Permeability and porosity images based on NMR, sonic, and...

Carbonate formations generally havea large distribution of pore sizes, rang-ing from microcrystalline to large vugs.Knowledge of these pore spaces andtheir connectivity is crucial to hydro-carbon reservoir characterization andto hydrogeological and near surfaceenvironmental applications. In thispaper, we present permeability andporosity images based on crosswellseismic measurements integrated withwell logs and petrography from a car-bonate aquifer underlying Palm BeachCounty, Florida, U.S. Petrography andcore analyses reveal relationshipsbetween the rock physical propertiesthat control the compressional- andshear-wave velocities of the formation.In addition, core data and petrographycharacterized the matrix permeabilityand pore spaces as well as the lithol-ogy. The lithology integrated with welllogs determined the hydraulic and rockproperties of a 500-ft zone interceptedby a borehole. We delineated vuggyand permeable/impermeable zones atthe borehole and interwell scales in theupper Floridan aquifer in south Floridaby inverting reflection seismic data forimpedance which, when correlatedwith borehole permeability and poros-ity logs, led to empirical relationshipsthat are used to transform impedanceimages to permeability and porosityimages. The images showed continuitybetween the major geologic units andlateral changes in the porosity image.The high-resolution reflectionsobserved at the field scale in the car-bonate formation are associated withchanges in porosity due to the pres-ence of vugs. This was corroboratedwith P-wave and borehole data, whichshowed that, as P-wave velocitydecreases, porosity increases. Theimages show that porous zones in thecarbonate aquifer are laterally contin-uous up to 200 ft from the well andthen become relatively discontinuous,and that these porous and permeableflow units are characterized by inter-connected vugs.

Pore structure. To analyze the porestructure of the carbonate rocks of theupper Floridan aquifer in South Florida,we processed x-ray CT and optical

1102 THE LEADING EDGE NOVEMBER 2003 NOVEMBER 2003 THE LEADING EDGE 0000

Permeability and porosity images based on NMR, sonic, and seismic reflectivity: Application to a carbonate aquiferJORGE O. PARRA and CHRIS HACKERT, Southwest Research Institute, San Antonio, Texas, U.S. MICHAEL BENNETT, South Florida Water Management District, West Palm Beach, Florida, U.S.HUGHBERT A. COLLIER, Collier Consulting, Stephenville, Texas, U.S.

Figure 2. An optical microscope (OM) thin section image of the matrix of core shown in Figure 1.The magenta background is open pore space of the matrix (porosity).

Figure 1. (a) 3D density image of avuggy carbonate core from the Floridanaquifer in South Florida. The imageshows connected, or touching, vugs inthe vertical direction of a full diametercore sample (in the direction of theborehole where the core was obtained ata depth of 1138 ft). (b) 2D densityimage obtained from the core end usedto produce the 3D density image. (c) Photograph of the end of the core.

a

b c

microscopic (OM) thin section imagesfrom core samples. Figure 1a shows, asan example, a 3D view of an x-ray CTimage of a full diameter core samplefrom a depth of 1138 ft. The figure illus-trates a typical interconnected vug sys-tem in the Eocene-aged OcalaLimestone. Vugs or vuggy porosity canbe defined as pore spaces larger than orwithin the particles of rock and com-monly present as leached particles, frac-tures, and large irregular cavities. Ahorizontal view of the end of the corewas obtained from CT data. Figure 1bshows calculated density from the x-ray CT data of a core slice. Figure 1cshows a photograph of the end of thecore for comparison. There is goodagreement between the vuggy pores inthe photograph and those visible in theCT cross-section. This sample has a ver-tical permeability of 4400 md and hor-izontal permeabilities of 904 and 3097md. Differences between Figure 1b and1c are ascribed to the lower resolutionand inherent smoothing of the tomo-graphic image. In addition, the CT sliceis 2 mm behind the core end. Overall,the core exhibits high vug connectivity

in the vertical direction. The matrixporosity of this carbonate rock sampleis observed in a photomicrograph(Figure 2) which clearly shows the inter-connected pores that correlate with highmatrix permeability and porosity. Thesample is best classified as a porous,calcareous packstone-to- grainstone,which denotes a texture that is grain-supported, but contains as much as 10%interstitial carbonate mud. The frame-work is dominated by skeletal grains,including abundant foraminifera tests.The internal structures of these skeletalgrains are well preserved, as indicatedby visible wall structures in corallinealgae and forams.The pore structureand petrography help characterize thelithology and hydraulics properties ofthe rock units intercepted by the bore-hole. The lithology is subsequentlyrelated to field images to delineate theflow units in the interwell region.

Velocity versus porosity and perme-ability: core scale. To relate velocity toporosity and permeability images at thefield scale, we examine first how the VPand VS velocities relate to porosity at the

core scale. We selected 24 full-diametercore samples from different lithofaciesintercepted by the borehole designated,well PBF-10, which was then used inconcert with well PBF-13 to record sonicand crosswell seismic data. Several rockpetrophysical measurements weremade on these core samples. Figure 3shows plots of VP and VS against poros-ity, including five facies. In general, P-and S-wave velocities decrease withincreasing porosity in all facies. Thisvelocity variation occurs because P- andS-wave velocities depend on the shearbulk moduli, or rigidity, of the rockmatrix. The shear bulk moduli in turncorrelates inversely to porosity, decreas-ing with increasing porosity. In effect,the pores reduce the structural integrityand hence the rigidity of the rock. Thus,flow units associated with connectedmoldic/vuggy-porosity are low-veloc-ity zones. Figure 4 shows plots of VP andVS versus horizontal/vertical perme-ability. Although the P-wave velocitydoes not show a clear correlationbetween the rock samples, it doesdecrease as permeability increases.There are two major clusters: the highpermeability samples in the regiongreater than 1000 md, which are uncor-related with VP, and the sandstones,which exhibit an increasing linear trendbetween VP and permeability. Thistrend is also observed at the boreholescale.

In the VS plot with permeability, ageneral increase occurs in permeabilityas S-wave velocity decreases. All pore-facies follow linear trends with a sim-ilar slope. The VS associated with theconnected moldic and vuggy faciesdecreases from 5000 to 4000 ft/s as per-meability increases from 700 to 6000md. In the isolated moldic facies, VSdecreases from about 9000 to 5000 ft/s,and permeability increases from 0.1-100 md. The S-wave velocity of thesandstones decreases from 7500 to 5000ft/s as permeability increases from 12to 700 md. This suggests that, as VS isreduced, the shear bulk modulidecreases and the pore structureschange, with the pores being intercon-nected and more permeable.

Well logs and lithology: boreholescale. To relate geology with rock phys-ical properties at the borehole scale, weused lithologic and geophysical welllogs, and petrographical data. Figure 5presents a sample of the lithology inter-cepted by well PBF-10. The permeabil-ity log is derived from the nuclearmagnetic resonance (NMR) well logusing a calibration method thatrequires a T2 cut off of 92 ms and cor-


Figure 3. VP and VS plotted against porosity for five lithofacies.

relations based on a data set contain-ing carbonate core measurements fromseveral reservoirs. Also shown are VP,VS, bulk density, log-derived porosity,and the NMR-determined bound watervolume. In this case we are interestedin the region between 1000 and 1200 ftbecause it has been identified as anaquifer storage and recovery (ASR)horizon. The lithology at this depth cor-relates with the permeability log. Forexample, the texture of the sandy car-bonate facies is very coarse-to-granu-lar with interconnected moldic porosity(based on cores and thin section analy-sis). Petrophysical core analyses indi-cate high porosity and permeability.The flow unit identified at 1020-1040 ftis part of the productive portion of theupper Floridan aquifer. Below this unit,a sandstone facies is observed that isfine-grained, slightly dolomitic, andwell cemented. It has a predominatelyinterparticle fabric and is characterizedby low permeability but high porosity.This unit has a high bound volume ofwater, and it represents the boundarybetween the upper and lower produc-tive horizons. Avuggy carbonate belowthe sandstone has a matrix with con-nected interparticle porosity and ischaracterized by very high permeabil-ity and porosity. The last zone in thisregion is a chalky carbonate of low per-meability, which serves as the lowerboundary of this targeted ASR horizon.

Figure 6 shows the correlation


Figure 4. VP and VS plotted against horizontal and vertical permeability for five lithofacies.

Figure 5. Lithology intercepted by well PBF-10 showing VP, VS, bulk density, log-derived porosity and NMR bound volume logs.

between the permeability log and thefive facies. Two thin sections producedfrom core samples at 1060.5 and 1126.5ft (20� magnification) show the porestructures of facies 3 and 4, respectively.The top thin section is representative ofthe very fine-grained, dolomitic, fos-siliferous sandstone lithofacies. Thisfacies has high, predominately inter-particle porosity with low permeabil-ity. The bottom thin section shows aforam-pellet packstone with very goodvuggy and interparticle porosity devel-opment responsible for the corre-sponding high permeability values.

Crosswell seismic: field scale.Crosswell seismic measurements wereconducted at a site in southern PalmBeach County, Florida. The field mea-surements were conducted betweenwells PBF-10R and PBF-13 at an inter-well spacing of 330 ft, using a TomoSeisadvanced piezoceramic X-series sourceand a 10-level hydrophone system. Thesurvey interval was from 550 to about

1225 ft below the surface and covereda series of flat lying limestones withsome interbedded sandstones. Thesweep length was 1.2 s at a samplingrate of 125 microseconds from 200-2000Hz. Source and receiver depth sam-pling spacing was 2.5 ft, resulting inabout 38 300 recorded seismic traces.Figure 7 shows the reflection image,velocity image, and well logs plottedin measured depth below land surfacefor well PBF-10, about 10 ft from wellPBF-10R, (no velocity logs were avail-able for well PBF-13). Actual reflectioncoverage below the total depth for eachwell was limited by well spacing. Thevertical resolution of the reflection datafor this profile was about 2 ft. There wasno access to receiver locations below1110 ft due to an obstruction in wellPBF-10R. This limited access reducedreflection coverage in the deeper partof the section and thus the amount ofreflection data available for mapping.The tomography image shows threeflow units beginning at depths of 970,

1020, and 1070 ft, respectively. The flowunit at 970 ft is continuous betweenwells PBF-10R and PBF-13 and is about10-ft thick. This flow unit has a low P-wave velocity with a moderate poros-ity averaging 28%. This flow unitcoincides with high natural gamma-ray emissions present in the lowerArcadia Formation, which contains 15-20% phosphatic sands. The second flowunit, at 1020 feet, is a continuous bedless than 10-ft thick, with an averageporosity of 20%. This unit, a sandy car-bonate of the Arcadia Formation, is ahigh velocity zone associated with alow gamma-ray anomaly. Core sam-ples from this unit are grainstones thatcontain separated vugs that may notcontribute to its overall permeability. Inthis flow unit, permeability is con-trolled primarily by the matrix of therock formation. The last flow unit is a60-ft thick, low velocity region presentwithin the Ocala Limestone at 1070 ft.It is a clean carbonate unit, as confirmedby the low natural gamma-ray emis-sions with interparticle porosity, whichvary from 28 and 43% in the interwellregion.

The reflection image in Figure 7 wasinverted for impedance using the band-limited method. Figure 8 shows theimpedance image between the PBF-10Rand PBF-13 wells at depths from 750 to1550 ft. The VP and density logs areoverlain on the impedance image, andthe image shows good correlation withthe well logs. In particular, the imped-ance clearly shows the main bound-aries of the upper and lower productivehorizons that correspond to the highimpedance zones (red). We analyzedthe impedance image in the regionbetween 950 and 1250 ft and plotted thepermeability and porosity log data withthe impedance at the borehole. Plots ofimpedance with permeability andporosity were used to derive empiricalrelationships (or impedance plot fitequations) for permeability (k) andporosity (φ) for depths of 950-1250 ft.These expressions in terms of the Zimpedance are given by

k=2•1014 exp(-1.6•ª10-3Z) (1)

and permeability for depths of 1024-1045 feet is given by

k=10-24Z6.28 (2)

Here, permeability is in md, poros-ity is in percent, and impedance is in(g/cm3)•(ft/s). Equations 1 and 2 areused to convert the impedance to pro-duce the overlaying permeability andporosity images. These images (Figure 9)


Figure 6. (a) Correlation between the permeability log and the five petrophysical facies. (b) and (c)Two thin sections at 20� magnification which show the pore structure of facies 3 and 4, respec-tively.

ab

c


Figure 7. Reflection and velocity images correlated with well logs from PBF-10 and plotted in measured depth below land surface (surveyed land sur-face elevation is 12.1 ft above sea level).

show continuous and discontinuousflow units. The lateral continuous flowunit (yellow) at 1020-1040 ft has anaverage permeability of 2000 md andan average porosity of 30% (blue in theporosity image at about 1020 ft). Thisflow unit was delineated as a continu-ous reflector in the reflection image inFigure 7.

The discontinuous flow unit showslateral permeability and porositychanges in the region between the 1070and 1140 ft. In this zone it is difficult toestimate the contribution of macrop-ores versus vugs to the overall perme-ability. However, a rough estimate canbe based on the relationship betweenVP and porosity as provided in Figure3a and by observing the permeabilityand porosity images. We know that P-wave velocity decreases as porosityincreases. This suggests that at the fieldscale (see Figure 7), seismic reflectionsbelow 1070 ft are associated with aporosity change due to the vuggy car-bonate. For example, the two porosity


Figure 8. Impedance image based on reflection data showing the VP and density logs.

Figure 9. Permeability and porosity images compared with lithology.

zones in the 1070-1140 ft interval inFigure 9 have been mapped with reflec-tion images. These two zones are lat-erally continuous up to 200 ft from thewell, and then become relatively dis-continuous. Based on core information,these two zones are vuggy in natureand correlate with high permeability,which suggests that their pore structureis formed by a network of intercon-nected vugs (see the core image inFigure 1). Therefore, these two zones(red in Figure 9) are characterized byvuggy porosity, and permeability in theorange, yellow, and light green zonesis probably controlled by macroporesof the rock matrix. These flow unitscarry most of the water flow in theinterwell region of the upper Floridanaquifer at this site.

Discussion. Lithologic and geophysi-cal log data indicated a high flow zonebetween 1060 and 1070 ft at a lithologicor formational contact where a moder-ately indurated limestone is overlain bypoorly indurated sandy limestone unit.This is seen on the geophysical logs bya enlarged borehole (caliper log), highlog-derived porosity (60%), and lowbulk density. Generally, within theFloridan aquifer, the majority ofupward flow is produced by a 5-15 ftsection of the borehole at lithologicboundaries (possibly due to sea levelchanges that control primary and sec-ondary porosity development-sequence stratigraphy concepts).Flowmeter log data have shown twopoints of increased flow (planar fea-ture), one at 1065 and the other at 1050ft (another change in lithology), whichdominate the contribution to upwardflow. The water density in this flowzone and above are higher than belowand the resulting water column (0-1065ft) may act to suppress the upward flowfrom the lower unit by acting as a waterstop or plunger effect. These flows mayalso overshadow any water productionbelow this point. Although, the over-all NMR permeability distribution isaccurate, it does not necessarily quan-tify the point flow sources. A goodapproach would be to integrate orrelate derived transmissivity data (ingallons per day/ft) to derived-NMRpermeability and crosswell reflectiondata.

Conclusions. A new data analysisapproach, from the pore to the fieldscale, allows us to characterize thehydraulic potential of a vuggy carbon-ate rock unit:

• Using a suitable calibration proce-dure, the NMR well log gives infor-mation on porosity, pore structure,and permeability.

• Plots between P-wave velocity andporosity core measurements demon-strate that velocity variation in thecarbonate formation is inversely pro-portional to porosity. This relation-ship is also observed at the boreholescale.

• The correlation between velocity andporosity at the core and boreholescales provides insight into how thehigh resolution (1000-2000 Hz) cross-well seismic data can capture changesin velocity, which are related toporosity changes in the formation.

• Based on the pore scale analysis, thehigh porosity zones are formed bylarge vugs, which can be either sep-arated or interconnected.

• The permeability, porosity, andimpedance images delineate flowunits that can be characterized asvery permeable, and laterally het-erogeneous discontinuous flow unitsthat are directly related to vuggyporosity development. The imagesalso delineate continuous, less per-meable flow units related to themacropores (interparticle porosity)of the rock matrix. These are the flowunits that carry most of the flow inthe interwell region of the upperFloridan.

• This study delineated a high-perme-ability region that is consistent withthe hydrogeologic data collectedfrom wells PBF-10 and PBF-13. Thereflection image-derived impedanceprovides the depth of the lowerboundary of the targeted ASR hori-zon as well as the lateral continuitywithin interwell region.

Suggested reading. “Quantitative char-acterization of carbonate pore systems bydigital image analysis,” by Anselmetti etal. (AAPG Bulletin, 1998). “Sonic velocityin carbonate sediments and rocks,” byAnselmetti and Ebertli (in CarbonateSeismology, SEG 1997). “Hydrologic inves-tigation of the Floridan aquifer systemwestern Hillsboro Basin Palm BeachCounty, Florida, by Bennett and Linton(Technical Publication WS-8, SouthFlorida Water Management District,2002). “Geological nomenclature and clas-sification of porosity in sedimentary car-bonates,” by Choquette and Pray (AAPGBulletin, 1970). “Simulating NMR mag-netization in real carbonate pore sys-tems,” by Hackert and Parra (Petrophysics,2002). “Estimating scattering attenuationfrom vugs and karsts,” by Hackert and

Parra (paper accepted for publication,GEOPHYSICS). “Petrophysical parametersestimated from visual description of car-bonate rocks: a field classification of car-bonate pore space,” by Lucia (Journal ofPetroleum Technology, 1983). “An inte-grated approach based on NMR/acoustictechniques to map permeability in car-bonate aquifers: from the pore to fieldscales,” by Parra et al. (paper accepted forpublication, NSG, Volume II, SEG); “Waveattenuation attributes as flow unit indi-cators,” by Parra and Hackert (TLE, 2002).“A methodology to integrate magneticresonance and acoustic measurements forreservoir characterization,” by Parra etal. (DOE/BC/ 15203-3 Report, 2001).“Seismic properties of carbonate rocks”by Wang (in Carbonate Seismology, SEG,1997). TLE

Acknowledgments: Florida aquifer data wereprovided by the South Florida WaterManagement District. Program work was sup-ported by contract DE-AC26-99BC15203 fromthe U.S. Department of Energy, NationalPetroleum Technology Office. The assistance ofP. Halder (DOE) is gratefully acknowledged. Wealso thank Hampson-Russell.

Corresponding author: [email protected]


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