A method to evaluate porestructures of fractured tightsandstone reservoirs usingborehole electrical image loggingLiang Xiao, Junran Li, Zhiqiang Mao, and Hongyan Yu

ABSTRACT

Fractures are important in improving tight sandstone pore con-nectivity and fluid flow capacity. However, the contribution offractures to pore connectivity and fluid flow capability cannotbe quantified using current methods. The objective of this study wasto develop a method to quantitatively characterize reservoir im-provement as a result of fractures. This method was proposed basedon the experimental results of 37 core samples recovered from theUpper Triassic Chang 8 tight sandstone in the Jiyuan area of theOrdos Basin, China. The morphological features of the porosityspectra, themercury injection capillary pressure curves, and the pore-throat radius distributions were analyzed. Accordingly, a method wasproposed to construct pseudocapillary pressure (Pc) curves from theporosity spectra to characterize the pore structure of fractured res-ervoirs and to establish corresponding models based on the classifiedpower function method. In addition, a model was developed topredict fracture formation permeability based on the Swansonparameter. The proposed method and models were applied infield applications, and the estimated results agreed well with thecore and drill-stem testing data. Fractured formations containedgood pore structure, high permeability, and oil production rata.The relative errors between the model-predicted pore structureevaluation parameters, permeability from Pc curves, and core-derived results are all within –30.0%. With the integrated studyof reservoir pore structure with permeability, the effective UpperTriassic Chang 8 fractured tight sandstone reservoirs with de-velopment potential were successfully identified.

AUTHORS

Liang Xiao ~ Key Laboratory of Geo-detection, China University of Geosciences,Beijing, People’s Republic of China; School ofGeophysics and Information Technology,China University of Geosciences, Beijing,People’s Republic of China; Department ofGeosciences, The University of Tulsa, Tulsa,Oklahoma; xiaoliang@cugb.edu.cn

Liang Xiao currently works as an associateprofessor and Ph.D. supervisor at the ChinaUniversity of Geosciences, Beijing. He has beenan associate editor for Acta Geophysica andthe Arabian Journal of Geosciences. Hisresearch interests include conventional andunconventional reservoirs pore-structurecharacterization using well logs. More than 30relevant papers have been published. Hereceived his Ph.D. in geological resources andgeological engineering in 2012. Currently, he isan associate editor of the Arabian Journal ofGeosciences and an editorial boardmember ofEnergy Sources, Part A: Recovery, Utilization,and Environmental Effects.

Junran Li ~ Department of Geosciences,The University of Tulsa, Tulsa, Oklahoma;junran-li@utulsa.edu

Junran Li obtained his B.Sc. in geology fromJilin University, Changchun, Jilin, China in 1998.He earned his Ph.D. of environmental sciencesfrom the University of Virginia, Charlottesville,Virginia in 2008. He is currently assistantprofessor of geosciences at The University ofTulsa. His current interests include aeoliangeomorphology and aeolian reservoirs,geochemical characterization of conventionaland unconventional reservoirs, and theenvironmental impacts of energy utilizationand exploration.

Zhiqiang Mao ~ State Key Laboratoryof Petroleum Resource and Prospecting,Beijing, People’s Republic of China; maozq@cup.edu.cn

Zhiqiang Mao works as a professor and Ph.D.supervisor at the China University ofPetroleum, Beijing. His interests includepetrophysics and evaluation of formationsusing well logs. He earned his Ph.D. in geologyand exploration for coal, oil, and natural gasfrom the postgraduate school of the Research

Copyright ©2020. The American Association of Petroleum Geologists. All rights reserved.

Manuscript received November 13, 2017; provisional acceptance March 12, 2018; revised manuscriptreceived April 28, 2018; revised manuscript provisional acceptance June 28, 2018; 2nd revisedmanuscript received August 10, 2018; 2nd revised manuscript provisional acceptance September 6,2018; 3rd revised manuscript received September 28, 2018; 3rd revised manuscript provisionalacceptance October 9, 2018; 4th revised manuscript received January 9, 2019; 4th revisedmanuscript provisional acceptance January 30, 2019; 5th revised manuscript received February 2,2019; final acceptance April 30, 2019.DOI:10.1306/04301917390

AAPG Bulletin, v. 104, no. 1 (January 2020), pp. 205–226 205

INTRODUCTION

The exploration and development of tight oil and gas sandstonereservoirs have become important in China and elsewhere (Zouet al., 2012). Compared with conventional reservoirs, tightsandstones have ultralow porosity (generally <10.0%) andpermeability (generally <0.5 md), high irreducible water satu-ration (ranges from 40.0% to 65.0%), and naturally developedfractures (Holditch, 2006; Zou, 2017). Frequently, intervals withlow porosity may yield good production, whereas zones with highporosity may not produce (Newberry et al., 1996; Ghafoori et al.,2009). As a result, reservoir validation prediction faces greatchallenges for tight sandstones (Fu et al., 2016).

In tight sandstone reservoirs, natural fractures are highlyrelevant to hydrocarbon accumulation and migration (Ameenet al., 2012; Zeng et al., 2013). Reservoirs with developed frac-tures generally contain a large pore-throat size and a serried porenetwork; thus, these reservoirs will have good pore structuresand fluid flow capacities (Burberry and Peppers, 2017). In contrast,nonfractured reservoirs tend to have small pore-throat sizes, poorpore structures, and low permeabilities (Santos et al., 2015).Therefore, the validation of tight sandstones is primarily determinedby the development of natural fractures (Lyu et al., 2016, 2017). Toimprove tight sandstone reservoirs identification and validationevaluation, quantitatively characterizing the pore structure and ac-curately predicting permeability are of great importance.

Borehole electrical image logs are typically used to charac-terize fracture development (Luthi and Souhaite, 1990; Yamadaet al., 2013; Damiani et al., 2016). Using this method, severalparameters of fractures, such as fracture porosity, width, length,gaping degree, and density, can be extracted (Ezati et al., 2018).Generally, formations with high fracture porosity, length,width, and density are considered productive (Ghafoori et al.,2009; Xie et al., 2015). However, borehole electrical imagelogs currently can only be used to macroscopically characterizereservoirs, and the microscopic relationships between fractureparameters and pore structure and permeability cannot bederived (Lai et al., 2017, 2018; Valentın et al., 2018).

Alternatively, formation pore structure may be evaluatedusing nuclear magnetic resonance (NMR) logs, which measurethe induced magnet moment of hydrogen protons containedwithin the reservoir rocks (Coates et al., 2000; Dunn et al.,2002). In recent years, numerous methods have been developedto evaluate pore structure using NMR logs (Looyestijn, 2001;Volokitin et al., 2001; Ouzzane et al., 2006; Olubunmi andChike, 2011; Xiao et al., 2016). However, these methods havesuffered from a number of limitations in fractured reservoirs.Xiao and Li (2011) pointed out that NMR logs are not effectivein pore structure evaluation for fractures with widths less than

Institute of Petroleum Exploration andDevelopment of Beijing in 1995.

Hongyan Yu ~ Northwest University,Xi’an, Shaanxi, People’s Republic of China;yuhy@nwu.edu.cn

Hongyan Yu received her Ph.D. in geologicalresources from China University of Petroleum(Beijing) in 2012. She is currently an assistantprofessor at Northwest University. Hongyan Yudeveloped her research in formationevaluation, geological and petrophysicalreservoir characterization, unconventionals(shale, coal), and x-ray microcomputedtomography.

ACKNOWLEDGMENTS

This research was supported by the NationalNatural Science Foundation of China (no.41302106); the China Postdoctoral ScienceFoundation (no. 2012M520347,2013T60147); the Fundamental ResearchFunds for the Central Universities, China (no.2-9-2016-007); and the Open Fund of KeyLaboratory of Geo-detection (ChinaUniversity of Geosciences, Beijing), Ministryof Education (no. GDL1204). The authorsthank Zhihao Jiang (China University ofPetroleum, Beijing) for providing the locationmap of the study area.

206 Pore Structure Evaluation of Fractured Tight Sandstone Reservoirs

2 mm because the fracture angle of dip has no re-sponse in NMR logs. In reality, the width of a ma-jority of natural fractures in tight sandstones is lessthan 2 mm, suggesting that the method based onNMR logs is invalid for these reservoirs (O’Hara

et al., 2017; Zhao et al., 2018). Additionally, theshape of the NMR spectrum is strongly affected byhydrocarbons that occupy the pore spaces, whichmakes it difficult to apply NMR logs to hydrocarbon-bearing formation pore structure evaluation (Mao et al.,

Figure 1. Location of the study area in the Ordos Basin (A), location of the Ordos Basin in northeast China (B), and the formationmember, thickness, and lithology of the Upper Triassic Yanchang Formation (C) (modified after Dou et al., 2017; Jiang et al., 2018). Fm. =Formation; Mbr. = Member.

XIAO ET AL. 207

2007; Xiao et al., 2018). Finally, the low longitu-dinal resolution of NMR logs makes them unsuit-able for distinguishing thin sandstones with relativehigh porosity and permeability (Coates et al., 2000;Dunn et al., 2002). Such formations, however,generally have high hydrocarbon production be-cause of high seepage capability.

Recently, the porosity spectra extracted fromborehole electrical image logging have been used tocharacterize porosity type (primary and secondaryporosity) and distribution in carbonate reservoirs(Akbar et al., 2000; Tyagi and Bhaduri, 2002; Wanget al., 2004). A consistency was found between theshape of the porosity spectrum and the productiondata (Ghafoori et al., 2009; Fu et al., 2016). De-spite the known advantages of this method, itcan only be used to qualitatively or semiquantita-tively characterize fractured reservoirs (Xiao et al.,2016). The parameters associated with pore struc-ture (e.g., pore-throat size and distribution, thresh-old pressure, median pressure, etc.) cannot beextracted, and the relationship between porosityspectra and permeability cannot be established(Xiao et al., 2016).

The purpose of this paper is to fill out theseknowledge gaps and to present a method to quan-titatively characterize the fractured reservoir pore

structure of tight sandstones based on boreholeelectrical image logging. In this method, a newmodelwas developed to construct the pseudocapillarypressure (Pc) curves and the pore-throat radius (Rc)distribution using the porosity spectrum, based ontypical tight sandstones of the Upper TriassicChang 8 in the Jiyuan area of the Ordos Basin inChina. A permeability prediction model, based onthe Swanson parameter, was also established toevaluate the permeability of fractured reservoirs.

GEOLOGICAL SETTINGS

The Ordos Basin, located in northcentral China,covers an area of more than 370,000 km2 (>143,000mi2) (Shi et al., 2011; Jiang et al., 2018) (Figure 1A,B). The elevation of this flat basin is higher in the eastthan in the west. The basin consists of six tectonicunits: the Yimeng uplift, the Jinxi folding belt, theYishan slope, the Tianhuang depression, the westernedge thrust belt, and the Weibei uplift (Dou et al.,2017; Jiang et al., 2018) (Figure 1A). The OrdosBasin is the second-largest sedimentary basin thatformed on the North China craton (Dou et al.,2017). The main oil-bearing reservoirs targeted forexploration and development in this basin include

Figure 2. Six diagenetic facies of the Upper Triassic Chang 8 in the Jiyuan area, west Ordos Basin, China. These six diagenetic faciescontain weak corrosion with chlorite mat (A), corrosion of unstable components (B), tectonic fracture (C), compaction density (D),kaolinite filling (E), and carbonate cementation (F). (A) to (C) are considered constructive diagenetic facies, and (D) to (F) belong todestructive diagenetic facies (modified after Shi et al., 2011).

208 Pore Structure Evaluation of Fractured Tight Sandstone Reservoirs

the Upper Triassic Chang 6, Chang 7, and Chang8 members (Dai et al., 2005). The Jiyuan area lies inthe western section of the Ordos Basin, and theChang 8 member in this area belongs to the Tian-huan depression, a major oil-producing area in theOrdos Basin. The main lithology in Chang 8 includesfine-grained sandstone, siltstone, and silty mudstone(Jiang et al., 2018) (Figure 1C). The matrix porosityof the Chang 8 member ranges from 3.0% to 15.0%,and the matrix permeability ranges from 0.01 to 5.0md (Wang et al., 2018).

The complicated pore structure and ultralowporosity and permeability of the Chang 8 tightsandstone were caused by diagenesis (Lai et al.,2013; Li et al., 2017), including compaction or ce-mentation that was unfavorable for the preservationof effective pore spaces and pore throats. Shi et al.(2011) reported that the diagenetic facies of theChang 8 tight sandstones have six subtypes (i.e.,weak corrosion with chlorite mat, corrosion of un-stable components, tectonic fracture, compactiondensity, kaolinite filling, and carbonate cementation)(Figure 2). According to their contributions to thesandstone’s history, these six diagenetic facies can

be further divided into constructive diagenetic faciesand destructive diagenetic facies (Shi et al., 2011).The constructive diagenetic facies, including weakcorrosion with chlorite mat, corrosion of unstablecomponents, and tectonic fractures, are a positivefactor in improving Chang 8 tight sandstone porestructure and pore connectivity. Compaction density,kaolinite filling, and carbonate cementation diage-netic facies are considered to be destructive to theChang 8 member. The tectonic stresses caused theChang 8 to develop many fractures. As a result,nearly no natural hydrocarbon production is presentin the intervals in which fractures are not developed(Zhang et al., 2017; Taleghani et al., 2018).

METHODS AND MODELS

Porosity Spectrum Extraction

The formation microresistivity scan image (for-mation microimager [FMI]) tool, a typical bore-hole electrical image method, contains 4 pads and4 flaps located around the borehole, and a total of192 button electrodes (Ekstrom et al., 1987; Luthi

Figure 3. An example of a formation microimager (FMI) image in fractured reservoirs and the corresponding porosity spectra derived using thetechniques shown by equation 3 in the Luo 60 well in the study area. The FMI image is shown in the second track, and the porosity spectrum isshown in the third track. For fractured formations, the FMI image exhibits dark sine curves (marked by red sine curves), and the porosity spectra havebimodal distributions. The first peak represents the matrix porosity distribution, and the second peak is the response of secondary porosity (fractureor vug). For nonfractured formations, the porosity spectra exhibit unimodal distributions. CM = centimeter; GAPI = the API unit of gamma ray-log;GR = gamma-ray log; VCAL = vertical caliper log; VSP = vertical spontaneous potential log.

XIAO ET AL. 209

and Souhaite, 1990). In practice, a total of 192formation conductivity data points can be equallyobtained around the borehole wall using 0.5-cm(0.2-in.)-wide electrodes and 0.25-cm (0.1-in.)longitudinal resolution (Williams-Stroud et al.,

2010; Aslanyan et al., 2015; Valentın et al., 2018).An imaging technique is then used to transform therecorded conductivity data to obtain the boreholeimage, and parameters associated with fracturedformations, such as fracture porosity, length, density,

Table 1. The Physical Properties and the Corresponding Mercury Injection Capillary Pressure Experimental Results for 37 Core SamplesDrilled from the Upper Triassic Chang 8 Tight Sandstone in the Jiyuan Area of the Ordos Basin, Northcentral China

Core No. Porosity, % Permeability, mdSwansonParameter

Maximal Pore-ThroatRadius, mm

MedianRadius, mm

MedianPressure, MPa

ThresholdPressure, MPa

1 6.57 0.09 8.44 0.37 0.07 10.01 2.012 6.75 0.13 3.33 0.13 / / 5.543 17.70 7.37 73.40 3.63 0.26 2.87 0.204 11.02 1.12 6.02 0.33 0.03 27.60 2.255 11.11 3.80 44.29 2.89 0.12 6.02 0.256 11.11 3.80 39.40 2.12 0.18 4.12 0.357 14.51 1.82 48.14 2.08 0.18 3.98 0.358 11.90 2.15 40.43 2.00 0.20 3.59 0.379 12.90 4.77 63.45 3.31 0.33 2.20 0.2210 13.60 5.80 69.02 3.51 0.23 3.15 0.2111 9.70 0.26 7.39 0.34 0.05 14.88 2.1712 12.10 0.78 24.79 1.10 0.25 2.92 0.6713 13.30 1.42 26.37 1.33 0.19 3.90 0.5514 6.50 0.09 3.69 0.16 0.03 21.35 4.4815 7.80 0.16 9.88 0.38 0.10 7.01 1.9416 7.60 0.16 8.66 0.37 0.10 7.53 1.9917 9.90 0.25 12.93 0.54 0.11 6.60 1.3518 7.40 0.14 7.90 0.38 0.04 16.46 1.9319 8.70 0.41 20.93 0.74 0.22 3.29 1.0020 8.90 0.16 13.99 0.58 0.16 4.46 1.2721 10.00 0.27 7.81 0.38 0.05 13.42 1.9422 7.80 0.10 7.43 0.35 0.06 11.51 2.0923 7.27 0.39 16.89 0.80 0.09 7.75 0.9224 12.78 0.09 3.65 0.20 0.03 24.60 3.6025 5.86 0.13 14.45 0.62 0.11 6.50 1.1926 7.80 0.06 6.03 0.23 0.07 11.24 3.1827 10.10 0.60 13.81 0.61 0.11 6.93 1.2028 11.80 0.79 24.40 1.05 0.27 2.69 0.7029 6.53 0.11 7.05 0.33 0.04 20.59 2.2330 7.08 0.07 7.43 0.31 0.08 9.50 2.3931 6.86 0.12 6.53 0.29 / / 2.5732 12.22 0.24 20.23 1.02 0.15 4.85 0.7233 12.99 0.57 10.97 0.55 0.08 8.85 1.3334 9.53 0.16 8.04 0.39 0.04 16.90 1.8935 11.30 0.85 33.53 1.28 0.43 1.70 0.5736 16.30 2.63 35.67 1.77 0.29 2.57 0.4237 8.85 3.55 29.95 1.16 0.29 2.52 0.63

Abbreviation: / = not applicable.

210 Pore Structure Evaluation of Fractured Tight Sandstone Reservoirs

Figure 4. Illustrations of a typical porosity spectrum (A), the casting thin section (B), the formation microimager (FMI) image (C), themercury injection capillary pressure (MICP) curve (D), and the corresponding pore-throat radius (Rc) distribution (E) in a formation withnatural fractures in the Huang 44 well. In a fractured formation, the porosity spectrum shows wide unimodal or bimodal distributions,fractures can be easily identified in the casting thin section, the FMI image exhibits a dark sine or cosine curve, the MICP curve lies at thebottom, and the Rc exhibits a wide bimodal distribution. GAPI = the API unit of gamma-ray log; GR = gamma-ray log.

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Figure 5. Illustrations of a typical porosity spectrum (A), the casting thin section (B), the formation microimager (FMI) image (C), themercury injection capillary pressure (MICP) curve (D), and the corresponding pore-throat radius (Rc) distribution (E) in a nonfracturedformation in the Luo 24 well. In this formation, the porosity spectrum is narrow with unimodal distribution, fractures cannot be identifiedin the casting thin section, the FMI image is bright, the MICP curve lies at the top, and the Rc exhibits a narrow unimodal distribution. GAPI =the API unit of gamma-ray log; GR = gamma-ray log.

212 Pore Structure Evaluation of Fractured Tight Sandstone Reservoirs

and width, can also be calculated (Cheung andHeliot, 1990; Sullivan and Schepel, 1995; Ezatiet al., 2018). High resolution makes FMI logs ap-plicable in the identification of thin beds (Harthyet al., 2010).

Assuming that the electrical images from theFMI tool are essentially a conductivity map of theborehole wall, primarily from within the mud-flushed zone, an expression derived from the clas-sic Archie’s equation that connected the effectiveporosity w, formation resistivity Rxo, mud filtrate

resistivity Rmf, and water saturation Sxo can bewritten as follows (Archie, 1942):

wm =abRmf

SnxoRxo(1)

In this equation, w can be estimated from con-ventional well log data (such as density, neutron,or sonic) (Wyllie et al., 1956; Widmyer andWood, 1958; Ellis, 2003); Rxo can be transformedfrom the recorded conductivity value of the FMItool; and a, b, m, and n are rock resistivity parameters,

Figure 6. An example of acquiring a reverse cumulative curve from a porosity spectrum in 2574.13 m (8445.31 ft) of the Huang 44 well.POR = porosity interval.

Figure 7. Principle of acquiring the value of 1/porosity interval (POR) for each mercury injection capillary pressure (Pc) increment. S0 =oil saturation; SHg = mercury injection saturation.

XIAO ET AL. 213

and their values can be estimated using rock re-sistivity experiments (Archie, 1942; Waxman andSmits, 1968; Waxman and Thomas, 1974).

By setting Sxo = 1, a = b = 1, and m = n = 2 inequation 1, Newberry et al. (1996) first trans-formed the FMI image into a porosity map usingthe following:

w =�Rmf

Rxo

�1 =

2

(2)

The assumption that the pore spaces are only occupiedby water (Sxo = 1) in a flushed zone is not always validbecause there are some unflushed hydrocarbonsremaining in the invaded zone (Fu et al., 2016).Under such circumstances, the value of Sxo is lessthan 1.0. Moreover, Rmf must be calibrated in thewater layer. A number of studies revised equation

2 and developed a method to derive a porosity mapfrom the FMI image (Akbar et al., 2000; Xie et al.,2015; Zhao et al., 2017):

wFMI =�abRmf

Snxo·Ci

�1=m

=�abRmf

SnxoRxo·Rxo ·Ci

�1=m

=�wm ·Rxo ·Ci

�1=m

= w ·�Rxo ·Ci

�1=m (3)

where wFMI is the calculated image porosity from theFMI image in a fracture, and Ci is the recordedelectrical conductivity of each FMI electrode in anFMI measurement. The value of Rxo is generallyobtained from a conventional shallow lateral or in-duction log.

By using equation 3, the conductivity of eachFMI button can be transformed into the porositydomain. Eventually, the porosity data from all FMIpads and flaps over a sliding window of 3 cm (1.18in.) that can be used to obtain a porosity spectrum. Byusing the procedures outlined above, a porosity spec-trum was extracted from the FMI data in the Luo 60well in the study area (Figure 3). In the porosityspectrum, the x-axis represents the porosity in-terval (POR), and the y-axis represents the fre-quency of occurrence for the specific micropores.The shape of the porosity spectra is associated withthe formation porosity types. Generally, forma-tions with developed fractures contain wide uni-modal or bimodal porosity spectra (the intervalof 2423.8–2424.1 m [7952.1–7953.1 ft] in Figure 3),and more-heterogenetic formations have wider porespectra. For nonfractured reservoirs, the porosityspectra display narrow and sharp unimodal patterns(up to 2422.5 m in Figure 3).

Figure 8. The relationships between 1/porosity interval (POR)and capillary pressure (Pc) for different core samples. Theserelationships can be fit with power functions for different coresamples.

Table 2. The Classification Criteria and the Corresponding Models of Constructing Pseudocapillary Pressure Curves from the PorositySpectra in the Upper Triassic Chang 8 Tight Sands of the Jiyuan Area, Ordos Basin

Type of Rock Range of Porosity, w

Established Models

Small Pore Throat (High Pc) Large Pore Throat (Low Pc)

1st w ‡ 12.8% y = 7e + 07x6.02 y = 85.14x1.51

2nd 8.0% £ w < 12.8% y = 270203x4.73 y = 5e + 09x8.86

3rd w < 8.0% y = 4811.3x2.99 y = 6e + 09x7.39

Abbreviation: Pc = pseudocapillary pressure.

214 Pore Structure Evaluation of Fractured Tight Sandstone Reservoirs

Relationship between Porosity Spectrumand Pore Structure

The FMI data acquired from six wells in the Jiyuanarea of the Ordos Basin were processed as outlinedabove (equations 1–3) to acquire the porosity spectra.Additionally, laboratory mercury injection experimentswere conducted to obtain mercury injection Pc (MICP)curves and the corresponding Rc distributions fora total of 37 core samples that were drilled inthe study area (Table 1). In the mercury injection ex-periment, core samples were first fully saturated withbrine, and mercury was then injected into the porespaces to simulate hydrocarbons. With the increase ofthe injection pressure, brine was gradually displaced.

The mercury injection saturation (SHg) under variousmercury injection pressures was recorded to obtainthe MICP data. The experimental data were thenprocessed using a method proposed by Tiab andDonaldson (2012) to obtain the Rc distributionsand the pore structure evaluation parameters. Inaddition to the mercury injection experiments,more than 80 casting thin sections were made toobserve the characteristics of fractures.

To obtain the relationship between the porosityspectrum and the pore structure, the FMI image andthe porosity spectra that were adjacent to the depthof the core samples were acquired. The FMI imageand the porosity spectra were analyzed side by sidewith the MICP curve, Rc distributions, and casting

Figure 9. The average mercury injection capillary pressure curves (A), average pore spectrum (B,) and corresponding average reversecumulative curve (C) for three rock types in the Upper Triassic Chang 8 tight sandstones of the Jiyuan area, Ordos Basin. POR = porosityinterval.

XIAO ET AL. 215

thin sections. For the fractured formations, fracturesare clearly identified from the casting thin sectionand the FMI image. The MICP curve shows a lowposition, and the Rc distribution displays bimodality,which indicates good pore structure (Figure 4). Fora tight sandstone formation without fractures, theporosity spectrum is narrow with unimodal distri-bution, and the position of the peak is located inthe left. The position of the MICP curve, how-ever, became high, and the Rc spectrum displaysunimodal distribution because of poor pore structure(Figure 5).

The MICP curve and Rc distribution acquired frommercury injection experiments of core samples arevaluable for pore structure quantitative evaluation in

the laboratory (Volokitin et al., 2001; Xiao et al.,2016). However, they cannot be used to evaluateconsecutive formation pore structure in field appli-cations because of the limited number of core sam-ples (Xiao et al., 2016). Additionally, formation porestructure cannot be evaluated by using MICP curveand Rc distribution in uncored wells. Figures 4 and 5illustrate that the MICP curve and Rc distributioncorrespond to the porosity spectrum both in frac-tured and nonfractured formations. However, thephysical significance of each is different. To charac-terize a fractured formation pore structure using theporosity spectrum, an effective model has to be es-tablished to transform the porosity spectrum as aPc curve and Rc distribution.

Figure 10. Models that are used to construct pseudocapillary pressure curves from the porosity spectra for three rock types in the studyarea. POR = porosity interval; R2 = correlation coefficient.

216 Pore Structure Evaluation of Fractured Tight Sandstone Reservoirs

Pore Structure Evaluation Model

Acquisition of a Reverse Cumulative Curve from aPorosity SpectrumTo establish a robust model to obtain a Pc curve fromthe porosity spectrum, the porosity spectrum wasfirst processed to obtain a reverse cumulative curve,which has a similar shape to the MICP curve(Figure 6). In this method, the amplitude of theporosity spectrum was reversely cumulated withporosity, decreasing from 100% to 0, and was nor-malized to obtain the reverse cumulative saturationdisplayed as the x-axis. Porosity was a token reciprocal

displayed in the y-axis to acquire the reverse cumu-lative curve.

Construction of a Pseudocapillary Pressure Curvefrom the Reverse Cumulative CurveTo transform the reverse cumulative curve to aPc curve, a relationship between Pc and 1/POR isestablished. Figure 7 displays a method of extractingthe value of 1/POR under each mercury injectionpressure increment (Pc). In this process, the reversecumulative curve and the MICP curve are plottedusing the same x-axis. From every injection pressure

Figure 11. Comparisons of synthetic pseudocapillary pressure (Pc) curves with measured results illustrate the reliability of the models.MICP = mercury injection capillary pressure.

XIAO ET AL. 217

increment, a line that contained the same saturationvalue was drawn to intersect with the reverse cu-mulative curve, and the corresponding 1/POR isacquired.

The values of 1/POR for each mercury injectionpressure increment were extracted and crossplottedwith the corresponding Pc value (Figure 8). Thisfigure suggests that a good power function re-lationship exists between 1/POR and Pc. However,it should be noted that no single relationship existsbetween 1/POR and Pc for all core samples or evenfor a single core sample. A classified power func-tion (CPF) may be used to accurately construct aPc curve using the porosity spectrum. This methodinvolves the following procedures.

1. Processing the FMI image logs using equation 3to obtain the consecutive porosity spectra.

2. Drilling a large number (‡20) of core samplesfrom the same region for mercury injection ex-periments to obtain MICP data and correspondingRc distribution and extracting the porosity spectraunder the same or adjacent depth with core sam-ples and then using the method displayed inFigure 6 to calculate the reverse cumulative curves.

3. Establishing a rock classification criterion to di-vide the MICP data and the corresponding reversecumulative curves into several types and calculating

the average MICP curves and reverse cumulativecurves for each type of core sample.

4. Extracting the values of 1/POR under every Pcvalue based on the average MICP and reversecumulative curves and establishing the rela-tionships between 1/POR and Pc based on powerfunctions. It should be noted that for each typeof rock, two power functions must be used toexpress the relationship between 1/POR and Pc.

For the same type of core sample, the Pc curvescan be related to 1/POR according to equation 4,based on the CPF method:

Pc = c ·�

1POR

�d

(4)

where c and d are the statistical model parameters,and their values can be calibrated by using the coreexperimental results. One needs to note that the porespaces must be first classified into two groups orclasses (small and large pore-throat sizes) in theCPF method, and for every part of the pore space,the respective involved model parameters are used.

The demarcation of small and large pore-throatsizes for a core sample was determined by the shapesof MICP curves and porosity spectra. Small pore-throat size corresponded with a relatively high Pcvalue and the first peak in the porosity spectrum,whereas large pore-throat size was associated with a

Figure 12. Model for predicting permeability from mercuryinjection capillary pressure curves based on the Swanson pa-rameter. R2 = correlation coefficient.

Figure 13. Regression relationship between routine core-derived porosity and permeability for 37 core samples usingthe conventional method. R2 = correlation coefficient.

218 Pore Structure Evaluation of Fractured Tight Sandstone Reservoirs

relative low Pc value and the second peak. Finally, bycombining the predicted Pc with the reverse cumu-lative saturation, Pc curves were synthetized. Oncethe established models were extended into fieldapplications, consecutive Pc curves could be con-structed in the intervals from which borehole elec-trical image data were acquired. Meanwhile, theclassic relationship between Pc and Rc expressed inequation 5 can be used to acquire Rc distributionfrom the constructed Pc curve:

Pc =2scosuRc

(5)

where Rc is the rock Rc (mm), s is the surface tensionbetween two phases fluid (dyn/cm), and u is thecontact angle (°).

Calibration of Model ParametersTo make the established models applicable to targetformations, the MICP curves and the correspondingporosity spectra that were extracted from the adja-cent depths of 37 core samples were classifiedinto 3 categories, according the effective porosity(Table 2). Accordingly, the average MICP curves,the average porosity spectra, and the correspondingaverage reverse cumulative curves were computed(Figure 9).

Figure 9 shows that with the decrease in poros-ity, the average MICP curves increase, and the av-erage porosity spectra become narrower and shiftto the left. Additionally, the corresponding averagereverse cumulative curves also increase with de-creasing porosity. By combining the average MICP

Figure 14. A field example of constructing pseudocapillary pressure (Pc) curves and pore-throat radius (Rc) distributions from theporosity spectra in fractured tight sandstone reservoirs with good hydrocarbon production in the Huang 15 well. In the first three tracks ofthis figure, conventional well log curves are displayed that were used for effective formation indication, reservoir porosity prediction, andfluid identification. Porosity spectra acquired from the formation microimager image log (POR_DIST) are displayed in the fifth track. Thesixth and seventh tracks display Pc curves constructed from porosity spectra (PC_DIST) and the corresponding Rc distribution (RC_DIST).In the eighth and ninth tracks, the estimated Swanson parameter (SWANSON) and permeabilities (PERMSWAN) from Pc curves with thosefrom core-derived results are compared, whereas permeabilities from porosities (PERM) was predicted using the conventional method. Inthe last four tracks, the extracted pore structure evaluation parameters (the maximum Rc of maximum pore-throat radius [Rmax], themedian Rc of R50, the threshold pressure (PD) and the median pressure of P50) are compared with those of core-derived results. Goodconsistency of the predicted parameters and core-derived results illustrated the validity of the proposed pore structure evaluation method.AC = acoustic log; CAL = caliper log; CNL = compensated neutron log; CP50 = core-derived median pressure; CPD = core-derivedthreshold pressure; CPERM = core-derived permeability; CR50 = core-derived median pore-throat radius; CRmax = core-derived maximumpore-throat radius; CSWANSON = core-derived Swanson parameter; DEN = density log; GR = gamma-ray log; RT = true formationresistivity; RXO = flushed zone formation resistivity; SP = spontaneous potential log.

XIAO ET AL. 219

curves and the corresponding average reverse cu-mulative curves for three rock types, the values of1/POR can be extracted under every Pc curve. Byplotting 1/POR and Pc for each rock type, theparameters involved in the models were in-dividually derived (Figure 10). These figures showthat power functions provide good fits between1/POR and Pc, with correlation coefficients greaterthan 0.95. The models that are used to transformthe porosity spectra into Pc curves are listed inTable 2.

Model Reliability Evaluation

The established models were evaluated by applyingthem to field conditions. Three typical Pc curves,

which were extracted from approximately the samedepth of core samples, were compared with theexperimental results (Figure 11). These results showthat the measured MICP curves match well with thesynthetic results. This ensures the reliability of theproposed model.

Permeability Prediction Model

Besides pore structure evaluation, another importantapplication of the Pc curve is permeability estimation(Swanson, 1981). Xiao et al. (2014) proposed apermeability prediction method, which was partic-ularly valuable for tight sandstones, based on theSwanson parameter. Based on this method, if the SHg

(x-axis), and mercury injection pressure increment

Figure 15. A field example of evaluating nonfractured formation pore structure by using the proposed techniques in tight sandstonereservoirs with no hydrocarbon production in the Luo 42 well. AC = acoustic log; CAL = caliper log; CNL = compensated neutron log;CP50 = core-derived median pressure; CPD = core-derived threshold pressure; CPERM = core-derived permeability; CR50 = core-derivedmedian pore-throat radius; CRmax = core-derived maximum pore-throat radius; CSWANSON = core-derived Swanson parameter; DEN =density log; GR = gamma-ray log; P50 = median pressure; PC_DIST = capillary pressure distribution; PD = threshold pressure; PERM =permeability; PERMSWAN = permeability predicted by using the Swanson parameter based model; POR_DIST = porosity spectrumdistribution; R50 = median pore-throat radius; RC_DIST = pore-throat radius distribution; RCmax = maximum pore-throat radius; RT =true formation resistivity; RXO = flushed zone formation resistivity; SP = spontaneous potential log; SWANSON = the Swansonparameter.

220 Pore Structure Evaluation of Fractured Tight Sandstone Reservoirs

(y-axis) is displayed in log–log coordinates, theMICPcurve can be presented as a hyperbolic curve, and theexpression of the hyperbolic curve is expressed asfollows:

Log10

�Pc

Pd

�· Log10

�SHg

SHg‘

�= C (6)

where Pd is the threshold pressure (MPa), SHg‘ is thenonwetting phase saturation under infinite mercuryinjection pressure (%), andC is the geometric prefactor.

The inflection point of the hyperbolic curverepresents the SHg threshold in the main pore system,and it is the primary control on fluid flow (Guo et al.,2004; Rezaee et al., 2012). This inflection point is the

cutoff point for large and small pore-throat size. Inthe primary stage of the MICP experiment, non-wetting phase mercury mainly occupies the con-nected large pore space because of the low mercuryinjection pressures. As the mercury injection pressuresincrease, it breaks through the inflection point, andmercury is injected into the small pore space or porecorners with irregular shapes, and the flow capacity ex-periences a dramatic decline (Thomeer, 1960; Swanson,1981). The Swanson parameter, which was defined asthe maximal value of mercury saturation per pressureand expressed as (SHg/Pc)max, was proposed to expressthe capacity of fluid flow (Xiao et al., 2014). Followingwith the proposed method by Xiao et al. (2014), a

Figure 16. The cross-plots of predicted pore structure evaluation parameters and permeability versus core-derived results: (A) theSwanson parameter; (B) the maximum pore-throat radius (Rmax); (C) the median pore-throat radius (R50); and (D) the permeability. Inthese figures, the solid red lines represent the discrepancy of the predicted parameters with those of the core-derived results. The two bluelines indicate a margin of relative error of 30.0%.

XIAO ET AL. 221

model, which predicts fractured reservoir perme-ability from a Pc curve based on the Swanson pa-rameter, was established (Figure 12). Meanwhile, theroutine core-derived porosities and permeabilities forthese 37 samples are used to establish a conventionalpermeability prediction model based on the exponen-tial function (Figure 13). The results show thatthe Swanson parameter-based permeability modelprovided a better prediction than that of the con-ventional method because of the consideration ofpore structure.

CASE STUDIES

The proposed methods were applied to the Huang15 well to derive Pc curves and Rc distribution usingporosity spectra and to calculate pore structure eval-uation parameters and permeability (Figure 14). Theresults show that for a majority of the studied in-tervals, the permeabilities are close to 0.1 md.However, for the intervals ranging from 2509.5 to2510.5 m (8233.3–8236.6 ft), 2512–2513m (8241.5–8244.8 ft), and 2516–2517 m (8254.6–8257.9 ft), thepredicted permeabilities from the Pc curves based onthe Swanson parameters are notably higher than 0.1md, suggesting that the formation fluid flow capacityis enhanced because of the contribution of fractures.Permeabilities estimated using the conventionalmethod did not show the contribution of thesefractures. The comparisons between the predictedpore structure evaluation parameters from the con-structed Pc curve and those of the core-derived resultsfurther show that the pore structure evaluation pa-rameters can be well predicted using the proposedmethod. This prediction was further verified by thedrill-stem test (DST) data in the interval of 2508 to2512 m (8228.3–8241.5 ft), which showed that ap-proximately 28 bbl of oil was produced per day withno water. As a comparison, this interval was consid-ered to be non–oil producing using the conventionalmethod because the predicted permeabilities arelower than the lower limit of the exploitable for-mations (Fu et al., 2014). Clearly, the proposedmethods of pore structure evaluation successfullyidentified some intervals worth exploiting thatwould have been overlooked by conventional evalua-tion methods.

For nonfractured reservoirs, the porosity spec-tra and Rc distributions all have narrow unimodaldistributions, with low POR and small pore-throatsize (Figure 15). The predicted permeabilities fromthe Pc curves and the conventional method aresimilar, with values less than 0.1 md. The pre-dicted pore structure evaluation parameters showthat the maximal pore-throat radii are less than0.3 mm and that the threshold pressures are all greaterthan 3.0 MPa. As a result, these formations are consid-ered nonproducing. These results were also confirmedby the DST data, which show that there was no fluidflow for the intervals of 2730–2731 m (8956.7–8960 ft)and 2732.5–2733.5 m (8964.9–8968.2 ft).

UNCERTAINTY ANALYSIS

To quantify the uncertainties associated with thepore structure evaluation parameters and perme-ability yielded by the modeling process, the relativeerrors between the predicted pore structure evalu-ation parameters and permeability with laboratoryexperimental results were evaluated according toequation 7:

re =jPredicted result - experimental resultj

experimental result· 100%

(7)

where re is the relative error between the pre-dicted pore structure evaluation parameters andpermeability, with laboratory experimental re-sults (%).

The predicted Swanson parameters maximumpore-throat radius, median pore-throat radius, andpermeability from constructed Pc curve and ex-perimental results of core samples were cross-plotted in Figure 16A–D. Considering the relationshipof the Pc and Rc expressed in equation 5, the thresh-old pressure and the median pressure correspond tothe maximal Rc and median Rc, respectively. Therelative errors of predicted threshold pressure andmedian pressure were not analyzed. The solid redlines in Figure 16A–D represent the diagonal lines,which clarify the discrepancy of the predicted re-sults with that of the core-derived results. Thesetwo thin blue lines indicate a margin of relativeerror of 30.0%.

222 Pore Structure Evaluation of Fractured Tight Sandstone Reservoirs

These comparisons show that the predicted porestructure evaluation parameters and permeabilityfrom the synthetized Pc curves are consistent withthose of the core-derived results. For the majority ofcore samples, the relative errors between the pre-dicted results and the core-derived results are lowerthan 30%. These results suggest that our proposedmethods are satisfactory and that the extractedporosity spectrum from FMI logs can be used toevaluate fractured tight sandstone reservoir porestructures.

CONCLUSIONS

The current borehole electrical image logging tech-nique only provides qualitative or semiquantitativeinformation about the pore structure of fracturedreservoirs. To evaluate the pore structure of frac-tured reservoirs in a more quantitative manner, po-rosity spectra can be processed to obtain Pc curvesand Rc distributions. In this study, a method is de-veloped to construct Pc curves from the porosityspectra based on a CPF method. By using thismethod, formation Pc curves can be consecutivelyconstructed, and the corresponding Rc distributionand parameters associated with the pore structureevaluation are precisely extracted.

This method was evaluated using the DST datafrom the Upper Triassic Chang 8 tight sandstones ofthe Jiyuan area in the Ordos Basin in China. Theresults suggest that this method is superior to existingmethods in that it accurately predicted the existenceof hydrocarbon-bearing layers where conventionalmethods failed to identify these zones.

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