Patent Publication Number: US-8116979-B2

Title: System and method for determining a more accurate resistivity model of a geological formation using time-lapse well logging data

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     The present application is a continuation-in-part of U.S. patent application Ser. No. 11/075,471 filed Mar. 9, 2005, the contents of which are incorporated herein by reference thereto. 
    
    
     BACKGROUND OF THE INVENTION 
     Petroleum engineers generally estimate an amount of hydrocarbons stored in a geological formation based on well logging data, including resistivity measurements, from the formation. Logging-while-drilling (“LWD”) sensors provide resistivity measurements of a geological formation as a wellbore is being drilled through the geological formation. Wireline (“WL”) sensors provide resistivity measurements of the geological formation after the wellbore has been drilled through the geological formation. For the purposes of this application, a wireline or WL sensor should be understood to include any sensor deployed in a pre-drilled borehole, such as those deployed on slick lines or coiled tubing. After the wellbore has been drilled, mud and other material can penetrate into the geological formation adjacent the wellbore, which is called an “invaded” zone. The invaded zone can distort resistivity measurements associated with the geological formation. 
     Because the WL resistivity measurements are strongly affected by several environmental effects, such as borehole rugosity, invasion, and shoulder-bed effects from adjacent layers, special modeling and inversion based interpretation techniques have been utilized to extract information about the formation properties from the WL resistivity measurements. Similarly, because the LWD resistivity measurements are also strongly affected by the foregoing environmental effects, special modeling and inversion based interpretation techniques have been utilized to extract information about the formation properties from the LWD resistivity measurements. 
     A problem associated with the current interpretation techniques, however, is that the techniques generate a model of a geological formation that may represent an equivalent solution of an inverse problem and therefore does not accurately represent an actual resistivity model of the geological formation. 
     Accordingly, there is a need for an improved system and method for determining a more accurate model of a geological formation using well logging data from both a LWD sensor and a WL sensor. 
     BRIEF DESCRIPTION OF THE INVENTION 
     A method for estimating a model of a geological formation in accordance with an exemplary embodiment is provided. The geological formation has a wellbore drilled therethrough. The method includes obtaining a first resistivity log associated with the geological formation from a LWD sensor or a similar immediate sensor in the wellbore. The first resistivity log comprises a plurality of resistivity measurements. The method further includes obtaining a second resistivity log associated with the geological formation from a WL or later-run sensor in the wellbore. The second resistivity log comprises a plurality of resistivity measurements. The method further includes calculating a plurality of horizontal resistivity values associated with the geological formation by utilizing a first inversion technique and the first resistivity log. The method further includes obtaining a plurality of invaded zone resistivity values obtained from a micro-resistivity measurement device in the WL sensor. The method further includes calculating a plurality of invaded zone thickness values proximate the wellbore by utilizing a second inversion technique and the second resistivity log, wherein the plurality of horizontal resistivity values are fixed values and the plurality of invaded zone resistivity values are fixed values, wherein the plurality of invaded zone thickness values, the plurality of invaded zone resistivity values, and the plurality of horizontal resistivity values comprise a first model of the geological formation. 
     A system for estimating a model of a geological formation in accordance with another exemplary embodiment is provided. The geological formation has a wellbore drilled therethrough. The system includes a database configured to store a first resistivity log associated with the geological formation from a LWD sensor or a similar immediate sensor in the wellbore. The first resistivity log comprises a plurality of resistivity measurements. The database is further configured to store a second resistivity log associated with the geological formation from a WL sensor or later-run sensor in the wellbore. The second resistivity log comprises a plurality of resistivity measurements. The database is further configured to store a plurality of invaded zone resistivity values obtained from a micro-resistivity measurement device in the WL sensor. The system further includes a computer operably coupled, permanently or temporarily, to the database. The computer is configured to calculate a plurality of horizontal resistivity values associated with the geological formation by utilizing a first inversion technique and the first resistivity log. The computer is further configured to calculate a plurality of invaded zone thickness values proximate the wellbore by utilizing a second inversion technique and the second resistivity log, wherein the plurality of horizontal resistivity values are fixed values and the plurality of invaded zone resistivity values are fixed values, wherein the plurality of invaded zone thickness values, the plurality of invaded zone resistivity values, and the plurality of horizontal resistivity values comprise a first model of the geological formation. 
     A method for estimating a model of a geological formation in accordance with another exemplary embodiment is provided. The geological formation has a wellbore drilled therethrough. The method includes obtaining a first resistivity log associated with the geological formation from a LWD sensor or a similar immediate sensor in the wellbore. The first resistivity log comprises a plurality of resistivity measurements. The method further includes obtaining a second resistivity log associated with the geological formation from a WL sensor or later-run sensor in the wellbore. The second resistivity log comprises a plurality of resistivity measurements. The method further includes calculating a plurality of horizontal resistivity values associated with the geological formation by utilizing a first inversion technique and the first resistivity log. The method further includes calculating a plurality of invaded zone resistivity values and a plurality of invaded zone thickness values proximate the wellbore by utilizing a second inversion technique and the second resistivity log, wherein the plurality of horizontal resistivity values are fixed values, wherein the plurality of invaded zone thickness values, the plurality of invaded zone resistivity values, and the plurality of horizontal resistivity values comprise a first model of the geological formation. 
     A system for estimating a model of a geological formation in accordance with another exemplary embodiment is provided. The geological formation has a wellbore drilled therethrough. The system includes a database configured to store a first resistivity log associated with the geological formation from a LWD sensor or a similar immediate sensor in the wellbore. The first resistivity log comprises a plurality of resistivity measurements. The database is further configured to store a second resistivity log associated with the geological formation from a WL sensor or later sensor in the wellbore. The second resistivity log comprises a plurality of resistivity measurements. The system further includes a computer operably coupled, temporarily or permanently, to the database. The computer is configured to calculate a plurality of horizontal resistivity values associated with the geological formation by utilizing a first inversion technique and the first resistivity log. The computer is further configured to calculate a plurality of invaded zone resistivity values and a plurality of invaded zone thickness values proximate the wellbore by utilizing a second inversion technique and the second resistivity log, wherein the plurality of horizontal resistivity values are fixed values, wherein the plurality of invaded zone thickness values, the plurality of invaded zone resistivity values, and the plurality of horizontal resistivity values comprise a first model of the geological formation. 
     A method for determining an invaded zone thickness value associated with a formation in accordance with another exemplary embodiment. The formation has a wellbore extending therethrough. The method includes obtaining a first measurement associated with the formation, utilizing a computer. The method further includes obtaining a second measurement and a third invaded zone measurement associated with the formation, after obtaining the first measurement, utilizing the computer. The method further includes calculating the invaded zone thickness value for the wellbore using a first inversion technique, based on the first measurement, the second measurement, and the third invaded zone measurement, utilizing the computer. The method further includes storing the invaded zone thickness value in a database, utilizing the computer. 
     A system for determining an invaded zone thickness value associated with a formation in accordance with another exemplary embodiment is provided. The formation has a wellbore extending therethrough. The system includes a database configured to store a first measurement associated with the formation. The database is further configured to later store a second measurement and a third invaded zone measurement associated with the formation. The system further includes a computer operably coupled to the database. The computer is configured to calculate an invaded zone thickness value for the wellbore using a first inversion technique, based on the first measurement, the second measurement, and the third invaded zone measurement. The computer is further configured to store the invaded zone thickness value for the wellbore in the database. 
     A method for determining an invaded zone resistivity value and an invaded zone thickness value associated with a formation in accordance with another exemplary embodiment is provided. The formation has a wellbore extending therethrough. The method includes obtaining a first measurement associated with the formation, utilizing a computer. The method further includes calculating the invaded zone resistivity value and the invaded zone thickness value for the wellbore by utilizing an inversion technique, based on the first measurement, utilizing the computer. The method further includes storing the invaded zone resistivity value and the invaded zone thickness value for the wellbore in a database, utilizing the computer. 
     A system for determining an invaded zone resistivity value and an invaded zone thickness value associated with a formation in accordance with another exemplary embodiment is provided. The formation has a wellbore extending therethrough. The system includes a database configured to store a first measurement associated with the formation. The system further includes a computer operably coupled to the database. The computer is configured to calculate the invaded zone resistivity value and the invaded zone thickness value for the wellbore by utilizing an inversion technique, based on the first measurement. The computer is further configured to store the invaded zone resistivity value and the invaded zone thickness value for the wellbore in the database. 
     Other systems and/or methods of the invention according to the embodiments will become or are apparent to one with skill in the art upon review of the following drawings and detailed description. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram of a system for estimating a model of the geological formation in accordance with an exemplary embodiment; 
         FIG. 2  is a schematic of an exemplary geological formation; 
         FIGS. 3-7  are flowcharts of a method for estimating a model of a geological formation in accordance with another exemplary embodiment; and 
         FIGS. 8-9  are flowcharts of a method for estimating a model of a geological formation in accordance with another exemplary embodiment. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to  FIG. 1 , a system  10  for determining a mathematical model of the geological formation is illustrated. The system  10  includes a computer  12 , an LWD sensor  14 , a WL sensor  16 , a database  18 , a display device  20 , and a keyboard  22 . 
     It will be appreciated by those skilled in the art that, although a computer  12  is referenced and depicted as a single unit, that several processors, within the same unit or residing distances apart, could work collaboratively as a computer and are considered a “computer” for purposes of this application. Similarly, a “computer” may comprise a processor only or be a unit hardwired into any unit that fulfills another function. 
     Similarly, it will be appreciated that, although LWD sensors describe a certain set of sensors in the art, in this application the term is used in its broadest sense to describe a sensor which takes a reading or measurement immediately or soon after drilling a wellbore. An LWD sensor would not, therefore, need to be a part of a bottom hole assembly (BHA) or adjacent to a drill bit. Indeed, a traditional wireline sensor could be used as the LWD sensor if it could be run through the wellbore quickly enough after drilling the wellbore. 
     It will be also appreciated that, although a WL sensor describes a certain set of sensors in the art, the definitions previously set out for that term apply within this application. The exact method of running the WL sensor is not definitive of a WL sensor; rather, the fact that the sensor is run later, after the borehole has been drilled, is of definitional importance to the WL sensor as that term is used in this application. 
     Referring to  FIG. 2 , before explaining the system  10  in greater detail, a brief explanation of a geological formation will now be described. The geological formation  40  includes layers  42 ,  44 ,  46 . Of course, the geological formation  40  can include a plurality of additional layers that are not shown. When drilling the wellbore  48  through the geological formation  40 , a region surrounding the wellbore  48  called an “invaded region” is partially filled with drilling mud and other material. Further, the invaded region has resistivity characteristics different than a portion of a layer outside of the invaded region. A mathematical model or Earth model of the geological formation  40  includes a plurality of parameters associated with each layer of the formation  40 . The model can comprise either an isotropic model or in anisotropic model. An isotropic model of a geological formation includes the following parameters for each layer: (i) a horizontal resistivity Rh, (ii) an invaded zone resistivity Rxo, and (iii) an invaded zone thickness Lxo. The anisotropic model of a geological formation comprises the foregoing parameters and further includes the vertical resistivity value Rv. The invaded zone resistivity Rxo corresponds to a resistivity of the invaded region of a layer of the geological formation  40 . The invaded zone thickness value Lxo corresponds to a thickness of the invaded region outwardly from the wellbore  48 . The horizontal resistivity value Rh corresponds to a resistivity of a portion of the layer that extends outwardly from the invaded region. The vertical resistivity value Rv corresponds to a vertical resistivity of a portion of the layer that extends outwardly from the invaded region. The term “resistivity” can be represented by ohms per meter or by any other number of convenient units of measure. 
     For purposes of discussion, when a plurality of model parameters are being discussed, the subscript “i” will be utilized. For example, a plurality of horizontal resistivity values is represented by Rh i , a plurality of invaded zone resistivity values is represented by Rxo i , and a plurality of invaded zone thickness values is represented by Lxo i , and a plurality of vertical resistivity values is represented by Rv i . 
     Referring to  FIG. 1 , the various components of system  10  will now be explained. The computer  10  is provided to obtain resistivity values from the LWD sensor  14 , and the WL sensor  16  and to generate first and second resistivity logs, respectively, which are a stored in the database  18 . It should be noted that in an alternative embodiment, the sensor  14  can comprise at least one of a wireline sensor, a nuclear magnetic resonance sensor, a density sensor, a tracer-based nuclear sensor, an acoustic sensor, a sensor disposed on a slickline, and a sensor disposed on a coil tubing. Further, in an alternative embodiment, the sensor  16  can comprise at least one of a nuclear magnetic resonance sensor, a density sensor, a tracer-based nuclear sensor, an acoustic sensor, a sensor disposed on a slickline, and a sensor disposed on a coil tubing. The computer  10  is further provided to determine a model of the geological formation  40 . In particular, computer  10  can calculate parameters representing an isotropic model or an anisotropic model of the geological formation  40 . The computer  10  is operably coupled to the LWD sensor  14 , the WL sensor  16 , the database  18 , the display device  20 , and the keyboard  22 . The coupling may be permanent or temporary, including wired, wireless or media couplings. “Coupling” is intended to encompass any means of data communication between the units. 
     The LWD sensor  14  is provided to generate one or more resistivity logs associated with the geological formation  40  when the wellbore  48  is being drilled through the geological formation  40  by a drilling rig (not shown). Each resistivity log comprises a plurality of resistivity measurements. The LWD sensor  14  comprises an induction sensor, known to those skilled in the art, which generates signals indicating apparent resistivity values of the geological formation  40 . 
     The WL sensor  16  is provided to generate one or more resistivity logs associated with the geological formation  40  after the wellbore  48  has been formed by a drilling rig (not shown). Each resistivity log comprises a plurality of resistivity measurements. The LWD sensor  14  comprises an induction sensor, known to those skilled in the art, which generates signals indicating apparent resistivity values of the geological formation  40 . In an alternate embodiment, the LWD sensor  14  comprises a galvanic sensor known to those skilled in the art. The WL sensor  16  is further configured to provide microresistivity measurements utilizing x-axis, y-axis, and z-axis coils therein. Other embodiments may use different manners of resistivity sensors. 
     The database  18  is provided to store the one or more resistivity logs associated with the LWD sensor  14  and one or more resistivity logs associated with the WL sensor  16 . The database  18  is configured to communicate with the computer  12 . It will be appreciated by those skilled in the art that “database” as it is used in this application is used in its broadest sense and may comprise one or more individual databases and may include database systems that store data in disparate locations. 
     The keyboard  22  is provided to allow a user to input information for inducing the computer  12  to determine a model of the geological formation  40 . The keyboard  22  is operably coupled to the computer  12 . 
     The display device  20  is provided to display parameters associated with a model of the geological formation  40 . The display device  20  is operably coupled to the computer  12 . 
     Referring to  FIGS. 3-7 , a method for estimating a model of a geological formation  41  in accordance with an exemplary embodiment will now be described. The method may be, in one embodiment, implemented utilizing a software program executed in the computer  12 . 
     At step  70 , the computer  12  stores a first plurality of resistivity logs associated with a geological formation  40  from a LWD sensor  14 , in the database  18 . Each resistivity log of the first plurality of resistivity logs comprises a plurality of resistivity measurements. Of course, alternately, the computer  12  could store only one resistivity log from the LWD sensor  14  if desired, instead of the first plurality of resistivity logs. 
     At step  72 , the computer  12  stores a second plurality of resistivity logs associated with the geological formation  40  from the WL sensor  16 , in the database  18 . Each resistivity log of the second plurality of resistivity logs comprises a plurality of resistivity measurements. Of course, alternately, the computer  12  could store only one resistivity log from the WL sensor  16  if desired, instead of the second plurality of resistivity logs. 
     At step  74 , the computer  12  calculates a plurality of horizontal resistivity values (Rh i ) associated with the geological formation  40  by utilizing an inversion technique and the first plurality of resistivity logs from the LWD sensor  14 . Each resistivity value of the plurality of horizontal resistivity values (Rh i ) is associated with a layer in the geological formation  40 . The inversion technique utilized in step  74 , and in other steps described herein, comprise a least-squares inversion technique (based on a local linearization of a non-linear inverse problem). The least squares inversion technique utilizes forward modeling during each iteration of the inversion technique in order to calculate a Jacobian matrix. For example, one or more of the inversion techniques described in commonly owned U.S. Pat. No. 5,889,729, which is hereby incorporated by reference in this entirety, can be utilized for each inversion technique discussed herein. Of course, any other inversion technique known to those skilled in the art can be utilized for each step utilizing an inversion technique discussed herein. 
     Referring to  FIG. 5 , the step  74  is implemented utilizing the steps  100 - 110 . At step  100 , the computer  12  estimates a first value for a horizontal resistivity value (Rh) associated with each layer of the geological formation  40 . 
     At step  102 , the computer  12  calculates a plurality of synthetic or estimated horizontal resistivity logs using mathematical modeling of the geological formation  40  and the first value for the horizontal resistivity value (Rh) of each layer. 
     At step  104 , the computer  12  calculates a data fit value using the plurality of synthetic horizontal resistivity logs and the first plurality of resistivity logs. The data fit value indicates how closely the plurality of synthetic horizontal resistivity logs approximate the first plurality of resistivity logs, and thus the accuracy of the mathematical model of the geological formation  40 . 
     At step  106 , the computer  12  makes a determination as to whether the data fit value is less than a threshold data fit value. If the value of step  106  equals “yes”, the method advances to step  108 . Otherwise, the method advances to step  110 . 
     At step  108 , the computer  12  indicates that a determined value for the horizontal resistivity value (Rh) of each layer is valid. After step  108 , the method advances to step  76 . 
     At step  110 , the computer  12  modifies the first value for the horizontal resistivity value (Rh) of each layer. After the step  110 , the method advances to step  102 . 
     Referring to  FIG. 3 , after step  74  is completed, the method advances to step  76 . At step  76 , the computer  12  stores a plurality of invaded zone resistivity values (Rxo i ) in the database  18 , obtained from a microresistivity log. The microresistivity log is generated by the WL sensor  16  disposed proximate an invaded zone of the geological formation  40  surrounding the wellbore  48 . Each resistivity value of the plurality of invaded zone resistivity values (Rxo i ) is associated with a layer in the geological formation  40 . 
     At step  78 , the computer  12  calculates a plurality of invaded zone thickness values (Lxo i ) proximate the wellbore  48  by utilizing an inversion technique and the second plurality of resistivity logs from the WL sensor  16 , wherein the plurality of horizontal resistivity values (Rh i ) are fixed values and the plurality of invaded zone resistivity values (Rxo i ) are fixed values. Each thickness value in the plurality of invaded zone thickness values (Lxo i ) is associated with a layer in the geological formation  40 . 
     Referring to  FIG. 6 , the step  78  is implemented utilizing the steps  120 - 130 . At step  120 , the computer  12  estimates a first value for the invaded zone thickness value (Lxo) associated with each layer of the geological formation  40 . 
     At step  122 , the computer  12  calculates a plurality of synthetic invaded zone thickness logs using mathematical modeling of the geological formation  40  and the first value for the invaded zone thickness value (Lxo) of each layer, wherein the plurality of horizontal resistivity values (Rh i ) are fixed values and the plurality of invaded zone resistivity values (Rxo i ) are fixed values. 
     At step  124 , the computer  12  calculates a data fit value using the plurality of synthetic invaded zone thickness logs and the second plurality of resistivity logs. The data fit value indicates how closely the plurality of synthetic invaded zone thickness logs approximate the second plurality of resistivity logs. 
     At step  126 , the computer  12  makes a determination as to whether the data fit value is less than the threshold data fit value. If the value of step  126  equals “yes”, the method advances to step  128 . Otherwise, the method advances to step  130 . 
     At step  128 , the computer  12  indicates that a determined value for the invaded zone thickness value (Lxo) of each layer is valid. After step  128 , the method advances to step  80 . 
     At step  130 , the computer  12  modifies the first value for the invaded zone thickness value (Lxo) of each layer. After step  130 , the method advances to step  122 . 
     Referring to  FIGS. 3 and 4 , after step  78  is completed, the method advances to step  80 . At step  80 , the computer  12  queries an operator as to whether an anisotropic model of the geological formation  40  is desired. If the value of step  80  equals “yes”, the method advances to step  84 . Otherwise, the method advances to step  82 . 
     At step  82 , the computer  12  stores the plurality of invaded zone thickness values (Lxo i ), the plurality of invaded zone resistivity values (Rxo i ), and the plurality of horizontal resistivity values (Rh i ), in the database  18 , which correspond to an isotropic model of the geological formation  40 . After step  82 , the method is exited. 
     At step  84 , the computer  12  stores a plurality of multi-component induction measurements obtained from x-axis, y-axis, and z-axis coils in the WL sensor  16 , in the database  18 . 
     At step  86 , the computer  12  calculates a plurality of vertical resistivity values (Rv i ) associated with the geological formation  40  by utilizing an inversion technique and the plurality of multi-component induction measurements from the WL sensor  16 , wherein the plurality of invaded zone thickness values (Lxo i ) are fixed values, the plurality of invaded zone resistivity values (Rxo i ) are fixed values, and the plurality of horizontal resistivity values (Rh i ) are fixed values. Each resistivity value of the plurality of vertical resistivity values (Rv i ) is associated with a layer in the geological formation  40 . 
     Referring to  FIG. 7 , the step  86  is implemented utilizing the steps  140 - 150 . At step  140 , the computer  12  estimates a first value for the vertical resistivity (Rv) associated with each layer of the geological formation  40 . 
     At step  142 , the computer  12  calculates a plurality of synthetic vertical resistivity logs using mathematical modeling of the geological formation  40  and the first value for the vertical resistivity (Rv) of each layer, wherein the plurality of invaded zone thickness values (Lxo i ) are fixed values, the plurality of invaded zone resistivity values (Rxo i ) are fixed values, and the plurality of horizontal resistivity values (Rh i ) are fixed values. 
     At step  144 , the computer  12  calculates a data fit value using the plurality of synthetic vertical resistivity logs and the plurality of multi-component induction measurements from the WL sensor  16 . The data fit value indicates how closely the plurality of synthetic vertical resistivity logs approximate the plurality of multi-component induction measurements. 
     At step  146 , the computer  12  makes determination as to whether the data fit value is less than a threshold data fit value. If the value of step  146  equals “yes”, the method advances to step  148 . Otherwise, the method advances step  150 . 
     At step  148 , the computer  12  indicates that a determined value for the vertical resistivity (Rv) of each layer is valid. After step  150 , the method advances to step  88 . 
     At step  150 , the computer  12  modifies the first value for the vertical resistivity (Rv) of each layer. After step  150 , the method advances to step  142 . 
     Referring to  FIG. 4 , after step  86  is completed, the method advances to step  88 . At step  88 , the computer  12  stores the plurality of vertical resistivity values (Rv i ), the plurality of invaded zone thickness values (Lxo i ), the plurality of invaded zone resistivity values (Rxo i ), and the plurality of horizontal resistivity values (Rh i ), in the database  18 , which correspond to an anisotropic model of the geological formation  40 . After step  88 , the method is exited. 
     Referring to  FIGS. 8-9 , a method for estimating a model of a geological formation  40  in accordance with another exemplary embodiment will now be described. The method is implemented utilizing a software program executed in the computer  12 . 
     At step  160 , the computer  12  stores a first plurality of resistivity logs associated with the geological formation  40  from the LWD sensor  14 , in the database  18 . Each resistivity log of the first plurality of resistivity logs comprises a plurality of resistivity measurements. Of course, alternately, the computer  12  could store only one resistivity log from the LWD sensor  14  if desired, instead of the first plurality of resistivity logs. 
     At step  162 , the computer  12  stores a second plurality of resistivity logs associated with the geological formation  40  from the WL sensor  16 , in the database  18 . Each resistivity log of the second plurality of resistivity logs comprises a plurality of resistivity measurements. Of course, alternately, the computer  12  could store only one resistivity log from the WL sensor  16  if desired, instead of the second plurality of resistivity logs. 
     At step  164 , the computer  12  calculates a third plurality of horizontal resistivity values (Rh i ) associated with the geological formation  40  by utilizing an inversion technique and the first plurality of resistivity logs from the LWD sensor  14 . Each resistivity value of the third plurality of horizontal resistivity values (Rh i ) being associated with a layer in the geological formation  40 . The step  164  is implemented utilizing steps similar to those described above with respect to step  74 . 
     At step  166 , the computer  12  calculates a fourth plurality of invaded zone resistivity values (Rxo i ) and a fifth plurality of invaded zone thickness values (Lxo i ) proximate the wellbore  48  by utilizing an inversion technique and the second plurality of resistivity logs from the WL sensor  16 , wherein the third plurality of horizontal resistivity values (Rh i ) are fixed values. 
     Referring to  FIG. 9 , the step  166  is implemented utilizing the steps  170 - 180 . At step  170 , computer  12  estimates a first value for an invaded zone thickness value (Lxo) and a second value for the invaded zone resistivity value (Rxo) associated with each layer of the geological formation  40 . 
     At step  172 , the computer  12  calculates a plurality of synthetic invaded zone thickness logs and a plurality of synthetic invaded zone resistivity logs using mathematical modeling of the geological formation  40  and the first value for an invaded zone thickness value (Lxo) and the second value for the invaded zone resistivity value (Rxo) of each layer. 
     At step  174 , the computer  12  calculates a first data fit value using the plurality of synthetic invaded zone thickness logs and the plurality of synthetic invaded zone resistivity logs and the second plurality of resistivity logs from the WL sensor  16 . 
     The first data fit value indicates how closely (i) the plurality of synthetic invaded zone thickness logs approximate the second plurality of resistivity logs, and (ii) the plurality of synthetic invaded zone resistivity logs approximate the second plurality of resistivity logs from the WL sensor  16 . 
     At step  176 , the computer  12  makes a determination as to whether the first data fit value is less than a threshold data fit value. If the value of step  176  equals “yes”, the method advances to step  178 . Otherwise, the method advances to step  180 . 
     At step  178 , the computer  12  indicates that a determined value for the invaded zone thickness value (Lxo) and a determined value for the invaded zone resistivity value (Rxo) of each layer are valid. After step  178 , the method advances to step  168 . 
     At step  180 , the computer  12  modifies the first value for an invaded zone thickness value (Lxo) and the second value for the invaded zone resistivity value (Rxo) of each layer. After step  180 , the method advances to step  172 . 
     Referring to  FIG. 8 , after step  166  is completed, the method advances to step  168 . At step  168 , the computer  12  stores the fifth plurality of invaded zone thickness values (Lxo i ), the fourth plurality of invaded zone resistivity values (Rxo i ), and the third plurality of horizontal resistivity values (Rh i ), in the database  18 , which correspond to an isotropic model of the geological formation  40 . After step  168 , the method is exited. 
     The system and the method for determining a model of a geological formation provide a substantial advantage over other systems and methods. In particular, the system and the method provide a technical effect for determining a unique and more accurate model of a geological formation using logging data from a WL sensor and logging data from a LWD sensor. 
     As described above, the present invention can be embodied in the form of computer-implemented processes and apparatuses for practicing those processes. The present invention can also be embodied in the form of computer program code containing instructions embodied in tangible media, such as floppy diskettes, CD ROMs, hard drives, or any other computer-readable storage medium, wherein, when the computer program code is loaded into and executed by a computer, the computer becomes an apparatus for practicing the invention. The present invention can also be embodied in the form of computer program code, for example, whether stored in a storage medium, loaded into and/or executed by a computer, or transmitted over some transmission medium, such as over electrical wiring or cabling, through fiber optics, or via electromagnetic radiation, wherein, when the computer program code is loaded into and/or executed by a computer, the computer becomes an apparatus for practicing the invention. When implemented on a general-purpose microprocessor, the computer program code segments configure the microprocessor to create specific logic circuits. 
     While the invention is described with reference to an exemplary embodiment, it will be understood by those skilled in the art that various changes may be made and equivalence may be substituted for elements thereof without departing from the scope of the invention. In addition, many modifications may be made to the teachings of the invention to adapt to a particular situation without departing from the scope thereof. Therefore, it is intended that the invention not be limited to the embodiment disclosed for carrying out this invention, but that the invention includes all embodiments falling with the scope of the intended claims. Moreover, the use of the terms first, second, etc. does not denote any order of importance, but rather the terms first, second, etc. are used to distinguish one element from another.