Patent Application: US-35340506-A

Abstract:
method and apparatus for monitoring growth of fracture during hydraulic fracturing treatment of a ground formation . a series of tiltmeters are positioned at spaced apart tiltmeter stations at which tilt changes due to hydraulic fracturing treatment are measurable by those tiltmeters . tilt measurements obtained from the tiltmeters at progressive times during the fracture treatment are compared with estimated tilt changes estimated from an assumed hydraulic fracturing propagation . useful values for initially undetermined values of parameters of the model are derived using an inverse procedure . the data analysis may be performed in real time as the hydraulic treatment progresses using differing propagation models to determine a most probable model .

Description:
in order to explain the operation of the preferred method and apparatus and according to the invention , it will be necessary to analyse in some detail the current state of the art in the operation of hydraulic fracture monitoring , especially tiltmeters , and the modelling and inverse techniques required to derive meaningful data from tiltmeter measurements . several techniques have been developed in order to image hydraulic fracture . three type of measurements are typically encountered in practice : 1 . well pressure monitoring 2 . passive seismic system recording acoustic emission during the fracturing process 3 . tiltmeters remotely located from the fracture measuring change of deformation as the fracture grows . well pressure monitoring is a simple measurement with a relatively low cost . when no pressure sensor is lowered down the injection well at the level of the injection interval , pressure is usually recorded on the surface rig together with the injected flow . in that case , corrections of the pressure drops due to viscous flow along the well have to be performed . the interpretation of well pressure with respect to hydraulic fracture growth can be rendered difficult due to damage around the well bore disturbing the fluid pressure gradients . typical analysis of pressure decline , shut - in and fall - off data ( g - plot etc .) can help estimating a number of characteristics of the fracture ( treatment efficiency , closure stress etc . ), economides and nolte , 2000 [ 5 ]. a number of simplifying assumptions are usually made in order to analyse pressure records . acoustic emission monitoring ( also sometimes call passive seismic ) consists of recording using precise accelerometers the seismic signal produced by the growth of the fracture . an array of geophones is used , and analysis of the signal enables to locate the seismic source . the velocity of seismic waves in the rock mass must be known . usually , operators calibrate a velocity model by recording the signal generated by a known source ( typically during the perforation of the casing ). this method can provide good results in homogeneous rock mass if the array of sensor covers well the fracture area . in the case , where natural joints are present in the vicinity of the hydraulic fractures , multiple shear events along the natural joints can occur . this can ‘ blur ’ the overall picture given by the analysis of the recorded signals . a tiltmeter ( which is tightly installed in the rock ) measures at its location changes of inclination in two orthogonal directions with a precision down to nanoradians . the tilts recorded are a direct measure of the small strain rotation at the apparatus location . in the field , tiltmeter fracture monitoring involves the deployment of a number of apparatus in the surroundings of the future fracture . typically , they are either located on the surface of the earth in shallow boreholes ( to minimize noise ), or in an off - set well ( downhole tiltmeter array ), even sometimes the injection well itself ( davis , 1983 [ 4 ]; evans , 1983 [ 7 ]; branagan et al ., [ 2 ]; warpinski et al ., [ 11 ]; wright et al . [ 13 ]). during a hydraulic fracture treatment , a measure of the different tiltmeters is recorded every 5 seconds or so , thus providing the effect of the fracture propagation on the elastic deformation field in the rock surrounding the fracture . fig4 displays for a given tiltmeter station , the two inclinations ( north - south and east - west ) recorded during a fracturing job . we clearly see the evolution of the inclination during the injection as well as the slow return toward their initial values after the end of the injection . this return is associated with the hydraulic fracture closing back on itself after injection stops . another representation of tiltmeter measurements is given in fig5 . in case of a surface array , the so - called tilt vectors provide a spatial view ( plan view ) of the recorded inclination at the different tiltmeter station at a particular time during the injection . the tilt vector is determined from a vector addition of the two orthogonal components of the rotation tensor measured by the two bubbles in the tiltmeter : v = ( ∂ u z ∂ x - ∂ u x ∂ z , ∂ u z ∂ y - ∂ u y ∂ z ) . such tiltmeter measurements are extremely precise and can furnish interesting data sets . in contrast to the relative simplicity of the measurement , the modelling necessary to quantitatively analyse tilt data pose difficult problems . despite the now common use of tiltmeters to map hydraulic fractures in the petroleum industry , there is a widespread misunderstanding of what information about the fracture can and cannot be obtained from such measurements . lecampion et al . [ 22 ] have shown that for measurement located at a distance twice the fracture characteristics length , tilt measurements only sense the effect of fracture volume and orientation . such situation occurs in the field when the tiltmeters are too far from the fracture : we are in a case of so - called far - field tiltmeter mapping . the specification of our international application pct / au2004 / 001263 discloses the use of a fundamental displacement discontinuity model by which it is possible to carry out a real - time analysis of the hydraulic fracture volume and the treatment efficiency , particularly for far - field tiltmeter mapping . the disclosure of that specification is imported here by reference . if the tiltmeter are sufficiently close to the fracture , the fracture shape starts to affect the recorded tilts : this is a case of near - field tiltmeter mapping . in near - field tiltmeter mapping , the use of simple static fracture model ( radial , elliptical , rectangular dd . . . ) faces the problem that these models do not have the correct boundary conditions on the fracture face , which can results in doubtful conclusions . by the present invention , an alternative method to analyse data recorded around hydraulic fractures is proposed . the method may use tiltmeter data but other data such as measurements of the injection pressure and acoustic emission can also be used . the method consists of coupling hydraulic fracture growth models ( which model the physical process of hydraulic fracturing either numerically or analytically depending on their assumptions ) to the recorded data , and to calibrate the parameters of the hydraulic fracture growth models from the data . in contrast to existing methods , where data are analysed sequentially at different times independently , here the analysis is carried out using the data over an entire time interval and uses physical models of the hf process , not just static fracture models like the ones described in warpinski 2000 ; [ 15 ]; evans , 1983 [ 7 ]. essentially the data recorded throughout the entire time interval are used in an inverse procedure to derive useful values for initially unknown values of parameters in the model . this will normally involve estimating data at the relevant time with differing assumed values of the parameters and comparing the various estimates with the recorded data to derive values which can then be used in the model to estimate evolution of the fracture . the propagation of a hydraulic fracture is a highly non - linear process . recent advances in the understanding of the key parameters controlling the growth of such fracture have shown that different regimes of propagation can be isolated ( see detournay , 2004 [ 17 ]; adachi , 2001 [ 1 ]; detournay et al . [ 18 ] for extensive discussions ). the propagation of a hydraulic fracture is governed by two competing dissipative processes associated with fracturing fluid viscosity and rock toughness , respectively and two competing components of the fluid balance associated with fluid storage in the fracture and fluid storage in the surrounding rock ( leak - off ). scaling laws as well as complete solutions for the propagation of hydraulic fractures have been recently obtained for simple fracture geometries such as a radial fracture and a plane strain fracture . this approach is useful for the design of hf treatment and has been described in reference [ 17 ]. also , complex and computationally efficient numerical models are now becoming available ( siebrits , e . and peirce , a . p . ; 2001 [ 9 ]). we have also to note that empirical growth models are sometimes used in the industry for practical purposes [ 5 ]. all these hydraulic fracture growth models furnish a solution at all times during the injection period for the fracture shape , fracture aperture and internal fluid pressure ( therefore well pressure ) etc . everywhere in the fracture . moreover , for a given fracture evolution , the corresponding tiltmeters at the different observation point and at the different time can be simply obtained from the solutions of an elasto - static problem ( eshelby , 1957 [ 6 ]) for each fracture configuration ( i . e . each time ). the location of seismic events obtained from acoustic emission can be qualitatively associated with the fracture front and the front of fluid leaking into the rock formation . typically , a particular fracture growth model depends on a number of parameters lumping physical properties of the rock , the layering structure , state of initial stress , the properties of the injected fluid driving the fracture as well as the pumping schedule . some , if not all , of these parameters are often poorly known . data recorded during the actual treatment can be used to back calculate these parameters . moreover , several growth models with different type of assumptions can be tested against the data recorded . for example , we can suppose a simple pkn model for the fracture growth ( see economides and nolte [ 5 ] for details ). this is a typical model use in the industry for a vertical fracture growing in a confined layer . according to this model , the half - length of the fracture and fracture aperture at the fracture center evolves as : l ⁡ ( t ) = 0 . 68 ⁢ ( e ′ ⁢ q o 3 2 ⁢ μ ⁢ ⁢ h 4 ) 1 / 5 ⁢ t 4 / 5 = 0 . 68 ⁢ ⁢ α × t 4 / 5 ( 1 ) w ⁡ ( 0 , t ) = 2 . 5 ⁢ ( 2 ⁢ μ ⁢ ⁢ q o 2 e ′ ⁢ h ) 1 / 5 ⁢ t 1 / 5 = 2 . 5 ⁢ ⁢ β × t 1 / 5 ( 2 ) where e ′ is the plane strain , μ the fluid viscosity , h the layer in which the fracture is developing and q o the fluid injection rate ( supposed constant ). t denotes the time from the beginning of the injection . for that particular growth model , the unknown parameters will be α = ( e ′ ⁢ q o 3 2 ⁢ μ ⁢ ⁢ h 4 ) 1 / 5 ⁢ ⁢ and ⁢ ⁢ β = ( 2 ⁢ μ ⁢ ⁢ q o 2 e ′ ⁢ h ) 1 / 5 . alternatively , we can assume that the created hydraulic fracture is radial and grows in the so - called toughness dominated regime ( detournay , 2004 [ 17 ]). when a newtonian fracturing fluid is injected at a constant rate , the radius and net pressure inside the fracture evolves as power law of time : r ⁡ ( t ) = l k ⁢ γ ko ⁡ ( t t c ) 2 / 5 ( 3 ) p ⁡ ( t ) = ɛ k ⁢ e ′ ⁢ π o ⁡ ( t t c ) - 1 / 5 ( 4 ) γ ko = ( 2 π ⁢ ⁢ 2 1 / 2 ) 2 / 5 , ⁢ π ko = π 8 ⁢ ( π 12 ) - 1 / 5 and the characteristic time t c is related to the injection rate , plane strain young &# 39 ; s modulus , fracture toughness and fracturing fluid viscosity : t c = ( μ ′ 1 / 5 ⁢ q o 3 ⁢ e ′ 13 k ′ 18 ) 1 / 2 the characteristic lengthscale l k and dimensionless number ε k are given by ( see detournay , 2004 [ 17 ]): l k _ = e ′ 3 ⁢ q o ⁢ μ ′ k ′ 4 ɛ k _ = ( k ′ 6 e ′ 5 ⁢ q o ⁢ μ ′ ) 1 / 2 for that radial fracture toughness dominated growth model , the unknown parameters to be identified during the inverse analysis of the tilt series data are α ={ overscore ( l k )}( t c ) − ⅖ and β ={ overscore ( ε k )}( t c ) ⅕ . of course , more complex numerical models with a larger number of parameters can be used . some parameters of the numerical simulation can also be isolated in order to be estimated in the inverse analysis . all the data from tiltmeters recorded during a time interval of the treatment can be used to perform an inverse calculations to estimates the parameters of a given growth models . eventually , the parameters of several competing models can be estimated and the different models quantitatively ranked using a bayesian model selection procedure as discussed in raftery , 1995 [ 21 ]. it is therefore possible to detect the regime of propagation in which the hydraulic fracture is growing during that time interval . let us describe the inverse procedure . consider a fracture growth model m , with parameters m =( α , β , etc . . . ). for a given value of its parameter , this model furnishes the fracture shape s , aperture w and pressure p at all time . it is therefore possible to compute , for this value of the parameters , the tilts at all the tiltmeter location for all time where the tilts are sampled . we shall denote the predicted tilts ( or eventually well pressure , or acoustic event location ) as a function of the unknown parameters of the model : g ( m ). if we have n tiltmeter stations , each recording two components of tilts , and p samples during the time interval for each stations , we have a data vector d of length 2 * n * p . the inverse procedure seeks to minimize the error between the predictions and the observation in order to obtain the best fit ( vogel , 2000 [ 10 ]; tarantola and valette , 1982 [ 19 ]): j ⁡ ( m ) = 1 2 ⁢  g ⁡ ( m ) - d  ( 5 ) prior knowledge on the parameters can be input in the procedure ( see tarantola and valette , 1982 [ 19 ]; ulrych t . j . et al . 2001 [ 20 ]). the minimization of the error can be done by using several methods ( random search , quasi - newton methods etc .). the best fit furnishes the best estimates for the model parameters . the knowledge of the best estimates of the model parameters allows to obtain the evolution of the fracture shape , aperture etc . during the injection period . the growth model is then calibrated . as an illustrating example , let consider the following synthetic case . the tiltmeter data corresponding to the growth of a hydraulic fracture of so - called pkn geometry ( with coefficients α = 2 , β = 2e − 3 , see eqns ( 1 )-( 2 )) . . . are simulated and noise is added to this synthetic data set . the data are logged by a borehole array located 200 meters from the fracture ( a far - field array ). tilts are sampled every minute . the synthetic data are then inverted using the same pkn model for the fracture growth model ( see eqns . ( 1 )-( 2 )). the parameters ( α , β ) are supposed unknowns and are retrieved via an inverse calculation using the simulated tilt data . the values of both parameters are retrieved accurately , we obtain α = 1 . 94 , β = 1 . 98e − 3 . the fit of the tilt data at a particular tilt station can be seen in fig6 . fig5 shows the time evolution fracture half - length and aperture at the fracture center obtained from eq . and the estimated values of the coefficients α and β . the estimated values of the model parameters allow to obtain fracture length and aperture . as a guideline , the practical steps of the analysis are typically the following : collect data at all the tiltmeter stations for all sampling times during the interval of interest t ∈[ t a , t b ], correct the tiltmeter data ( drift , earth tides , rotation to the geometrical coordinate system ); perform the identification procedure for a particular fracture propagation model using the tilt data at the different instrument locations over the time interval of interest in order to estimate the model parameters ; and eventually repeat the preceding step with a different propagation model and compare the different fracture propagation models . we have to note that the computational speed of the models make it possible to carry out a real - time analysis , as described above , during the treatment . for example , the analysis can be performed on the first five minutes of the treatment , then on the first ten minutes of treatment and so on , eventually allowing design changes to be performed according to the calibrated model . adachi j . i . fluid - driven fracture in a permeable rock . phd thesis , university of minnesota , 2001 . branagan p . t ., wilmer r . h ., warpinski n . r ., and steinfort t . d . measuring a deformation of a rock mass around the vicinity of a fracture in a well drilled offset from proposed fracture region . u . s . pat . no . 5 , 934 , 373 - a , 1999 . assignee : gri . cipolla c . l . and wright c . a . diagnostic techniques to understand hydraulic fracturing : what ? why ? and how ? soc . petrol . eng . 59735 , 2000 . davis p . m . surface deformation associated with a dipping hydrofracture . j . geophys . res ., 88 : 5826 - 5838 , 1983 . economides m . j . and nolte k . g ., editors , reservoir stimulation , schlumberger , john wiley & amp ; sons , 2000 . eshelby j . d . the determination of the elastic field of an ellipsoidal inclusion and related problems . proc . roy . soc . series a , 241 : 376 - 396 , 1957 . evans k . on the development of shallow hydraulic fractures as viewed through the surface deformation field : part 1 - principles . j . petrol . tech ., 35 ( 2 ): 406 - 410 , 1983 . okada y . surface deformation due to shear and tensile faults in a half plane . bull . seismol . soc . am ., 75 ( 4 ): 1135 - 1154 , 1985 . siebrits e . and pierce a . p . an efficient multi - layer planar 3d fracture growth algorithm using a fixed mesh approach . int . j . numer . meth . engng , 53 : 691 - 717 , 2002 . warpinski n . r ., steinfort t . d ., branagan p . t ., and wilmer r . h . apparatus and method for monitoring underground fracturing . u . s . pat . no . 5 , 934 , 373 , january 1997 . assignee : gri . wright c ., davis e ., ward j ., samson e ., wang g ., griffin l ., demetrius s ., and fisher k . treatment well tiltmeter system , for monitoring fluid motion in subsurface strata from active well , comprises tiltmeter array within borehole , with tiltmeter sensor . wo2001181724 - a ; wo2001181724 - a1 ; au2001157342 - a , 2001 . assignee : pinnacle technologies inc . wright c . a ., weijers l ., davis e . j ., and mayerhofer m . understanding hydraulic fracture growth : tricky but not hopeless . soc . petrol . eng . 56724 , 1999 . larson m . c ., arthur verges m ., and keat w . q ( 1999 ) non destructive identification of three dimensional embedded cracks in finite bodies by inversion of surface displacements . eng . frac . mech ., 63 : 611 - 629 . warpinski n . r ( 2000 ) analytic crack solutions for tilt fields around hydraulic fractures . j geophys . res , 105 ( b10 ): 23463 - 23478 . cheng a . h . d and detournay e ( 1998 ) on singular integral equations and fundamental solutions of poroelasticity . int . j . solids structures , 35 ( 34 - 35 ): 4521 - 4555 . detournay , e . 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