Patent Application: US-201515300759-A

Abstract:
an example method includes acquiring two - dimensional or three - dimensional digital images of a rock sample . the method also includes selecting a subsample within the digital images . the method also includes deriving a trend or petrophysical property for the subsample . the method also includes applying the trend or petrophysical property to a larger - scale portion of the digital images .

Description:
fig1 a shows a two - dimensional digital representation of a material , while fig1 b shows a three - dimensional digital representation . these representations are hereafter referred to as images . while it is possible to use raw images , the disclosed methods are facilitated by classifying each pixel as one of multiple phases , e . g ., pore space , solid . some embodiments may include additional phases indicating intermediate levels of porosity between open pore space and fully filled solid space , e . g ., low density porous matrix , high density porous matrix . within each image , a number of subsample positions are selected . the selection may be made randomly or systematically , and in an overlapping or non - overlapping fashion . typically , the subsample regions are square ( for two - dimensional images ) or cubes ( for three - dimensional images ). the method then determines the properties of interest for each subsample . properties commonly subjected to trend analysis in the petroleum industry are porosity vs . permeability , porosity vs . formation factor , and permeability vs . formation factor . the property measurements for all subsamples are then collected and analyzed to discern trend information . fig2 shows a crossplot of two properties that suggests the presence of a trend , and further shows a parameterized curve that might be fit to the points representing the properties for each subsample . in at least some embodiments , the extracted trend information is presented in a mathematical form expressing the relationship between two properties . due to its computerized implementation , the digital rock physics ( drp ) approach offers a way to generate trends in fast , safe , and repeatable fashion . most importantly , owing to the use of subsampling , trends can be generated with far fewer samples than most experimental methods , possibly as few as one sample . however , existing drp methods assume that the sample is relatively homogeneous sample , i . e . the properties can be represented using unimodal distribution such as that shown in fig3 a or 3c . consequently , these method yield only one trend for each sample ( ramstad et al ., 2010 , khalili et al ., 2012 , khalili et al ., 2013 , de prisco et al ., 2013 ) and inevitably fail to properly characterize relatively heterogeneous samples . as most formation rocks / reservoirs possess a high degree of heterogeneity , this circumstance creates difficulties . bimodal distributions , such as those shown in fig3 b or 3d , trimodal distributions , or even higher , are typical . it would be desirable to have a trend analysis method that properly accounts for the heterogeneity and complexity of most samples . the proposed method accomplishes this by treating the property measurement distribution as a mixture of component distributions and subjecting the overall distribution to a statistical analysis that extracts the component distributions . for example , fig4 a shows a trimodal distribution that is expressible as a weighted sum of three unimodal distributions . the statistical analysis determines the number of components , the position of each component , the size ( variance ) of each component , and the fraction ( weight ) of each component . ( suitable statistical analysis methods are discussed further below .) once each component is identified , the points associated with that distribution may be determined , enabling the individual distributions to be mapped to the corresponding subsample positions as indicated in fig4 b . note that the subsamples associated with a given component need not be contiguous . having identified the components and their associated subsamples , a separate trend analysis may be performed for each component , as indicated in fig5 . a parameterized curve may be fit to the measurement points of each given component . note that the fit of a single curve to the full set of measurement points would have obscured the sample &# 39 ; s heterogeneity . fig6 a is a flow diagram of an illustrative trend determination method . in block 602 , the method obtains a two dimensional or three dimensional image of a sample . in block 604 , the image is pre - processed to remove noise and other artifacts of the imaging process . in block 606 , the image is segmented , meaning that each pixel of the image is classified in to one of multiple possible categories , including at least pore ( open space ) and solid ( filled spaced ), and depending on resolution at the chosen magnification , possibly further including matrix phases of intermediate porosities between the two extremes . in block 608 , the method determines a statistically large number of subsamples , selecting their locations in a random or systematic and overlapping or non - overlapping fashion . given the anticipated heterogeneity of the sample , it is desirable to have the density of subsample locations spread relatively evenly throughout the sample . the statistical largeness can be determined using well known statistical principles such as confidence levels and confidence intervals , or if feasible , the method may simply position the subsample locations to achieve complete ( and possibly overlapping ) coverage of the sample . the size of the sub - samples may be selected arbitrarily or systematically ( see , e . g . de prisco et al ., 2013 ) depending on the desired scale of information . in block 610 , the method computes the selected primary properties for each subsample . examples of primary properties include porosity , pore structure , composition of porous matrices , and the computation may provide measurement of one or more such properties . in block 612 , the distributions of the computed primary properties are determined and analyzed . such distributions are typically multi - modal due to the typical sample &# 39 ; s level of complexity and heterogeneity , and if multiple properties are measured , the distribution is multivariate . ( fig3 a - 3d are examples of unimodal and multimodal as well as univariate and multivariate distributions .) suitable statistical analyses are those that can be applied to uni - or multi - modal and / or uni - or multi - variate distributions to determine the number of component distributions and the parameters associated with each . the analysis of a multimodal distribution should not result in only one mean value and standard deviation value , but rather it should yield a set of means , standard deviations , and relative weighting for each of multiple component distributions presented in the sample . the number of distributions indicates the number of distinct regions characterized by the chosen primary properties . accordingly , regions with different characteristics can be identified within the sample by associating each individual subsample with a corresponding distribution and thereby mapping the distributions to specific locations in the image ( block 614 ). it is possible for distinct regions to share a common distribution . for more information regarding property distribution analysis options , reference may be had to radompon sungkorn et al ., “ representative elementary volume determination via clustering - based statistics ”, atty . docket no . ingra - 011b , pct application serial number ______ and filed ______ , and hereby incorporated herein by reference in its entirety . in block 616 , the method processes the subsamples associated with each component distribution in turn , to determine the desired secondary properties of those subsamples . examples of secondary properties include permeability , formation factor , capillary pressure and relative permeability . various numerical techniques such as finite volume method ( fvm ), finite element method ( fem ) and lattice boltzmann method ( lbm ) can be used for the computation of these properties . for each given component distribution , the method associates the secondary property measurements with the primary property measurements ( block 618 ) and applies a regression analysis to determine the relationships ( block 620 ) between the primary and secondary properties . for example , one commonly used trend analysis employs a linear least square regression technique with a power function ( y = ax b + c ) to derive the relationship between porosity and permeability . fig5 shows an example of a system with three distinct structures / patterns ( i . e . tri - modal distribution having three component distributions ). the relationships between property i and property ii are analyzed separately for each structures , yielding three trends for the sample . the trends identified by the method of fig6 a are expected to vary based on the subsample size . if it is desired to obtain trends that are relatively insensitive to subsample size , the method may be augmented as shown in fig6 b to find trends associated with the representative elementary volume ( rev ). blocks 602 - 620 are the same as in fig6 a . blocks 622 - 628 are added to provide a loop in which the trends are found for multiple subsample sizes . in block 622 , the parameters of the mathematical expression ( e . g ., a , b , c , of the regression function y = ax b + c ) for each trend are compared to those of the previous loop iteration . if no previous iteration was performed , or if the parameters or the number of trends do not match the previous iteration , a decision is made in block 624 to repeat the loop . the method enlarges the subsample size in block 626 and blocks 610 - 624 are repeated with the new subsample size . once a match is detected ( indicating that the trends have converged to stability ), the method outputs the trend information and the minimum corresponding subsample size in block 628 . as an alternative to comparing expression parameters for the convergence test , the method may compare parameters of the component distributions identified by the analysis in block 612 , and reserve the operations of blocks 614 - 620 for performance only after a suitable subsample size has been identified . the foregoing trend determination methods enable a new framework for upscaling petrophysical properties , i . e ., deriving large - scale properties from small scale samples analyzed with digital rock physics ( drp ) imaging . fig7 shows sample images acquired at three different scales : large scale ( low resolution ), intermediate scale ( intermediate resolution ), and small scale ( high resolution ). the use of small scale samples to derive the petrophysical properties of the large scale sample yields an enormous gain in computational efficiency . each sample image reveals the presence of multiple , distinguishable entities which can be identified using the foregoing methods , image processing - based techniques ( e . g . liang , 2012 , unser & amp ; eden , 1989 ), or statistical analysis ( see e . g . christopher , 2003 , barker , 1998 ). each entity can be classified as resolved or unresolved , the former indicating that the entity is substantially void ( empty space ) or substantially impermeable solid ( filled space ), and the latter indicating that the entity is a collection of porous matrices ( partially filled space ). as the relevant properties of the resolved entities are already apparent , subsequent analysis focuses on the unresolved entities . the unresolved entities are selected arbitrarily or identified based on visual inspection or statistical analysis ( potentially using the methods explained above ). one or more higher - resolution samples are taken from each entity . in the example of fig7 , this yields the intermediate scale image which is not fully resolved . the process is repeated until , as shown by the small scale image on the right side of fig7 , a fully resolved sample is obtained . two magnifications were employed in fig7 , and hence the upscaling process set out below will be repeated twice to obtain the desired petrophysical properties for the large scale image . fig8 a - 8d shown the three phases associated with the first upscaling process . the first phase , represented by the arrow from fig8 a to fig8 b , is the obtaining of high resolution images from each of the unresolved entities . in the second phase , as represented by the arrows from fig8 b to fig8 c , the high resolution images are processed to measure their properties and to derive their inter - relationships using the trend - identification methods set out previously . as set out previously , subsamples of the image are taken and sorted based on their structures / patterns and their location . various numerical techniques such as finite volume method ( fvm ), finite element method ( fem ) and lattice boltzmann method ( lbm ) can be used to solve the governing equations of these properties . it is desirable to solve multi - scale governing equations , such as darcy equations , brinkman equations or brinkman - forchheimer equations for permeability . the relationships between properties are derived using a regression analysis techniques with a selected mathematical function , see fig8 c . this populating operation may employ an image registration technique , i . e . a method to transform multiple images into similar frame of reference , but this is not necessary if the exact location of entities in the large sample are known . as indicated at fig8 d , the method then relates a property value of the larger scale image to the properties measured at the smaller scale , optionally in terms of a linear translation . for example , the pixel intensity of the larger scale image may be related to the porosity measured in a corresponding part of the smaller scale image . such linear translations may be employed to map the properties revealed by the small scale trends of fig8 c to corresponding locations in the image of fig8 a , thereby providing petrophysical property measurements for each of the previously - identified ( unresolved ) entities of fig8 a . as part of the trend - mapping , the third phase performs an aggregation operation . as shown in fig9 , each pixel of the larger scale image corresponds to multiple pixels of the smaller scale image . as the trend properties associated with the different small scale pixels may not be identical ( e . g ., at the boundary between entities ), the aggregation operation combines the different trend properties to provide a suitable aggregated property measurement value . direct area / volume averaging may be used or a wavelet decomposition technique may be employed . the trend information , together with the aggregation and translation processes , provide a transitive relationship for mapping petrophysical properties onto the larger scale image . this third phase may hereafter be referred to as “ populating ” the larger scale sample . once the upscaling process has been performed for each of the entities identified in each of the intermediate scale samples , the upscaling operation is performed again , using the populated intermediate scale samples as inputs as represented in fig1 a - 10d . the resulting populated large - scale sample can be used to resolve large - scale petrophysical properties and / or trends . if desired the method can be extended to ever - larger scales . the foregoing methods may be computer implemented . for context , fig1 - 12 demonstrate an illustrative context for the use of these methods . fig1 shows an illustrative high - resolution focused ion beam and scanning electron microscope 120 having an observation chamber 122 in which a sample of material is placed . a computer 124 is coupled to the observation chamber instrumentation to control the measurement process . software on the computer 124 interacts with a user via a user interface having one or more input devices 126 ( such as a keyboard , mouse , joystick , light pen , touchpad , or touchscreen ) and one or more output devices 128 ( such as a display or printer ). for high resolution imaging , the observation chamber 122 is typically evacuated of air and other gases . a beam of electrons or ions can be rastered across the sample &# 39 ; s surface to obtain a high resolution image . moreover , the ion beam energy can be increased to mill away thin layers of the sample , thereby enabling sample images to be taken at multiple depths . when stacked , these images offer a three - dimensional image of the sample to be acquired . as an illustrative example of the possibilities , some systems enable such imaging of a 40 × 40 × 40 micrometer cube at a 10 nanometer resolution . however , the system described above is only one example of the technologies available for imaging a sample . transmission electron microscopes ( tem ) and three - dimensional tomographic x - ray transmission microscopes are two other technologies that can be employed to obtain a digital model of the sample . regardless of how the images are acquired , the foregoing disclosure applies so long as the resolution is sufficient to reveal the porosity structure of the sample . the source of the sample , such as in the instance of a rock formation sample , is not particularly limited . for rock formation samples , for example , the sample can be sidewall cores , whole cores , drill cuttings , outcrop quarrying samples , or other sample sources which can provide suitable samples for analysis using methods according to the present disclosure . fig1 is an example of a larger system 200 within which the scanning microscope 120 can be employed . in the larger system 200 , a personal workstation 202 is coupled to the scanning microscope 120 by a local area network ( lan ) 204 . the lan 204 further enables intercommunication between the scanning microscope 120 , personal workstation 202 , one or more high performance computing platforms 206 , and one or more shared storage devices 208 ( such as a raid , nas , san , or the like ). the high performance computing platform 206 generally employs multiple processors 212 each coupled to a local memory 214 . an internal bus 216 provides high bandwidth communication between the multiple processors ( via the local memories ) and a network interface 220 . parallel processing software resident in the memories 214 enables the multiple processors to cooperatively break down and execute the tasks to be performed in an expedited fashion , accessing the shared storage device 208 as needed to deliver results and / or to obtain the input data and intermediate results . typically , a user would employ a personal workstation 202 ( such as a desktop or laptop computer ) to interact with the larger system 200 . software in the memory of the personal workstation 202 causes its one or more processors to interact with the user via a user interface , enabling the user to , e . g ., craft and execute software for processing the images acquired by the scanning microscope . for tasks having small computational demands , the software may be executed on the personal workstation 202 , whereas computationally demanding tasks may be preferentially run on the high performance computing platform 206 . when adapted for use in the illustrative systems , the methods may be modified to enable one or more of the operations to be carried out concurrently to exploit the availability of parallel processing resources . moreover , the order of the steps may vary , with some of the steps carried out in a potentially speculative fashion . such variations are within the scope of the claims . potential advantages of the disclosed systems and methods include the use of drp to overcome the obstacles presented by traditional experimental approaches and instead provide an accurate , safe , repeatable determination of petrophysical properties the accounts for the typical complexity and heterogeneity / anisotropy of the rocks / reservoirs . it provides a universal framework to establish trends between petrophysical properties , e . g . porosity , permeability , formation factor , elasticity , relative permeability . the following references are hereby incorporated herein by reference in their entirety : barker , s . a ., image segmentation using markov random field models , dissertation , university of cambridge , 1998 . christopher , l ., bayesian segmentation of three dimensional images using the em / mpm algorithm , dissertation , purdue university , 2003 . de prisco et al ., digital rock analysis systems and methods that reliably predict a porosity - 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