Patent Publication Number: US-8126646-B2

Title: Perforating optimized for stress gradients around wellbore

Description:
BACKGROUND 
     The invention generally relates to perforating that is optimized for stress gradients around the wellbore. 
     For purposes of producing well fluid from a formation, the formation typically is perforated from within a wellbore to enhance fluid communication between the reservoir and the wellbore. In the perforating operation, a perforating gun typically is lowered downhole (on a string, for example) inside the wellbore to the region of the formation to be perforated. The perforating gun typically contains perforating charges (shaped charges, for example) that are arranged in a phasing pattern about the longitudinal axis of the gun and are radially oriented toward the wellbore wall. After the perforating gun is appropriately positioned, the perforating charges are fired to pierce the well casing (if the well is cased) and produce radially extending perforation tunnels into the formation. 
     The formation is subject to tectonic forces, which produce stress on the formation. The stress has multidirectional components, one of which is a maximum horizontal stress. Quite often, the perforating charges are generally aligned with the direction of maximum horizontal stress for purposes of avoiding sand production and/or preparing the formation for subsequent fracturing operations. 
     SUMMARY 
     In an embodiment of the invention, a technique includes determining a stress tensor in a formation that surrounds a wellbore. The stress tensor varies with respect to the wellbore. The technique includes running a perforating charge into the wellbore to perforate the formation and performing at least one of selecting the perforating charge and orienting the perforating charge in the wellbore based at least in part on the determination of the stress tensor. 
     In another embodiment of the invention, a technique includes determining a stress tensor in a formation that surrounds a wellbore and based on the determination of the stress tensor, modeling formation damage near the wellbore. The formation damage that is predicted by the model varies with respect to the wellbore. The technique includes running a perforating charge into the wellbore to perforate the formation and orienting the perforating charge based at least in part on the model. 
     Advantages and other features of the invention will become apparent from the following description, drawing and claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWING 
         FIG. 1  is an illustration of principal components of a stress tensor according to an embodiment of the invention. 
         FIG. 2  is a cross-section of a wellbore, illustrating stress concentrations in the formation that surrounds the wellbore according to an embodiment of the invention. 
         FIG. 3  depicts the performances of different perforating charges versus a stress parameter according to an embodiment of the invention. 
         FIG. 4  is a flow diagram depicting a technique to select and orient a perforating charge based on a stress tensor according to an embodiment of the invention. 
         FIG. 5  depicts a model of formation damage near a wellbore according to the prior art. 
         FIG. 6  illustrates a model of formation damage near a wellbore according to an embodiment of the invention. 
         FIG. 7  is a flow diagram depicting a technique to orient a perforating charge based on a model of formation damage derived from a stress tensor determination according to an embodiment of the invention. 
         FIG. 8  is a schematic diagram of a well according to an embodiment of the invention. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  depicts an infinitesimal unit  10  of a reservoir rock, or formation. The formation is subject to tectonic forces that produce stress gradients in the formation. The stress on the unit  10  may be characterized by a stress tensor that has three independent principal stress components, which generally differ in magnitude: a vertical, or overburden stress component  12  (called “σ V ” in  FIG. 1 ); a minimum horizontal stress component  14  (called “σ h ” in  FIG. 1 ); and a maximum horizontal stress component  16  (called “σ H ”) in  FIG. 1 . 
     For purposes of producing well fluid from the formation, a wellbore is drilled into the formation. Neglecting the stress concentrations that are induced by the wellbore itself, the mean total stress (to be defined subsequently) is identical in every azimuthal direction around the wellbore. However, the direction of the stress tensor varies with respect to the azimuth. In the context of this application, references to “azimuth,” “azimuthal” and the like mean a particular angular orientation with respect to the longitudinal axis of the wellbore. 
     The wellbore induces stress concentrations in the formation near the wellbore. As a more specific example,  FIG. 2  is a cross-sectional view of an exemplary wellbore  30 , depicting stress concentrations  20  about the wellbore  30 . As depicted in  FIG. 2 , along an axis that is oriented with respect to maximum horizontal stress components  34 , the formation surrounding the wellbore  30  has pronounced magnitude stress lobes  36 , indicating stress decrease relative to far field values. Similarly, along an axis that is aligned with minimum horizontal stress components  32 , the formation exhibits pronounced stress lobes  33 , indicating stress increase relative to far field values. Between the lobes  33  and  36 , stress approaches the far field value, as indicated by the stress concentrations approaching unity. Thus, near a wellbore, the total stress magnitude azimuthally varies. In general, the penetration depth of a perforating charge depends on the target rock&#39;s strength and in-situ stress. Conventionally, penetration depth has been gauged as being related to the effective stress of the formation. The effective stress is derived from the mean total stress, which is described below: 
                     Stress     mean   ⁢           ⁢   total       =       1   3     ·     (       σ   v     +     σ   H     +     σ   h       )               Equation   ⁢           ⁢   1               
where “σ V ,” “σ H ,” and “σ h ” represent the overburden, maximum horizontal and minimum horizontal principal stress components, respectively. From the mean total stress, the effective stress may be derived as follows:
 
Equation 2
 
Stress effective =Stress meantotal =alpha·fluid pore pressure
 
where “alpha” is Biot&#39;s constant and is generally equal to or slightly less than unity.
 
     Conventionally, the effective stress, a scalar quantity, is calculated and has a general correspondence to a perforating penetration depth, as described in pending U.S. patent application Ser. No. 11/162,185 entitled, “PERFORATING A WELL FORMATION,” filed on Aug. 31, 2005, having Brenden M. Grove as the inventor. 
     It has been discovered, however, that perforating charge performance may be further enhanced by considering the specific stress tensor, not just the mean total stress. In other words, it has been discovered that the performance of a perforating charge may be enhanced by considering the stress tensor for the region of the formation, which is being perforated by the charge. 
     For a particular stress tensor, one perforating charge may outperform other perforating charges. For example,  FIG. 3  depicts a perforating charge performance chart  48  for a given formation stress tensor type or category. Thus, the chart  48  may be used for cases in which the stress tensor for the targeted formation region falls within a certain directional or magnitude range. The chart  48  includes, by way of example, a relationship  50  for a particular perforating charge, depicting the penetration depth of the charge versus a particular stress parameter. Likewise,  FIG. 3  depicts an exemplary relationship  60  for another perforating charge (i.e., a perforating charge of a different type), depicting the penetration of that perforating charge versus the stress parameter. 
     It is understood that many different types of perforating charges are available due to variations in liner geometries, variations in liner materials, variations in charge explosive compositions, variations in charge casing geometries, variations in charge case materials, variations in casing cap designs, variations in casing cap materials, etc. 
     The “stress parameter” of the chart  48  of  FIG. 3  may be one of a number of different parameters, depending on the particular embodiment of the invention. For example, in some embodiments of the invention, the stress parameter may be the mean total stress for a particular stress tensor and thus, may be average of its vertical, minimum horizontal and maximum horizontal principal components. As another example, in other embodiments of the invention, the stress parameter of  FIG. 3  may be an average of only two of the principal stress components; and as yet another example, in some embodiments of the invention, the stress parameter may be one of the principle stress components, such as the maximum horizontal stress component (as an example). Many other variations are possible and are within the scope of the appended claims. 
     Regardless of the technique that is used to calculate the stress parameter, different perforating charge types have different penetration performances versus the stress parameter. Thus, as shown in  FIG. 3  by way of example, for a first given stress parameter (called “SP 1 ,” in  FIG. 3 ), a penetration depth  62  of the relationship  60  is greater than a corresponding penetration depth  61  of the relationship  50 . Therefore, if the targeted formation region exhibits the stress parameter SP 1 , then the perforating charge that corresponds to the relationship  60  is chosen, as the perforating charge has the greater penetrating depth. 
     It is noted, however, that the perforating charge type that corresponds to the relationship  50  may be chosen in other applications. Thus, as depicted in  FIG. 3 , if the targeted formation region exhibits another exemplary stress parameter (called “SP 2 ,” in  FIG. 3 ), the relationship  50  depicts a larger penetration depth  54  than a corresponding penetration depth  64  that is depicted by the relationship  60 . Therefore, for this particular application, the perforating charge type that corresponds to the relationship  50  is chosen. 
     Therefore, the perforating charge that is selected depends on a particular stress parameter for the targeted formation region. Furthermore, the azimuthal directions of the perforating charges of a perforating gun may be selected to aim the perforating charges toward regions of the formation where perforation depth is maximized. Thus, empirical tests may be conducted to produce charts, such as the chart  48  that is depicted in  FIG. 3 , for purposes of detecting which stress tensors are desired for optimizing perforating performance. Therefore, knowledge of the stress tensor may be used to select such parameters as the perforating charge type, orientation of the perforating charge, the carrier used to convey the perforating charge downhole, etc. 
     To summarize, in general,  FIG. 4  depicts a technique  100  in accordance with some embodiments of the invention. The technique  100  includes determining (block  102 ) a stress tensor in a formation near a wellbore. The stress tensor azimuthally varies in direction and magnitude with respect to the wellbore. It is noted that the stress tensor may also and/or alternatively vary longitudinally with respect to the wellbore (i.e., vary along the longitudinal axis of the wellbore). The stress tensor may be calculated or at least estimated by knowledge of tectonic forces. Next, in accordance with the technique  100 , a perforating charge is selected (block  104 ) based on the stress. The technique  100  includes running the selected perforating charge downhole and orienting the charge toward the region of the formation to be perforated, as depicted in block  106 . The selected perforating charge is then fired, as depicted in block  108 . 
     Knowledge of the stress tensor may be used for purposes other than the purpose of maximizing penetration depth. For example, in accordance with some embodiments of the invention, the knowledge of the stress tensor may be used for purposes of avoiding damaged regions of the well near the wellbore. In this regard, formation damage typically occurs near the wellbore due to fluid invasion, such as the invasion of drilling fluid. In general, more formation stress means less fluid invasion, and conversely, less stress means greater fluid invasion. 
       FIG. 5  depicts a model  160  of formation damage near an exemplary wellbore  150  according to the prior art. As shown, the model  160  is conventionally perceived to be generally uniform and thus, generally circularly cylindrical about the wellbore  150 . Therefore, conventionally, regardless of the azimuthal orientation of perforating charges, the resulting perforation tunnels  154  are expected to experience the same depth of damaged formation. 
     However, the above-described conventional depiction of formation damage does not account for the perturbation of the formation stress due to the existence of the wellbore. Referring to  FIG. 6 , in accordance with some embodiments of the invention, the stress tensor is used to develop a formation damage model  170  that accounts for the anisotropic variation in stress around the wellbore  150 . As depicted in  FIG. 6 , due to this anisotropic stress variation, the formation damage model  170  may be elliptically symmetrical (as an example), in some embodiments of the invention. Thus, depending on the azimuthal variation about the wellbore  150 , the formation damage may be radially thinner in some directions than in other directions. For example,  FIG. 6  depicts a perforation tunnel  154   a  that extends through more formation damage relative to a perforation tunnel  154   b  that extends through relatively a smaller amount of formation damage. Therefore, for this example, the perforation tunnel  154   a  is generally less effective than the perforation tunnel  154   b . It is noted that the formation damage may likewise vary in a longitudinal direction along the wellbore. 
     Thus, in accordance with some embodiments of the invention, the stress tensor is used to develop a formation damage model for purposes of optimizing perforation. More specifically, referring to  FIG. 7 , in accordance with some embodiments of the invention, a technique  200  generally includes determining (block  202 ) a stress tensor in a formation near a wellbore. Next, according to the technique  200 , a model of formation damage near the wellbore is developed (block  204 ) based at least in part on the stress tensor. The perforating charge is then oriented based on the model, as depicted in block  206 . Subsequently, once in this orientation and positioned in the segment of the well to be perforated, the perforating charge may then be fired. 
     As yet another variation, in accordance with other embodiments of the invention, the type of perforating charge that is selected may be based on the above-described formation damage model and azimuthal direction of perforation. Thus, similar to the techniques that are described above, performance charts (charts that graph penetration depth versus stress parameters) may be used to select the perforating charges for a given application. 
       FIG. 8  generally depicts a perforating system according to some embodiments of the invention. Referring to  FIG. 8 , in accordance with some embodiments of the invention, the system is used in a well  230 , which includes an exemplary vertical wellbore  232 . A string  240  of the perforating system extends into the wellbore  232  for purposes of penetrating a casing string  234  and the surrounding formation of the wellbore  232 . Although  FIG. 8  depicts the wellbore  232  as being cased, it is noted that the perforating system may be likewise used in an uncased wellbore, in other embodiments of the invention. Furthermore, although  FIG. 8  depicts a vertical wellbore  232 , it is noted that the perforating system may be used in a lateral or horizontal wellbores in other embodiments of the invention. 
     The string  240  includes a perforating gun  250  that includes a firing head  252  and perforating charges  254  (shaped charges, for example). The particular phasing of the shaped charges  254 , as well as the type of the perforating charges  254  are selected based on stress tensor of the formation region to be perforated, as described above. For purposes of orienting the perforating charges  254 , the string  240  includes an orientation mechanism  242 . 
     Depending on the particular embodiment of the invention, all of the perforating charges  254  may be the same, groups of the perforating charges  254  may be the same type, or all of the perforating charges  254  may be different types. Thus, many variations are possible and are within the scope of the appended claims. Furthermore, in accordance with the particular embodiment of the invention, the selection of the carrier for the perforating charges  254  and the phasing pattern for the perforating charges  254  depends on the determined stress tensor in the formation being perforated. Likewise, in some embodiments of the invention, a particular region of the formation may be targeted, and thus, the perforation orientation may target this region. 
     Although  FIG. 8  depicts that the perforating gun  250  is lowered downhole on a string, other conveyance mechanisms may be used, in other embodiments of the invention. In this regard, depending on the particular embodiment of the invention, the perforating charge  250  may be lowered downhole via a wireline, a slickline, coiled tubing, etc. 
     The firing head  252  may be hydraulically, mechanically or electrically operated, depending on the particular embodiment of the invention. Furthermore, various techniques may be used to establish communication between the firing head  252  and the surface of the well. Thus, a wired connection (an optical or electrical cable, as examples) may be established between the firing head  252  and the surface of the well. Alternatively, a wireless communication path (i.e., a communication path that uses pressure pulses, electromagnetic communication, acoustic communication, etc.) may be used to establish communication between the firing head  252  and the surface of the well. Other variations are possible and are within the scope of the appended claims. 
     While the present invention has been described with respect to a limited number of embodiments, those skilled in the art, having the benefit of this disclosure, will appreciate numerous modifications and variations therefrom. It is intended that the appended claims cover all such modifications and variations as fall within the true spirit and scope of this present invention.