Fracture-frequency prediction from borehole · Fracture response of wireline logs The presence of fractures is known to affect wireline logs in a variety of ways. Density and resistivity

$Page 1: Fracture-frequency prediction from borehole · Fracture response of wireline logs The presence of fractures is known to affect wireline logs in a variety of ways. Density and resistivity$
Fracture-frequency prediction from boreholewireline logs using artificial neural networks1

Elaine M. FitzGerald,2 Christopher J. Bean2 and Ronan Reilly3

Abstract

Borehole-wall imaging is currently the most reliable means of mapping discontinuitieswithin boreholes. As these imaging techniques are expensive and thus not alwaysincluded in a logging run, a method of predicting fracture frequency directly fromtraditional logging tool responses would be very useful and cost effective. Artificialneural networks (ANNs) show great potential in this area. ANNs are computationalsystems that attempt to mimic natural biological neural networks. They have the abilityto recognize patterns and develop their own generalizations about a given data set.Neural networks are trained on data sets for which the solution is known and tested ondata not previously seen in order to validate the network result. We show that artificialneural networks, due to their pattern recognition capabilities, are able to assess thesignal strength of fracture-related heterogeneity in a borehole log and thus fracturefrequency within a borehole. A combination of wireline logs (neutron porosity, bulkdensity, P-sonic, S-sonic, deep resistivity and shallow resistivity) were used as inputparameters to the ANN. Fracture frequency calculated from borehole televiewer datawas used as the single output parameter. The ANN was trained using a back-propagation algorithm with a momentum learning function. In addition to fracturefrequency within a single borehole, an ANN trained on a subset of boreholes in an areacould be used for prediction over the entire set of boreholes, thus allowing the lateralcorrelation of fracture zones.

Introduction

Fracture zones play an important role in our understanding of fluid flow within theearth’s crust, for example in hydrology, recovery of hydrocarbons or transport ofcontaminants. A knowledge of fracture distribution is also important for ourunderstanding of material strength. Boreholes offer one of the best opportunities tosample fracture populations, albeit in 1D. In fact, fractures in boreholes often play apivotal role in hydrocarbon recovery and related problems.

In this contribution we use an artificial neural network (ANN) scheme to assess thesignal strength of fracture-related heterogeneity in a variety of borehole logs and to

q 1999 European Association of Geoscientists & Engineers 1031

Geophysical Prospecting, 1999, 47, 1031–1044

1 Received June 1998, revision accepted March 1999.2 University College Dublin, Department of Geology, Belfield, Dublin 4, Republic of Ireland.3 University College Dublin, Department of Computer Science, Belfield, Dublin 4, Republic of Ireland.

identify packages of fracturing. ANNs have previously been used to invert for fracturedensities from field seismic velocities (Boadu 1998) and have also been used in theborehole environment to predict lithofacies (Rogers et al. 1992; Westphal andBornholdt 1996), porosity and permeability (Huang et al. 1996; Huang andWilliamson 1997; Wong et al. 1997). Other researchers have successfully appliedANNs on trace-editing tasks (McCormack, Zaucha and Dushek 1993), seismicinversion (Roth and Tarantola 1994), first-break picking (Murat and Rudman 1992;Dai and MacBeth 1997) and feature detection (Poulton, Sternberg and Glass 1992).

The interpretation of wireline data for fracture-frequency prediction can beunderstood as pattern recognition where particular combinations of geophysicalvalues correspond to a particular fracture frequency. Here, we assess the potentialwhich ANNs possess as a fracture-frequency prediction tool.

Data set

Borehole wireline log data obtained from UK NIREX Ltd were used in this study.Three boreholes, namely RCF1, RCF2 and RCF3, were utilized. RCF1 and RCF2 are~ 400 m apart while RCF3 is located midway between them. The boreholes areinclined at an angle of 608 to the horizontal at depths of 300 mbrt (metres below rotarytable) to a final depth of 1000–1100 mbrt. A complete suite of wireline logs, boreholeteleviewer (BHTV) data and core data were available. All interpretations of both theBHTV and core data, for fractures, were carried out prior to our obtaining the datafrom UK NIREX Ltd. The boreholes intersect three major geological units. A fluvial,fine to medium-grained sandstone is uppermost in the stratigraphy. The sandstonepasses down into a poorly sorted, matrix-supported breccia. This unconformablyoverlies volcanic rocks, a series of tuffs, lapilli tuffs and pyroclastic breccias. Someandesite sills also occur. The base of the volcanics was not reached in either borehole.The breccia and volcanic section of the logs were chosen for analysis as they were moreheavily fractured than the sandstones and it was felt that including the sandstonesection would increase the complexity of the task.

The BHTV data interpreted in conjunction with an almost complete core hasinformation on both the type and origin of discontinuities in the borehole (Barton andMoos 1988; Pezard and Luthi 1988; Barton and Zoback 1992). Several types ofdiscontinuity have been identified: bedding, cleavage, veins, joints, fractures, andfaults. Of these we were concerned only with faults, fractures and joints. These datawere then divided into two data sets: those discontinuities which were natural breaks(NFO) and those which were related to drilling (DIF). Breaks related to drilling alsoincluded those which exploit an existing weakness in the borehole wall and those whichare due entirely to drilling.

Fracture response of wireline logs

The presence of fractures is known to affect wireline logs in a variety of ways. Densityand resistivity values will decrease where fractures are present, while acoustic transit

1032 E.M. FitzGerald, C.J. Bean and R. Reilly

q 1999 European Association of Geoscientists & Engineers, Geophysical Prospecting, 47, 1031–1044

times (P-sonic and S-sonic) and porosity will increase in fractured rock (Moos andZoback 1983; Bremer, Kulenkampff and Schopper 1992; Holliger 1996). Thesetrends can be difficult to see on a simple plot of log response and fracture location.Cumulative sum plots of the various logs and fracture frequency per metre provide aclearer picture of long-term trends in the borehole (Leary 1991; Dolan, Bean andRiollet 1998). The cumulative sum is a point-by-point integral of the logs corrected tozero mean and unit standard deviation. These plots demonstrate quite well the effectwhich the presence of fracture zones has on the individual log responses (Fig. 1), forexample as fracturing increases so does porosity (Fig. 1b). In addition, cumulativesum plots were generated for which the fracture-frequency data were randomizedrelative to their respective log measurements, prior to calculating their cumulativesum (Fig. 2). By randomizing the fracture location, the signal within the data shouldbe removed and thus the cumulative sum of the fracture frequency should not trackthe wireline-log trends. This clearly demonstrates that it is the fracture-frequencydistribution which has a significant effect on the wireline-log response. In the nextsection we aim to obtain a more quantitative picture of fracture distribution usingwireline logs and ANNs.

Preprocessing

In this study six wireline logs were used as input parameters to the ANN, and theinterpreted BHTV data for fracture frequency were used as the desired output. Thelogs utilized were: neutron porosity (nphi), bulk density (rhob), deep laterolog (lld),shallow laterolog (lls), P-sonic (dtco) and S-sonic (dtsm). In order to use these datasets for ANN training some preprocessing was performed. The original samplinginterval of the wireline logs was ~ 0.15 m. The log data were resampled at 1 m intervals,by simple decimation, as properties are effectively averaged over logging-tool lengths(i.e. ~ 1 m) during data acquisition (Bean 1996). The fracture data from the boreholeteleviewer were now processed so that fracture frequency per metre corresponded, indepth, to the correct wireline-log pick. Resistivity logs were transformed to log10. Allinputs and outputs are scaled between 0 and 1. This makes the data more suitable forthe neural network. When different input parameters deviate from each other by morethan an order of magnitude, the network tends to be dominated by the parameter withthe highest values. Training then becomes more difficult. The data were partitionedrandomly into three sets of equal size in order to remove any depth bias: a training set, avalidation set and a test set. The ANN was trained on the training set up to the pointwhere performance on the validation set started to deteriorate. All tests on theperformance of the ANN were carried out using the test set.

Training

Network architecture for this study consisted of six input neurons, one output neuronand 20 hidden neurons. A back-propagation algorithm with a momentum learning

Fracture-frequency prediction 1033




Figure 1. Cumulative sum of the normalized, zero mean and unit standard deviation wirelinelogs (solid line) and fracture frequency (dotted line) in RCF2 natural fractures only (NFO). (a)Bulk density, (b) neutron porosity, (c) deep laterolog, (d) shallow laterolog, (e) P-sonic (transittime), (f) S-sonic (transit time).



Figure 2. Cumulative sum of the normalized, zero mean and unit standard deviation wirelinelogs (solid line) and fracture frequency (randomized to incorrect locations prior to cumulativesum calculation) (dotted line) in RCF2/NFO. (a) Bulk density, (b) neutron porosity, (c) deeplaterolog, (d) shallow laterolog, (e) P-sonic (transit time), (f) S-sonic (transit time).

function was utilized in training (Rumelhart, Hinton and Williams 1986; Muller,Reinhardt and Strickland 1995). The learning algorithm was implemented using theStuttgart Neural Network Simulator (Zell et al. 1995). Back-propagation works by trialand error, back-propagating the error, and repeating the trial. The purpose of themomentum learning function is to speed up training and eliminate flatspots from theerror curve. One hidden layer was used. The number of hidden neurons used waschosen after preliminary testing with varying numbers of hidden neurons. Twentyhidden neurons was found to be the most suitable. Prior to training on the actualfracture data, training was carried out using data sets which contained the samefracture frequency per metre values but were not associated with the correct wirelinemeasurements, i.e. the fracture locations were randomized to incorrect depths. Theserandomized data sets were used in the training process as a control on the networkoutput for data with the same statistics as our original data set, but containing no signal.Thirty of these control data sets were generated for each fracture population in eachborehole and ANNs were trained using each control data set. The development of thenetwork error was observed over 100 000 epochs and the point of minimum error wasidentified, i.e. where the performance of the validation set starts to deteriorate. Notethat the validation set was not used for training the network. The evaluation of thetrained network was carried out using only the test set. For the actual fracture data sets,three realizations of each fracture population in both boreholes was undertaken usingthe same initial ANN. To investigate the ANN’s potential for predicting fracturefrequency within a borehole in which it was not trained, we generated a third trainingset by combining wireline log and BHTV data from RCF1 and RCF2. By combiningthe two data sets, it was hoped to create a more widely applicable ANN. The trainedANN was then used to predict fracture frequency within RCF3 (borehole data notpreviously seen by the ANN).

Results

ANN performance must be assessed in order to determine if the ANN training wassuccessful and if the ANN can be used with any degree of confidence as a predictivetool. The accuracy of the ANN’s fracture-frequency prediction is best assessed bycomparing it directly with the desired fracture frequency. We can analyse the ANNperformance by calculating the percentage of times that the ANN predicts accuratelywithin a defined error margin and plotting these percentages against defined errormargins. The error margin is effectively a measure of the amount of absolutedeviation from the correct value which can still be considered a ‘correct’ prediction.Using this method of calculating ANN accuracy, we plot the accuracy of the actualfracture data together with the control data (i.e. fracture locations randomized toincorrect depths) for both fracture populations in each borehole (Fig. 3). This helpsus to determine whether results from the actual data were obtained simply by chance(i.e. only noise), or if the ANN was learning from a signal in the wirelinemeasurements.



RCF1: natural fractures only (RCF1/NFO)

Of this 449 m long profile, 41% of the profile contains fractures, i.e. of the 449 m longintervals in the data set, 184 (41%) of those intervals contain fractures. The maximumnumber of fractures per metre is 8. From the plot of percentage accuracy versus errormargin (Fig. 3a), it can be clearly seen that the ANN has identified a definite signal inthe data. With an error margin of > 0.02, the actual data lie outside one standarddeviation of the control data.

RCF1: natural fractures and drilling-induced fractures (RCF1/NFO&DIF)

This profile is the same length as that used for the NFO data set and 79% of the profilecontains fractures. The maximum number of fractures per metre is 16. On comparison



Figure 3. Percentage accuracy against error margin for: (a) RCF1 natural fractures only (NFO);(b) RCF1/NFO and drilling-induced fractures (DIF); (c) RCF2/NFO; (d) RCF2/NFO&DIF.The error margin represents the amount of absolute deviation from the correct fracture-frequency value which is still considered an accurate prediction. (*) indicates three realizations ofthe actual data performance; (f) indicates mean and standard deviation of control dataperformance.

with the control data performance, it can be seen that the network has performed quitepoorly for the actual data (Fig. 3b).

RCF2: natural fractures only (RCF2/NFO)

This profile is 455 m in length and encounters the same stratigraphic units as RCF1.However, only 20% of this profile contains fractures. The maximum number offractures per metre is again 8. At low error margins, the difference in accuracy betweenthe actual fracture data and the control data is evident, but as the error margin isincreased the two data sets appear to converge (Fig. 3c). As the error margin isincreased, the control data set appears to perform better than the actual data set, whichclearly shows that the network has no predictive power.

RCF2: natural fractures and drilling-induced fractures (RCF2/NFO&DIF)

When the drilling-induced fractures are included, the amount of fractures in theprofile increases to 76% with the maximum number of fractures per metre having avalue of 12. This result is practically identical to that produced from RCF 1 (Figs 3band d).

RCF1&2: natural fractures only (RCF1&2/NFO)

The two borehole data sets combined result in a data set which has 30% naturallyoccurring fractures. The maximum number of fractures per metre is again 8. TheANN performance is well above the randomized fracture location data set withpredictive power increasing as error margin is increased (Fig. 4a).

RCF1&2: natural fractures and drilling-induced fractures (RCF1&2/NFO&DIF)

This data set contains 77% fractures. The result is very similar to that of RCF1 andRCF2 for the equivalent fracture population (NFO&DIF). The ANN possesses littleor no predictive power (Fig. 4b).

The above observations leave us with several points which need to be addressed:1 Why does the ANN trained on RCF1/NFO perform better than that trained on theequivalent fracture set in RCF2?The primary difference is fracture density. RCF1/NFO has 41% fractures whileRCF2/NFO has 20% fractures. To test the influence of the number of fracturespresent in the data set, we generated a data set from RCF1/NFO which had the samenumber of fractures as RCF2/NFO, by randomly resampling the RCF1/NFO dataset. The ANN trained using this data set produced results similar to those of RCF2/NFO (Fig. 5). Thus, as expected from our prior analysis using cumulative sums,which shows a close relationship between fracture distribution and wireline-log



response, the number of fractures present in the data has a significant effect on theANN performance.2 How does the inclusion of drilling-induced fractures (DIF) affect the ANNperformance?When the DIF are included in the data set the predictive power of the ANN decreasessignificantly (Figs 3b and d). The ANN is not able to predict the fracture frequency toan acceptable level of accuracy, i.e. to achieve a higher percentage of correctpredictions than the control data set. The inclusion of the DIFs decreased the signal-to-noise ratio in the data therefore making it substantially more difficult for the ANN todevelop generalizations. This is a strong indication that drilling-induced fractures donot play a significant role in controlling log response in these data. This is to beexpected as it is known that drilling-induced fractures do not generally penetratedeeper than the invaded zone in a borehole, therefore they will have a significantlyweaker effect, relative to the naturally occurring fractures, on the wireline-log response.Also, if one compares cumulative sum plots for the two fracture populations (i.e.



Figure 4. Percentage accuracy against error margin for (a) combined RCF1&RCF2/NFO and(b) combined RCF1&RCF2/NFO&DIF data sets.

natural and drilling-induced fractures) and the wireline-log responses, it is evident thatthe data set which contains both the naturally occurring fractures and those related todrilling does not track the log response very well (Figs 6a and b).3 Can an ANN trained using a subset of boreholes in an area be applied to theremaining boreholes in order to predict fracture frequency?This would be of particular importance where only a subset of the boreholes in an areahad televiewer and core data. On a local scale the ANN trained in RCF2 was used topredict RCF1/NFO fracture frequency from RCF1 wireline data. The results are veryencouraging. Despite the limitations of the RCF2/NFO network due to low fracturedensities (Fig. 3c), the network performs quite well when presented with RCF1wireline data (Fig. 7). The general highs and lows of fracture frequency have beenpredicted although the actual fracture frequencies are not directly comparable. Giventhat the RCF2/NFO network was trained on one-third of the RCF2 data set and wasused to predict over 400 m of RCF1, the results are very promising. On a wider scale,the ability of an ANN trained on a combination of borehole data (RCF1&2) to predictthe fracture frequency in a borehole (RCF3) was also found to be reasonablysuccessful. Again, in general, the ANN has been able to match the occurrence offracturing in the borehole (Fig. 8).

Conclusion

We have successfully used an ANN scheme to predict fracture frequency within aborehole. We would expect ANN performance as a fracture-frequency predictive toolto improve if total fracture aperture per metre were used rather than the total numberof fractures per metre. Aperture data would give a more accurate measure of the



Figure 5. Percentage accuracy against error margin for the resampled RCF1/NFO data set. Notethe difference between this and Fig. 3a and the similarity with Fig. 3c. (*) indicates threerealizations of the actual data performance; (f) indicates mean and standard deviation of controldata performance.



Figure 6. Cumulative sum of the normalized, zero mean and unit standard deviation wirelinelogs (solid line) and fracture frequency (dotted line) in RCF2/NFO&DIF. (a) Bulk density, (b)neutron porosity, (c) deep laterolog, (d) shallow laterolog, (e) P-sonic (transit time), (f) S-sonic(transit time).

wireline-log response to the presence of fractures. Aperture data were not available tous for this study.

From this work we can conclude that the signal produced by natural fractures inwireline-log responses dominates over that produced by drilling-induced fractures.The drilling-induced fractures do not seem to have a quantifiable log response. Theinclusion of the DIFs has been shown to alter radically the ANN’s predictive power,making it impossible for the ANN to recognize a coherent pattern in the fracture dataset. In addition, the total number of fractures in a borehole has a significant role toplay in the ability of an ANN to learn. Also, the possibility exists that an ANNtrained using a small number of boreholes could be applicable on a widergeographical area.

Acknowledgements

We thank Robin Brereton (BGS) for discussions and UK NIREX Ltd for data. We also



Figure 7. RCF1 (natural fractures only) fracture frequency predicted using a network trained onRCF2 borehole data.

thank the Institute for Parallel and Distributed High Performance Systems (IPVR),University of Stuttgart, for SNNS, Version 4.1.

References

Barton C.A. and Moos D. 1988. Analysis of macroscopic fractures in the Cajon Pass scientificdrillhole: over the interval 1829–2115 metres. Geophysical Research Letters 15, 1013–1016.

Barton C.A. and Zoback M.D. 1992. Self-similar distribution and properties of macroscopicfractures at depth in crystalline rock in the Cajon Pass scientific drillhole. Journal of GeophysicalResearch 97, 5181–5200.

Bean C.J. 1996. On the cause of 1/f power spectral scaling in borehole logs. Geophysical ResearchLetters 23, 3119–3122.

Boadu F.K. 1998. Inversion of fracture densities from field seismic velocities using artificialneural networks. Geophysics 63, 534–545.

Bremer M.H., Kulenkampff J. and Schopper J.R. 1992. Lithological and fracture response ofcommon wireline logs in crystalline rocks. In: Geological Applications of Wireline Logs 11 (eds



Figure 8. RCF3/NFO fracture frequency predicted using a network trained on a combination ofborehole data from RCF1 and RCF2.

A. Hurst, C.M. Griffiths and P.F. Worthington), Geological Society Special Publication No.65, pp. 221–234. Geological Society.

Dai H. and MacBeth C. 1997. The application of back-propagation neural network to automaticpicking seismic arrivals from single-component recordings. Journal of Geophysical Research102, 15105–15113.

Dolan S.S., Bean C.J. and Riollet B. 1998. The broad-band fractal nature of heterogeneity in theupper crust from petrophysical logs. Geophysical Journal International 132, 489–507.

Holliger K. 1996. Upper crustal seismic velocity heterogeneity as derived from a variety ofP-wave sonic logs. Geophysical Journal International 125, 813–829.

Huang Z., Shimeld J., Williamson M. and Katsube J. 1996. Permeability prediction with artificialneural network modelling in the Venture gasfield, offshore eastern Canada. Geophysics 61,422–436.

Huang Z. and Williamson M.A. 1997. Determination of porosity and permeability in reservoirintervals by artificial neural network modelling, offshore eastern Canada. Petroleum Geoscience3, 245–258.

Leary P.C. 1991. Deep borehole log evidence for fractal distribution of fractures in crystallinerock. Geophysical Journal International 107, 615–627.

McCormack M.D., Zaucha D.E. and Dushek D.W. 1993. First-break refraction event pickingand seismic data trace editing using neural networks. Geophysics 58, 67–78.

Moos D. and Zoback M.D. 1983. In situ studies of velocity in fractured crystalline rocks. Journalof Geophysical Research 88, 2345–2358.

Muller B., Reinhardt J. and Strickland M.T. 1995. Neural Networks: an Introduction, 2nd edn.Springer-Verlag, Inc. (Physics of neural networks)

Murat M.E. and Rudman A.J. 1992. Automated first arrival picking: a neural network approach.Geophysical Prospecting 40, 587–604.

Pezard P.A. and Luthi S.M. 1988. Borehole electrical images in the basement of the Cajon Passscientific drillhole, California; fracture identification and tectonic implications. GeophysicalResearch Letters 15, 1017–1020.

Poulton M.M., Sternberg B.K. and Glass C.E. 1992. Location of subsurface targets ingeophysical data using neural networks. Geophysics 57, 1534–1544.

Rogers S.J., Fang J.H., Karr C.L. and Stanley D.A. 1992. Determination of lithology from welllogs using a neural network. AAPG Bulletin 76, 731–739.

Roth G. and Tarantola A. 1994. Neural networks and inversion of seismic data. Journal ofGeophysical Research 99, 6753–6768.

Rumelhart D.E., Hinton G.E. and Williams R.J. 1986. Learning representations by back-propagating error. Nature 323, 533–536.

Westphal H. and Bornholdt S. 1996. Lithofacies prediction from wireline logs with geneticalgorithms and neural networks. Zeitschrift der Deutschen Geologischen Gesellschaft 147, 465–474.

Wong P., Tamhane D. and Wang L. 1997. A neural-network based approach to knowledge-basedwell interpolation: a case study of a fluvial sandstone reservoir. Journal of Petroleum Geology 20,363–372.

Zell A., Mamier G., Vogt M., Mache N., Hubner R. and Doring S. 1995. SNNS: StuttgartNeural Network Simulator, Version 4.1. Institute for Parallel High Performance DistributedSystems, University of Stuttgart.



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Fracture-frequency prediction from borehole · Fracture response of wireline logs The presence of fractures is known to affect wireline logs in a variety of ways. Density and resistivity