Patent Publication Number: US-2005115711-A1

Title: Method and system for determining an optimum pumping schedule corresponding to an optimum return on investment when fracturing a formation penetrated by a wellbore

Description:
CROSS REFERENCE TO RELATED APPLICATIONS  
      This application claims benefit of U.S. Provisional Patent Application No. 60/481,623 filed on Nov. 11, 2003. 
    
    
     BACKGROUND OF INVENTION  
      The subject matter of the present invention relates to a system and method for real time control of hydraulic fracturing treatments of a formation penetrated by a wellbore, and, in particular, a system and method for determining an optimum pumping schedule which corresponds to an optimum production rate and an optimum return on investment when fracturing a perforated formation penetrated by a wellbore.  
      When fracturing a formation penetrated by a wellbore, a particular pumping schedule is utilized for pumping fracturing fluid into a plurality of perforations in a formation penetrated by the wellbore. Oil and other hydrocarbon deposits will produce from the fractured perforations in response thereto, the oil and other hydrocarbon deposits flowing uphole. A particular production rate corresponds to the particular pumping schedule, the particular production rate representing the rate at which the oil and other hydrocarbon deposits flow uphole. A particular return on investment corresponds to the particular production rate of the hydrocarbon deposits flowing uphole, the particular return on investment representing the amount of a client&#39;s profits being derived from a producing well in connection with the particular production rate of the oil and other hydrocarbon deposits being produced from the well and flowing uphole in relation to the costs for fracturing and producing that well.  
      A client will want to know whether a particular return on investment, associated with a particular production rate and a particular pumping schedule for a single well is an “optimum” one. The term “optimum” is defined by the client. Therefore, it is desirable to determine in advance for a particular well, before a fracturing operation is completed, whether a selected pumping schedule is an “optimum” pumping schedule which, when utilized, will fracture a well in a particular manner such that oil and other hydrocarbon deposits will be produced at an “optimum” production rate thereby generating an “optimum” return on investment for the client.  
     SUMMARY OF INVENTION  
      One aspect of the invention involves a method of determining a pumping schedule adapted for fracturing a formation penetrated by a wellbore, comprising the steps of: defining a selected pumping schedule to include an initial portion and a remaining portion; interrogating a pump data model in response to at least one of the initial portion and the remaining portion thereby generating a return on investment; deciding if the return on investment is an acceptable return on investment; and determining the pumping schedule to be the initial portion and the remaining portion of the selected pumping schedule when the return on investment is an acceptable return on investment.  
      Another aspect of the present invention involves a method of determining a pumping schedule corresponding to a particular return on investment for a particular wellbore, the pumping schedule including an initial pumping schedule and a remaining pumping schedule, comprising the steps of: (a) fracturing one or more perforations in a formation penetrated by the particular wellbore, thereby creating one or more fractures in the formation, in accordance with the initial pumping schedule; (b) analyzing a set of fracture characteristics associated with the one or more fractures in response to the fracturing step; (c) interrogating a pump data model in accordance with the remaining pumping schedule; and (d) determining a particular return on investment for the particular wellbore in response to the interrogating step, the pumping schedule corresponding to the particular return on investment for the particular wellbore when the pump data model is interrogated in accordance with the remaining pumping schedule.  
      Another aspect of the present invention involves a method of determining a return on investment associated with a particular wellbore before completing a fracturing of a formation penetrated by the wellbore, the formation being fractured in response to a particular pumping schedule, a pump data model generating one or more values indicative of the return on investment when interrogated by at least a portion of the pumping schedule, the method comprising the steps of: (a) before completing the fracturing of the formation, interrogating the pump data model in response to at least a portion of the pumping schedule; and (b) generating one or more values indicative of the return on investment in response to the interrogating step.  
      Another aspect of the present invention involves a method of determining a return on investment associated with a particular wellbore before completing a fracturing of a formation penetrated by the wellbore, the formation being fractured in response to a particular pumping schedule, a pump data model generating one or more values indicative of the return on investment when interrogated by at least a portion of the pumping schedule, the method comprising the steps of: (a) calibrating the pump data model; (b) before completing the fracturing of the formation, interrogating the calibrated pump data model in response to at least a portion of the pumping schedule; and (c) generating one or more values indicative of the return on investment in response to the interrogating step.  
      Another aspect of the present invention involves a method of determining a pumping schedule adapted for fracturing a formation penetrated by a wellbore, the pumping schedule including an initial pumping schedule and a remaining pumping schedule, comprising the steps of: (a) fracturing the formation penetrated by the wellbore in accordance with the initial pumping schedule thereby generating fractures in said formation; (b) interrogating a pump data model in response to the remaining pumping schedule thereby generating a return on investment; (c) in response to the interrogating step, deciding whether the return on investment is an acceptable return on investment; and (d) in response to the deciding step, determining the pumping schedule to be the initial pumping schedule and the remaining pumping schedule when the return on investment is an acceptable return on investment.  
      Further scope of applicability of the present invention will become apparent from the detailed description presented hereinafter. It should be understood, however, that the detailed description and the specific examples, while representing a preferred embodiment of the present invention, are given by way of illustration only, since various changes and modifications within the spirit and scope of the invention will become obvious to one skilled in the art from a reading of the following detailed description. 
    
    
     BRIEF DESCRIPTION OF DRAWINGS  
      A full understanding of the present invention will be obtained from the detailed description of the preferred embodiment presented hereinbelow, and the accompanying drawings, which are given by way of illustration only and are not intended to be limitative of the present invention, and wherein:  
       FIG. 1  illustrates a perforating gun perforating a formation penetrated by a wellbore;  
       FIG. 2  illustrates how a fracturing fluid is pumped into the perforations in the formation and fracturing the formation in accordance with a pumping schedule;  
       FIG. 3  illustrates how oil or other hydrocarbon deposits are produced from the fractured perforations in the formation and flow uphole, the hydrocarbon deposits flowing uphole having a production rate in barrels/day and a return on investment corresponding to the production rate;  
       FIGS. 4, 5 , and  6  illustrate three separate wells wherein, by way of example, three separate pumping schedules associated with the three separate wells are used before an “optimum” pumping schedule is realized which corresponds to an “optimum” return on investment;  
       FIGS. 7 and 8  illustrate one particular well wherein one pumping schedule is used for the purpose of determining an “optimum” pumping schedule which corresponds to an “optimum” return on investment;  
       FIGS. 9 and 10  illustrate three separate “time line merged” inputs that are input to a computer system in a well logging truck situated near the particular well of  FIGS. 7 and 8 , the three separate inputs being an initial pumping schedule, tiltmeter data originating from sensors disposed near a fracture in a formation, and micro-seismic data also originating from sensors disposed near the fracture in the formation;  
       FIG. 11  illustrates a construction of the computer system in the well logging truck of  FIGS. 9 and 10 ;  
       FIG. 12  illustrates a block diagram representing a functional operation that is practiced by the computer system of  FIG. 11 , the computer system including a memory which stores a pump data model;  
       FIG. 13  illustrates how and why it is sometimes necessary to calibrate the pump data model;  
       FIGS. 14 through 16  illustrate how an “optimum” pumping schedule which corresponds to an “optimum” return on investment is determined, a remaining pumping schedule being used (and possibly iteratively modified) to interrogate the calibrated pump data model in order to determine an “optimum” production rate and an “optimum” return on investment. 
    
    
     DETAILED DESCRIPTION  
      Referring to  FIG. 1 , a perforating gun  10  is disposed in a wellbore  12  and a packer  14  isolates a plurality of shaped charges  16  of the perforating gun  10  downhole in relation to the environment uphole. The shaped charges  16  detonate and a corresponding plurality of perforations  18  are produced in a formation  20  penetrated by the wellbore  12 .  
      Referring to  FIG. 2 , when the formation  20  is perforated, a fracturing fluid  22  is pumped downhole into the perforations  18  in accordance with a particular pumping schedule  24 . An example pumping schedule is illustrated in  FIGS. 9 and 14 . In response thereto, the formation  20  surrounding the perforations  18  is fractured (see  FIG. 9  for an example of a fracture surrounding the perforations  18  in the formation  20  which is created in response to the pumping of the fracturing fluid  22  into the perforations  18  in accordance with the pumping schedule  24 ).  
      Referring to  FIG. 3 , when the formation  20  surrounding the perforations  18  is fractured, oil or other hydrocarbon deposits  26  begin to flow from the fractures, into the perforations  18 , into the wellbore  12 , and uphole to the surface. The oil or other hydrocarbon deposits flow at a certain “production rate”  28  (in barrels/day) thereby generating a “return on investment”  30 . A client or owner of the wellbore  12  will want to know the return on investment  30  in connection with the production rate  28  of  FIG. 3  in order to further determine whether to continue producing the hydrocarbon deposits  26  from the wellbore  12 . In fact, the client has an “optimum” return on investment in mind and hopes that the wellbore  12  of  FIG. 3  will achieve an “optimum” production rate  28  that corresponds to the “optimum” return on investment.  
      Referring to  FIGS. 4, 5 , and  6 , one method for determining an “optimum” pumping schedule for producing oil or other hydrocarbon deposits at an “optimum” production rate and thereby achieving an “optimum” return on investment is illustrated.  
      In  FIG. 4 , a fracturing fluid  22   a  is pumped into perforations  18  in the formation  20  in accordance with a first pumping schedule (pumping schedule  1 )  24   a.  Responsive thereto, oil and other hydrocarbon deposits  26  begin to flow from the fractured formation  20 , into the perforations  18 , into the wellbore  12 , and uphole to the surface at a first production rate (production rate  1 )  28   a  thereby achieving a first return on investment (return on investment  1 )  30   a.  However, assume that the first return on investment (return on investment  1 )  30   a  is not an “optimum” return on investment from the client/wellbore owner&#39;s point of view. Therefore, the first pumping schedule (pumping schedule  1 )  24   a  is not the “optimum” pumping schedule. As a result, in  FIG. 5 , the method of  FIG. 4  (i.e., the method for determining an “optimum” pumping schedule for producing oil or other hydrocarbon deposits at an “optimum” production rate thereby achieving an “optimum” return on investment) is repeated with a different pumping schedule (pumping schedule  2 ) in an effort to determine an “optimum” pumping schedule for achieving the client/wellbore owner&#39;s “optimum” return on investment.  
      In  FIG. 5 , a fracturing fluid  22   b  is pumped into perforations  18  in the formation  20  in accordance with a second pumping schedule (pumping schedule  2 )  24   b.  Responsive thereto, oil and other hydrocarbon deposits  26  begin to flow from the fractured formation  20 , into the perforations  18 , into the wellbore  12 , and uphole to the surface at a second production rate (production rate  2 )  28   b  thereby achieving a second return on investment (return on investment  2 )  30   b.  However, assume that the second return on investment (return on investment  2 )  30   b  is not an “optimum” return on investment from the client/wellbore owner&#39;s point of view. Therefore, the second pumping schedule (pumping schedule  2 )  24   b  is not the “optimum” pumping schedule. As a result, in  FIG. 6 , the method of  FIGS. 4 and 5  (i.e., the method for determining an “optimum” pumping schedule for producing oil or other hydrocarbon deposits at an “optimum” production rate thereby achieving an “optimum” return on investment) is repeated again with a different pumping schedule in an effort to determine an “optimum” pumping schedule for achieving the client/wellbore owner&#39;s “optimum” return on investment.  
      In  FIG. 6 , a fracturing fluid  22   c  is pumped into perforations  18  in the formation  20  in accordance with a third pumping schedule  24   c.  Responsive thereto, oil and other hydrocarbon deposits  26  begin to flow from the fractured formation  20 , into the perforations  18 , into the wellbore  12 , and uphole to the surface at a third production rate  28   c  thereby achieving a third return on investment  30   c.  Assume now that the third return on investment  30   c  is an “optimum” return on investment from the client/wellbore owner&#39;s point of view. Therefore, the third pumping schedule  24   c  is the “optimum” pumping schedule. As a result, in  FIG. 6 , although the aforementioned method of  FIGS. 4 through 6  (for determining an “optimum” pumping schedule for producing oil or other hydrocarbon deposits at an “optimum” production rate thereby achieving an “optimum” return on investment) was repeated a plurality of times in connection with a corresponding plurality of wellbores, that method did successfully determine the “optimum” pumping schedule for achieving the client/wellbore owner&#39;s “optimum” production rate and the client/wellbore owner&#39;s “optimum” return on investment. However, one disadvantage associated with the method of  FIGS. 4 through 6  relates to the fact that three wellbores (in our example) were fractured in an attempt to determine the “optimum” pumping schedule that achieves the “optimum” return on investment.  
      Referring to  FIGS. 7 through 16 , the aforementioned disadvantage associated with the method of  FIGS. 4 through 6  (for determining an “optimum” pumping schedule for producing oil or other hydrocarbon deposits at an “optimum” production rate achieving an “optimum” return on investment) is eliminated when the method of  FIGS. 7 through 16  (for determining an “optimum” pumping schedule for producing oil or other hydrocarbon deposits at an “optimum” production rate achieving an “optimum” return on investment) is utilized. Recall that the aforementioned disadvantage associated with the method of  FIGS. 4 through 6  relates to the fact that a “plurality of wellbores” (three wellbores in our example) were fractured in an attempt to determine the “optimum” pumping schedule that achieves the “optimum” return on investment. In  FIGS. 7 through 16 , the advantage of the method (for determining an “optimum” pumping schedule for producing oil or other hydrocarbon deposits at an “optimum” production rate achieving an “optimum” return on investment) of  FIGS. 7 through 16  relates to the fact that a “single wellbore” is fractured in an attempt to determine the “optimum” pumping schedule for achieving the “optimum” return on investment; and, during the fracturing of that “single wellbore” of  FIGS. 7 through 16 , the “optimum” pumping schedule for achieving the “optimum” return on investment is determined. Therefore, a method associated with a “single wellbore” for determining an “optimum” pumping schedule for producing oil or other hydrocarbon deposits from the “single wellbore” at an “optimum” production rate thereby achieving an “optimum” return on investment is discussed in the following paragraphs with reference to  FIGS. 7 through 16  of the drawings.  
      In  FIGS. 7 and 8 , referring initially to  FIG. 7 , a fracturing fluid  32  is pumped into the perforations  18  of a wellbore  12  in accordance with a pumping schedule  34 . In  FIGS. 7 and 8 , the wellbore  12  is referred to as a “particular well 36” in order to emphasize the fact that “one single wellbore” is being fractured during the practice of a new and novel method in accordance with the present invention for determining an “optimum” pumping schedule that achieves an “optimum” production rate and an “optimum” return on investment, where the word “optimum” as in “optimum return on investment” represents a term which can only be defined by the owner of the particular well  36 . In  FIG. 8 , in response to the fracturing fluid  32  which was pumped into the perforations  18  of the particular well  36 , oil and other hydrocarbon deposits  38  are produced from the particular well  36 , the oil or other hydrocarbon deposits  38  flowing from the fractures in the formation  20 , into the perforations  18 , into the wellbore, and uphole to the surface. The oil or other hydrocarbon deposits  38  flow at a production rate  40  in barrels per day. A graph of that production rate  40  is illustrated in  FIG. 8 . In  FIG. 8 , the y-axis of the graph of that production rate  40  is the production rate (“prod rate”) in barrels/day and the x-axis of the graph of that production rate  40  is “time”. The graph of the production rate  40  is divided into two parts: an “actual” production rate  40   a  associated with an “initial portion of the pumping schedule”  34  of  FIG. 7 , and two “predicted” production rates  40   b  and  40   c  which would be associated with a “remaining portion of the pumping schedule”  34  of  FIG. 7 : a first “predicted” production rate  40   b  and a second “predicted” production rate  40   c.  The “actual” production rate  40   a  (of the oil or other hydrocarbon deposits  38  produced from the particular well  36 ) reflects the rate at which the oil or other hydrocarbon deposits  38  were actually produced from the particular well  36  in response to the “initial portion of the pumping schedule”  34 , that “initial portion of the pumping schedule”  34  representing the actual pumping of the fracturing fluid  32  into the perforations  18  of the particular well  36 . The first “predicted” production rate  40   b  and the second “predicted” production rate  40   c  (of the oil or other hydrocarbon deposits  38  produced from the particular well  36 ) each reflect the rate at which the oil or other hydrocarbon deposits  38  may, sometime in the future, be produced from the particular well  36  in response to the “remaining portion of the pumping schedule”  34 , that “remaining portion of the pumping schedule”  34  representing a “future potential pumping” of the fracturing fluid  32  into the perforations  18  of the particular well  36 , the “future potential pumping” taking place sometime in the future. Therefore, in  FIG. 8 , the “actual” production rate  40   a  is the result of the actual pumping of a fracturing fluid  32  into the perforations  18  in response to an “initial portion of the pumping schedule”  34  and one of the two “predicted” production rates  40   b  and  40   c  may result from the “future potential pumping” of the fracturing fluid  32  into the perforations  18  in response to the “remaining portion of the pumping schedule”  34 , where the “remaining portion of the pumping schedule”  34  has not yet been implemented. If the first “predicted” production rate  40   b  will follow the “actual” production rate  40   a  (sometime in the future) in response to the “remaining portion of the pumping schedule”  34 , a “first return on investment”  42  will be the result; however, if the second “predicted” production rate  40   c  will follow the “actual” production rate  40   a  (sometime in the future) in response to the “remaining portion of the pumping schedule”  34 , a “second return on investment”  44  will be the result. The client/owner of the wellbore will want to “avoid an undesirable return on investment” (see element numeral  46  in  FIG. 8 ). Assuming that the “second return on investment”  44  is the undesirable one, the client/owner of the wellbore may want to either stop any further pumping of the fracturing fluid  32  into the perforations  18  in accordance with the “remaining portion of the pumping schedule”  34  because of an undesirable return on investment, or that owner of the wellbore may want to modify the “remaining portion of the pumping schedule”  34  for the purpose of achieving a desirable return on investment. The following discussion with reference to  FIGS. 9 through 16  will set forth a method and system by which the owner of the wellbore can determine if an “optimum remaining pumping schedule” associated with pumping schedule  34  can be determined (for the particular “single” well  36 ) that will achieve an “optimum” production rate and an “optimum” return on investment.  
      In  FIGS. 9 and 10 , the pumping schedule  34  includes an “initial pumping schedule”  34   a  and a “remaining pumping schedule”  34   b.  In  FIG. 9 , fracturing fluid and proppant  48  is pumped into the perforation(s)  18  of the particular well  36  in accordance with the “initial pumping schedule”  34   a.  In response thereto, a fracture system  50  is created in the formation around the perforations(s)  18 . In  FIG. 9 , micro-seismic data sensor(s)  52  and tiltmeter data sensor(s)  54  are located adjacent the fractures  50 . The micro-seismic data sensor(s)  52  and the tiltmeter data sensor(s)  54  are adapted to respectively generate output signals  52   a  and  54   a  in response to the creation and further development of the fractures  50 , the output signals  52   a  and  54   a  being communicated to the surface. In  FIGS. 9 and 10 , the micro-seismic data sensor(s)  52  are adapted to generate output signals  52   a  that are communicated to the surface (in response to the creation and further development of the fractures  50 ) representing “micro-seismic data”  52   b;  and the tiltmeter data sensor(s)  54  are adapted to generate output signals  54   a  that are communicated to the surface (in response to the creation and further development of the fractures  50 ) representing “tiltmeter data”  54   b.  In  FIGS. 9 and 10 , the “initial pumping schedule”  34   a,  the tiltmeter data  54   b,  and the micro-seismic data  52   b  are “time line merged” via a “time line merging” block  56  in  FIGS. 9 and 10  wherein a first portion of the tiltmeter data  54   b  and a first portion of the micro-seismic data  52   b  are associated with a first time of the initial pumping schedule  34   a,  and a second portion of the tiltmeter data  54   b  and a second portion of the micro-seismic data  52   b  are associated with a second time of the initial pumping schedule  34   a,  and a third portion of the tiltmeter data  54   b  and a third portion of the micro-seismic data  52   b  are associated with a third time of the initial pumping schedule  34   a,  etc. That is, the tiltmeter data  54   b  and the micro-seismic data  52   b  are synchronized with respective times on the initial pumping schedule  34   a.  In response thereto, a signal representing a “time line merged initial pumping schedule, tiltmeter data, and micro-seismic data”  58  is provided as “input data” to a computer system  60  located in a well logging truck  62  situated at the earth&#39;s surface.  
      In  FIG. 11 , the computer system  60  of  FIGS. 9 and 10  is illustrated. The computer system  60  includes a processor  60   a  operatively connected to a system bus, a recorder or display device  60   b  operatively connected to the system bus, and a program storage device  60   c  operatively connected to the system bus. The “time line merged initial pumping schedule, tiltmeter data, and micro-seismic data” (plus other data including downhole temperature and bottom hole pressure)  58  is provided as “input data” to the computer system  60 . The program storage device  60   c  stores a “bottom hole sensors answer product software”  60   c   1 , the “bottom hole sensors answer product software”  60   c   1  further including a “pump data model”  60   c   2 . When the processor  60   a  of the computer system  60  executes the “bottom hole sensors answer product software”  60   c   1  stored in the program storage device  60   c,  the recorder or display device  60   b  will record or display a “diagnostic display”  60   b   1 . The “pump data model”  60   c   2  and the “diagnostic display”  60   b   1  will be discussed later in this specification. The computer system  60  of  FIG. 11  may be a personal computer (PC), a workstation, or a mainframe. Examples of possible workstations include a Silicon Graphics Indigo 2 workstation or a Sun SPARC workstation or a Sun ULTRA workstation or a Sun BLADE workstation. The program storage device  16   c  is a memory or other computer readable medium which is readable by a machine, such as the processor  60   a.  The processor  60   a  may be, for example, a microprocessor, microcontroller, or a mainframe or workstation processor. The program storage device  60   c,  which stores the Bottom Hole Sensor Answer Product software  60   c   1 , may be, for example, a hard disk, ROM, CD-ROM, DRAM, or other RAM, flash memory, magnetic storage, optical storage, registers, or other volatile and/or non-volatile memory.  
      In  FIG. 12 , a block diagram is illustrated which represents a functional operation that is performed when the “bottom hole sensors answer product software”  60   c   1  is executed by the processor  60   a  of the computer system  60  of  FIG. 11 . In  FIG. 12 , when the “bottom hole sensors answer product software”  60   c   1  is executed by the processor  60   a  of the computer system  60  of  FIG. 11 , the received “input data” (representing the “time line merged initial pumping schedule, tiltmeter data, and micro-seismic data”  58 ) is split into three parts: the initial pumping schedule  34   a,  the tiltmeter data  54   b,  and the micro-seismic data  52   b,  the initial pumping schedule  34   a  being provided as “input data” to the “pump data model”  60   c   2 . The “pump data model”  60   c   2 , which constitutes a portion of the “bottom hole sensors answer product software”  60   c   1 , is a modeling or simulation program. In response to the initial pumping schedule  34   a,  the “pump data model”  60   c   2  portion of the “bottom hole sensors answer product software”  60   c   1  will generate a set of “pump data model fracture characteristics”  64 . The “pump data model fracture characteristics”  64  include the following information representing characteristics of the fracture  50  in  FIG. 9  (see element numeral  64   a  in  FIG. 12 ): fracture length (the length of fracture  50  shown in  FIG. 9 ), fracture height, fracture width, fracture volume (hydraulic and propped), treating pressure, net pressure, bottom hole pressure, temperature, tilts from modeling, and/or pump parameters. In response to the tiltmeter data  54   b,  the “bottom hole sensors answer product software”  60   c   1  will generate a set of “tiltmeter data fracture characteristics”  66 . The “tiltmeter data fracture characteristics”  66  include the following information representing characteristics of the fracture  50  in  FIG. 9  (see element numeral  66   a  in  FIG. 12 ): fracture length, fracture height, fracture width, fracture volume, and/or orientation with respect to the tiltmeter  54  in  FIG. 9 . In response to the micro-seismic data  52   b,  the “bottom hole sensors answer product software”  60   c   1  will generate a set of “micro-seismic data fracture characteristics”  68 . The “micro-seismic data fracture characteristics”  68  include the following information representing characteristics of the fracture  50  in  FIG. 9  (see element numeral  68   a  in  FIG. 12 ): fracture length, fracture height, fracture width, fracture volume and/or orientation with respect to the micro-seismic data sensor  52  in  FIG. 9 . In response to the “pump data model fracture characteristics”  64 , the “tiltmeter data fracture characteristics”  66 , and the “micro-seismic data fracture characteristics”  68 , the “bottom hole sensors answer product software”  60   c   1  will then generate the “diagnostic display”  60   b   1  which is recorded or displayed on the “recorder or display device”  60   b  of the computer system  60  of  FIG. 11 . However, if the “pump data model fracture characteristics”  64  do not substantially match the “tiltmeter data fracture characteristics”  66  and the “micro-seismic data fracture characteristics”  68 , the “pump data model”  60   c   2  itself may need to be calibrated.  
      In  FIG. 13 , a block diagram is illustrated which represents a calibration procedure for calibrating the “pump data model”  60   c   2 . In  FIG. 13 , it was noted above that, if the “pump data model fracture characteristics”  64  do not substantially match the “tiltmeter data fracture characteristics”  66  and the “micro-seismic data fracture characteristics”  68 , the “pump data model”  60   c   2  itself may need to be calibrated.  FIG. 13  represents a calibration procedure for calibrating the “pump data model”  60   c   2 . In  FIG. 13 , refer to step  70 : if the “pump data model fracture characteristics  64  do not substantially match the tiltmeter fracture characteristics  66  and the micro-seismic data fracture characteristics  68 , calibrate the “pump data model”  60   c   2 . In step  72 , when calibrating the “pump data model”  60   c   2 , monitor the diagnostics display  60   b   1  and simultaneously change at least some of the characteristics of the “pump data model”  60   c   2  thereby creating a “modified” pump data model  60   c   2 ; for example, change the following characteristics of the “pump data model”  60   c   2 : (1) the “rock properties”, and (2) the “friction of the proppant in the wellbore”. In step  74 , interrogate the “modified” pump data model  60   c   2  using the initial pumping schedule  34   a  (a step which is shown in  FIG. 12 ) thereby creating a “modified” set of “pump data model fracture characteristics”  64 . In step  76 , do the “modified” set of “pump data model fracture characteristics”  64  substantially match the “tiltmeter data fracture characteristics”  66  and the “micro-seismic data fracture characteristics”  68 ? If no, repeat steps  72 ,  74 , and  76 . If yes, step  78  indicates that the “pump data model”  60   c   2  is now calibrated.  
      Now that the “pump data model”  60   c   2  is properly calibrated, the “remaining pumping schedule”  34   b  of  FIG. 9  will now be used to interrogate the calibrated “pump data model”  60   c   2  for the purpose of determining the “pump data model fracture characteristics”  64  associated with the “remaining pumping schedule”  34   b  including the “production rate” and the “return on investment” associated with the particular well  36  of  FIG. 9 . In response thereto, the owner of the particular well  36  can determine whether the particular well  36  will ultimately produce an “optimum” return on investment.  
      In  FIG. 14 , the pumping schedule  34  of  FIG. 9  is illustrated again. The pumping schedule  34  includes an initial pumping schedule  34   a  and a remaining pumping schedule  34   b.    
      In  FIG. 15 , the remaining pumping schedule  34   b  is used to interrogate the pump data model  60   c   2  (in the manner illustrated in  FIG. 12 ) to determine a production rate and a return on investment for the particular well  36  of  FIG. 9 . The owner of the particular well  36  hopes: (1) that the production rate will be an “optimum” production rate, and (2) that the return on investment will be an “optimum” return on investment. In  FIG. 15 , if all goes well, in steps  80 ,  82 ,  84 , and  86 , the “remaining pumping schedule”  34   b  of  FIG. 14  (step  80 ) interrogates the “pump data model”  60   c   2  of  FIG. 12  (step  82 ) thereby producing a production rate which, hopefully, is an “optimum” production rate (step  84 ) and a return on investment which, hopefully, is an “optimum” return on investment (step  86 ).  
      However, if the aforementioned production rate of step  84  in  FIG. 15  is not an “optimum” production rate, and if the aformentioned return on investment of step  86  in  FIG. 15  is not an “optimum” return on investment, it may be necessary to change some of the characteristics of the remaining pumping schedule  34   b  in  FIG. 14  in order to ensure that the “pump data model”  60   c   2  of step  82  in  FIG. 15  will produce an “optimum” production rate and an “optimum” return on investment.  
      In  FIG. 16 , therefore, when the “pump data model”  60   c   2  of step  78  in  FIG. 13  is properly calibrated, the following steps should be taken in order to ensure that the “pump data model”  60   c   2  produces an “optimum” or “acceptable” production rate and an “optimum” or “acceptable” return on investment. In step  88  of  FIG. 16 , when the “pump data model”  60   c   2  is calibrated, determine the “remaining pumping schedule”  34   b  and use the “remaining pumping schedule”  34   b  to interrogate the “pump data model”  60   c   2 . In step  90 , interrogate the “pump data model”  60   c   2  using the “remaining pumping schedule”  34   b.  In step  92 , determine a new set of “pump data model fracture characteristics”  64  of  FIG. 12  corresponding to the “remaining pumping schedule”  34   b.  In step  94 , determine a “production rate” corresponding to the “remaining pumping schedule”  34   b.  In step  96 , determine a “return on investment” corresponding to the “production rate”. In step  98 , is the “return on investment” determined in step  96  an “acceptable” or “optimum” return on investment? If no, in step  100 , recalling from  FIG. 14  that the “pumping schedule”  34  includes a “frac fluid” column and a “proppant” column, change the proportions of “frac fluid” and “proppant” in the “remaining pumping schedule”  34   b  to determine a “new remaining pumping schedule”. In step  102 , use the “new remaining pumping schedule” to interrogate the “pump data model”  60   c   2  (in the manner illustrated in  FIG. 12 ). Repeat steps  90 ,  92 ,  94 , and  96  to determine a “new return on investment”. In step  98 , is the “new return on investment” an “acceptable” or “optimum” return on investment? If yes, in step  104 , the “new remaining pumping schedule”, which produced the “new return on investment”, corresponds to an “acceptable” or “optimum” return on investment.  
      A functional description of the operation of the present invention will be set forth in the following paragraphs with reference to  FIGS. 1 through 16  of the drawings.  
      The present invention pertains to a method and system for determining an optimum pumping schedule corresponding to an optimum return on investment when fracturing a formation penetrated by a wellbore. A pumping schedule is selected for pumping fracturing fluid into a plurality of perforations in a formation penetrated by a wellbore. When the formation is fractured, a production rate and a return on investment is determined for the particular well. However, that production rate and return on investment is a function of the pumping schedule selected. If an “optimum” pumping schedule is selected for fracturing the plurality of perforations in the formation penetrated by the wellbore, an “optimum” production rate (i.e., the rate at which the oil or other hydrocarbon deposits are produced from the fractured perforations) is produced and, as a result, an “optimum” return on investment is the result, where the term “optimum” is determined by the owner of the wellbore. The “optimum” pumping schedule has been determined by selecting a plurality of pumping schedules for a respective plurality of wellbores and, after fracturing the perforations in those plurality of wellbores, eventually determining the “optimum” pumping schedule that corresponds to the “optimum” return on investment”. However, a plurality of wellbores are utilized during the above-referenced practice of determining the “optimum” pumping schedule that corresponds to the “optimum” return on investment.  
      A better method (for determining an “optimum” pumping schedule that corresponds to an “optimum” production rate and an “optimum” return on investment) would involve determining the “optimum” pumping schedule that corresponds to the “optimum” return on investment for “one particular wellbore”, and not for a plurality of wellbores as previously described. According to this better method, a “particular pumping schedule”  34  is divided into an “initial pumping schedule”  34   a  and a “remaining pumping schedule”  34   b;  and “one particular wellbore”  36  is selected to be fractured in accordance with that “particular pumping schedule”  34 . The Earth formation penetrated by the “one particular wellbore”  36  is perforated in the manner described above with reference to  FIG. 1  of the drawings. Then, the resulting perforations  18  in the formation penetrated by the “one particular wellbore”  36  are fractured in accordance with the “initial pumping schedule”  34   a  in the manner described above with reference to  FIGS. 2 and 9  of the drawings thereby producing a fracture system  50  in the formation. A set of micro-seismic data sensor(s)  52  and a set of tiltmeter data sensor(s)  54  are placed adjacent the fractures  50 , as shown in  FIG. 9  of the drawings. The micro-seismic data sensor(s)  52  generate a plurality of micro-seismic data  52   a  and the tiltmeter data sensor(s)  54  generate a plurality of tiltmeter data  54   b.  The “initial pumping schedule” includes a plurality of times, as shown in  FIG. 9  of the drawings. The “initial pumping schedule”  34   a,  the tiltmeter data  54   b,  and the micro-seismic data  52   b  then undergo “time line merging”  56  of  FIG. 9 , wherein, the plurality of tiltmeter data  54   b  and the plurality of micro-seismic data  52   b  which corresponds, respectively, to the plurality of times of the “initial pumping schedule”  34   a  are determined. As a result of the aforementioned “time line merging”  56 , a “time line merged initial pumping schedule, tiltmeter data, and micro-seismic data” output signal  58  is generated. The “time line merged initial pumping schedule, tiltmeter data, and micro-seismic data” output signal  58  is provided as an “input signal” to a computer system  60  of a well logging truck  62 , as shown in  FIGS. 9 and 10 . In response to the “time line merged initial pumping schedule, tiltmeter data, and micro-seismic data” output signal  58 , the processor  60   a  of the computer system  60  in the well logging truck  62  executes a stored software called the “Bottom Hole Sensors Answer Product Software”  60   c   1  that includes a “pump data model”  60   c   2 . In response to the execution of the stored software  60   c   1  by the processor  60   a,  as shown in  FIG. 12 , the “initial pumping schedule”  34   a  will interrogate the “pump data model”  60   c   2  and thereby generating the “pump data model fracture characteristics”  64 , the tiltmeter data  54   b  will generate the “tiltmeter data fracture characteristics”  66 , and the micro-seismic data  52   b  will generate the “micro-seismic data fracture characteristics”  68 . In  FIG. 12 , the “pump data model fracture characteristics”  64 , the “tiltmeter data fracture characteristics”  66 , and the “micro-seismic data fracture characteristics”  68  will collectively generate a “diagnostic display”  60   b   1  that is recorded or displayed on the recorder or display device  60   b  of the computer system  60  disposed in the well logging truck  62 . If the “pump data model fracture characteristics”  64  of  FIG. 12  do not substantially match the “tiltmeter data fracture characteristics”  66  and the “micro-seismic data fracture characteristics”  68 , the “pump data model”  60   c   2  of  FIGS. 11 and 12  must be calibrated in the manner described above with reference to  FIG. 13  of the drawings. When the “pump data model fracture characteristics”  64  of  FIG. 12  substantially matches the “tiltmeter data fracture characteristics”  66  and the “micro-seismic data fracture characteristics”  68 , the “pump data model”  60   c   2  is calibrated. At this point of the novel method of the present invention, referring to  FIGS. 14 and 15 , the “remaining pumping schedule”  34   b  of the pumping schedule  34  interrogates the calibrated “pump data model”  60   c   2  and, hopefully, an “optimum” production rate for the particular well  36  of  FIG. 9  is determined and an “optimum” return on investment for the particular well  36  of  FIG. 9  is also determined. In  FIG. 16 , if the “optimum” production rate and the “optimum” return on investment is not determined when the “remaining pumping schedule”  34   b  of  FIG. 14  fractures the perforations  18  of the particular wellbore  36  of  FIG. 9 , as shown in  FIG. 16 , change the proporations of the “frac fluid” and the “proppant” in the “remaining pumping schedule”  34   b  of  FIG. 14  (see block  100  of  FIG. 16 ) to thereby create a “new remaining pumping schedule” and then use the resultant “new remaining pumping schedule” to interrogate the “pump data model”  60   c   2  (see block  102  of  FIG. 16 ). If the resultant “production rate” and the resultant “return on investment” are acceptable (i.e., an “optimum” production rate and an “optimum” return on investment are generated), the owner of the particular wellbore  36  of  FIG. 9  must now consider whether or not to continue to actually fracture the particular wellbore  36  using either the “remaining pumping schedule”  34   b  or the “new remaining pumping schedule” in the manner described above with reference to  FIG. 2  of the drawings.  
      Functional Specification for the Bottom Hole Sensors Answer Product Software  60   c   1   
      A functional specification associated with the “Bottom Hole Sensors Answer Product Software”  60   c   1  of  FIG. 11  will be set forth in the following paragraphs:  
      User interactions are performed through the Recorder or Display Device  60   b  in  FIG. 11 . Where a specification indicates a display, it refers to this device and where it refers to the User doing something it infers interaction with this device. The display is a terminal screen and the input device can be a keyboard, mouse or a touch screen.  
      Where the input device is a touch screen, the input device and the terminal screen are the same thing.  
      Timeline merging ( 56  in  FIG. 10  and  58  in  FIG. 11 )  
      1. The pump parameters are treated as the Primary Source, this serves as the timeline for the merged dataset.  
      2. All other sources (e.g. microseismic, tiltmeter, bottom hole pressure, temperature etc.) are considered as Secondary Sources.  
      3. Data from Secondary Sources is intially buffered.  
      4. The time location for an observation in the Secondary Source is read from the buffer.  
      5. The corresponding time is located in the Primary Source  
      6. The information from the Secondary Source buffer is appended to the Primary Source information at the correct time, creating the Merged Data Set.  
      7. This operates continuously during real-time data acquisition so that the Merged Data is continuously available for processing.  
      8. If Secondary Source data appears with timestamps more recent than the more recent Primary Source data, it is buffered until needed.  
      9. If the Primary Source ends (or fails), one of the Secondary Sources will be selected, by the user, to become the Primary Source so that data-merging can continue.  
      Pump Data Model Fracture Characteristics ( 64  and  64   a  in  FIG. 12  and  60   c   2  in  FIG. 11 )  
      1. The forward model includes information on rock properties, such as Young&#39;s Modulus, in-situ stress, Poisson&#39;s Ratio, permeability, reservoir pressure etc.  
      2. There are multiple available fracture models (1-, 2- and 3-dimensional) and the user selects whichever is most appropriate for the current job.  
      3. This is a numerical model based on physical principles  
      4. The model is used to create predictions of the possible observables such as the examples listed in  64   a  of  FIG. 12 .  
      5. These output predictions are stored ready for display along-side observations for comparison.  
      Tiltmeter Data Fracture Characteristics ( 66  in  FIG. 12 )  
      1. An inversion algorithm is used to calculate the size and shape of the distortion that resulted in the tilt.  
      2. There are multiple such algorithms avialable and the user selects whichever is most appropriate for the current job.  
      Microseismic Data Fracture Characteristics ( 68  and  68   a  in  FIG. 12 )  
      1. The user can view the microseismic event locations in three orthogonal two-dimensional views (East vs. North, North vs. Depth and East vs. Depth).  
      2. Interactively the user may draw a box around a sub-set of the microseismic points, relating to the hydraulic fracture.  
      3. The interpretation in step 2 allows the experienced user to differentiate microseismic events from the fracturing from, say, events generated by movement of an existing fault plane nearby.  
      4. The microseismic points lying inside a particular interpretation box are considered as an interpretation set.  
      5. For each interpretation set, the minimum-distance least-squares line through the points is considered to be the interpreted axis of the fracture.  
      6. The center of the fracture is considered to be located at the mean position of the microseismic events in the interpretation box.  
      7. The length of the fracture is determined by the furthest distance of a microseismic event along the interpreted axis in either direction.  
      8. The length is stored in each direction as a half-length, so that asymmetry of the fracture may be determined.  
      9. The height of the fracture is determined by the further distance of a microseismic event perpendicular to the axis along the minimum-distance least-squares plane through the points.  
      10. The height is stored in each direction from the center as a half-height, so that again symmetry can be analyzed.  
      11. The elliptical area of the fracture is determined from the length and height information.  
      12. The rectangular area of the fracture is determined from the length and height information.  
      13. The orientation of the fracture is determined as the orientation of the interpreted axis.  
      14. The fracture characteristics determined from the microseismic information are stored (by  60   c  in  FIG. 11 ).  
      Diagnostic Display ( 60   b   1  in  FIG. 11  and  FIG. 12 )  
      1. The diagnostic display is completely configurable in terms of which graphs are displayed.  
      2. The configuration for a particular job contains graphs that compare stored information. This can be observations, results from the Pump Data Model ( 64  and  64   a  in  FIG. 12 ), results from the Tiltmeter Data ( 66  and  66   a  in  FIG. 12 ), results from the Microseismic Data ( 68  and  68   a  in  FIG. 12 )  
      3. The interaction for the user to intepret fracture characteristics from microseismic described above, can be achieved using a diagnostic plot.  
      4. Diagnostic plots can carry automatic alarms. These alarms can be triggered by any information trigger (for example greater-than, less-than a value; difference between modeled and observed values of the same property etc.) see  70  in  FIG. 13   
      5. The alarms alert the user immediately to early-warning signals that the original operation is not producing the desired results.  
      6. Alarms can be set for any observation, any fracture characteristic derived from observation, or any model output.  
      7. Alarms can be created for any mathematical combination of the values described in step 6.  
      8. The Diagnostic Displays can show predictions based on the portion of the pump schedule not yet pumped.  
      9. The Diagnostic Displays can show results from production simulation and return on investment.  
      Calibration of the pump model ( 72 ,  74 ,  76  and  78  in  FIG. 13 )  
      1. The user decides to perform a calibration, and so clicks on the “Calibrate” button to initiate the process.  
      2. The pump schedule is split into the fixed portion (that which has been pumped so far  34   a  in  FIG. 14 ) and the remaining portion (that which is yet to be pumped  34   b  in  FIG. 14 ).  
      3. Concentrating on the fixed portion, the user can further split the pumpshcedule into calibration intervals.  
      4. The user selects a match-point within each calibration interval (in time) where the obesrvations and the model will be compared.  
      5. The user selects the appropriate quantity (rock properties or friction of the proppant) to vary to achieve the match.  
      6. The program iteratively adjusts the appropriate quantity to improve the match at the define match-points until the root-mean-square difference between the modeled and measured values is below a user-defined limit. This is an iterative optimization.  
      7. Once the match is good as defined in step 6, the Pump Data Model is considered to be calibrated and useful for predictions.  
      Optimizing the remaining pump schedule  
      1. The fixed portion and remaining portion of the pump schedule ( 80  in  FIG. 15 ) are used with the Pump Data Model to provide a prediction for the current job.  
      2. The output from the Pump Data Model includes a propped fracture length and a fracture conductivity. It is the fracture characteristics resulting from completing the current job with the remaining portion of the pump schedule ( 90  in  FIG. 16 )  
      3. The fracture length and conductivity, along with rock properties are inputs to a production simulator ( 84  in  FIG. 15 ).  
      4. The production simulator is a numerical simulator that uses mass-balance and flow equations to model the predicted flow of hydrocarbons through the well during reservoir production.  
      5. There are several production simulators available and the user selects the most appropriate one for this job.  
      6. The production simulator uses specified well controls (for example a constant draw-down pressure) to numerically model the production expected from the fractured well.  
      7. The output of the production simulator is the production vs. time (commonly known as the Decline Curve (the “Production Rate” in  94  of  FIG. 16 ). It may also include other production parameters, such as water-cut versus time.  
      8. The outputs from the production simulator are forwarded to the Return On Investment calculation ( 86  in  FIG. 15 ).  
      9. The return on investment considers the cost of the fracture treatment and the monetary value of the decline curve, plus any costs associated with handling unwanted production (such as the water-cut). These are the known costs.  
      10. The return on investment simulator is a numerical simulator that provides a monetary value over time for the results of the fracturing.  
      11. There are several ways to calculated return on investment available. The user selects the most appropriate.  
      12. The return on investment provides an output of return versus time from the production data and the known costs. ( 96  on  FIG. 16 )  
      13. An adjustment is made to the fluid and proppant pumped in the remaining portion of the pump schedule.  
      This is made under the constraint of the total materials available at the well-site minus the total materials pumped so far ( 102  on  FIG. 16 ).  
      14. Steps from 1 through 13 are repeated iteratively to improve the return on investment in line with the client&#39;s definition of an “optimum” return. ( 98  on  FIG. 16 ). The results of each iteration are used in calculating the best updates to make in step 13, so that this scheme converges to the optimum solution over a few iterations.  
      15. The remaining portion of the pump schedule that has been determined by the above scheme represents an optimum alternative to the original remaining portion of the pump schedule ( 104  in  FIG. 16 ).  
      16. A graphical display contrasts the return on investment for continuing with the original remaining portion or, instead, using the newly determined remaining portion.  
      17. The client is then able to select between the alternatives, and any changes are relayed to the pump operator.  
      18. This calibration and optimization scheme can be recalculated at any time during the job. The portion of fixed schedule being determined at the time the user begins to calibrate.  
       19 . The calibration and optimization are rapid operations compared to the length of the pump schedule.  
      The invention being thus described, it will be obvious that the same may be varied in many ways. Such variations are not to be regarded as a departure from the spirit and scope of the invention, and all such modifications as would be obvious to one skilled in the art are intended to be included within the scope of the following claims.