Abstract:
A method for determining effects of perforation on a rock formation includes obtaining a sample of the rock formation. A perforation tunnel is created in the sample of the rock formation. The core sample is either subdivided into subsamples and a three dimensional tomographic image is made of each subsample and/or a three dimensional tomographic image is made of the sample of rock formation and the image thereof is segmented into sub images of selected subvolumes of the rock formation sample. At least one physical property of the rock formation is estimated from each tomographic image.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    Priority is claimed from U.S. Provisional Application No. 61/227,651 filed on Jul. 22, 2009. 
     
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
       [0002]    Not applicable. 
       BACKGROUND OF THE INVENTION 
       [0003]    1. Field of the Invention 
         [0004]    The invention relates generally to the field of estimating material properties of porous media. More specifically, the invention relates to methods for estimating such properties using computer tomographic (CT) images of porous media such as subsurface rock formation. 
         [0005]    2. Background Art 
         [0006]    Estimating materials properties such as effective elastic moduli, electrical resistivity and fluid transport properties of porous media, an example of the latter being mobility of hydrocarbon in subsurface rock formations, has substantial economic significance. Methods known in the art for identifying the existence of subsurface hydrocarbon reservoirs, including seismic surveying and well log analysis, need to be supplemented with reliable methods for estimating how fluids disposed in the pore spaces of the reservoir rock formations will flow over time in order to characterize the economic value of such reservoir rock formations. 
         [0007]    One method known in the art for estimating fluid transport properties is described in U.S. Pat. No. 6,516,080 issued to Nur. The method described in the Nur patent includes preparing a “thin section” from a specimen of rock formation. The preparation typically includes filling the pore spaces with a dyed epoxy resin. A color micrograph of the section is digitized and converted to an n-ary index image, for example a binary index image. Statistical functions are derived from the two-dimensional image and such functions are used to generate three-dimensional representations of the rock formation. Boundaries can be unconditional or conditioned to the two-dimensional n-ary index image. Desired physical property values are estimated by performing numerical simulations on the three-dimensional representations. For example, permeability is estimated by using a Lattice-Boltzmann flow simulation. Typically, multiple, equiprobable three-dimensional representations are generated for each n-ary index image, and the multiple estimated physical property values are averaged to provide a result. 
         [0008]    It is also known in the art to use x-ray computer tomographic (CT) images of samples of rock for analysis. CT images are input to a computer program that segments the images into rock grains and pore spaces. The segmented image can be used as input to programs such as the Lattice-Boltzmann program described above to estimate formation fluid transport properties. 
         [0009]    Wellbores drilled through subsurface formations typically have a pipe or casing cemented in place after drilling the wellbore is completed. The casing hydraulically isolates and protects the various rock formations and provides mechanical integrity to the wellbore. The wellbore is hydraulically connected to a formation from which fluid is to be withdrawn or injected by a process known as “perforating.” Perforating is typically performed by inserting an assembly of explosive shaped charges into the wellbore and detonating the charges. See, for example, U.S. Pat. No. 5,460,095 issued to Slagle et al. The process of shaped charge perforating creates a tunnel or flow conduit that allows reservoir fluids to enter the wellbore and subsequently flow or be pumped out of the wellbore. However, by creating the perforation tunnels the physical parameters of the rocks surrounding the tunnel are often altered in such a manner as to restrict or reduce flow. 
         [0010]    It is known in the art to test the effectiveness and performance of shaped charges. Testing is typically performed by the shaped charge manufacturer using a procedure specified by the American Petroleum Institute, Washington, D.C. (“API”) known as Recommended Practice 43 (“RP43”). In performing RP43, a target material, typically in the shape of a cylinder, is placed proximate the shaped charge undergoing testing. A steel casing segment or plate and a layer of typical casing cement may be disposed between the target material and the shaped charge. The target material is typically a rock formation known as the Berea sandstone. After detonation of the shaped charge, the dimensions of the perforation made in the target are measured, and the fluid transport properties of the target may be measured in a laboratory. Laboratory evaluation of fluid transport properties can be difficult and expensive. Laboratory evaluation of perforated cores can also be highly inaccurate due to the presence of unknown fractures or heterogeneities within the core. 
         [0011]    It is desirable to be able to estimate or determine fluid transport properties of perforation test targets without the need for full laboratory evaluation. 
       SUMMARY OF THE INVENTION 
       [0012]    A method according to one aspect of the invention for determining effects of perforation on a rock formation includes obtaining a sample of the rock formation. A perforation tunnel is created in the sample of the rock formation. The core sample is either subdivided into subsamples and a three dimensional tomographic image is made of each subsample and/or a three dimensional tomographic image is made of the sample of rock formation and the image thereof is segmented into sub images of selected subvolumes of the rock formation sample. At least one physical property of the rock formation is estimated from each tomographic image. 
         [0013]    Other aspects and advantages of the invention will be apparent from the following description and the appended claims. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0014]      FIG. 1A  shows a side view of an example Berea sandstone perforating test target core. 
           [0015]      FIG. 1B  shows the core of  FIG. 1A  after a shaped charge is detonated therethrough. 
           [0016]      FIG. 1C  shows an end view of the core of  FIG. 1B  to illustrate altered rock formation in an annular volume surrounding the perforation tunnel. 
           [0017]      FIG. 1D  shows an example of well drilling to obtain core samples. 
           [0018]      FIG. 1E  shows an example of a completed wellbore with cemented in place casing having perforations therein in a reservoir formation. 
       
    
    
     DETAILED DESCRIPTION 
       [0019]      FIG. 1A  shows a side view of an example test core  110  made of a rock formation known as Berea sandstone as discussed in the Background section herein. The test core  110  may be prepared according to the test procedure API RP43 referred to in the Background section herein. While test procedure API RP43 specifies Berea sandstone, the present invention is equally applicable to testing of other rock formations.  FIG. 1B  shows the test core  110  after detonation of a shaped charge in a test performed, for example, according to RP43. A perforation tunnel  112  is created by the action of the shaped charge upon detonation. Operation of shaped charges and how they create perforation tunnels is explained, in a non-limiting example, in U.S. Pat. No. 5,567,906 issued to Reese et al. An end view of the core sample  110  is shown in  FIG. 1C  to illustrate a zone  114  that occupies a roughly annular volume surrounding the perforation tunnel  112  in which the structure of the rock formation is altered to some extent by the action of the “jet” created by the shaped charge detonation. Such alteration within the zone  114  may also affect the fluid transport properties of the rock formation. 
         [0020]    An example of drilling a wellbore to obtain samples of rock formations for evaluation by examples of a method according to the invention will be explained with reference to  FIG. 1D . A drilling unit or “rig”  10  is disposed at the Earth&#39;s surface. The rig  10  includes lifting equipment (not shown separately) for raising and lowering one of several types of device used to rotate a drill string  14 . The device, shown at  18  in the present example may be a top drive, although the use of a top drive is not a limit on the scope of the invention. The drill string  14  is assembled by threadedly coupling segments of drill pipe end to end. A drill bit  16  is disposed at the lower end of the drill string  14  and cuts through subsurface rock formations  11  to form a wellbore  12 . During the drilling of the wellbore  12 , the rig  10  is operated to cause some of the axial load (weight) of the drill string  14  to be applied to the drill bit  16 . The top drive  18  rotates the drill string  14  and the drill bit  16  at the lower end thereof. The combination of axial load and rotation causes the drill bit  16  to cut through the formations  11 . 
         [0021]    The rig  10  includes a tank or pit  22  having drilling fluid (“mud”)  20  stored therein. A pump  24  lifts the mud  20  and discharges it through suitable flow lines  26  so that the mud  20  passes through an internal passage in the drill string  14 , whereupon it is discharged through suitable orifices or courses in the drill bit  16 . The discharged mud  20  cools and lubricates the drill bit  16  and lifts the cuttings generated by the bit  16  to the Earth&#39;s surface. The cuttings and mud thus lifted enter separation and cleaning devices, shown generally at  28  and including, for example, devices known as “degassers” and “shale shakers” to remove the cuttings and contamination from the mud  20 . The mud after such cleaning is returned to the pit  22  for subsequent use in drilling the wellbore  12 . 
         [0022]    When the wellbore reaches a depth proximate a particular formation of interest, the drill bit  16  may be replaced by a core drilling bit (not shown) that may recover a substantially cylindrical core sample of the rock formation of interest. The core sample ( 110  in  FIG. 1A ) may be prepared into one or more perforation test cores shaped as explained with reference to  FIGS. 1A ,  1 B and  1 C, and perforated according to the conditions specified in RP43. It will be appreciated by those skilled in the art that to use a drilled core sample of the rock formation, it is desirable for the diameter of the core sample to be sufficient to enable perforation testing to be performed in a direction transverse to the axis of the core sample. This is because a drilled core sample is obtained by drilling along the axis of the wellbore, while typical wellbore perforations are made in a direction transverse to the axis of the wellbore. Thus, to simulate how the particular formation will actually be affected by perforation, the directionality of the rock sample with respect to the perforation direction can be important. 
         [0023]    In other examples, samples of rock may be obtained from surface outcrops of the formation or near surface deposits of the rock formation. Such samples may be perforation tested in a direction that is expected to be similar to the direction of perforations in a wellbore drilled and cased through such formation. At present, using samples obtained from surface outcrops of rock formations is preferred. It is also known in the art to drill samples of the formation through the wellbore wall transverse to the wellbore axis using a specialized drilling instrument. 
         [0024]      FIG. 1E  shows the wellbore after the drilling operations explained with reference to  FIG. 1D  have been completed. At the end of the drilling procedure, a steel pipe or casing  100  may be inserted into the wellbore  12 . Cement  102  is then typically pumped through the interior of the casing  100 , whereupon it travels through the bottom end thereof, and into the annular space between the wall of the wellbore  12  and the exterior of the casing  100 . After the cement  102  has sufficiently cured, the remaining components of the wellbore  12  may be installed. In one procedure, an annular sealing element  106  called a packer is inserted into the casing  100  to a selected depth, typically above a depth of a reservoir formation  11 A in the subsurface formations  11 . A tubing  108  may be sealingly engaged with the packer  106 , and wellhead equipment  110  may be installed at the top of the casing  100  and tubing  108 . The wellhead equipment  110  may include control valves and may ultimately be coupled to a discharge conduit  112 . Perforations  104  may be made through the casing  100 , cement  102  and into the reservoir formation  11 A. The perforations  104  may be made prior to inserting the packer and tubing using, for example, a casing perforating gun assembly (not shown). The perforations  104  may alternatively be made with a “tubing conveyed” perforating gun assembly (not shown) that is installed simultaneously with the tubing  108 , and actuated, for example by applying fluid pressure to the tubing  108  or dropping an actuation tool (not shown) into the tubing  108 . Alternatively, the perforations  104  may be made after insertion of the packer and tubing using a “through tubing” perforating gun assembly. Other methods for creating the perforations  104  are known in the art. The method of the present invention is intended to determine how the creation of the perforations  104  changes one or more petrophysical properties of the reservoir formation  11 A, in particular the fluid transport properties. 
         [0025]    In the present example, a perforated test core sample (e.g.,  110  in  FIG. 1A ) may have taken therefrom small samples of the formation beginning laterally near the perforation tunnel ( 112  in  FIG. 1 ) and continuing successively laterally outwardly. One or more samples may be taken near the lateral edge of the core sample near the back end thereof, where the perforation tunnel may not have caused material effect on the fluid transport properties of the rock formation. Alternatively, samples may be taken from unperforated core (e.g., as  110  in  FIG. 1A ). If samples from an unperforated test core are used, a perforation may be created in the test core, and subsequent samples may be taken from the perforated test core for comparative analysis. 
         [0026]    The samples may be transported to a computer tomographic (“CT”) scanner  30 , which may use x-rays for analysis of internal structure of the cuttings, for generation of three dimensional (3D) images of the test core sample ( 110  in  FIG. 1A ). The images so generated may be in numerical form and their content will be further explained below. After CT scanning, the test cores may be saved for further analysis or may be suitably discarded. 
         [0027]    In a practical implementation of core analysis according to the invention, the state of the rock formation prior to perforating can be determined by extracting relatively small portions of the core sample after the test perforating is performed. The state of the rock formation after perforation can be characterized by CT scanning the small samples and estimating fluid transport properties of the foregoing small samples as explained below. 
         [0028]    In an alternative example, a CT image of the entire core may be made using suitable CT imaging devices. The CT image may be made prior to creating the perforation tunnel, and thereafter, or the CT image may be made only after creating the perforation tunnel. The CT image(s) may be segmented into sub images of the entire volume of the core sample similar in volume and position to the physical small samples taken from the entire core sample as explained above. 
         [0029]    The extent to which the rock has been affected by perforating by examination (i.e., CT scan and analysis of the CT scan images thereof) of the small volume samples of the core obtained at progressively greater radial distances from the perforation tunnel axis until the determined fluid transport properties are substantially equal to those of the unaltered rock formation. It is thus possible to quantify the lateral extent of and the magnitude of the formation alteration caused by perforating and to map its radial distribution with respect to the perforation tunnel axis 
         [0030]    CT scan imaging of the test core small samples can be used in the invention to produce a numerical object that represents the material sample digitally in the computer  32  for subsequent numerical simulations of various physical processes, such as viscous fluid flow (for permeability estimation); stress loading (for the effective elastic moduli); electrical current flow (for resistivity); and pore size distribution for nuclear magnetic resonance relaxation time properties, including distribution of relaxation time. 
         [0031]    The CT scan images produced by the CT scanner may be stored or displayed in a computer and can be used as input to one or more rock property characterization models. In the present example, the Lattice-Boltzmann method can be used to numerically solve Navier-Stokes equations for flow simulation. Such solution may be used to calculate permeability of simulated 3D volumes. The Lattice-Boltzmann method is a robust tool for flow simulation, particularly in media with complex pore geometry. See, for example. Ladd,  Numerical Simulations of Particulate Suspensions via a discretized Boltzmann Equation, Part  1:  Theoretical Foundation , J. Fluid Mech., v 271, 1994, pp. 285-309; Gunstensen et al., “ Lattice Boltzmann Model of Immiscible Fluids , Phys. Rev. A., v. 43, no. 8, Apr. 15, 1991, pp. 4320-4327; Olsen et al.,  Two fluid Flow in Sedimentary Rock Simulation, Transport and Complexity , J. Fluid Mechanics, Vol. 341, 1997, pp. 343-370; and Gustensen et al.,  Lattice - Boltzmann Studies of Immiscible Two - Phase Flow Through Porous Media,” J. of Geophysical Research, V.  98, No. B4, Apr. 10, 1993, pp. 6431-6441). 
         [0032]    The Lattice-Boltzmann method simulates fluid motion as collisions of imaginary particles, which are much larger than actual fluid molecules, but wherein such particles show almost the same behavior at a macroscopic scale. The algorithm used in the Lattice-Boltzmann method repeats collisions of these imaginary particles until steady state is reached, and provides a distribution of local mass flux. In accordance with the present invention, the Lattice-Boltzmann method is applied successfully for many pore structures, including cylindrical tubes, random densely packed spheres, and 3D rock samples digitized by CT scanning as explained above. See, for example, U.S. Pat. No. 6,516,080 issued to Nur. 
         [0033]    It is also possible to estimate capillary pressure related flow characteristics from the pore structure determined using the 3D images processed as explained above. See, for example, U.S. Pat. No. 7,277,795 issued to Boitnott. Other properties of the rock formation that may be modeled include, without limitation, electrical formation resistivity factor, and compressional-wave and shear-wave acoustic velocity. Any or all of the foregoing estimated physical properties may be stored and/or displayed in the computer ( 32  in  FIG. 1 ). 
         [0034]    In a particular application of the foregoing technique for analyzing perforation test core samples, the fluid transport properties determined above on perforated core samples (e.g.,  FIG. 1B ) of a formation of interest can be input into conventional reservoir simulator computer programs to derive an estimate of expected fluid production from the wellbore. In a particular application of the foregoing technique, the foregoing image and fluid transport property determination may be made on an unaltered test core sample ( FIG. 1A ), and/or as explained above on a portion of the perforated test core obtained sufficiently distant from the perforation tunnel so as to have essentially unaltered petrophysical properties. A shaped charge may then be detonated to create a perforation tunnel ( FIG. 1B ). The imaging and fluid transport property determination may then be repeated on small samples of the perforated test core at successively larger radial distances from the perforation tunnel axis as explained above. 
         [0035]    Once a reservoir model is developed using the segmented images of the perforated test core, a number of other applications that use the images become possible, such as predicting changes in rock formation flow capacity resulting from changes in relative permeability. Relative permeability may change due to water invasion or gas coning, chemical or other stimulation, re-perforating the casing in a selected formation or blockage of existing perforations in the wellbore 
         [0036]    Methods according to the invention also can enable shaped charge manufacturers to determine how changes in shaped charge explosive type and weight, geometry, and materials affect the flow properties of various rock formations in addition to those commonly used for testing and QC purposes. The topology of the perforation tunnel can be mapped in detail using the segmented images The thickness of the damaged zone ( 14  in  FIG. 1C ) can be measured and quantified in terms of grain sizes and distribution compared to the unaffected portion of the core sample. Location of metal debris from the shaped charge jet in the perforation tunnel ( 112  in  FIG. 1B ) is also facilitated. 
         [0037]    End users (operators) can develop specialized techniques for the use of perforating systems during well completion or repair. The amount of pressure differential (underbalance or overbalance), standoff, shot density (numbers of shaped charges used per unit axial length of wellbore casing), and selection of shaped charge type can also be evaluated. Such evaluated may enable optimization of perforating system cost by potentially reducing the number of perforations required and the total amount of explosive used. It may also be possible to optimize perforation techniques in a particular wellbore to compensate for the relative attitude of the formation (the direction of the bedding planes with respect to the wellbore axis). 
         [0038]    While the example implementation herein is described in terms of jet perforating using explosive shaped charges, it should be clearly understood that the process described herein also applies to other methods of creating hydraulic openings in a well casing into a rock formation, including, without limitation, bullet perforating, hydraulic jetting, laser perforating, rotary boring, etc. 
         [0039]    While the invention has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of this disclosure, will appreciate that other embodiments can be devised which do not depart from the scope of the invention as disclosed herein. Accordingly, the scope of the invention should be limited only by the attached claims.