an angle of 60 degrees. Thus, the initiation of each wellbore fracture is carried out sequentially in a different direction corresponding to the different radial spacings of the pistons. A previous fracture is allowed to close before initiating a subsequent fracture so that each measured breakdown pressure is independent of the others. 
     FIG. 4 better illustrates the stacking relationship of the platens such that each platen is vertically offset from the others by a convenient amount. The length of the jack 62 is not critical as long as the length does not exceed the thickness of the formation being fractured. Generally a length for the jack 62 of about two to about five feet is satisfactory. 
     Hydraulic fracturing of subterranean formations is well known. The present invention relates to determining the in-situ stress conditions at a desired depth in a borehole and includes inducing three independent fractures of the subterranean formation. The method of the present invention is best illustrated with reference to FIG. 5, which shows three breakdown pressures at 80, 82 and 84 required to fracture a formation in different radial directions at a desired depth in a borehole. More specifically the method includes positioning the downhole jack, which is part of the drill string, at a selected borehole depth such that the jack is disposed at the depth of the formation to be measured and the orientation of the platens is noted. Measurement of the pressure exerted on the borehole wall by the drilling fluid is recorded as illustrated by the solid portion 86 of the plot shown in FIG. 5. Next the first platen is extended to contact and bear against the borehole wall with pressure exerted on the wall gradually increased until a fracture is initiated. Pressure on the wall exerted by the first platen is illustrated by the dash line 88 in FIG. 5. Once the first fracture is initiated, as indicated at 80 in FIG. 5 by a sudden reduction in pressure, the platen is retracted and the borehole pressure is allowed to leak off as illustrated by the portion of the curve 90. The change in slope of the curve illustrated at 92 indicates closure of the fracture created by the first platen. The above procedure is repeated for the second and third platens to obtain breakdown pressures as shown at 82 and 84. 
     In accordance with this invention the downhole tool is used to obtain quantitative values for σ max  and σ min  which are defined as the maximum and minimum normal plane stresses that operate in a plane perpendicular to a borehole axis. 
     In vertical and near vertical boreholes the maximum and minimum normal plane stresses are the maximum and minimum horizontal principal stresses operating in rock formation surrounding the borehole. The downhole tool measures three radial stresses required to initiate three independent fractures oriented 60 degrees apart relative to the axis of the borehole. The three stresses, hereinafter referred to as S i , S j , and S k , are used to calculate R max  and R min  which are the maximum and minimum values for radial stresses necessary to fracture the borehole wall. Versions of the &#34;Kirsch&#34; equation for stresses surrounding a cylindrical hole in stressed solids are used to calculate σ max  and σ min , the maximum and minimum normal plane stresses that operate in a plane that is normal to the borehole axis. For more details concerning the &#34;Kirsch&#34; equation see the text: Roegiers, Jean-Claude (1989), &#34;Elements of Rock Mechanics&#34;, p. 2-1 through p. 2-22 found in Economides, M. J. and Nolte, K. G., Editors, &#34;Reservoir Stimulation&#34;, Second Edition, Prentice Hall, which is incorporated herein by reference. 
     In accordance with the present invention the maximum and minimum principle horizontal stresses operating in a subterranean formation are determined by first ascertaining the maximum and minimum values for radial stresses required to initiate a fracture in the subterranean formation using the equations: ##EQU1## where: S=stress applied by the downhole jack, psi 
     i, j, k=indexes for direction of stress relative to some specified direction or azimuth, and 
     S i  &gt;S j  &gt;S k . 
     The maximum value for radial stress caused by the downhole jack R&#39; max  is given by R&#39; max  =A+B, and likewise 
     R&#39; min  =A-B where the &#34;R&#34; refers to radial stress and A and B are defined above. 
     The computed maximum and minimum radial stresses, R max  and R min  respectively, are obtained by adding the borehole pressure (bp) to the maximum and minimum radial stress as follows: 
     R max  =R&#39; max  +bp 
     R min  =R&#39; min  +bp 
     where 
     bp=borehole pressure i.e., drilling fluid (mud) pressure. 
     The orientation of R max  is given by the angle theta (θ) in degrees which is drawn anticlockwise from the i direction. ##EQU2## 
     Finally the maximum and minimum principal stresses σ max  and σ min  operating the normal plane are computed using the maximum and minimum radial stresses in the following &#34;Kirsch&#34; equations that relate radial and tangential stresses surrounding a borehole to the principal stresses operating in the normal plane. 
     σ max  =3R max  /8+R min  /8+P p  /2 
     σ min  = R min  +σ max  +P p  !/3 
     where: 
     P p  =formation pore pressure. 
     The downhole jack of this invention is designed to be applicable to a wide variety of subterranean materials ranging from sandy compositions to hard rock. Accordingly it should be noted that the jack may be used repeatedly at different depths within a borehole to determine stress conditions surrounding the borehole at different depths. 
     In this disclosure there is shown and described only the preferred embodiment of this invention which is applicable to oil production or exploration. It is to be understood that the invention is applicable to various other combinations and environments, accordingly various changes or modifications possible by those skilled in the art are within the scope of the inventive concept as expressed herein.