Soclety of Petroteum Engineers

SPE 35737

CT Scan and Neural Network Technology for Construction of DetailedDistribution of Residual Oil Saturation During WaterfloodingA. Garg’, A.R. Kovscek2, M. Nikravesh*, L. M. Castanie$ and T. W. Patzek’2‘Department of Materials Science and Mineral Engineering, Universi(v of California. Berkelev2Earth Sciences Division, Lawrence Berkeley National Laboratory‘Department of Petroleum Engineering, Stanford University

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AbstractWe present an integrated approach to imaging the progress ofair displacement by spontaneous imbibition of oil intosandstone. We combine Computerized Tomography (CT)scanning and neural network image processing. The mainaspects of our approach are I) visualization of the distributionof oil and air saturation by CT, 11) interpretation of CT scansusing neural networks, and III) reconstruction of 3-D images ofoil saturation from the CT scans with a neural network model.The neural networks developed here construct 3-D images offluid distribution at any time and/or location within the core.One neural network model interpolates between the CT imagesfor a given position at different time levels and extrapolatesbeyond the interval of time during which the images werecollected. Likewise, the network interpolates spatially betweenimages at a given time, After interpolation and extrapolation,other network models have been developed to reconstruct thethree-dimensional distribution of oil in the core. Excellentagreement between the actual images and the neural networkpredictions is found.

IntroductionAn increasing global demand for energy and simultaneousdepletion of conventional hydrocarbon reserves impose aformidable challenge for efficient recovery fromnonconventional rock systems, such as naturally hcturedreservoirs. Fractured petroleum reservoirs provide over 20 ?ZO of

the world oil reserves [ 1]. Examples of prolific fmcturedreservoirs are: the Monterey Shales in California (estimatedtens of billions of barrels of oil-in-place); the CaliforniaDiatomites (estimated fifteen billion barrels of oil-in-place);the West Texas Carbonates; the North Sea Chalks; and theAsmari Limestones in Iran.

Hydrocahon recovery from naturally fractured reservoirs isnot yet fully understood. This is mainly due to the lack of acomplete understanding of multiphase flow through fracturedporous media. Two- or three-phase flow in a fractured reservoirdepends on the combined nonlinear effects of hydraulicconnectivity and physiochemical properties of fractures,relative permeabilities to multiphase flow in the fractures,rock-matrix nature, matrix block size, capillary forces andfracture closure stress. The nonlinear interplay of all thesefactors determines the ultimate hydrocarbon recovery fromfractured reservoirs. In contrast, most of the published datahave been produced in controlled experiments that have focusedon one or more of the above factors considered in isolation.These data are then upscaled in numerical simulators to modelthe coupled nonlinear behavior of fractured reservoirs. As aresult, current numerical simulation models of fracturedreservoirs lack firm predictive capability and must be tuned foreach field case with the available data.

Thus, itmight be helpful to undertake a systematicexperimental and theoretical study of joint effects of all thefactors governing multiphase fluid flow in a fractured porousrock. Of course, such a study is beyond the scope of thispaper. Nevertheless, we have undertaken a study to evaluate theinfluence of four major factors on hydrocarbon recovery. Theseare: fracture configuration, rock-matrix block size, nettabilitycharacteristics of the rock, and fluid flow rates. This paperreports our progress on a scoping study of spontaneousimbibition of a hydrocarbon (kerosene) into a single air-filledblock of rock matrix (Berea sandstone). Our experiments are apreamble to a more difficult study of the most importantproduction mechanism in fractured reservoirs during

2 CT SCAN AND NEURAL NETWORK TECHNOLOGY FOR CONSTRUCTION SPE 35737TURATIO N

waterflooding, i.e., counter-current imbibition of water todisplace oil and gas from the matrix. Here, we want tounderstand the pattern of imbibition from the distribution offluid saturations and to design a neural network model of in-situ fluid saturations obtained directly from a CT scanner, Themodel is then used to generate three-dimensional time-lapseimages of kerosene imbibition. Finally, we intend toincorporate the experimental results into our integrated-finitedifference simulator, M2NOTS (Multiphase MulticomponentNon Isothermal Organics Transport Simulator [2]), to allowfor a more realistic simulation of multiphase flow throughfractures. The mathematical formulation of M2NOTS does notrely on a global coordinate system; therefore, it naturallyextends the method of Multiple Interacting Continua [3] formodeling flow in fractured media to multiphase andmulticomponent systems.

In this project, we use high resolution X-ray computerizedtomography to obtain images of the cross-sectionaldistribution of kerosene and air in Berea sandstone cores as afunction of time. Scans perpendicular to the axis of the cotewere made using a high resolution EMI 5005 (secondgeneration) CT scanner. Each CT slice consists of a series ofvolume elements (voxels). Every voxel has its owncharacteristic attenuation, and can be mapped into a 2-D imagematrix of picture elements (pixels). Using standard computersoftware, the 2-D fluid distributions at specific times adlocations m visualized for each CT slice. CT is a fast, non-destructive imaging technique for determining in-situ fluidsaturation with excellent 3-D resolution. Using this technique,attenuation differences as small as 0.17’0with a cross sectionalresolution of less than 1 mm~ can be realized. Forextrapolating and interpolating between different slicesobtained, neural network models were developed.

Neural networks are very useful in modeling nonlinear,complex, and multi-dimensional data and find wide applicationin analyzing experimental, industrial, and field data. Neuralnetworks, unlike regression analysis, do not requirespecification of a structural relationship between the input adoutput data and they can be trained easily by using sufficientdata from the system under study. In addition, neural networkshave the ability to infer general rules and extract typicalpatterns from specific examples. These properties give theneural networks the ability to interpolate between typicalpatterns or data and generalize their learning in order toextrapolate to a region beyond their training domains.

Principles of CT ImagingVarious visualization methods have been used for fluidsaturation determination during laboratory core fledexperiments [4]. Some of the more common ones in use aretransparent models [5], resistivity [6], microwave attenuation[7], NMR, MRI, X-ray, and gamma ray attenuation [8]. Whilemost of these methods provide only average saturation andimpose restrictions on experimental techniques, CT is a very

fast and accurate technique with few restrictions onexperimental conditions and offers fine spatial resolution [9].Earlier investigators [10- 16] have illustrated the importance ofcomputerized X-ray tomography as a powerful tool forpetroleum industry researchers,

To obtain a CT slice of an object, an X-ray source iscollimated to provide a thin beam which is received by an arrayof crystal detectors, X-ray photons which strike these crystalscause them to fluoresce with an intensity proportional to thenumber of photons received. When a body is placed in thebeam between the source and detector array, only thosephotons that are not absorbed by the body reach the detectors.Fig. la illustrates the principles of X-ray tomography. Thevalues attained when the detectors are read represent the beamattenuation by an object placed in the path of the X-rays. Thedetectors are in a stationary array surrounding the object. TheX-ray bmms are always directed through the object aperture asthe source moves around it in a circular path. The detectors arermd at small rotational intervals and the resulting data arestored in a computer. This rotational excursion is called a passand the total data acquired during this pass are termed a slice.After all readings for a slice have been acquirwl and stored in acomputer, a cross-sectional image or matrix of attenuationcoefficients P(X, y) is created. Radon [17] established themathematical foundation for image reconstruction fromprojection data, The basic synthetic unit is the volume elementor voxel. The CT slice is composed of many voxels, each withits own characteristic attenuation, which are displayed as a 2-Dimage matrix of picture elements (pixels), shown in Fig. la.

CT measures linear attenuation coefficients /.L, which aredefined by Beer’s law:

-(p / p)px

I/Z. = e ......................(1)

where 1{, is the source X-ray intensity, I is the intensitymeasured by the detectors, w is the linear attenuationcoefficient, p is the density of the medium, p/p is the linearmass attenuation coefficient, and x is the thickness of thematerial, If several materials are placed in the path of the X-raybeams, Beer’s law can be generalized as:

Illo=e ‘XPi f Pi )Pxi............... (2)

where i is the material considered. If the object contains amixture of components, the overall mass attenuationcoefficient of the mixture is given by:

Pm, =~o 1 . . . . . . . . . . . . . . . . . . . . . . . .(3)

where S, is the saturation of the phase i, i.e., Si is the volume

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SPE 25737 A. GARG, A. R. KOVSCEK, M. NIKRAVESH, L. M. CASTANIER AND T.W. PATZEK 3

fraction of component i such as water, oil or gas.Different mechanisms are involved in the adsorption of X-

rays, The relative importance of these mechanisms depends onthe energy level of the incident X-rays. In general, y dependson both electron density, p, and atomic number, Z. If theenergy is above 100 keV, y depends mostly on the electrondensity (Compton scattering). For energy below 100 keV,photo-electric adsorption is the main mechanism, dependingmostly on the atomic number Z of the material studied. Thus,

~=p(a+bZ38/E32 )..................(4)

where a is the Klein-Nishira coefficient, p is the electrondensity, E is the energy level in keV, Z is the atomic number,

and b is a constant with a value of 9.8x 10-Z4keVJ 2. Some

conclusions that can be drawn from Eq. (4) are, I) heavierelements will attenuate more than the lighter ones, II) thecoefficient of adsorption, V, for a given material changes withthe energy level of the source and this change depends mostlyon the atomic number of the element considered, and III) bymeasuring adsorption at two or more energy levels, one canobtain two independent measurements. This will help insolution of three phase problems as discussed in the SaturationDetermination section,

Since it is impractical to deal with the X-ray attenuationcoefficient, U, a new scale is defined based on the internationalstandard unit of Hounsfield (H or CT number). On this scale,water has a value of zero and air has a value of -1000. Hence,each CT unit represents about a 0.1 % change in theattenuation coefficient. Equation (5) defines the CT number

CT= PX‘flwafrr Xl f)()() (5). . .P w.,,,

where ~x is the calculated X-ray attenuation coefficient. In

most CT scanners, the range of CT unit varies from -1000,representing air, to 4000, representing very dense materials.Reservoir rocks typically fall in the range of 1000 to 2000 onthis scale.

Saturation DeterminationIn order to obtain fluid saturations, Eq. (I) can be written as:

where Pfi is the adsorption of the rock, p~ is the density of therock, I+ is the adsorption of the fluids, P, is the density of thefluids, and @ is the porosity. For two phases (kerosene-airsystem), the governing equation is given by

PB# =#RPR(l- @)+@@kPk +Y.P. )...........(7)

where pg is the bulk density of the system, fl~ is adsorptioncoefficient of kerosene, p~ is the density of kerosene, M. is theadsorption coefficient of air, and pa is the density of air. From

the measurement of an evacuated core, /.4RP ~ (] – f#J) is

obtained, With ~~ and p. known, there are two equations withtwo unknowns:

jt=),lksk+jlsa a . . . . . . . . . . . . . . . . . . . . . . .

(8)

where Sk and Su are the saturation of kerosene and airrespectively. Also,

Sk+so=l........... . ..........(9)

For three phase saturation (water-kerosene-air system),since there are three unknowns, an additional, independentmeasurement is required. This is done by scanning at adifferent energy level. The system of equations for three phasesaturation determination are given by

PI ‘Pklskl ‘~WIswI ‘~aIsc/I . . . . . . . . ..(10)

at energy level 1 (100 keV), and

~~ ‘~k2sk2 ‘~w2sw2 ‘pa2sa2 ......... (Ill

at energy level 2 (> 100 keV). Finally,

Sk+sw+sa=l.. . . . ,(12)

By scanning a fully kerosene saturated core, a fully watersaturated core, and a fully air saturated core, ~~, vW, and I.Lucmbe obtained.

Neural NetworksImaging the process of spontaneous imbibition in a Berea coreusing CT scanning methods has many limitations. One suchlimitation is the number of slices thaf can be obtained in spaceand time, For this study, only 4 sections perpendicular to thecore axis were scanned at 20 mm separation and at only a fewtime intervals. In order to obtain fluid saturation distributionin space and time throughout the core, a neural network modelwas developed to interpolate between the CT images for agiven position versus time and to extrapolate beyond theinterval of time during which the images were collected. Inthis paper, only multi-layer perception networks with a back-propagation learning algorithm were used.

Historically, the development of neural networks followedthe philosophy of emulating the brain. Many engineers and

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4 CT SCAN AND NEURAL NETWORK TECHNOLOGY FOR CONSTRUCTION SPE 35737~ ED DISTRIBUTION RESIDUAL OIL R

scientists believed that if the functions of the brain could beemulated, many of the problems which are difficult and seeminsoluble by traditional methods could be solved. During thelast decade, a great number of neural network softwarepackages and tools were developed. It is important to mentionthat the new interest in neural networks is due, in part, toadvances in computer technology which have made it possibleto bring together a large number of nodes and massiveinterconnections of simple neurons, much like the humanbrain. However, developing a proper neural network model thatis an accurate representation of the process of interest stillrequires a combination of art, science, and technology.

During the past several years, successful applications ofneural networks to solve complex problems have increasedexponentially. Considerable attention has been devoted to theuse of neural networks as an alternative approach tointerpolation and extrapolation, pattern recognition [ 18],statistical, and mathematical modeling. For example, back-propagation neural networks [19] were used to develop processmodels as substitutes for complicated empirical admathematical models [20]. These models can be used as analternative to statistical and time series analysis. Neuralnetwork analysis, unlike regression, does not requirespecification of structural relationships between the input andoutput data. However, identification using neural networks ismore useful when large amounts of data are available. Once thenetworks are trained using sufficient information, they achieveexcellent predictive capability and show excellentgeneralization performance. Neural networks may be trained toanalyze, predict, and opt imize waste management,electrochemical, reservoir, and chemical processes [21 ]. Selforganization maps, such as Kohonen networks [22], are usedto classify different patterns of processes. Auto associatednetworks, such as Hopfield networks [23], are also used inpattern recognition.

Multi-layer perception networks with a back-propagationlearning algorithm are perhaps the most widely used forprocess modeling, identification, pattern recognition, andpattern classification. The typical network has an input layer,where data are presented to the network, an output layer, whichholds the response of the network to a given input, and at leastone hidden layer, which connects the input layer to the outputlayer. There is no theoretical limit on the number of hiddenlayers, but typically there will be one. Each layer is fullyconnected to the succeeding layer with corresponding weights.The values of the weights represent the current state ofknowledge of the network. These weights are adjusted toimprove the network performance. They are either determinedvia an off-1ine algorithm such as the back-propagationalgorithm [24], or adjusted on-line via a learning process [20,25].

Experimental StudiesAn EMI 5005 (second generation) CT scanner at Stanford

University was used in this study. Fig. lb displays thescanner components. The scanner consists of a mainframe,rotational elements, and scanner electronics. The mainframehouses the X-ray source, detector array, and beam shapingelements, The scanner assembly consists of a support table forpositioning the core. The generator group is responsible forgenerating the X-rays, A combined Viewer/Operator Consoleconsists of a video console, an interactive keyboard forviewing, initiating image generation, and for imagemanipulation. The computation unit performs sequencing,interprets instructions, and executes them, The VideoGenerator accepts image information in digital form adconverts it to the image seen on the viewing monitors. A DiskDrive stores these images. The Magnetic Tape Unit recordsimages from the Disk Drive for long term storage ofinformation.

The cores were scanned at an energy level of 140 keV and afield size of 13 cm. A small field of scan was used to obtainbetter spatial resolution, as the number of pixels availableremain constant. Slice thickness was made as small aspossible, i.e., 3 mm (it varies from 1-10 mm), in order tominimize errors and maximize resolution. Greater slicethickness results in greater measurement error. Also a scanangle of 398” was used as it produces the highest resolutiondue to an overscan of 38”.

The core holder/experimental cell was constructed fromacrylic which is relatively X-ray transpment. A schematic ofthe experimental setup is shown in Fig. 2a. The core holder,6.4 cm in diameter and 2 I cm long, is provided with two endcaps for fluids to flow in and out of the core holder, The inletendcap is connected to a fluid tank through a rubber tube. Acontrol valve attached to the tank controls the flow of fluidfrom tank to coreholder. The outlet endcap is connected to ameasuring vessel. The axis of the cylindrical Berea sandstonecore was aligned with the axis of the core holder so that thecore was exposed to uniform fluid saturation on all the sides.The sandstone used for this study has a porosity of 22% and apermeability of 300 md. Kerosene used as the hydrocarbon forthis study has a specific gravity of 0.80 and viscosity of 1.152cp at 21(’C. Kerosene-air surface tension is 23-32 dynes/cm at21(’C.

Core preparation prior to the start of the experimentinvolved firing the cores for 24 hours at 750(~C. This was doneto remove effects of clay swelling and migration from theimbibition process. The cores were initially at 1 atm pressureand saturated with air. At the onset of the experiment, the firstimages were scanned at four different axial locations within theair-filled core holder in a single run to obtain dry core CTvalues (CTJrY).Four 3 mm thick axial scans were taken at 20mm spacing. Location of the four faces with reference to thetwo end faces are shown in Fig, 2b. Later, the valve attachedto the fluid tank was opened and kerosene filled the core holderuntil the whole core was uniformly submerged in kerosene. X-ray scanning was done along the core at the same locations to

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SPE 25737 A. GARG, A. R. KOVSCEK, M. NIKRAVESH, L. M. CASTANIER AND T.W, PATZEK 5

obtain CT values (CT,,P) at times of 1, 5, 10, 15, 25, 35, 50minutes, and at every 60 minutes for next 240 minutes allerthe core was exposed to kerosene to obtain temporaldistribution of kerosene within the core. The scanningprocedure determined the average saturation of the core sampleat each location. Scanning was also conducted at 24 hours and48 hours after the start of kerosene imbibition. Weight of thecore was measured at the beginning and end of the experimentfor mass-balance calculations. Scanning was performed al thesame axial locations in all the runs to obtain the spatialdistribution of kerosene.

ResultsFor brevity, we only report images obtained at 5, 10, 15, and25 minutes after the start of kerosene imbibition. This isbecause most of the observable dynamics of keroseneimbibition were found to have occurred in first 15 minutes ofthe experiment. An analysis of images obtained at later periodsshowed only very small changes in the overall kerosenesaturation of the core.

For calculating kerrssene saturation in any slice of the core,Eq, (13) is applied to each pixel of the slice:

L lkero~ene– t, I,xps‘erase”’= Cqe,o,ene–Cqy ““””””””””””””

(13)

and

s,,,=1–skerosene . . . . . . . . . . . . . . . . . . . . . .

(14)

CTke,,,$enFis the CT value for a fully kerosene saturated core. Inthis study, slices obtained from X-ray scanning after 48 hoursof kerosene imbibition were used to determine the fullykerosene saturated core CT values. After 48 hours of keroseneimbibition, the core appeared to have reached irreducible airsaturation, as no further changes were noticed in the CTvalues. From mass-balance calculations, the final kerosenesaturation in the core is 80%. Thus to obtain accuratesaturation values, values obtained from Eq. (13) weremultiplied by a factor of 0.8. We are currently developing abetter method of resealing the images directly from the raw X-ray altenuarion aha.

There were also problems using the CTJ,, values obtainedfrom scanning the core surrounded only by air. All the otherimages were scanned after filling the core holder with kerosene.Differences in densities of the surrounding media causedifferences in the absolute values of attenuation coefficient pinside the core. For obtaining the CTJ,,, values to be used inEq. ( 13), inner dry portions of the slices obiained after 1minute of kerosene imbibition were used. To obtain kerosenesaturation profiles, average kerosene saturation was calculatedin annular rings of each slice, within circles at increasing radii,

and finally in sectors. This averaging procedure is illustrated inFig. 2c.

Fig. 3 shows a series of images obtained after thekerosene has imbibed into the core for 5, 10, 15, and 25minutes at the four axial sections of [he core, The imagesrepresent the distribution of kerosene saturation inside the core.In all these images, white represents zero kerosene saturation,and black represents the maximum kerosene saturation or100%. Figs. a- I through d-1 are the images of Berea core after5, 10, 15 and 25 minutes of kerosene imbibition at section 1,located 2 mm from the core face. In these images, there is aclear lack of an oil front, because axial flow dominates overradial flow in this section. Thus at all times, the whole sliceappears uniformly saturated. There is the possibility of akerosene front at very early times. However, nothingconclusive can be said from the information available. Also,kerosene saturation increases uniformly but consistently withtime from image a-1 to d-1. Image d-1 appears to 80 70 oilsaturated.

Berea slices obtained at section 2, 22 mm away from theleft core face, are shown in images a-2 through d-2. Due tolocation of the slices far away from the core faces, radial flowdominates in this section. This is seen as a clear front observedat early times and represented by a dark annulus at the edge ofthe slice. Image a-2 obtained after 5 minutes of keroseneimbibition shows a very sharp front, that gradually changes toa more diffuse front in image b-2, and finally disperses after 15minutes as seen in images c-2 and d-2. In image a-2, keroseneis imbibing uniformly into the core from all the sides adimbibes radially into the sample as a sharp front. Analysis ofthe saturation-matrix shows that the front is dispersed over 3-4mm range. In image b-2, the kerosene saturation annulusappears to be moving radially inside the core and has thickenedas compared to image a-2. There is also a gradual increase inthe kerosene saturation towards the core edges as would kexpected. Image c-2 shows the kerosene saturation in Bereacore after 15 minutes of imbibition, The kerosene front hasdispersed by this time. High kerosene saturation values in thecenter of the section show that the kerosene has reached thecenter of the core. The kerosene saturation distribution after 25minutes of imbibition is shown in image d-2. The image &2shows that approximately 80’%0kerosene saturation is obtaineduniformly throughout the core and stays constant.

Again in section 3, 25 mm from the right face of the core,an imbibition pattern in time similar to that of section 2 isobserved. Radial flow dominates and hence changes in keroseneconcentration are observed radially with time. A sharp kerosenefront in image a-3 changes to a slightly less sharp front inimage b-3 and finally disperses in images c-3 and d-3.

A similar kerosene imbibition history is seen in imagesobtained at section 4, 5 mm from the right face of the core.Section 4, however, is quite different from section 1,especially at the early stages of the imbibition process. This isalso due to a predominance of radial flow. A clear pattern can

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6 CT SCAN AND NEURAL NETWORK TECHNOLOGY FOR CONTSTRUCTION SPE 35737OF DETAILED DISTRIBUTION OF RESIDUAL OILS ATURATION

be seen from a-2 to a-4, and b-2 to b-4. A sharp front exists inthe early part of the imbibition, then it diffuses slightly at-dfinally disappears after 15 minutes, as shown in Figs. 3c-4 and3d-4. However, the distribution of kerosene saturation insection 4 differx from those in sections 2 and 3, Around 10minutes of imbibition, axial effects combine with radial flow.This cannot be seen in images 3c-4 and 3d-4 as the corEreaches uniform saturation distribution and the axial flow effectis masked. In summary, the behavior of section 4 in the earlystages of the imbibition process is similar to the behavior seenin section 2 and 3. In the late stages of imbibition, it is acombination of the behaviors of sections 1, 2 and 3.

To illustrate the imbibition pattern of kerosene in Bereasandstone more clearly, saturation profiles along the diameterof the core at each section are presented in Fig. 4. Figures 4a-I through 4d-1 show kerosene saturation profiles obtained insection 1 at 5, 10, 15 and 25 minutes. In agreement with theimages of Fig. 3, the saturation profiles 4a-1 to 4d indicatethat axial flow dominates. A consistent increase in kerosenesaturation is observed as we go horn Fig. 4a-1 to 4d- 1. Ananalysis of Figs. 4a-2 to 4d-2, representing kerosene saturationprofiles with time at section 2, show the progression of a verysharp radial front extending over a range of 3-4 pixels or 1.1 to1.5 mm. The kerosene front width increases to 7-10 pixels or2.6 to 3.7 mm at 10 minutes in Fig. 4b-2, and finallydisappears after 15 and 25 minutes in Figures 4c-2 and 4d-2.

History of average kerosene saturation in a circular annulusof the core at different radii is shown in Fig. 5. Here, averageannular kerosene saturation is plotted as a function of radialdistance and time. It shows the movement of a kerosene front,the knowledge of which is extremely important forinterpolation between the images. In Fig. 5a through 5d, whiteshading represents zero kerosene saturation and black shadingrepresents 100% kerosene saturation. Shades of gray representintermediate saturations. Trends found in Figs. 5a through Mare similar to those shown earlier in Figs. 3 and 4. At sectionI in Fig. 5a, 2 mm from the left face, at times 5-15 minutes,no change in kerosene saturation occurs radially due topredominant axial flow. Uniform increases in kerosenesaturation between 5 and 15 minutes is observed. After 15minutes, no further change in kerosene saturation occurs eitherradially or with time. Figs. 5b, 5c, and 5d at sections 2, 3, and4, respectively, exhibit a similar trend in kerosene imbibitionand a trend similar to that seen in Figs. 3 and 4 in sections 2,3, and 4. Kerosene imbibition at 5 minutes occurs only at aradiaf distance of 20 mm, i.e., near the edge of the core.Kerosene first reaches the center of the core at 12 minutes.Also, a sharp kerosene front is seen during the first 15minutes, after which the front disappears.

In order to smooth the kerosene saturation distribution,average kerosene saturation within a circle is presented as afunction of time and radial distance in Fig. 6. The purpose ofthese plots is to show minute changes in the kerosenesaturation fronts. Kerosene imbibition patterns observed earlier

in Figs. 3, 4 and 5 are exactly similar to those shown in Fig.6 at all the four sections. A lack of front is seen in Fig. 6a atsection 1, and sharp fronts in Figures 6b, 6c, and 6d atsections 2, 3, and 4 until 12 minutes. Beyond 15 minutes, thekerosene front becomes non-existent.

Fig. 7 is a plot of percent kerosene saturation versus axialdistance from the closest core face at different times, In Fig. 7at section 1, the core is saturated. Kerosene saturations rangefrom 45 % to 82 % afier 5 to 25 minutes of keroseneimbibition.

Plots of average kerosene saturation in a specific annularring versus time is shown in Fig. 8-la through 8-id. Anearly uniform kerosene saturation is observed in Fig. &la,representing section 1, at all times. Kerosene saturationsincrease from the edge to the center of the core at 5, 10, and 15minutes. The change in saturation with radial distance at 25minutes is very small indicating that the core has reached asteady state. Figures 8-1 b through 8-Id show a very sharpfront at 5 minutes that changes to more diffuse front at 10minutes and no front at times 15 minutes and 25 minutes.Similar trends can be observed in Figs. 8-lc and 8- ld, i.e.,sections 2 and 3, respectively, and similar to that in Fig. 8- ld,i.e., section 4 at earlier times. However, the trend is differentfrom Fig. 8-Id at later times and is a combination of sections1, 2, and 3 at times 15 and 25 minutes.

Average oil saturation within a specific annulus as afunction of radial distance versus time is plotted in Fig. 8-2.A smaller profile band width in Fig. 8-2a, representing section1, shows uniform imbibition all throughout the core which isdue to the axial flow pattern at section 1, 2 mm from the leftface of the core. Figs. 8-2b through 8-2d representing sections2, 3, and 4, respectively, show a wide profile band widthindicating that a radial flow pattern is more prevalent in thesesections as there is a large change in saturation with radialdistance. However, all the profiles converge to a very narrowregion beyond 15 minutes as most of the imbibition processends before 15 minutes. Figures 8-2b arrd 8-2c have a similarwidth as compared to Fig. 8-2d at earlier times. At later times,i.e., after 15 minutes, profile width pattern in Fig. t3-2dbecomes a combination of those in Figures 8-2b and 8-2c.

Design of Neural Network ModelsThe network model for axial mapping has two nodes in theinput layer representing the axial coordinate and elapsed time,both scaled uniformly between O and 1. It has 3 nodes in thebidden layer with nonlinear transfer function, and one node inthe output layer predicting the total average saturation in eachcircular cross section, and also with nonlinear transferfunction. The data in Fig. 7 were used to train the network.Due to the limited volume of data available, all the data wereused in the training. The model was trained until the predictionsuffered upon continued learning. Figs. 7a and 7b show theperformance of the network model for predicting the averageoil saturation as a function of time and axial position. The

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SPE 25737 A, GARG, A. R. KOVSCEK, M. NIKRAVESH, L. M. CASTANIER AND T.W. PATZEK 7

results show perfect mapping and excellent prediction of thesaturation for the training data set. Even though only 4 imageswere available in the axial direction, the model had excellentperformance. Therefore, better performance with higheraccuracy and confidence level will be expected if more axialinformation is introduced into the network model.

To model the radial behavior presented in Figs. 8-1a to 8-1d, and Figs. 8-2a to 8-2d, a different neural network wasdesigned. This network has three nodes in the input layerrepresenting the axial coordinate, radial coordinate, and elapsedtime, all scaled uniformly between Oand 1. It has 15 nodes inthe hidden layer with nonlinear transfer function, and one ndein the output layer representing the average saturation in acircular ring. Data presented in Figs. 8-1a through 8-Id wereused for training and testing the network model. The availabledata were divided into two groups, a testing and a training dataset. The test data set was presented to the network, and themodel was trained until the prediction suffered upon continuedtraining. Figs. 8-1 e through 8- Ih show the performance of thenetwork prediction for both the test and training data set. Themean error in the training data set is equal to 0.000249 withstandad deviation equal to 0.000343. The mean error in testdata set is equal to 0.000520 with standard deviation equal to0.001257. Comparing Figs. 8-la to 8-id with Figs. 8-le to 8-lh, and Figs. 8-2a to 8-2d with Figs. 8-2e to 8-2f, one can seethat the network for radial mapping has excellent prediction forboth the test and training data set. We conclude that the radialnetwork is trained with sufficient information and with datathat span a wide range of system behavior; therefore, it is anexcellent predictive tool.

3-D Reconstruction of ImagesThe network model developed earlier can be used for 3-Dreconstruction of CT images and prediction of kerosene

saturation. Our neural network methodology was used toreconstruct image d-4 in Fig. 3. This particular neural networkmodel can predict the saturation of kerosene at each pixel as afunction of axial and radial coordinate at a fixed time. The errorpredicted for reconstructing the 3-D images of the saturationdistribution is less than 5 percent.

To show the usefulness of the model to predict the oilsaturation at any point (axial and radial location and time)image b-2 in Fig. 3 is used. Fig. 9a shows the actual data.Fig. 9b shows the reconstruction of Fig. 9a based on linearinterpolation in time. Figs. 3a-2 and 3c-2 were used for thisinterpolation. Comparing Fig. 9a with 9b, one can see that thetwo images are not similar, and the linear interpolation failedto reconstruct the actual data. As a remedy, the results from theIinear interpolation were used in conjunction with the neuralnetwork prediction of the average saturation in each concentricring with a thickness of 4 pixels. The result is shown in Fig.9c. Comparison of Fig. 9a with 9C demonstrates that themodel accurately reconstructed the actual image. The meanerror in this case study is less than 10~0 with a standard

deviation of 2.57.. To reduce the error further, a neural networkmodel was developed to calculate the average saturation in asector of 2 pixels in the radial direction and 10 degrees in theazimuthal direction. In addition, the axial images were aIsoincluded into the interpolation model. In this study, images ~2, c-2, b-3, and b-4 in conjunction with the network modelwere used to reconstnrct the image 9d. Comparing image 9aand 9d, one can see that the model reconstructed the actualimage almost perfectly. The maximum expected error based onthis technique is less than 5%.

ConclusionsKerosene imbibition in a dry Berea core was successfullyimaged using CT scans and correct fluid saturations werecomputed. Images scanned in the interior of the core show asharp front propagating radially at short times. The frontgradually diffuses and disperses totally after 15 minutes, as theentire cross-section fills with kerosene. Spontaneousimbibition of kerosene in an air-saturated Berea core withdiameter 5.46 cm and length 6.7 cm is a comparatively fastprocess with most of the observable dynamics ending in 15minutes. A relatively fast and accurate technique for imagingfluid flow in a porous medium, such as CT scanning, is quiteadequate for tracking kerosene imbibition and for measuringthe distribution of in-situ fluid saturations. However, CTexperiments must be carefully designed to avoid excessiveexperimental error in a limited number of images that can beobtained in time and space. As most of the observabledynamics of kerosene imbibition were over in 15 minutes, itwas imperative to obtain images at several short timeintervals. Also, it is important to scan all the images with asimilar medium surrounding the core. A core imaged insurrounding media of different densities has different absolutevalues of attenuation coefficient, y. CT values of such imageslead to improper determination of saturations.

To train the neural networks for proper prediction of spatialand temporal distribution of fluids, a large number of datapoints are needed. Due to scanner limitations (heating up ofcathode-ray tube), images could only be obtained at 4 timeintervals during the first 15 minutes. Thus, data obtained fromsuch experiments are in general quite insufficient for properneural network modeling. Axial information was sparse ad

even though our network interpolated properly between theexisting images we are uncertain as to its extrapolative qualityat core ends. Fortunate y, the homogeneous Berea sandstonecore behaved predictably, and we obtained sufficient radialinformation to train the network.

Nomenclaturea = Klein-Nishira coefficient, (-)b = constant in Eq. (4), 9.8x 10”24,mL2/t2, keVq2E = energy level, mL’/t2, keV1 = detected X-ray intensity, I/t, counts/rein1(,= incident X-ray intensity, l/t, counts/rein

701

8 CT SCAN AND NEURAL NETWORK TECHNOLOGY FOR CONTSTRUCTJON SPE 35737

OF DETAILED DISTRIBUTION OF RESIDUAL OIJ , SATURATI ON

0= porosity, percentagep = density, n-rfL3, grrrfcc

Si = saturation of the phase i, ‘ZO PVp = linear attenuation coefficient, L“’, cm’l

x = thickness of material, L, mmZ = atomic number

AcknowledgmentsThis work was supported by the Assistant Secretary for

Fossil Energy, Office of Gas and Petroleum Technology, under

contract No. DE- AC03-76FSOO098 to the Lawrence Berkeley

National Laboratory of the University of California and is

funded through the Natural Gas and Oil TechnologyPartnership. Support for the CT scan experiments wasprovided by the SUPRI-A Heavy Oil Industrial Affiliates

Program and by U.S. Department of Energy under contract No.DE-FG 19-87BC 14126 to Stanford University.

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19. Nikravesh, M., A. R. Kovscek, T. W. Patzek, and R. M,Johnston: “Prediction of Formation Damage During FluidInjection into Fractured, Low Permeability Reservoirs viaNeural Networks,”. Paper SPE 31103, SPE Formation DamageSymposium, Lafayette, LA, 1996.

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SPE 25737 A. GARG, A. R. KOVSCEK, M. NIKRAVESH, L. M. CASTANIER AND T.W. PATZEK 9

22. Kohonen, T.: Self-Organization arrd Associa[e Memory, 2nd 24. Rumelhart D.E., G.E. Hinton, R.J. Williams: “LearningEdi[ion, Berlin, Springer-Verlag, 1987. Internal Representations By Error Propagation, ” Rumelhart

and J. McClelland, editors. Parallel Dara Processing, Vol 1,23 .Hopfield, J. J.: “Neural Networks and Physical Systems With Chapter 8, Cambridge, MA: the M.1.T. Press, 318-362

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703

10 CT SCAN AND NEURAL NETWORK TECHNOLOGY FOR CONSTRUCTION SPE 35737OF DETA ILED DISTRIBUTIONN OF RESIDUAL OIL SATURATION

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