geologic modeling of eagle ford facies continuity based on ...pared with those of an outcrop data...

Geologic Modeling of Eagle Ford FaciesContinuity Based on Outcrop Images

and Depositional ProcessesPejman Tahmasebi, (currently with the University of Wyoming), Farzam Javadpour, and Gregory Frebourg

(currently with Thermal Energy Partners), University of Texas at Austin

Summary

Geologic modeling of mudrock reservoirs is complicated by the presence of multiscale heterogeneities and lithofacies lateral disconti-nuity. The resolution of wireline logs is also too low to capture many small-scale heterogeneities that affect fluid flow. In addition, thelarge distance between logged wells results in uncertain long-range correlations. Supplementary to wireline log data, high-resolutionoutcrop images offer a direct representation of detailed heterogeneities and lithofacies connectivity. We used high-resolution panoramicoutcrop images to collect data on lithofacies heterogeneity and the role that depositional processes play in this heterogeneity. We thenused these data in different classes of reservoir algorithms—two-point-based, object-based, and higher-order statistics—to build a geo-logic model. To present our methodology, we used data collected from Eagle Ford outcrops in west Texas. We found the higher-order-statistics method to be especially efficient, capable of reproducing details of heterogeneity and lithofacies connectivity.

Introduction

Mudrock depositional systems are a controlling factor in the development of major reservoir properties such as porosity and permeabil-ity. These data are generally extracted from well data (e.g., wireline logs, core samples, and drill cuttings) limited to the near-wellborespace domain and therefore do not contain sufficient information regarding the long-range connectivity and spatial correlations of facies(Sahimi 2011). On the other hand, outcrop images provide a unique and direct representation of geologic features, offering a clear illus-tration of the geometry and spatial continuity that allows visual inspection of the existing structures. However, because most outcropdata are limited to 2D sections, information from the third dimension is therefore needed to build 3D models with true spatial continu-ity. In this study, we used sedimentation-process theories to extract information for the third dimension of an outcrop. We used twoEagle Ford outcrops in west Texas to develop our methodology (Frebourg et al. 2016).

For outcrop images, we used different scales. From large-scale images, we extracted information about lateral lithofacies continuityand determined the statistical properties of stratigraphic horizons such as lens length and thickness. From small-scale images, weextracted vertical information such as ash-bed thickness and spacing. Although 2D outcrop images are an important source of data,extending such information to 3D modeling is not straightforward. Because we needed additional information about the distribution offacies in the third dimension, we used our understanding of the early compaction history of pelagic carbonate sand bodies for our EagleFord example (Frebourg et al. 2016). In this paper, we present a novel framework that is based on a combination of outcrop-data andsedimentation-process theories in reservoir algorithms to generate 3D geologic models.

Uncertainty in facies-distribution study is considerable, particularly for mudrock reservoirs. In statistics, problems with limited in-formation are known as ill-posed problems. Among different models that use all existing data, stochastic techniques have been foundto provide efficient and reliable solutions by using extracted data and producing various equiprobable realizations (Journel andHuijbregts 1978).

Available methods for facies modeling can be divided into two groups: pixel-based and object-based. In pixel-based methods, foreach loop in a simulation, only one cell of the geomodel is constructed; therefore, each single cell needs to be visited separately. Thesealgorithms account for short-range connectivity because they consider pixels (Deutsch and Journel 1998). On the other hand, object-based methods require the direct use and assembly of some predefined objects (e.g., channel, ellipses) in building a stochastic model(Deutsch and Wang 1996; Holden et al. 1998). Pixel-based algorithms honor the well data when dense wells or any conditioning dataare being considered. These methods, however, produce models that are different from actual structures (e.g., disconnected structures).Object-based modeling can compensate for the issue of disconnected structures in geomodels, but such modeling requires extra work tomatch the conditioning data. An approach that alleviates such issues and produces both long-range connectivity and conditioning datais multiple-point statistics (MPS). In our study, various stochastic-modeling approaches were used, and their performances were com-pared with those of an outcrop data set from an Eagle Ford mudrock formation.

The work flow used in this paper follows this hierarchical scheme:1. First, geologic data from outcrop images are extracted.2. Next, morphologic properties of objects, such as length and thickness, are carefully extracted and described in terms of mean and

variance.3. Then, because they only work with numerical information, variogram- and object-based methods are fed with statistical data

extracted from outcrop images. The MPS method, however, is used directly on the available outcrop images.4. Then, the modeling is extended to 3D space, which is challenging for the implemented methods. In 2D modeling, a strategy simi-

lar to the previous Step 3 is used for variogram- and object-based methods. The model generated by the object-based method isalso used for the MPS method because outcrop data are not available in 3D form.

5. Finally, a set of synthetic acoustic impedance (i.e., seismic data) is synthesized and integrated within the MPS method, and theresults are compared quantitatively.

In the Stochastic Modeling Techniques section, we describe the stochastic modeling used. Available 2D outcrop images andextracted information are discussed in the Data From Eagle Ford Outcrops section. In the Results and Discussion section, we

Copyright VC 2018 Society of Petroleum Engineers

Original SPE manuscript received for review 28 March 2017. Revised manuscript received for review 6 November 2017. Paper (SPE 189975) peer approved 9 November 2017.

J189975 DOI: 10.2118/189975-PA Date: 9-February-18 Stage: Page: 1 Total Pages: 13

ID: jaganm Time: 14:36 I Path: S:/J###/Vol00000/170130/Comp/APPFile/SA-J###170130

2018 SPE Journal 1

demonstrate the performance of various stochastic algorithms and compare results quantitatively with those of the proposed method inthis paper. Next, we use synthetic acoustic impedance (equivalent to 3D-seismic data) to demonstrate multivariable data integration.The paper is summarized in the Conclusions section,which lists some of the advantages of the proposed work flow.

Stochastic-Modeling Techniques

Two-Point-Based Statistics. Two-point-based statistical methods, also known as variogram-based techniques, consider only correla-tions between two points. Basically, a variogram measures the average dissimilarity between data that are separated by a vector, h, andcalculates half the average squared difference between each data pair (Goovaerts 1997; Deutsch and Journel 1998; Pyrcz and Deutsch2014). A variogram, as a two-point descriptor, is used for measuring spatial continuity and variability, and is therefore unable to realisti-cally model the geologic features; final models often appear too heterogeneous. Another disadvantage is that linking variogram modelsto complex geologic features such as curvilinearity, sinuosity, and outcrop data is difficult.

Indicator Kriging, one facies-modeling method used in this study, is a two-point-based algorithm that provides an efficient frame-work for facies modeling and conditional simulation. As explored in this paper, conditional simulation occurs when a geologic model isbuilt using information such as well and seismic data, into which conditioning data also can easily be integrated. An algorithm startswith a single pixel and simulates the visiting point according to a Monte Carlo approach, drawing a random value that is based on aprobability-distribution function. This probability function is constructed on the basis of previously simulated points—available welldata and secondary (e.g., seismic) information.

Object-Based Modeling. Object-based algorithms are preferred when more-realistic models are required. In object-based algorithms,geologic structures are replaced with predefined objects based on available data on size, orientation, thickness, and other morphologicproperties. Then, various stochastic models can be generated with given distributions in each of these mentioned parameters. Object-based methods can also be conditioned to other data, such as well, seismic, and proportional maps. For example, a global proportioncan be defined for each object (e.g., populating the simulation grid until a set of conditions is met). Results of object-based algorithmsare satisfying in terms of reproducing many realistic geomodels. Object-based techniques, however, require extensive iterations whendense, hard, or additional secondary data are considered, and even then, convergence is not guaranteed.

Multiple-Point Statistics. Development of realistic geostatistical approaches for simulating large-scale porous media has been moti-vated partly by a current challenge in such modeling—namely, the question of how to include complex patterns and data in the models.Most of the geostatistical models in the past, as already discussed, relied on traditional two-point geostatistics, which have been demon-strated to be inadequate descriptors of structures that contain complex features and variability. Therefore, MPS methods were developedto address the limitations of traditional methods. MPS methods are based partly on the use of a training image (TI), representing a con-ceptual framework for the most important features of a system and the given prior geologic information. It is worth mentioning that noconditional data (e.g., secondary and well data) should be used for building the TI.

MPS methods were first introduced approximately 2 decades ago (Journel 1992; Guardiano and Srivastava 1993; Srivastava 1994).Original methods were not, however, computationally feasible. The first practical method, the single-normal equation simulation(SNESIM) algorithm, which used a search-tree structure, was introduced by Strebelle (2002). This method, because the computationaltime was dramatically lower than for that of the original MPS algorithm, helped in the investigation of further applications of MPSto practical problems. Since that breakthrough, several other MPS algorithms have been proposed (for a comprehensive review, seeTahmasebi and Sahimi 2016a, b). For example, Arpat and Caers (2007) introduced a pattern-based simulation (SIMPAT) algorithm thatwas based on patterns of heterogeneities and a distance function measuring differences between model and data. This method, however,requires highly intensive computations. To make the model computationally efficient, Zhang et al. (2006) proposed a method that simu-lated patterns with filters (FILTERSIM) that were predefined and fast-searching; they used a classification method to reduce the numberof patterns. However, this technique suffers from extreme pattern reduction, which we refer to as pattern smoothing. Meanwhile, adirect-sampling algorithm was introduced—essentially identical to the SIMPAT, differing only in that it does not require extensivescanning of the TI—based on adding one pixel at a time to the model instead of to a pattern (Mariethoz et al. 2010). This algorithmuses only a fraction of the patterns in the TI and ignores the rest. However, using only a small part of the TI produces the realization ofa system without many specific features such that many details may be neglected complexities.

More recently, patch-based algorithms capable of efficient pattern reproduction have become more popular. One of the most recentof such methods is a cross-correlation-based simulation—by which the TI is reconstructed and is denoted by T, whereas DT(u) is thedata event at position u in T. We use data event instead of data because during the reconstruction, DT changes as the algorithm pro-gresses. Finally, OL represents the overlap region between neighboring templates. We can describe the cross-correlation function(CCF) and the reconstruction algorithm for 2D systems, after which the extension to 3D media will be clear.

Suppose that TI ðx; yÞ represents the datum at point ðx; yÞ of a TI of size ðTx;TyÞ, with x 2 f0;…;Tx � 1g and y 2 f0;…;Ty � 1g.When the TI is examined, a portion DT(u) is focused on, with size OLx � OLy; it is regenerated based on the data, such that it matchesthe corresponding part in the TI. Euclidean distance between a TI and DT (u) is calculated as

ETI;DTði; jÞ ¼

XOLx�1

x¼0

XOLy�1

y¼0½TDðxþ i; yþ jÞ � DTðx; yÞ�2; ð1Þ

with i 2 ½0 Tx þ OLx � 1� and j 2 ½0 Ty þ OLy � 1� and i; j 2 Z. The i and j represent shift steps in the x- and y-direction. Therefore,the acceptable candidates (cand) can be expressed as

ðicand; jcandÞE ¼ mincand½ETI;DT

ði; jÞ�: ð2Þ

Eq. 1 can be rewritten and expanded as

ETI;DTði; jÞ ¼

XOLx�1

x¼0

XOLy�1

y¼0

½TDðxþ i; yþ jÞ2 þ DTðx; yÞ2 � 2TDðxþ i; yþ jÞDTðx; yÞ�

¼ CTD þ CDT� 2CTD;DT

: � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ð3Þ

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



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Because CDTand CTD are not dependent on any data event or TI, they are therefore constant. A CCF to quantify the similarity between

the TI and DT is thus introduced as

Cði; jÞ ¼XOLx�1

x¼0

XOLy�1

y¼0

TDðxþ i; yþ jÞDTðx; yÞ: ð4Þ

Eq. 4 indicates that the desired position of ði; jÞ—the best match with the TI—is one that maximizes Cði; jÞ. If the size of the TI isnot too large, all computations are conducted in the spatial domain. When the TI is large, calculations in the Fourier space can greatlyreduce central-processing-unit time (Tahmasebi et al. 2017).

Ways of creating the TI include (1) sketches that are based on physical facts that explain the geologic character of the outcrop; (2)remote-sensing data for identifying spatial relationships and topology in a depositional model; and (3) core description and seismic data toinfer fine/large-scale relationships between different layers and structures. In addition, unconditional, object-based methods and those thatare based on physical processes that occur in an outcrop can provide high-quality TIs that contain more-realistic, more-complex patterns.

For the sake of simplification, we considered unconditional simulation—a simulation in which the algorithm does not have to honorany specific hard (quantitative) data (HD) exactly in the TI. G is partitioned into (square) blocks of size Tx � Ty (in three dimensions, Gis partitioned into cubes). Between every two neighboring blocks is an OL region of size ‘x � ‘y representing DT, in which OLxðOLyÞ ¼TxðTyÞ and OLyðOLxÞ � TyðTxÞ, where the OL region is between two templates that are neighbors in the x (y) direction (Fig. 1). Sup-pose, for example, that the 1D raster path is along the vertical (y) direction. The algorithm begins at the origin of the path in G—forexample, the leftmost bottom template in G—and moves along the path. A realization of the disorder in the TI, equal in size to T, is gen-erated and inserted into the first block of G along the path, part of which represents the OL region with the next block.

The purpose of the OL region is to preserve the continuity near the common boundary between the two blocks. The aim is then togenerate a suitable realization of the disorder for the next neighboring block along the path with a bottom section—the OL region—thatmakes a seamless transition between the two. If, however, several realizations of the disorder have the same degree of similarity to OL,one of them is selected at random. The procedure continues until inspection of the first vertical column of the raster path is finished.The algorithm then moves forward, beginning with the bottom block of the next vertical column of G, and uses the same procedure,considering its OL region with the neighboring block on the left. The next block is more complex because it has two OL regions—atthe bottom and on the left. More details about the CCSIM algorithm can be found in Tahmasebi and Sahimi (2016a, b).

Data From Eagle Ford Outcrops

The Eagle Ford Group (Boquillas Formation west of the Pecos River) crops out along Highway 90 in Val Verde and Terrell Counties(Fig. 2). The middle Boquillas Member (Lock and Peschier 2006) is the outcrop equivalent of producing Eagle Ford strata in the sub-surface. Three main lithologies are observed: organic-matter-rich, globigerinid wackestones; pelagic grainstone beds and lenses; andash beds. The succession represents a low-productivity, low-accumulation-rate system, in which the globigerinid wackestones representaverage conditions. After deposition of ash beds and subsequent release of iron in the water, blooms of planktonic productivity increasetrophic levels, and result in an increase of coarse-grained, planktonic, skeletal sediment (Frebourg et al. 2016). Deposition and rework-ing by bottom currents below the storm wave base are responsible for the lateral discontinuity of pelagic grainstone beds and lenses andash beds (Frebourg et al. 2016).

Several outcrops, even though intensely weathered, provide the opportunity to observe and measure the vertical and lateral varia-tions of the exposed strata. However, because of the orientation of these outcrop sections, observation of the sedimentary bodies in threedimensions is not possible. Outcrops of the Boquillas Formation in the Ernst Tinaja, Big Bend National Park, Brewster County (Fig. 3),on the other hand, provide a unique opportunity for observation of the lateral continuity of the lithologies in three dimensions.

Using this set of exposures, we measured the lateral and vertical variation and stratal relationships of the lithofacies of the EagleFord/Boquillas succession and extracted statistics to serve as input and control data for the model. The main issue encountered duringthis process resulted from the irregular surface of some of the outcrops. Although uneven surfaces helped provide 3D information at theErnst Tinaja outcrops, irregular surfaces can create artifacts when mixed with the perspective associated with photographs. Data-set ac-quisition and processing had to be adapted to minimize artifacts and ensure correct measurements.

Coarse-Scale Data Set of Outcrops. This study provides parameters extracted from a data set presented in Frebourg et al. (2016)—a220-m-long (722-ft) exposure at outcrop Section 13 (Fig. 2). This data set was generated from a combination of nine high-resolution

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

cand1

candk

cand2

OL

(a) (b)

Fig. 1—(a) Raster path, (b) overlap regions OL, and templates on a 2D grid.



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GigaPans (with resolution ranges from 1 to 0.25 mm per pixel) and a lidar mosaic acquired through a focus on the geometry of laterallydiscontinuous pelagic grainstone beds and lenses. On the basis of these high-resolution photographs and controlled by field observa-tions, eight lithological logs were traced. Using lidar mosaics supplemented by the high-resolution pictures, we measured the thicknessand length of the pelagic grainstone beds and lenses with JMicroVision image-analysis software (Roduit 2008). The precision of thelidar mosaic is within 1 cm (0.39 in.). The high resolution provided by these data sets allowed some of the thicker ash beds (>1 cm) andother stratigraphic horizons to be traced. Thinner ash beds required a finer-scale data set. Detailed measurements made on the pelagicgrainstone lenses at Section 13 (Fig. 2) provided the statistical variability in thickness and length of these sediment bodies. Statisticalproperties of their occurrence along the stratigraphic horizons are summarized in Table 1.

Austin Gp

Boquillas/Eagle Ford

Sect. 51

Sect. 54MEXICO

TEXAS

Rio G

randeNEW

MEXICOTEXAS

MEXICO

29°30′N

29°50′N

101°

10′ W

101°

30′ W

101°

50′ W

Del Rio

Langtry

N

Comstock

US 90

US 277

US

277

US 90

Lozier

Val V

erde Co.

Canyon

Terrell Co.

US

377

River

Devil’s

River

Pecos

River

Sect. 42

Sect. 13Buda/Del Rio

Segovia

Devils River

Salmon Peak

Mi

km

0 20

300

Fig. 2—Geologic map showing outcrop study area in west Texas (modified from Ruppel et al. 2012).

Undifferentiated Quaternary alluvium depositsHolocene and Pleistocene

Paved road

MEXICO

MEXICO

5 miles

TEXAS

TEXASN

Big BendNational Park

NEWMEXICO

Dirt road

Flowing river

29°11′N1 mile

29°13′N

ErnstTinaja

Tornillo Creek

Hot SpringsRio Grande

29°15′N

Ernst B

asin

Old O

re Rd.

Cuesta C

arlota

103°

02′ W

103°

W

Ephemeral stream

Main fault

Very old alluviumLower Pleistocene and Pliocene

Aguja FormationUpper Cretaceous

Upper Cretaceous

Upper Cretaceous

Upper Cretaceous

Upper Cretaceous

Upper Cretaceous

Lower CretaceousSanta Elena Limestone

Buda Limestone

Del Rio Clay

Pen Formation

San Vicente Member - Boquillas Formation

Ernst Member - Boquillas Formation

Fig. 3—Geologic map showing study area in Big Bend National Park (Brewster County) (modified from Turner et al. 2011). Locationof measured section noted by black circle.



4 2018 SPE Journal

Study of these geometrical sedimentary bodies began at the Ernst Tinaja location (Fig. 3). Observations made at the Ernst Tinaja(Fig. 2 and Fig. 4) show that the morphology observed on the vertical faces of the roadcuts (X, Z plane) could be propagated in depthalong the Y-plane. At this location, a creek has eroded through inclined layers of the Boquillas Formation, allowing observation of thebedding geometry (Fig. 5a).

Fine-Scale Data Set of Outcrops. A finer-scale data set was used to provide high-resolution and detailed TI for the model. Roadcut 54(Fig. 2) along Highway 90 was chosen for this purpose because it has one of the least irregular surfaces of all the outcrops. Still, theirregularity of the outcrop surface did not allow tracing of contours of the different lithologies directly without artifacts being createdthat would have had a significant and negative impact on the model. This issue was resolved by our tracing 20 regularly spaced verticalsections on an image corrected for perspective and correlating them with a high-resolution image background (Fig. 4). This image wasspatially calibrated, yielding a 4.7-m-wide (15.4-ft-wide) data set. The resulting TI (Fig. 4b), at a resolution of 1,200 dpi, correspondsto a resolution of 0.47 mm (0.0185 in.).

Results and Discussion

The three stochastic methods described were used to build a 3D model from an Eagle Ford outcrop data set. A comparison of resultsfrom the different methods is presented. The fine-grained character of mudrocks and associated weathering commonly result in pooroutcrop expression, making lithological contrast for observing stratal relationships and architecture for building geologic models hardto perceive. The goal of this study was to provide morphologic data, including vertical- and lateral-variability statistics, for thethree main lithologies found in the Eagle Ford Formation, as a framework for building a 3D geologic model that is based on 2Doutcrop images.

As previously described, the collected outcrop data are restricted to 2D outcrop images. However, these images were acquired fromseveral different sections and at different scales, thus providing useful statistical information about bedding and facies features in thethird dimension. Such spatial morphologic information can be used in the first two described methods, the variogram-based and object-based methods. Using the extracted information, we constructed various 2D and 3D models. Because the MPS method requires a

Elevation (m) Number of Lenses Average Lens

Length (m) STD DV Lens

Length (m) Average Lens Thickness (m)

STD DV LensThickness (m) Lens/Length

10.53 32 0.84 0.28 0.09 0.03 17%

10.15 38 1.18 0.56 0.16 0.04 29%

9.66 22 0.98 0.28 0.15 0.03 14%

9.55 26 1.53 0.58 0.15 0.05 26%

8.98 43 2.85 2.41 0.12 0.03 80%

7.98 40 3.29 2.59 0.19 0.02 86%

7.27 86 0.98 0.48 0.18 0.03 55%

6.43 15 9.70 7.89 0.14 0.02 95%

6.33 52 0.97 0.46 0.17 0.04 33%

5.14 55 1.80 0.91 0.14 0.03 65%

N 409

Averages 40.90 2.41 1.64 0.15 0.03 50%

STDVs 19.23 2.56 2.23 0.03 0.01 29%

Table 1—Statistical properties of stratigraphic horizons in this study. STD DV 5 standard deviation.

(a) (b)

Fig. 4—(a) Outcrop of part of Boquillas Formation Section 54 and 20 vertical sections. Globigerinid wackestones shown in brown,pelagic grainstones in blue, and ash beds in red. (b) Interpolated TI in grayscale for ease of visualization. Globigerinid wacke-stones shown in white, pelagic grainstones in gray, and ash beds in black. Both photos 4.7 m (15.4 ft) wide, with true vertical scale.



2018 SPE Journal 5

physical representation of the input geologic model, however, this method could be applied only in 2D modeling because of the avail-ability of the outcrop data in two dimensions. Some attempts have nevertheless been made to use the 2D images to reconstruct 3D mod-els that were mostly limited to fine-scale porous media (Tahmasebi et al. 2015, 2016a,b, 2017). Variogram-based, object-based, andMPS-method models are presented in Figs. 6, 7, and 8, respectively. These models are generated on the basis of the data provided inTable 1 and the outcrop image in Fig. 4.

(a) (b)

(c) (d)

Fig. 5—Photos of Ernst Member of Boquillas Formation at Ernst Tinaja site (Big Bend National Park, Brewster County) showingbedding styles. (a) View of southern wall of Ernst Tinaja Canyon showing good lateral continuity of pelagic grainstone (competentbeds) along cut axis. (b) Straight sand ridge. Red lines frame upcurrent and downcurrent boundaries of sand ridge, red dottedlines underline internal stratification, and white arrow points at inflection between stoss and lee sides (crest). Direction of progra-dation from bottom-right corner toward top-left corner. (c) Sand ridge. Red lines frame upcurrent and downcurrent boundaries ofsand ridge; red dotted lines underline internal stratification. Direction of progradation from bottom-left corner toward top-right cor-ner. (d) Crescentic (barchanoid) dune. Red dotted line follows top surface at middle of dune, showing progradation direction, frombottom-right corner toward top-left corner. All photos: Phone is 10 cm (4 in.) long.

(a) (b)

Globigerinid wackestones

Pelagic grainstones

Ash beds

Fig. 6—Results of variogram-point-based statistics for (a) 2D (160 3 160 cells 5 40 3 40 ft2), and (b) 3D (160 3 160 3 80cells 5 40 3 40 3 10 ft3) models of Eagle Ford Formation. Some inconsistencies of facies distributions in terms of their similaritywith structures in Fig. 4b shown with yellow arrows.



6 2018 SPE Journal

The variogram-based model (Fig. 6) does not show geologic features in the outcrop. In fact, reproducing a similar distribution ofhorizontal layers and ellipses is not achievable with this method. Note that unrealistic distribution of facies is also observed.

Results from object-based techniques produce a slightly more realistic distribution of morphologic properties compared with that ofthe outcrop. Not all complexities or spatial information is expressed in simulated models; considerable simplification can be observedby comparing Fig. 4b and Fig. 6a.

On the other hand, results from the MPS method seem more realistic and similar to spatial features observed in the outcrop image.One reason for this significant similarity is the direct use of outcrop data. The other two methods require the extraction of necessary in-formation to build the 2D/3D model. Clearly, inference of all complexities and spatial information from the outcrop elements is impos-sible. The MPS method, however, does not extract any of this information and instead directly uses outcrop data.

Our conceptual understanding of the geometry of the pelagic grainstone sedimentary bodies in three dimensions was based on fieldmeasurements and observations made along Highway 90 (Fig. 2) and the Ernst Tinaja location (Fig. 3). The length and thickness of thevertical section of 409 pelagic grainstone sedimentary bodies were measured at Section 13 of Fig. 2 (Fig. 9; see Frebourg et al. 2016for methods and details). These measurements were used to define the vertical and lateral extent of the pelagic grainstone sedimentarybodies along their progradation axis, along with the amount of variation of these two dimensions. The width of the pelagic grainstonesedimentary bodies perpendicular to the progradation axis was derived from observations collected at the Ernst Tinaja location (Fig. 3).At this outcrop, note that, with the exception of the barchanoid morphology of isolated hydraulic dunes (Fig. 5d), the pelagic grainstonesedimentary bodies are laterally elongated perpendicular to their progradation axis (Figs. 5b and 5c).

The biconvex shape of the pelagic grainstone sedimentary bodies is associated with compaction phenomena linked to the slowingdown and stopping of the prograding pelagic sand body (Fig. 10). As this process ends, underlying pelagic mud dewaters under the pe-lagic sand body’s weight, and the latter sinks into the mud, changing its shape into the lenticular or biconvex appearance observed incores and in outcrop (Figs. 10a, 10b). This lenticular or biconvex shape can appear on all cuts through the barchanoid hydraulic dunesediment bodies and all cuts of sand ridges, but along the axis perpendicular to the progradation (Fig. 11). Using field observations, weinterpreted the pelagic grainstone sedimentary bodies to consist of either barchanoid hydraulic dunes or sand ridges with varying degreeof sinuosity, with a possibility of the sand ridges coalescing.

We generated a new facies-distribution model with outcrop descriptions in the object-based method (Fig. 12). Note the three distinctregions in the model. For example, the upper part of the model, as expected, represents disconnected barchans that are found only in theregion. Similarly, the channels in the middle and lower parts of the model represent two different structures in terms of their morpho-logic properties.

(a) (b)

Fig. 7—Simulated facies model using object-based method. (a) 2D section of generated model, and (b) 3D model. Both images4.7 m (15.4 ft) wide with true scales in other directions.

(a) (b)

Fig. 8—Results of MPS method for 2D models of outcrop section illustrated in Fig. 4b. (a,b) Representations of two realizations,both 4.7 m (15.4 ft) wide with true vertical scale.



2018 SPE Journal 7

The model shown in Fig. 12 indicates a nonstationary distribution of the objects. The models that used 2D outcrop data in the previ-ous section can be categorized as stationary models because the statistical properties of a region do not change much and the entiremodel displays similar distribution. The model based on 3D data, however, does not show a stationary distribution of objects. Forinstance, the statistical properties in the upper region differ completely from those of the lower one. Such behavior, called nonstationar-ity, requires a different treatment. To add more complexity to this example, the initial model (Fig. 12) was used. This model is anunconditional model that we consider the reference model for generating the necessary data. For example, a synthetic acoustic imped-ance image using a moving average method was constructed with the model shown in Fig. 12. To mimic the noise associated with theactual seismic data, we added a random noise to the acoustic impedance data. Likewise, well data were extracted along a vertical direc-tion at random locations in the models shown in Fig. 12. In other words, the facies values in these random locations are selected andconsidered well data for the next steps. The produced well and acoustic impedance data are shown in Fig. 13. The size of this systemwas considered 160� 160� 80 cells (40� 40� 10 ft3). Note that we used synthetic acoustic impedance because of the lack of actualseismic data. All the following simulations are performed on a similar size.

Because two-point-based statistical methods cannot reproduce the complex morphologies of channels and barchans, not one hasbeen used for our case. And, although object-based methods can provide a realistic representation of the geology, a simultaneous condi-tioning to well and seismic data in these methods is not practical. For example, they cannot reproduce well data completely. In this pa-per, 45% of well data was not reproduced with the object-based method. Furthermore, considering seismic data for each facies is notstraightforward. Such limitations have been extensively discussed in previous literature (Shmaryan and Journel 1999; Journel 2002;Gringarten et al. 2005; Hauge et al. 2007; Guo and Deutsch 2010; Pyrcz and Deutsch 2014; Tahmasebi 2017a). The higher-order statis-tics method, however, can incorporate well and seismic data into a single model. This method can reproduce the entire complexity ofthe outcrop-defined facies, even in the presence of various conditioning data (Fig. 8). An unconditional model generated by the object-based method, similar to the one shown in Fig. 12, was therefore considered as the TI (Fig. 14).

Dealing with a geologic system that contains multiple facies requires extraction of different probability maps from the seismic data.In other words, the probability of having any of the existing facies should be extracted from the seismic data. For this to happen,the Bayesian rule was used, by which the probability of each of the facies, given well and impedance data, was calculated (Doyenet al. 1994):

0

0.1

0.2

0.3

0.4

1 2 3 4 5 6 7

Length (m)

Max

imum

Thi

ckne

ss (

m)

(Ave

rage

= 0

.149

; ST

D D

V =

0.0

27)

7 points not shown

10.4%25.9%

47.6%

Maximum for barchanoid hydraulic dunes (A = L/4.23)N = 409

Minimum for barchanoid hydraulic dunes (A = L/10)

16.1% Megaripples (A = L /25)A

B

CD

(Average = 2.41; STD DV = 2.56)

8 9 10

Fig. 9—Plot of length vs. thickness of pelagic grainstone bodies measured on their vertical cuts at Section 13 (Fig. 2). (a) Pelagicgrainstone sedimentary bodies with concretionary overgrowth. (b) Hydraulic dunes and/or sand ridges. (c) Megaripples or coa-lesced sand ridges. (d) Sand sheets (from Frebourg et al. 2016).

(a) (b)

Fig. 10—Early compaction history in formation of pelagic sand bodies (vertical section). (a) Dune/sand ridge prograding over soft,water-filled, uncompacted, pelagic muds resulting from action of seafloor bottom currents (white arrow points in current direction,closely spaced dotted lines underline foresets, solid lines underline pelagic mud bedding planes). (b) After progradation, pelagicsand body’s weight presses on uncompacted muds, which lose volume through dewatering. Pelagic sand body sags into com-pacted mud, adopting biconvex geometry observed at outcrop (white arrow points at sagging direction, dashed lines underlineforesets, plain lines underline pelagic mud bedding planes).



8 2018 SPE Journal

Pð fnjIÞ ¼PðIj fnÞPð fnÞ

PðIÞ ; ð5Þ

where Pð fnÞ represents the probability of facies f and PðIÞ is the probability of impedance values.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Background facies

Lensoid facies

Sinuous crested sand ridge type 1

Sinuous crested sand ridge type 2

Fig. 12—Example of generated geologic model using object-based method. Grid contains 160 3 160 3 80 cells (40 3 40 3 10 ft3).

Lensoidmorphology

Lensoidmorphology

Pinch-and-swellmorphology

Sinuous crestedsand ridges

Isolatedbarchans

Fig. 11—Dimensionless representation of geometrical objects associated with outcrop observation of pelagic sand bodies. Somelaterally continuous bodies can appear discontinuous, depending on cut.

(a) (b)

Fig. 13—(a) Extracted well data for three locations. Well data contain information about type of facies. (b) Synthetic acoustic im-pedance equivalent to seismic data.



2018 SPE Journal 9

Three probability maps were extracted from the seismic data (synthetic acoustic impedance in Fig. 13) with the Bayesian equation,and results are shown in Fig. 15.

Probability maps indirectly divide the geologic system into three stationary regions. The simulation grid was divided into three sepa-rate regions based on the available facies, and another set of data, called auxiliary region data, was also added to the input data. TheTI, well data, extracted probability maps, and auxiliary region data were all used stochastically to generate different realizations(Tahmasebi and Sahimi 2015). Using the described algorithm, we generated 50 realizations; two are shown in Fig. 16. An ensemble av-erage map over the generated realizations was also created for checking the quality of well-data reproduction (Fig. 16). It should benoted that all the used well data are reproduced in this simulation.

Finally, the accuracy of the generated realizations was compared with the TI. For this purpose, variograms and multiple-point con-nectivity were calculated for realizations and the TI (Krishnan and Journel 2003). The multiple-point connectivity quantifies the proba-bility pðh; nÞ of having a sequence of connected n facies/pixels in a specific direction h:

pðh; nÞ ¼ Prob½IðuÞ ¼ 1; Iðuþ hÞ ¼ 1;…; Iðuþ hnÞ ¼ 1�; ð6Þ

where indicator function IðuÞ is defined by

IðuÞ ¼1; u 2 facies i

0 otherwise:

�� ð7Þ

Results show good agreement with the TI (Fig. 17).

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Fig. 14—3D TI used in higher-order statistics. TI shown in different states of full three dimensions, intersection, and transparent view.

Fig. 15—Extracted probability maps from synthetic acoustic impedance data for each facies at top, middle, and bottom layers.

(a) (b)

Fig. 16—Results of CCSIM algorithm. (a) Two conditional realizations. (b) Ensemble average map over 50 conditional realizations.



10 2018 SPE Journal

Conclusions

The Eagle Ford Group is one of the most important and extensively studied energy resources in Texas. Statistical properties of the out-crop data have generally been extracted from collected images that are used to build similar models. Such statistical properties, how-ever, are insufficient to include all complexities. In this paper, three different methods were used to generate 2D and 3D geologicmodels from Eagle Ford outcrop data. Two-point-based (variogram-based) techniques were unable to capture the complexity and long-range connectivity of data because of their high level of heterogeneity and layering; thus, they were poor choices for studying EagleFord outcrop data. Results from object-based techniques were more realistic and reproduced spatial continuity, but the method canhardly produce shapes such as those in Fig. 4. In general, this class of facies modeling can be used for specific and simple geometriessuch as circles, ellipses, and channels. Conditioning object-based techniques to well and secondary data is not straightforward. In con-trast, when outcrop images are used directly, the MPS (higher-order statistics) method produces high-quality and realistic realizations.The MPS method used can produce high-quality models while it assimilates all available conditioning data.

The current MPS methods are limited to perform a direct modeling, meaning that adding the third dimension to 2D outcrop imagesis challenging. Although this has been performed in the fine-scale porous-media modeling with isotropic assumption (Tahmasebi et al.2015, 2016a,b), repeating a similar exercise for large-scale reservoir modeling can be challenging. Thus, as future work, one can con-sider using outcrop data at different directions and establish a meaningful 3D correlation between the 2D data. Another issue in the cur-rent pattern-based MPS method is reproducing the conditioning point data (i.e., well information). Recently, a new hybrid method thatis based on a combination of pixel- and pattern-based methods has been proposed (Tahmasebi 2017b), but this new direction requiresfurther research.

Nomenclature

C ¼ cross-correlationcand ¼ candidate number

DT ¼ data eventETI;DT

¼ Euclidean distance between TI and DT

G ¼ simulation gridblock

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 10 20 30 40 50 60 70

Var

iogr

am

Lag(a) (b)

(c) (d)

(e) (f)

0.25

0.27

0.29

0.31

0.33

0.35

0.37

1 21 41 61 81 101

p (r

)

r

0

0.2

0.4

0.6

0.8

1

1.2

0 10 20 30 40 50 60 70

Var

iogr

am

Lag

0.17

0.19

0.21

0.23

0.25

0.27

0.29

0.31

1 21 41 61 81 101

p (r

)

r

1

1.5

2

2.5

3

3.5

4

0 10 20 30 40 50 60 70

Var

iogr

am

Lag

0

0.05

0.1

0.15

0.2

0.25

1 21 41 61 81

p (r

)

r

Fig. 17—Comparison between TI (red curve) and generated realizations (gray curves) in terms of variogram and multiple-point con-nectivity. Representations of behavior of facies (a, b) at bottom; (c, d) at middle; and (e, f) at upper part of realizations. a, c, and erepresent variogram; b, d, and f represent multiple-point connectivity. p(r) represents probability of multiple-point connectivityfunction. Both Lag and r indicate sequence of points/pixels.



2018 SPE Journal 11

h ¼ lag distanceI(u) ¼ indicator value at location uOL ¼ overlap regionTI ¼ training imageTx ¼ template size in x-directionu ¼ visiting cell

Acknowledgments

This work was supported partly by the NanoGeosciences laboratory and by the Mudrock Systems Research Laboratory (MSRL) consor-tium at the Bureau of Economic Geology, Jackson School of Geosciences, the University of Texas at Austin. MSRL member companiesare Anadarko, Apache, Aramco Services, BHP, BP, Cenovus, Centrica, Chesapeake, Cima, Cimarex, Chevron, Concho, ConocoPhil-lips, Cypress, Devon, Encana, Eni, EOG, Exco, ExxonMobil, FEI, Geosun, Hess, Husky, IMP, Kerogen, Marathon, Murphy, Newfield,Oxy, Penn Virginia, Penn West, Pioneer, QEP, Repsol, Samson, Shell, Sinopec, StatOil, Talisman, Texas American Resources,The Unconventionals, University Lands, US EnerCorp, Valence, and YPF. Instructive comments by S. Ruppel are appreciated.Stephanie Jones and Lana Dieterich edited the manuscript. Publication was authorized by the Director, Bureau of Economic Geology(https://doi.org/).

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Pejman Tahmasebi is in the Department of Petroleum Engineering at the University of Wyoming. Previously, he was a research sci-entist at Stanford University, the University of Texas at Austin, and the California Institute of Technology, working on porousmedia/materials reconstruction, granular materials and advanced computational methods. Tahmasebi’s current interestsinclude computational geomechanics, coupled and multiphysics modeling, subsurface characterization, inverse problems,and data mining. He has authored or coauthored more than 45 technical papers. Tahmasebi holds BSc and MSc degrees fromAmirkabir University of Technology and a PhD degree in modeling of subsurface reservoirs and porous media from the Universityof Southern California. He is an SPE member and is the recipient of the 2017 Vistelius Research Award from the International Asso-ciation for Mathematical Geosciences.

Farzam Javadpour has worked as a reservoir engineer in industry and is currently working as a research scientist at the Bureau ofEconomic Geology (Jackson School of Geosciences, University of Texas at Austin). He is the coprincipal investigator of an indus-trial consortium and leads research works on novel techniques of reserves and permeability estimations as well as oil and gasproduction in shale systems. Javadpour is also studying the fundamentals of nanoparticle transport in porous media for EOR andreservoir-engineering applications. He teaches shale-gas characterization and production at the University of Texas at Austin.Javadpour has authored or coauthored more than 50 peer-reviewed journal papers and 25 SPE conference proceedings ontopics related to shale gas, CO2 injection, and transport in porous media. He holds a BS degree with distinction in petroleumengineering and MS and PhD degrees in chemical and petroleum engineering, respectively, from the University of Calgary.Javadpour’s work on the development of apparent permeability formulation for shale-gas systems appeared as a DistinguishedAuthor publication in Journal of Canadian Petroleum Technology (JCPT) in 2009. He served as an associate editor for JCPT andwas the recipient of the award for the best paper published in JCPT in 2008, the SPE Outstanding Service Award in 2010, and theSPE A Peer Apart Award in 2014.

Gregory Frebourg is a partner and the chief geologist of Thermal Energy Partners, where he focuses on geothermal exploration,research and development, and reservoir characterization. Previously, Frebourg worked as a research associate at the Bureauof Economic Geology, the University of Texas at Austin, for 6 years, during which he also lectured. Frebourg holds a BS degree,an MS degree, and a PhD degree, all in sedimentology, from the Department of Earth Sciences and Environment at the Univer-sity of Geneva, Switzerland.



2018 SPE Journal 13

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geologic modeling of eagle ford facies continuity based on ...pared with those of an outcrop data...

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