METHOD OF ESTIMATING THE REGION OF DAMAGE DUE TO COLLAPSE IN THE WALL OF A BOREHOLE DURING THE DRILLING OPERATION

Abstract

The present invention relates to a method of estimating the region of damage due to collapse in the wall of a well during the drilling operation, normally using drilling fluid, where said well can, for example, be intended either for the injection or else for the production of a gas or oil reservoir. Other uses can be found in mining and in civil engineering work. This method is characterized by a set of analytical steps that allow establishing, for example, optimal drilling parameters so as to allow the fastest possible drilling speed that is also safe enough to allow is charging the collapse material without jamming the drilling tool. This method likewise allows assessing both the width and depth of damage in the wall of the well.

Claims

1. A method of estimating a region of damage due to collapse in a wall of a well during a drilling operation, and comprising the steps of: a) generating a geomechanical model of a domain comprising a path of the well to be drilled at least incorporating rock data and mechanical properties of said rock for a pre-specified in situ stress field; b) generating a fluid flow model of the same domain at least incorporating drilling fluid data, where said fluid flow model models the rock as a porous medium and comprises a pore pressure in said porous medium; c) establishing a vertical height z at which it is located a circular section S of the well in which the region of damage due to collapse in the wall of said well is to be estimated, section S being transverse to the drilling path of the well, and establishing an orientation of the normal of said section S; d) determining a pressure of the drilling fluid, should there be any, pore pressure p.sub.p, maximum stress .sub.max, minimum stress .sub.min and the mechanical properties of the rock in the section based on the geomechanical model; e) determining a stress state () of the rock on a periphery of section S of the borehole at least according to the data from the preceding step, where: i. is the scalar value of the equivalent stress, ii. is the angle with respect to a system of axes located in section S of the drilling, centered in the center of said section S and with an orientation on the plane containing section S, such that (=0)=.sub.min and (=/2)=.sub.max; f) determining a collapse angle .sub.br as the angle centered in =/2 and covering an arc of the periphery of section S where the stress () is greater than an allow able stress of the rock; g) defining a family of ellipses of eccentricity e contained on the plane of section S, wherein eccentricity e is defined as a ratio of the semi-minor side to a semi-major side of the ellipse, such that: i. an ellipse corresponding to the value of eccentricity e=1 is a circumference established by the circular section S of the well; and ii. an intersection between another ellipse and said circular section S of the well is established at least at points /2.sub.br/2 and /2.sub.br/2 as well as at their symmetrical points /2+.sub.br/2 and /2.sub.br/2, respectively; h) defining a factor of safety
F=.sub.ext/.sub.res where .sub.ext is the sum of external forces on the rock at a given point of the rock, depending at least on in situ stresses, on the density () of the drilling fluid should there be any, on the elastic properties of the rock and on the pore pressure p.sub.p; and where .sub.res is a sum of resistance forces of the rock at the same point, depending on a stress tensor, on resistance properties of the rock and on an angle of internal friction of the rock; i) determining a function F(,e) as a factor of safety F evaluated at a point of the ellipse defined by the eccentricity e for a value of the angle , j) establishing a cut-off threshold value .sub.0</2; k) determining the value of eccentricity e.sub.0 closest to one verifying F(.sub.0,e.sub.0)=f.sub.0, where f.sub.0 is a pre-established reference value close to one, l) establishing the intersection region between the ellipse of eccentricity e.sub.0 and a circumference of section S of the well as the region of damage, according to section S of the well and at vertical height z.

2. The method according to claim 1, wherein an estimation of a depth of damage b.sub.d in the wall is calculated as a difference between the semi-major side b of the ellipse of eccentricity e.sub.0 and a radius of the circumference of section S of the well.

3. The method according to claim 1, wherein an estimation of a width angle of damage in the wall is calculated as an angle covering the intersection points between the ellipse of eccentricity e.sub.0 and the circumference of the section of the well.

4. A well-drilling method using a drilling bit for drilling a well of a well-drilling diameter D at a drilling speed (v) and, injecting a drilling fluid with a density () and flow rate (Q) during the drilling process, for the injection or production of a gas or oil reservoir, comprising the steps of: 1. carrying out steps a) and b) of claim 1; 2. establishing the well-drilling diameter D and the bore path through the geomechanical model and the fluid flow model of the reservoir; 3. establishing a discretization t.sub.i=1 . . . N of a coordinate (t) along the drilling path; 4. determining, for each t.sub.i, a transverse section S.sub.i of diameter D, and in said section S.sub.i, for a plurality of values of density of the drilling fluid .sub.j.sup.l,j=1 . . . M, determining in section S.sub.i the region R.sub.j.sup.i(.sub.j.sup.l,S.sub.i) of damage according to claim 1, and the value of the area A.sub.j.sup.i(.sub.j.sup.l,S.sub.i)=R.sub.j.sup.i(.sub.j.sup.l,S.sub.i) of said region R.sub.j.sup.i(.sub.j.sup.l,S.sub.i); 5. establishing, for each coordinate (t) of the discretization t.sub.i=1 . . . N: a correspondence V.sup.i(.sub.j.sup.l) between the discrete values of density of the drilling fluid .sub.j.sup.l,j=1 . . . M and the value of the area A.sub.j.sup.i(.sub.j.sup.l,S.sub.i) of the region R.sub.j.sup.i(.sub.j.sup.l,S.sub.i), the latter being interpreted as a detachment volume (V) of the wall of the well per unit of drilled length; a combination of drilling speed (v), density () of the injected drilling fluid and flow rate (Q) thereof, such that it establishes a volume of material V.sub.e(v,,Q) to be discharged, material being cut by the bit plus the collapse material V.sup.i(.sub.j.sup.l), less than that determined by the drilling system, so as to allow removing the volume of material from the well without a drilling bit collapsing; 6. drilling the well according to the values of drilling speed (v), density () of the injected drilling fluid and flow rate (Q) thereof for each coordinate of the drilling path.

5. A non-transitory computer program product computer-implementable instructions, which, when executed by a computer, cause the computer to carrying out the method according to claim 1.

Description

DESCRIPTION OF THE DRAWINGS

[0071] The foregoing and other features and advantages of the invention will be more clearly understood based on the following detailed description of a preferred embodiment, provided only by way of illustrative and non-limiting example in reference to the attached drawings.

[0072] FIG. 1 shows a scheme for making a well in an oil reservoir, defined by a wellbore trajectory, where a section S on which the region of damage is to be determined is established at a given point of the path.

[0073] FIG. 2 shows a scheme for making a well in a sectional view, as well as a pair of ellipses with different eccentricity used in the calculation steps according to the invention.

[0074] FIG. 3 shows a graph of stresses on the periphery of a family of ellipses. The family of ellipses is represented by means of a plurality of curves identified with an arrow in which the direction in which the eccentricity increases is shown. The x-axes show the angle in the section taking the point of minimum stress as a reference.

[0075] FIG. 4 shows an image of a vertical segment of the well in which the width of the damage has been measured according to the vertical height. Regions with damage are darker.

[0076] FIG. 5 shows two graphs related to one another. The graph on the left shows a drawing with the factor of safety F according to the eccentricity e with a value of one to consider the factor of equilibrium between the external forces and resistance forces. After having determined the eccentricity, the graph on the right shows the ellipse with said eccentricity determining the transverse area of the damage.

[0077] FIG. 6 partially reproduces FIG. 1 as an embodiment where the determination of damage is performed in a discrete set of the drilling path for subsequently evaluating the collapse volume, and therefore for performing drilling according to the parameters estimated according to an embodiment.

DETAILED DESCRIPTION OF THE INVENTION

[0078] According to the first inventive aspect, the present invention relates to a method of estimating the region of damage due to collapse in the wall of a well during the drilling operation for the injection or production of a gas or oil reservoir.

[0079] FIG. 1 schematically shows the section of a reservoir with oil reserves, where the upper line represents the surface of the reservoir and the volume of the reservoir identified by the lower line (Rs), a well (P) being demarcated therein.

[0080] The well (P) is a borehole having a circular section S extending along a path depicted by a curve. The curve is shown in FIG. 1 beginning at the surface, descending in an almost vertical path, and after increasing its inclination ending in an almost horizontal segment.

[0081] The region of damage in a section S located at a height z is to be calculated along this path. At this height z, the tangent n to the path coincides with the normal to the transverse plane of section where the region of damage is to be determined.

[0082] This same drawing depicts by means of a dashed line the plane transverse to the drilling path of the well at a pre-established point.

[0083] FIG. 2 schematically shows a circumference in a thick line representing the theoretical wall of the borehole in the plane of section S.

[0084] In order to determine the region of damage, a geomechanical model of the reservoir at least incorporating the rock data and the mechanical properties of said rock is generated in a computational system and the in situ stress field is established. The geomechanical model establishes a relationship between the field of acting forces at a given point of the domain and the properties of the material.

[0085] For each case, the forces acting at a point must be determined, such forces including those caused by the fluids which are stored under pressure in porous rocks, or also the pressures due to the drilling fluid injected while drilling the well, should there be any fluid injected.

[0086] Additionally, a fluid flow model of the same reservoir which at least models the porous medium suitable for housing liquid is generated in this example in the computational system. If drilling fluid is used in the borehole, then the fluid flow model must likewise incorporate this fluid and the interaction with the walls of the well. The fluid flow model includes the pore pressure in the porous medium.

[0087] Given that deformations of the porous media give rise to changes in the fluid flow model, and the forces thereof influence the geomechanical model, both models must be coupled to one another.

[0088] It is possible to determine the pore pressure p.sub.p, stress state and mechanical properties of the rock in section S through the geomechanical and fluid flow models. It is also possible in particular to determine the pressure of the borehole fluid should one be used.

[0089] Given the direction normal to the plane of section S, by means of rotation about said normal, it is established a direction where stress is minimum .sub.min and a direction which is perpendicular to the preceding direction, where stress is maximum .sub.max. These directions are those used as the axes of reference for establishing the site where damage occurs and its extent.

[0090] After having established the axes, the stress state in the rock along the curve defined by the circumference corresponding to the wall of the drilling is determined based on the geomechanical model. The value of the equivalent stress is calculated based on the stress state determining the arc of a curve where said equivalent stress is greater than the allowable stress of the rock.

[0091] This arc is centered in /2 due to the way of constructing the axes of reference and the width thereof is the collapse angle .sub.br.

[0092] FIG. 2 shows both axes which are axes that will correspond to the major and minor sides of a family of ellipses. This family of ellipses is parameterized by means of the eccentricity e. For a value of eccentricity equal to 1, the ellipse is the circumference having a radius R corresponding to the circumference representing the wall of the well according to section S. For increasing values of eccentricity e, ellipses having one end of the major side penetrating the rock while the minor side being smaller than the radius of the well R, are obtained. Of the ellipses thus obtained, the part of the ellipse which penetrates the rock and which will be the curve defining the region of damage will be of special interest.

[0093] The points where the collapse angle starts and ends are the points where the intersection between the circumference and any of the ellipses of the parameterized family in e is established.

[0094] The values of 2a and 2b in FIG. 2 identify the length and width of a given ellipse. Two ellipses of eccentricity e.sub.1 and e.sub.0 are also shown.

[0095] The factor of safety is used to determine the ellipse defining the region of damage

F=.sub.ext/.sub.res

where .sub.ext is the sum of external forces on the rock at a given point of the rock, depending at least on the in situ stresses, on the density of the drilling fluid () should there be any, on the elastic properties of the rock and on the pore pressure p.sub.p; and
where .sub.res is the sum of resistance forces of the rock at the same point, depending on the stress tensor, on the strength properties of the rock and on the angle of internal friction of the rock.

[0096] This factor of safety depends on the angle and on the factor of eccentricity where the value of one identifies the equilibrium between the forces and the resistance capacity. Damage is deemed to exist when this equilibrium is broken. Nevertheless, it is possible for a person skilled in the art to select values f.sub.0 other than but close to one as the factor of safety, for example. Valid f.sub.0 values are those comprised in the [0.7, 1.3] range, and more preferably in the [0.8, 1.2] range, and more preferably in the [0.9, 1.1] range and more preferably in the [0.95, 1.05] range.

[0097] FIG. 3 shows a graph of stress according to the angle where for values close to /2, identified in the drawing as close to 90 given that it is expressed in degrees instead of radians, the stress acquires asymptotically high values as eccentricity increases.

[0098] This fact renders useless the approach according to the state of the art for the estimation of damage since in no case would it consider that a safe situation exists.

[0099] With this hypothesis, the area of the end of the ellipse reaches unacceptable values in almost any case which would invalidate this method of determining the region of damage. Nevertheless, it has been found that if this bias is overcome by eliminating values above the pre-specified value .sub.0</2, then the method predicts with great precision the region of damage.

[0100] After having established .sub.0</2, the value of eccentricity e.sub.0 closest to one is determined, verifying F(.sub.0,e.sub.0)=f.sub.0, where f.sub.0 is the pre-established reference value close to one.

[0101] FIG. 4 shows an image of the perforated wall in a well, showing the areas where damage has occurred. The letters N, E, S and W identify North, East, South and West, respectively, and correspond to a perimetral development of 360 degrees (2 radians).

[0102] The image is taken a posteriori, once the well has been drilled or obtained by sensing during drilling. The dark spots are areas of damage in the wall based on which it is possible to determine the width of damage at a given vertical height z but they do not allow establishing the depth in the wall or providing the determination thereof before drilling is performed.

[0103] FIG. 5 shows a graph of the function F(.sub.0,e)=f.sub.0=1 with eccentricity e as a free parameter. It is where the function takes this value f.sub.0=1, i.e., the value which determines the eccentricity e which in turn defines a single ellipse of the family of ellipses defined above.

[0104] In this embodiment, the ellipse has an eccentricity of 0.4. The right side of the drawing shows a quarter of a circumference, the circumference representing the section of the wall of the well, and also a quarter of the ellipse having an eccentricity of 0.4. The inner area of the ellipse having an eccentricity of 0.4 is established as the region of damage.

[0105] Given this region of damage, it is possible to repeat the method for a plurality of sections S distributed along the wellbore path. By means of interpolating the sections of damage along a segment of the wellbore path, it is possible to determine the collapse volume in that segment before drilling is performed.

[0106] With the collapse volume, it is possible to establish drilling fluid injection parameters which allow discharging the collapse volume. Otherwise, the method allows recalculating the collapse volume by changing the pressure conditions established by the drilling fluid. For example, if the density of the drilling fluid increases, pressure on the walls of the well increases and compensates for the stresses exerted by the eliminated rock on the drilling and giving rise to the free surface, given that they now no longer perform a structural function. The region of damage is thereby reduced given that the pressure forces against the wall exert this compensating force.

[0107] This force has a limit since an excessive increase in the density of the drilling fluid can cause a pressure that is too high to be withstood by the wall of the well, generating cracks.

[0108] Therefore, this embodiment shows how the region of damage depends on the parameters used in the calculation of the stress state at the point where the plane of section S has been plotted out, and particularly on the pressure of the drilling fluid.

[0109] It is possible to simulate different conditions of damage for a plurality of densities of the drilling fluid and establish those that give rise to a collapse volume less than the acceptable limit by the means installed in the well.

[0110] One application of the method of determining damage, according to an embodiment is to establish a drilling method.

[0111] In this method, as shown in FIG. 6, a discretization t.sub.i=1 . . . N of the coordinate (t) along the wellbore path is established. If the wellbore is vertical, the parameter t coincides with the vertical coordinate z.

[0112] Once having established the well-drilling diameter D and a wellbore path through the geomechanical model and of the fluid flow model of the reservoir, the transverse section S.sub.i of diameter D is determined for each t.sub.i, and in said section S.sub.i, for a plurality of values of density of the drilling fluid .sub.j.sup.l,j=1 . . . M, the following steps are carried out: [0113] i determining the pore pressure p.sub.p, maximum stress .sub.max, minimum stress .sub.min and the mechanical properties of the rock; [0114] ii. determining the stress state of the rock in said section S.sub.i at least according to the data from the preceding step; [0115] iii. determining in section S.sub.i the region R.sub.j.sup.i(.sub.j.sup.l,S.sub.i) of damage according to the method already described and the value of the area A.sub.j.sup.i(.sub.j.sup.l,S.sub.i)=R.sub.j.sup.i(.sub.j.sup.l,S.sub.i) said region R.sub.j.sup.i(.sub.j.sup.l,S.sub.i);

[0116] Then for each coordinate (t) of the discretization t.sub.i=1 . . . N: [0117] iv. a correspondence V.sup.i(.sub.j.sup.l) between the discrete values of density of the drilling fluid .sub.j.sup.l,j=1 . . . M and the value of the area A.sub.j.sup.i(.sub.j.sup.l,S.sub.i) is determined, the latter being interpreted as the detachment volume (V) of the wall of the well per unit of drilled length; [0118] v. a combination of drilling speed (v), density () of the injected drilling fluid and flow rate (Q) thereof, such that it establishes a volume of material V.sub.e(v,,Q) to be discharged, material being cut by the bit plus the collapse material V.sup.i(.sub.j.sup.l), less than that determined by the drilling system, so as to allow removing the volume of material from the well without a drilling bit collapsing.

[0119] After having determined the drilling parameters, the well is drilled according to the values of drilling speed (v), density () of the injected drilling fluid and flow rate (Q) thereof for each coordinate of the drilling path.

[0120] The drilling operation discharges the sum of two volumes of material, the material being cut by the bit plus the material being collapsed near the bit because the damaged area corresponds to material showing a stress greater than the allowable stress of the rock in that location and then it further collapses. The sum of the two volumes is discharged by the injected drilling fluid.

[0121] The material being cut by the bit is determined by the drilling speed (v) and the section of well being drilled.

[0122] An skilled person on drilling systems, according to his practice, determines the maximum volume of material to be discharged by the drilling system taking into account at least the density () of the injected drilling fluid and flow rate (Q)) this is, he knows how much material can be removed by the drilling system under such drilling conditions, specifically those related to the drilling fluid being injected. It is to be noted that, apart from the variables related to the drilling fluid to be injected, the skilled person, according to his practice, may use further variables related to the drilling system per se such as the piping dimensions or pump characteristics, in order to tune-up the maximum volume of material to be discharged by the drilling system.

[0123] The invention provides the correspondence V.sup.i(.sub.j.sup.l), the volume being detached when drilling, to the skilled person and therefore solves the problem of determining accurately the volume of material to be discharged. This material to be discharged is less than that determined by the drilling system. The rest of the feature is just a clarification indicating that the result of using the combination of parameters (drilling speed (v), density () of the injected drilling fluid and flow rate (Q) fulfilling the specified condition allows removing the volume of material from the well without a drilling bit collapsing.

[0124] According to the invention, the skilled person can determine the drilling speed (v), the density () of the injected drilling fluid and flow rate (Q) for each coordinate of the well path as for each density () he knows the volume of the collapsing material V.sup.i(.sub.j.sup.l).

[0125] A second application of the method according to the invention is the estimation of the depth of the damage in the wall of the well (known as caliper). Given that, by hypothesis, the configuration of the region of the damage has been determined as elliptical, the value of bR, i.e., the difference between the semi-major side of the ellipse and the radius of the wall of the well, is taken as an estimated value of the depth of the damage.