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TECHNICAL FIELD 
       [0001]    This invention relates generally to systems and methods for monitoring a well. 
       BACKGROUND 
       [0002]    Monitoring the state of a well and the state of the surrounding formation remains difficult. Information about the state of the well and the state of the formation is useful, for example, to detect issues at an early stage where changes in operation can be made and remedial action can be implemented to prevent partial or complete loss of a well. 
       SUMMARY 
       [0003]    The present disclosure provides systems and methods for monitoring a well. The systems and methods are configured to identify or analyze various issues affecting the well including corrosion, cement quality, and fluid migration. One advantage of systems and methods that are described herein is the ability to continuously monitor a well. Another advantage is that systems and methods monitor more area of a well and with greater resolution. The systems and methods also simplify certain operations. 
         [0004]    According to an exemplary embodiment, a method for monitoring corrosion of a casing of a well includes measuring internal pressure of the casing, measuring strain of the casing with a system comprising at least one string of interconnected sensors that is arranged such that the sensors are distributed along a length and the circumference of the casing, and determining the thickness of the casing as a function of internal pressure and strain. A system configured to monitor corrosion of a casing of a well includes a pump configured to control internal pressure of the casing, a gauge configured to measure internal pressure of the casing, at least one string of interconnected sensors that is arranged such that the sensors are distributed along the length and circumference of the casing and configured to measure strain of the casing, and a computing unit configured to receive measurements of internal pressure and strain and to determine thickness of the casing as a function of internal pressure and strain. 
         [0005]    According to another exemplary embodiment, a method for analyzing cement in the annulus of a well includes controlling internal pressure of a casing of the well, measuring internal pressure of the casing, measuring strain of the casing with a system comprising at least one string of interconnected sensors that is arranged such that the sensors are distributed along a length and the circumference of the casing, the measured strain being a function of internal pressure, and determining the quality of the cement as a function of strain of the casing and internal pressure. Another method for analyzing cement in a well annulus includes measuring strain of a casing in the well with a system including at least one string of interconnected sensors that is arranged such that the sensors are distributed along a length and the circumference of the casing, and, after pumping cement into the well annulus, establishing a baseline that is a function of steady state strain measurements within a first time period, and identifying strain measurements that substantially deviate from the baseline during a second time period. 
         [0006]    According to another exemplary embodiment, a method for identifying fluid migration or inflow associated with a wellbore tubular includes measuring strain of the wellbore tubular with a system comprising at least one string of interconnected sensors that is arranged such that the sensors are distributed along a length and the circumference of the wellbore tubular, establishing a baseline that is a function of steady state strain measurements within a first time period, and identifying fluid migration or inflow where strain measurements substantially deviate from the baseline within a second time period. 
         [0007]    According to yet another exemplary embodiment, a method for analyzing fluid proximate an injection well includes turning an injector on or off, determining temperature along a casing of the well during a first time period, and associating a rate of temperature change during the first time period with a fluid. 
         [0008]    The foregoing has broadly outlined some of the aspects and features of the present disclosure, which should be construed to be merely illustrative of various applications of the teachings. Other beneficial results can be obtained by applying the disclosed information in a different manner or by combining various aspects of the disclosed embodiments. Other aspects and a more comprehensive understanding may be obtained by referring to the detailed description of the exemplary embodiments taken in conjunction with the accompanying drawings, in addition to the scope defined by the claims. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0009]      FIG. 1  is a schematic illustration of an exemplary injection operation. 
           [0010]      FIG. 2  is a partial cross-sectional view of a well reinforced with a casing according to an exemplary embodiment. 
           [0011]      FIG. 3  is a partial elevational view of the casing of  FIG. 2  and a monitoring system according to an exemplary embodiment. 
           [0012]      FIG. 4  is a graphical illustration of an exemplary response of a strain string of the monitoring system of  FIG. 3 . 
           [0013]      FIG. 5  is a graphical illustration of an exemplary response of strain strings of the monitoring system of  FIG. 3 . 
           [0014]      FIG. 6  is a partial cross-sectional view of the casing of  FIG. 2  including a corroded area. 
           [0015]      FIG. 7  is a graphical illustration of thickness along the length of the casing of  FIG. 6 . 
           [0016]      FIG. 8  is a graphical illustration of thickness at a point on the casing of  FIG. 6  at different times. 
           [0017]      FIG. 9  is a partial cross-sectional view of the casing of  FIG. 2  that is undergoing a minifrac treatment. 
           [0018]      FIG. 10  is a graphical illustration of strain and internal pressure of the casing of  FIG. 9 . 
           [0019]      FIG. 11  is a partial cross-sectional view of the casing of  FIG. 2  illustrating flow migration along the outside of the casing. 
           [0020]      FIG. 12  is a graphical illustration of strain over time along the length of the casing of  FIG. 11 . 
           [0021]      FIG. 13  is a graphical illustration of a horizontal gravel pack according to an exemplary embodiment. 
           [0022]      FIG. 14  is a graphical illustration of strain of a gravel pack screen of the gravel pack of  FIG. 13 . 
           [0023]      FIG. 15  is a partial cross-sectional view of a well reinforced with concentric casings illustrating exemplary flows moving along the outside of the outermost casing and between the casings. 
           [0024]      FIG. 16  is a graphical illustration of pressure difference and temperature corresponding to strain strings on each of the concentric casings of  FIG. 15 . 
           [0025]      FIG. 17  is a partial cross-sectional view of the casing of  FIG. 2  including permeable beds of carbon dioxide and water. 
           [0026]      FIG. 18  is a graphical illustration of temperature at different points along the length of the casing of  FIG. 17  over time. 
           [0027]      FIG. 19  is a partial cross-sectional view of the casing of  FIG. 2  where cement pumped into an annulus is partially cured. 
           [0028]      FIGS. 20 and 21  are graphical illustrations of temperature and external pressure at a point on the casing of  FIG. 19  during an exemplary curing process. 
           [0029]      FIG. 22  is a graphical illustration of external pressure at different times along the length of the casing of  FIG. 19 . 
       
    
    
     DETAILED DESCRIPTION 
       [0030]    As required, detailed embodiments are disclosed herein. It must be understood that the disclosed embodiments are merely exemplary of the teachings that may be embodied in various and alternative forms, and combinations thereof. As used herein, the word “exemplary” is used expansively to refer to embodiments that serve as illustrations, specimens, models, or patterns. The figures are not necessarily to scale and some features may be exaggerated or minimized to show details of particular components. In other instances, well-known components, systems, materials, or methods have not been described in detail in order to avoid obscuring the present disclosure. Therefore, specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a basis for the claims and as a representative basis for teaching one skilled in the art. 
         [0031]    For purposes of teaching, the systems and methods of this disclosure will be described in the context of monitoring a well, wellbore tubular, and the surrounding formation. However, the teachings of the present disclosure are also useful in other environments, such as to monitor pipes and the surrounding environment in refineries, gas plants, pipelines, and the like. 
         [0032]    As used herein, a wellbore tubular is a cylindrical element of a well. Wellbore tubulars to which the systems and methods can be applied include a well casing, a non-perforated tubular, a perforated tubular, a drill pipe, a joint, a production tube, a casing tube, a tubular screen, a sand screen, a gravel pack screen, combinations thereof, and the like. The wellbore tubular can be formed from steel or other materials. 
         [0033]    The systems and methods are configured to monitor the wellbore tubular during production or non-production operations including injection, depletion, completion, cementing, gravel packing, frac packing, production, stimulation, waterflood, a gas miscible process, inert gas injection, carbon dioxide flood, a water-alternating-gas process, liquefied petroleum gas drive, chemical flood, thermal recovery, cyclic steam injection, steam flood, fire flood, forward combustion, dry combustion, well testing, productivity test, potential test, tubing pressure, casing pressure, bottomhole pressure, downdraw, combinations thereof, and the like. An exemplary injection operation is illustrated in  FIG. 1 . Here, injection wells  10   a  include injectors or fluid pumps  2  that inject fluid  4  into a permeable bed  6  of a formation  12  to drive oil toward a production well  10   b.    
         [0034]    The systems and methods are configured to investigate downhole well problems such as those indicated by changes in production. Such problems include crossflow, premature breakthrough, casing leaks, fluid migration, corrosion, tubing leaks, packer leaks, channeled cement, other problems with cement quality, blast joint leaks, thief zones, combinations thereof, and the like. The systems and methods facilitate identifying the points or intervals of fluid entry/exit, the flow rate at such points, the type of fluid at such points, and the origin of the fluids coming into the well. The systems and methods are further configured to investigate the integrity of a well as part of a routine maintenance operation. 
         [0035]    Herein, a suffix (a, b, c, etc.) or subscript (1, 2, 3, etc.) is affixed to an element numeral that references like elements in a general manner so as to differentiate a specific one of the like elements. For example, strain string  22   a  is a specific one of strain strings  22 . 
         [0036]    Referring to  FIG. 2 , a well  10  includes a borehole  11  that is drilled in a formation  12 . To prevent well  10  from collapsing or to otherwise line or reinforce well  10 , well  10  includes a string of casings  14  that are inserted and cemented in borehole  11 . Cement  16  is pumped up an annulus  15  between casing  14  and the wall of borehole  11  to provide bonded cement sheath  16  that secures casing  14  in borehole  11 . Alternatively, well  10  may be formed according to other methods. Referring momentarily to  FIG. 15 , string of casings  14  includes concentric casings  14   a,    14   b.    
         [0037]    Continuing with  FIG. 2 , for purposes of teaching, coordinate systems are now described. A Cartesian coordinate system can be used that includes an x-axis, a y-axis, and a z-axis that are orthogonal to one another. The z-axis corresponds to the longitudinal axis of casing  14  and any position on casing  14  can be established according to an axial position z and a position in the x-y plane, which is perpendicular to the z-axis. In the illustrated embodiment, casing  14  is cylindrical and any position on casing  14  can be established using a Cylindrical coordinate system. Here, the z-axis is the same as that of the Cartesian coordinate system and a position lying in the x-y plane is represented by a radius r and a position angle α and referred to as a radial position rα. Radius r defines a distance of the radial position rα from the z-axis and extends in a direction determined by position angle α to the radial position rα. Here, position angle α is measured from the x-axis. A bending direction represents the direction of a bending moment on casing  14 . The bending direction is represented by a bending angle rβ that is measured relative to the x-axis. A reference angle φ is measured between bending angle rβ and position angle α. 
       Monitoring System 
       [0038]    Referring now to  FIGS. 2 and 3 , a monitoring system  20  is configured to monitor casing  14  and formation  12 . Monitoring system  20  includes strain strings  22  that include interconnected sensors  24 . Strain strings  22  are wrapped around casing  14  so as to position sensors  24  along the axial length and circumference of casing  14 . As such, strain strings  22  are integral to well  10  and configured to measure strain of casing  14  at a range of azimuth angles and a range of depth locations. Grooves  30  are formed in casing  14  and strain strings  22  are recessed in grooves  30 . In alternative embodiments, strain strings  22  are deployed on the inside of casing  14  and may be permanently or temporarily attached. Strings  22  can be laminated to casing  14  or pressed against casing  14  by a covering or expandable layer of material. 
         [0039]    In the illustrated embodiments, monitoring system  20  includes a plurality of strain strings  22   a ,  22   b  and each strain string  22   a ,  22   b  winds substantially helically at least partially along the length of casing  14 . Strain strings  22   a ,  22   b  are arranged at different constant inclinations that are hereinafter referred to as wrap angles θ 1 , θ 2 . Illustrated wrap angles θ 1 , θ 2  are measured with respect to x-y planes although equivalent alternative formulations can be achieved by changing the reference plane. In alternative embodiments, strings include a series of segments that are arranged at different inclinations so as not to intersect one another. 
         [0040]    In general, wrapping strain strings  22  at wrap angle θ is beneficial in that strain strings  22  experience a fraction of the strain experienced by casing  14 . Additionally, each wrap angle θ 1 , θ 2  is effective for a range of strain and the use of multiple strain strings  22   a ,  22   b  with different wrap angles θ 1 , θ 2  expands the overall range of strain that monitoring system  20  can measure. For example, strain string  22  with wrap angle θ of 20° may fail at one level of strain while strain string with wrap angle θ of 30° or more may not fail at the same level of strain or at a slightly higher level of strain. The use different wrap angles θ also facilitates determining unknown parameters, as described in further detail below. Another advantage of wrapping casing  14  with multiple strain strings  22   a ,  22   b  is that there is added redundancy in case of failure of one of strain strings  22 . The additional data collected with multiple strain strings  22  makes recovery of a 3-D image an overdetermined problem thereby improving the quality of the image. 
         [0041]    Referring again to  FIG. 15  where casings  14   a ,  14   b  are concentric, strain strings  22  are wrapped around each of concentric casings  14   a ,  14   b . Such an arrangement is useful in certain applications, as described in further detail below. Otherwise, strain strings  22  are generally wrapped around outermost casing  14   a  as geomechanical deformations are best transferred to outermost casing  14   a  from formation  12 . Alternatively, strain strings  22  can be coupled to outermost casing  14   a  by cementing, centralization, or other movement limiters. 
         [0042]    Continuing with  FIGS. 2 and 3 , monitoring system  20  includes a temperature string  32  of sensors  33 . As such, monitoring system  20  is configured to operate as a distributed temperature sensing (DTS) system. Illustrated temperature string  32  is positioned against casing  14  and configured to take temperature measurements along the length of casing  14  and independently of strain strings  22 . Alternatively, temperature string  32  can be wrapped around casing  14  as described above with respect to strain strings  22 . Temperature strings  32  and strain strings  22  are used in combination according to certain exemplary methods as described in further detail below. 
         [0043]    Monitoring system  20  further includes single point pressure gauges  34  and temperature gauges  36  that are positioned to measure pressure and temperature independently of strain strings  22  and temperature strings  32 . For example, internal pressure from fluid levels and well head annular pressure is measured with a pressure gauge  34  that is positioned inside casing  14 . Alternatively, other independent means of measuring or calculating temperature and pressure can be used. 
         [0044]    Monitoring system  20  further includes a data acquisition unit  38  and a computing unit  40 . Illustrated data acquisition unit  38  collects the response of each of strain strings  22 , temperature strings  32 , and single point gauges  34 ,  36 . The response and/or data representative thereof are provided to computing unit  40  to be processed. Computing unit  40  includes computer components including a data acquisition unit interface  42 , an operator interface  44 , a processor unit  46 , a memory  48  for storing information, and a bus  50  that couples various system components including memory  48  to processor unit  46 . 
       Strain Strings 
       [0045]    Strain strings  22  are now described in further detail. There are many different suitable types of strain strings  22  that can be associated with monitoring system  20 . For example, strain strings  22  can be waveguides such as optical fibers and sensors  24  can be wavelength-specific reflectors such as periodically written fiber Bragg gratings (FBG). An advantage of optical fibers with periodically written fiber Bragg gratings is that fiber Bragg gratings are less sensitive to vibration or heat and consequently are more reliable. In alternative embodiments, sensors  24  can be other types of gratings, semiconductor strain gages, piezoresistors, foil gages, mechanical strain gages, combinations thereof, and the like. For purposes of illustration, according to a first exemplary embodiment described herein, strain strings  22  are optical fibers and sensors  24  are fiber Bragg gratings. 
         [0046]    Referring to  FIGS. 4 and 5 , a wavelength response λ n  of strain string  22  is data representing reflected wavelengths λ r  at sensors  24 . The reflected wavelengths λ r  each represent a fiber strain ε f  measurement at a sensor  24 . Here, wavelength responses λ n , are plotted with respect to axial positions z of sensors  24  or along the longitudinal axis of casing  14 . 
         [0047]    Generally described, reflected wavelength λ r  is substantially equal to a Bragg wavelength λ b  plus a change in wavelength Δλ. Reflected wavelength λ r  is equal to Bragg wavelength λ b  when fiber strain ε f  measurement is substantially zero and, when fiber strain ε f  measurement is non-zero, reflected wavelength λ r  differs from Bragg wavelength λ b . The difference is change in wavelength Δλ and thus change in wavelength Δλ is the part of reflected wavelength λ r  that is associated with fiber strain ε f  . Bragg wavelength λ b  provides a reference from which change in wavelength Δλ is measured at each of sensors  24 . The relationship between change in wavelength Δλ and fiber strain ε f  is described in further detail below. 
         [0048]    Fiber strain ε f  may be due to forces including axial forces, shear forces, ovalization forces, and compaction forces. Such forces may be exerted, for example, by formation  12 , by the inflow of fluid between formation  12  and casing  14 , and by a pressure difference across the wall of casing  14 . Fiber strain ε f  also may be due to changes in temperature. Referring to  FIGS. 4 and 5 , fiber strain ε f  due to such forces and changes in temperature can have both a constant (DC) component and sinusoidal (AC) components. Referring to  FIG. 5 , axial forces, temperature changes, and pressure differences across the wall of the casing  14  are observed in the constant component (wavelength response λ n  that is observed as a constant (DC) shift from Bragg wavelength λ b ). Here, the different constant components correspond to different strain strings  22   a ,  22   b  wrapped at different wrap angles θ 1 , θ 2 . Referring to  FIG. 4 , bending of casing  14  at a radius of curvature R or ovalization of casing  14  due to hoop forces are observed in the sinusoidal component. 
       Relationship Between Change in Wavelength and Strain 
       [0049]    An equation that may be used to relate change in wavelength Δλ and fiber strain ε f  imposed on sensors  24  is given by Δλ=λ b (1−PE)Kε f . As an example, Bragg wavelength λ b  may be approximately  1560  nanometers. The term (1−P e ) is a fiber response which, for example, may be 0.8. P e  is a photoelastic coefficient. Bonding coefficient K represents the bond of sensor  24  to casing  14  and, for example, may be 0.9 or greater. 
       Relationships Between Fiber Strain and Axial Strain, Hoop Strain, Temperature, and Pressure 
       [0050]    The constant component of measured fiber strain ε f  is related to axial strain ε a  and hoop strain ε h  of casing  14  according to: 
         [0000]      ε f   =K ·(−1+√{square root over (sin(θ) 2 ·(1−ε a ) 2 +cos(θ) 2 ·( 1+vε   a ) 2 )}{square root over (sin(θ) 2 ·(1−ε a ) 2 +cos(θ) 2 ·( 1+vε   a ) 2 )}{square root over (sin(θ) 2 ·(1−ε a ) 2 +cos(θ) 2 ·( 1+vε   a ) 2 )}{square root over (sin(θ) 2 ·(1−ε a ) 2 +cos(θ) 2 ·( 1+vε   a ) 2 )}) and
 
         [0000]      ε f   =K ·(−1+√{square root over (sin(θ) 2 ·( 1−vε   h ) 2 +cos(θ) 2 ·(1+ε h ) 2 )}{square root over (sin(θ) 2 ·( 1−vε   h ) 2 +cos(θ) 2 ·(1+ε h ) 2 )}{square root over (sin(θ) 2 ·( 1−vε   h ) 2 +cos(θ) 2 ·(1+ε h ) 2 )}{square root over (sin(θ) 2 ·( 1−vε   h ) 2 +cos(θ) 2 ·(1+ε h ) 2 )})
 
         [0000]    where K is the bonding coefficient of the fiber to the tubular, θ is wrap angle, and v is Poisson&#39;s ratio. The constant component of measured fiber strain ε f  is a function of the difference between the internal pressure P i  and the external pressure P o  of casing  14  that is given in terms of hoop strain ε h  by: 
         [0000]    
       
         
           
             
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         [0000]    where D is inner diameter of casing  14 , w is wall thickness, and E is Young&#39;s modulus of the casing material. The constant component of measured fiber strain ε t  is further a function of change in temperature given by: 
         [0000]      ε f ρΔT
 
         [0000]    where p is the coefficient of thermal expansion. 
         [0051]    Where bending is present, fiber strain ε f  may be associated with axial strain ε a  at a sensor  24  position on casing  14  according to: 
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         [0000]    Here, fiber strain ε f  measured by sensor  24  at a position on casing  14  is a function of axial strain ε a  at the position, radius of curvature R at the position, Poisson&#39;s ratio v, wrap angle θ, and radial position which is represented in the equation by radius r and reference angle φ. Fiber strain ε f  is measured, wrap angle θ is known, and radius r is known. Poisson&#39;s ratio v is typically known for elastic deformation of casing  14  and unknown for non-elastic deformation of casing  14 . Radius of curvature R, reference angle θ, and axial strain ε a  are typically unknown and are determined through analysis of wavelength response λ n . Similarly, Poisson&#39;s ratio v can be determined through analysis of wavelength response λ n , where Poisson&#39;s ratio v is unknown. 
         [0052]    In general, signal processing can be used along with the equations to determine axial strain ε a , radius of curvature R, reference angle φ, Poisson&#39;s ratio v, hoop strain ε h , temperature T (relative to calibrated temperature), internal pressure P i , and external pressure P o  from fiber strain ε f  measured along the length and circumference of casing  14 . Examples of applicable signal processing techniques include deconvolution and inversion where a misfit is minimized and turbo boosting. Using the constant component of fiber strain ε f , signal processing can be used to determine pressure and temperature profiles along the length of casing  14 . The pressure and temperature profiles provide information that is useful for monitoring casing  14  and formation  12 . In general, thermal strains and strain due to fluid pressure changes are much less than geomechanical strain due to the formation  12 . 
         [0053]    Exemplary monitoring methods that are used during operations such as injection, depletion, completion (cement curing), and the like are described below. In addition, exemplary monitoring methods that are used to detect features such as corrosion, flow or leaks, fluid migration, and the like are described below. 
       Corrosion Monitoring 
       [0054]    Referring to FIGS.  3  and  6 - 8 , exemplary methods of monitoring corrosion with monitoring system  20  are now described. Using a modified version of an equation introduced above, wall thickness w of casing  14  can be determined according to: 
         [0000]    
       
         
           
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         [0000]    As decrease in thickness w reflects corrosion, casing  14  can be monitored for corrosion by monitoring the thickness w of casing  14  over time or with respect to the original thickness w. For example, the thickness w calculated at some point in time t 1 , t 2  can be compared to the original thickness w(t 0 ) of casing  14  (or to a previously calculated thickness w or some other baseline thickness) to determine how much corrosion has taken place and the rate of corrosion. Corrosion may be internal, external, or both. In  FIG. 6 , corrosion C is illustrated in an area A and the corresponding thickness w that is determined from fiber strain ε f  measurement is shown in  FIG. 7 . Multiple calculations of thickness w at a point z 1  in area A at different times t 1 , t 2  are shown in  FIG. 8  to illustrate the rate of corrosion. 
         [0055]    According to an exemplary method, internal pressure P i  is controlled with a fluid pump  2  (see  FIG. 1 ) as well  10  is shut-in. Internal pressure P i  is measured with internal pressure gauge  34 , the diameter D and Young&#39;s modulus E of casing  14  are known, and hoop strain ε h  is determined from fiber strain ε f  measured with the strain strings  22  of monitoring system  20 . Here, thickness w and external pressure P o  are unknown parameters that are found using the thickness equation along with measurements of internal pressure P i  and hoop strain ε h . Multiple measurements of hoop strain ε f  are utilized to be able to determine both external pressure P o  and thickness w with the equation. For example, multiple measurements of hoop strain ε h  can be determined for each of multiple internal pressures P i . Where internal pressure P i  is can be determined along casing  14  and strain strings  22  make hoop strain ε h  measurements along casing  14 , thickness w can be found along the length and around the circumference of casing  14  all at once. As another example, multiple measurements of hoop strain ε h  can be determined by multiple strain strings  22  at different wrap angles θ 1 , θ 2 . 
         [0056]    Alternatively, using an external pressure gauge  34 , an independent measurement of external pressure P o  can be combined with a measurement of each of internal pressure P i  and hoop strain ε h  to calculate thickness w at the position of the pressure gauge  34  or along casing  14  where external pressure P o  along casing  14  is constant or calculable using one or more point measurements of external pressure P o . 
         [0057]    According to yet another method, where annulus  15  is uncemented and there is access to annulus  15  at the wellhead, internal and external pressures P i , P o  are held constant such that hoop strain ε h  and thickness w are inversely proportional to one another. Here, the following equation can be used to relate hoop strain ε h  and thickness w at two different times t 1 , t 2 : 
         [0000]    
       
         
           
             
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               2 
             
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       Cement Quality Analysis 
       [0058]    Referring to  FIGS. 9 and 10 , an exemplary method of monitoring the quality of cement  16  with monitoring system  20  during a minifrac, leak-off, or formation integrity test is now described. As used herein, a minifrac treatment is a fracturing treatment performed before a main hydraulic fracturing treatment to acquire data and confirm a predicted response. In a formation integrity test, internal pressure P i  is increased to a preset value that is less than the anticipated formation break-down test. The formation integrity test can be used as a cement integrity test. In a leak-off test, internal pressure P i  is increased until part of formation  12  that is exposed to open borehole  11  starts to break down. During each of these tests, internal pressure P i  is increased and fluid may seep into formation  12  if formation  12  has sufficient permeability. 
         [0059]    In general, an extended leak-off test or minifrac operation can be used to determine the mechanical properties of formation  12 . The mechanical properties can be determined with information gained from the leak-off test or minifrac operation. For example, such information includes limit pressure, leak-off pressure, fracture opening pressure, uncontrolled fracture pressure, fracture propagation pressure, instantaneous shut-in pressure, fracture closure pressure, stable fracture propagation, unstable fracture propagation, fracture closure phase, and backflow phase. A pressure response curve is typically plotted to get such information. The pressure response curve is internal pressure P i  versus time or cumulative volume of fluid pumped. 
         [0060]    Monitoring system  20  is used to monitor cement  16  during the extended leak-off test or minifrac operation to facilitate differentiation between fracture of cement  16  and fracture of formation  12 . For example, such a differentiation may be difficult to determine from a pressure response curve. As internal pressure P i  increases, fiber strain ε f  is monitored to determine the quality of cement  16 . Referring to  FIG. 10 , if cement  16  is and remains competent, hoop strain ε h  is and remains substantially proportional to internal pressure P i , moving along line  60 , and external pressure P o  remains substantially constant. If cement  16  is weak and breaks apart or if channels or other fluid pathways exist in cement-filled annulus  15 , hoop strain ε h  will deviate from the line of proportionality  60  with respect to internal pressure P i . For example, hoop strain ε h  will move along line  62  so as to deviate from line  60  above a certain internal pressure P i,x . Here, where such deviation occurs along line  62 , hoop strain ε h  decreases as external pressure P o  changes toward the value of internal pressure P i . 
         [0061]    Certain information that is determined from the pressure response curve can similarly be determined from the pressure strain curve shown in  FIG. 10 . For example, where cement  16  is competent, uncontrolled fracture pressure of formation  12  or the point at which stable fracture growth ends can be identified as the highest internal pressure P i  measured. In such a case, measurements move up and then back down line of proportionality  60  during a leak-off test. 
       Fluid Monitoring 
       [0062]    Referring to  FIGS. 11-18 , exemplary methods of detecting the presence of fluid, fluid migration, and inflow proximate well  10  are now described. Such monitoring methods can be used to investigate operations such as injection, depletion, production, and the like. 
         [0063]    Referring to  FIGS. 11 and 12 , pressure difference across the wall of casing  14  changes where fluid  74  migrates in formation  12  or annulus  15  along the outside of the wall of casing  14 . Fluid may flow from a perforated area or leak in casing  14 . The fluid may additionally or alternatively flow from a permeable bed  70  or fracture  72  as shown in  FIG. 11 . The pressure change in permeable bed  70  may either be negative from a reservoir undergoing depletion or positive from a reservoir undergoing injection of fluids for purposes such as waste or carbon dioxide disposal or water flooding for oil production. 
         [0064]    Referring to  FIG. 11 , permeable bed  70  is undergoing a pressure change and fluid  74  changes the external pressure P o  applied to casing  14  and the associated fiber strain ε f  response. Referring to  FIG. 12 , fluid pressure and migration can be identified by deviation of fiber strain ε f  from a baseline  78  and extension of the deviating measurements along casing  14 . Baseline  78  can be determined from measurements of fiber strain ε f  that are substantially constant or steady-state for a certain time period. The time period used to determine baseline  78  is generally distinct from the time period in which fluid  74  changes external pressure P o . 
         [0065]    Illustrated fluid  74  migrates up annulus  15  with the front end boundary  76  of fluid  74  reaching different positions z 1 , z 2 , z 3 , z 4  along the length of casing  14  at different times t 1 , t 2 , t 3 , t 4 . The extent, direction, and rate of fluid  74  migration can be determined by monitoring boundaries  76  of fluid  74  over time and space. As shown in  FIG. 12 , boundaries  76  can be identified where fiber strain ε f  measurement deviates from baseline  78 . The extent of fluid  74  is the position of front end boundary  76  or the distance between front and rear end boundaries  76 , the flow rate is the change in position of front end boundary  76  over time, and the flow direction is given by the change in position of the front end boundary  76 . Front end boundary  76  is tracked with line  79 . An independent pressure gauge can facilitate determining the direction of pressure migration and the location (inside or outside). Referring to the time greater than time t 4  of  FIG. 12 , front end boundary  76  does not move and the flow rate approaches zero. This is illustrated by the flattening of line  79  and can indicate that fluid  74  is trapped. In other words, fluid  74  with a rate that approaches zero can indicate that fluid  74  is trapped. 
         [0066]    Strain strings  22  can further be used to determine the location of fluid  74  where fluid  74  changes the temperature of casing  14  so as to expand or contract the casing  14  and change fiber strain ε f . For example, temperature changes can be measured by strain strings  22  where flow rate is substantially high and where significant Joule-Thompson effects are involved. 
         [0067]    Similarly, referring to  FIGS. 13 and 14 , flow through a gravel pack  80 , including gravel pack screen  82  and gravel  84 , can be monitored where strain strings  22  are wrapped around a gravel pack screen  82 . Here, the inflow of fluid  74  changes the temperature of gravel pack screen  82  to create thermal strain such that the measurement of fiber strain ε f  deviates from baseline  78 . Greater fiber strain ε f  deviation can indicate point of entry into gravel pack screen  82 . 
         [0068]    Referring to  FIGS. 15 and 16 , flow detection with a monitoring system  20  including strain strings  22  on concentric casings  14   a ,  14   b  is described.  FIG. 15  shows fluid  74  migrating up annulus  15   a  between outer casing  14   a  and inner casing  14   b  as well as up annulus  15   b  between outer casing  14   a  and the wall of borehole  11 . Here, the material in annulus  15   a,    15   b  may be permeable or fluid  74  may move through a microannulus, channel, or void. As used herein, the term microannulus refers to the space between cement  16  and wall of casing  14  or wall of borehole  11 . A fluid migration detection method is similar to the methods described above. Here, the responses of strain strings  22  on concentric casings  14   a ,  14   b  can be compared to determine the location, rate, and direction of flow. Referring to  FIG. 16 , the change in pressure difference ΔP (P i −P o ) and the change in temperature T on each of casings  14   a ,  14   b  is illustrated. The changes in temperature T and pressure difference ΔP are reflected in fiber strain ε f  measurements as previously described. In general, flow that is closer to one of casings  14   a ,  14   b  will have a greater effect on the pressure and temperature components of fiber strain ε f  of that casing  14   a ,  14   b . Also, radial flow may be indicated by inversely proportional responses of strain strings  22  on concentric casings  14   a ,  14   b . 
         [0069]    The responses of strain strings  22  and temperature string  32  are used together to determine where the flow is located or the size of the flow. In general, larger and closer flows result in greater temperature and pressure responses while smaller and farther flows result in lesser temperature and pressure responses. Strain strings  22  are more sensitive to flow at a greater distance from casing  14  than temperature string  32 . For example, if strain string  22  response shows a pressure increase and the temperature string  32  response doesn&#39;t show a temperature increase (e.g., relative to geothermal temperature T G ), then the fluid flow path of a certain size is within a range of distances from casing  14 , the closer boundary being defined by the sensitivity range of the temperature string  32  and the farther boundary being defined by the sensitivity range of the strain string  22 . If a temperature anomaly is not detected by temperature string  32  and a pressure increase is not detected by the strain string  22 , any flow of any size is at a distance outside the sensitivity range of strain string  22  and temperature string  32 . The use of additional tracing methods such as oxygen activation can further facilitate determining the boundaries on an area in which flow is occurring. Tracers in the flow, such as those created by a pulsed-neutron logging tool that causes oxygen activation, can determine fluid velocity but not volumetric or mass rates. Using this information along with temperature-calculated mass flow rate can give an indication of either flow size or distance from casing  14 . 
         [0070]    Referring to  FIGS. 17 and 18 , monitoring system  20  can differentiate between fluids that have different effects on the rate of temperature change of casing  14 . For example, carbon dioxide (CO 2 ) and water (H 2 O) affect the rate of temperature change differently. According to an exemplary method, temperature change is monitored after beginning and ending injection operations. Here, injection fluids are colder than formation  12 . Referring to  FIG. 18 , when well injection begins (time t 2 ), well  10  cools down. When well injection is stopped (time t 1 ) warmback of well  10  occurs. During the life of injector  2  (see  FIG. 1 ), injector  2  will be turned off many times for scheduled or unscheduled maintenance. Every such cycle produces a perturbation of the temperature of well  10 . The local rate of temperature change of casing  14  is a function of the concentration of the fluid surrounding casing  14  in the area, such as beds of carbon dioxide CO 2  and water H 2 O shown in  FIG. 17 . As such, monitoring the rate of temperature change according to this method provides an indication of what fluids are located at certain positions along casing  14 . Measurements taken over time can be used to monitor migration of such fluids and the rate of migration. 
         [0071]    Monitoring system  20  can measure axial strain along casing  14 , which is related to reservoir compaction/dilation. For example, when injecting carbon dioxide, there is generally reservoir dilation. Monitoring system  20  can be used to quantify this and calibrate geomechanical models, which indicate that injected carbon dioxide is going where intended. 
       Cement Quality Analysis 
       [0072]    Referring to  FIGS. 19-22 , monitoring system  20  can further be used to determine the quality and effectiveness of cement  16 . Strain strings  22  and temperature string  32  can be used individually or in combination to continually or periodically monitor the quality of cement  16  without running a tool or other well intervention. For example, the curing process is monitored and the integrity of the cement  16  is monitored after cement  16  has cured. Objectives of cement  16  placement monitoring include detecting the top of cement  90  and determining the quality of the cementation (zonal isolation). 
         [0073]    Referring to  FIG. 20 , cement  16  cures by an exothermic reaction where the heat given off and rise in temperature is substantially proportional to the volume of cement  16  curing. In addition to the rise in temperature that accompanies cement curing, conventional cements shrink as they hydrate. Referring to  FIG. 21 , this shrinkage and hydration results in a decrease in external pressure P o  applied to casing  14 . Initially, liquid cement  16  applies hydrostatic pressure P o,1  to casing  14 . As liquid cement  16  cures, the pressure applied by cement  16  permanently changes and the pressure P o,2  applied by cured cement  16  is approximately the fluid pressure applied by fluids in formation  12 . The early time in  FIG. 21  shows the external pressure P o  at a point z 1  on casing  14  when cement  16  was pumped. Late time in  FIG. 21  shows external pressure P o  at point z 1  on casing  14  after cement  16  has cured and has effectively lowered the external pressure P o  applied to casing  14  at point z 1 . 
         [0074]    It should be understood that monitoring system  20  gathers data for multiple points having different depths and azimuth angles (not shown) and therefore provides complete coverage of casing  14  and any variations in cured cement  16 .  FIG. 22  illustrates the response of monitoring system  20  to partially cured cement  16  along the length of casing  14 . Top of cement  90  reaches point z 1  at time t 1 . In the uncured or poorly cured portions of cement  16 , the hydrostatic pressure in annulus  15  has not been reduced by hydration and shrinkage of cement  16 . The response of monitoring system  20  differentiates between cured and uncured cement  16  and can monitor the position of the top of cement  90  during the curing process. Cured cement is represented by fiber strain ε f,2  and uncured cement is represented by fiber strain ε f,1 . 
         [0075]    In the case of cement  16  curing in annulus  15  bounded by concentric casings  14   a ,  14   b , strain strings  22  on each of concentric casings  14   a ,  14   b  observe hoop strain changes in opposite directions due to the change in annulus  15  pressure. Where the curing cement  16  is outside casing  14 , the external pressure decreases. Where the curing cement  16  is internal to casing  14 , the internal pressure decreases. 
         [0076]    The temperature history from the temperature string  32  can be combined with other logs such as caliper logs to determine the cross sectional area of a channel or microannulus or otherwise the quality of cement  16 . For example, the temperature increase during curing can be used to determine the volume of cement placed and the volume can then be compared was expected to be used based on a caliper log or another determination of hole volume as a function of depth. Volume of cement  16  is determined based on the temperature change, the heat capacities of the various components, and the heat transfer characteristics of formation  12 , cement  16 , and casing  14 . When the cement volume estimated from the temperature substantially equals that from the caliper, there are no large voids. When the temperature-estimated volume is less than the caliper-calculated volume, there is indication of a void, channel, or microannulus. Knowledge of the size (cross section) of the channel or microannulus is useful for estimating “leakage rate” when monitoring injection or production processes or other logging measurements such as water flow log which give a velocity. 
         [0077]    The above-described embodiments are merely exemplary illustrations of implementations set forth for a clear understanding of the teachings and associated principles. Variations, modifications, and combinations may be made to the above-described embodiments without departing from the scope of the claims. All such variations, modifications, and combinations are included herein by the scope of this disclosure and the following claims.

Summary:
Systems ( 20 ) and methods for monitoring a well ( 10 ) are configured to identify or analyze various issues affecting the well ( 10 ) including corrosion, cement quality, inflow, and fluid migration.