3D Fracture Analyses of Various Rock Samples Through X-Ray Micro-Tomography

3D FRACTURE ANALYSES OF VARIOUS ROCK SAMPLES THROUGH X-RAY MICRO-TOMOGRAPHY

Aswien Dwarkasing

October 2016

3D fracture analyses of various rock samples through x-ray micro-tomography

Aswien Dwarkasing

in partial fulfilment of the requirements for the degree of

Master of Science

in Petroleum Engineering and Geosciences

at the Delft University of Technology,

to be defended publicly on Monday 10 October , 2016 at 14:00u

Supervisor: Dr. A. Barnhoorn

Thesis committee: Prof. dr.P.L.J. Zitha TU Delft

Dr. N.J.Hardebol TU Delft

This thesis is non-confidential and can be made public.

An electronic version of this thesis is available at http://repository.tudelft.nl/.

Abstract

Hydrocarbon reservoirs are currently declining. Reservoirs are becoming depleted, and production needs to satisfy the demand and supply of hydrocarbons. For tight reservoirs such as shales, fracturing will become the main source of improving the permeability. It is therefore vital to conduct research into the behavior of fractures in the reservoir. The aim is to study how fractures develop in terms of fracture size, coalescence, patterns and in which dimensions they often occur. Often the importance of the behavior of these fractures and their contribution to flow in reservoirs also formed part of this research.

In this investigation, the Posidonia shale core was examined using three different layering orientations. The three different layer orientated shale cores were subjected to axial loading in order to induce fracturing. These induced fractures were created in two ways. The first was by axial loading until the core reached maximum failure. The second involved loading in stages and scanning the core after each loading stage in the micro-CT scanner. This procedure was repeated until maximum failure was reached. An Indiana limestone core and sandstone core were also analyzed.

The behavior, coalescence, frequently seen fracture patterns, angle with respect to the z-axis and apertures of the fractures were studied and compared. This was performed in both a quantitative and qualitative matter using the commercial Avizo® Fire software at TU Delft. A small part of this study touch on the modeling of the observed shear fracture pattern from a shale core preformed in Abaqus. The results from the fracture analyses shows that the largest fractures are seen in the shale cores, for which the fracture initiation was created by one loading stage until failure. Another observation shows that there is clear set of different fractures that is seen for each distinctive layered core. From the observed patterns a simple 2D simulation is built in Abaqus. From the simulation is seen that for cracks under a certain angle, the master fracture is intersected by a 300 smaller fracture, the results in opening of the master fracture. This is also the case in the 2D slice, which is a representation of the 2D-model fracture configuration.

Keywords: Posidonia Shale, Sandstone, Limestone, Fracture analyses,Avizo®Fire,Fracture mode, Fracture angle, Abaqus modeling.

Acknowledgements

This thesis is a continuation of work performed by former students. By using the information they had gathered and drawing on the challenges they faced, some of the problems that were encountered concerning fracture analyses were solved.

First of all, this thesis would not have been possible without the help of my supervisor, Auke Barnhoorn, who showed tremendous patience in the progress of the work. Auke has always been available when challenges or setbacks arose, and he helped me think and guided me to solutions, and also provided guidance when writing the thesis.

I would also like to thank Nico Hardebol and Quiten Boersma, for their great support in the modelling in Abaqus at the last moment. Nico also introduced me to Jurgen Foegen, who was willing to help with the Avizo Fire and share his experience. Special thanks go to Jurgen. Thank you also goes to Joost van Meel and Guus Lohlefink for allowing me to use their workstation and office to analyze the cores. Thanks also go to the graduated students who had stored their data carefully and clearly. In the end a special thanks to my father for the support and believe, also a special thanks to my wife for the support and our newly born son.

Table of contents

Abstract ...... 3 Acknowledgements ...... 4 Table of contents ...... 5 List of figures ...... 7 List of tables ...... 10 1. Motivation ...... 11 2 Research question ...... 14 3 Methodology ...... 15 § 3.1 shales cores ...... 16 § 3.2 Sandstone sample ...... 17 § 3.4 Indiana limestone sample ...... 17 4. Fracture analysis in Avizo® Fire and modelling in Abaqus ...... 18 §4.1.0 Image processing and segmentation ...... 19 § 4.1.1 Fracture characterization ...... 23 §4.1.3 Quantification of orientation ...... 28 §4.2 Modeling in Abaqus ...... 31 §4.2.1 Objective for modelling? ...... 31 §4.2.2 Building a 2D-model in Abaqus ...... 32 5. Results ...... 33 §5.1 Qualitative analyses ...... 33 §5.1.0 Comparison of fracture patterns with different layering orientations ...... 38 §5.1.1 Fracture interaction (coalescence) ...... 38 §5.1.2 Frequently observed fracture patterns ...... 40 §5.2Quantitative analyses ...... 45 §5.2.1 Sandstone sample ...... 47 §5.2.2 Limestone sample ...... 49 §5.2.3 Shale sample 53B ...... 50 §5.2.4 Shale sample 36A ...... 52 §5.2.5 Shale_JV ...... 53 §5.2.4 Comparison of the quantified results ...... 54 §5.3 Modeling fracture geometry ...... 56 6. Discussion ...... 58

§6.1 Aperture ...... 58 §6.2 Fracture length ...... 58 §6.3 Fracture angle ...... 58 §6.4 Comparison of the quantitative and qualitative analyses ...... 59 §6.5 Contribution to flow ...... 59 §6.6 Setbacks ...... 59 §6.7 Comparison of fracture patterns on field scale ...... 61 §6.8 Comparison of the quantified data ...... 62 7. Conclusions and recommendations ...... 65 §7.1 Conclusion ...... 65 §7.2 Recommendations ...... 66 8. Appendix ...... 67 §8.1 Flow chart Avizo Fire ...... 67 §8.2 Analyzed data ...... 69 §8.2.1 shale_JV...... 69 §8.2.2 Sample 36A ...... 71 §8.2.3 Limestone ...... 74 §8.2.4 Sample 53B ...... 77 9. Bibliography ...... 78

List of figures

FIGURE 1 THIS CHART SHOWS THE PRODUCTION OF NATURAL GAS FROM THE GRONINGEN GAS FIELD. THE X-AXIS INDICATES THE YEARS; THE Y-AXIS INDICATES THE BILLION CUBIC METERS. THE GREEN BARS INDICATE GAS PRODUCTION, AND THE BLUE BARS INDICATE THE EXPECTED NATURAL GAS PRODUCTION FROM THE GRONINGEN GAS FIELD (SOURCE: HTTP://WWW.NLOG.NL). 11 FIGURE 2 A MAP OF THE NETHERLANDS SHOWING THE SHALE FORMATIONS. THE LIGHT BLUE SECTIONS INDICATE THE POSIDONIA SHALE FORMATION, AND THE LIGHT GREEN INDICATES THE GEVERIK LAAGPAKKET. SOURCE: HTTP://AARDGAS-IN- NEDERLAND.NL/ ------13 FIGURE 3 THE SANDSTONE CORE ON WHICH FRACTURE ANALYSIS WAS DONE USING THE AVIZO® FIRE SOFTWARE. ------17 FIGURE 4 AN EXPLANATION OF THE MEDIAN FILTER. THIS FILTER REPLACED THE VOXEL VALUE OF 10 TO 4 BY TAKING THE MEDIAN VALUE OF THE NEIGHBORING VOXEL SIZES. ------19 FIGURE 5 A MICRO-CT SCAN OF A SHALE CORE FROM THE POSIDONIA SHALE FORMATION, DETAILING THE DIFFERENT PROCESSING STEPS USED TO OBTAIN FRACTURE ANALYSIS FOR QUANTITATIVE ANALYSIS. A. RAW IMAGE. B. RESULT OF THE MEDIAN FILTER; THE EFFECT OF THE FILTER IS NOT SEEN CLEARLY IN THIS IMAGE. C. DEBLUR OPERATOR USED TO SHARPEN THE IMAGE. D. EROSION. E. OPENING AND F. CLOSING. THE RED BOXES ARE ENLARGED IMAGES, WHICH CAN BE SEEN IN FIGURE 6. THE NEXT STEP IS IMAGE SEGMENTATION AND FRACTURE CHARACTERIZATION. THIS SAMPLE IS HORIZONTALLY LAYERED SHALE. VOXEL SIZE: 0.04X0.04X0.040 MM. VIEW: XY. ------20 FIGURE 6 A. RAW DATA. B. MEDIAN FILTER OPERATION. C. DEBLUR IMAGE. D. EROSION. E. OPENING. F. CLOSING.------21 FIGURE 7. EROSION. THIS IMAGE IS A BINARY IMAGE, FIGURE A HAS NOT BEEN ERODED. THE IMAGE IN THE FIGURE B ILLUSTRATES THE EROSION OPERATION, AND FIGURE C IS THE RESULT OF APPLYING EROSION. THE VALUE OF THE OUTPUT PIXEL WAS THE MINIMUM VALUE OF ALL THE PIXELS IN THE INPUT PIXEL'S NEIGHBORHOOD. IF THE MINIMUM VALUE WAS 0, THEN THE PIXEL VALUE WAS CHANGED TO 0 AFTER EROSION (FIGURE B &FIGURE C). IN AVIZO, THE SAME WAS DONE FOR THE VOXELS. THE NEIGHBORHOODS WERE CHOSEN TO BE 6, 18, OR 26. THE 6 MEANS THAT THE VOXELS WITH A COMMON FACE WERE CONSIDERED TO BE CONNECTED. THE 18 VOXELS MEANS THAT AT LEAST ONE COMMON EDGE WAS CONSIDERED TO BE CONNECTED, AND THE 26 MEANS THAT AT LEAST ONE COMMON VERTEX WAS CONSIDERED TO BE CONNECTED. THIS ANALYSIS WAS PERFORMED WITH 26 VOXELS. ------22 FIGURE 8 OPENING. THIS MORPHOLOGICAL OPERATION CLEANED UP SMALL LOCAL PROTRUSIONS AFTER THE IMAGE HAD BEEN ERODED. THIS FILTER REMOVES SMALL OBJECTS THAT CANNOT CONTAIN THE STRUCTURED ELEMENT DEFINED BY THE NEIGHBORHOOD. THIS CAN BE SEEN IN THE BINARY IMAGE IN FIGURE A; AFTER THE APPLYING THE FILTER, THE RESULT IS SEEN IN THE BINARY IMAGE IN FIGURE C. ------22 FIGURE 9 CLOSING. THIS MORPHOLOGICAL FILTER WAS USED TO REMOVE SMALL HOLES THAT CANNOT CONTAIN THE STRUCTURED ELEMENT DEFINED BY THE NEIGHBORHOOD AND THE SIZE. THIS FILTER IS USUALLY USED AFTER A DILATION OPERATION. IN THIS CASE, THIS WAS AFTER USING THE OPENING FILTER. FIGURE A, A BINARY IMAGE IS DILATED; AFTER APPLYING THE CLOSING FILTER, THE RESULT CAN BE SEEN IN FIGURE C. ------23 FIGURE 10 A OVERVIEW OF THE TOOLS USED FOR FRACTURE ANALYSIS. ------24 FIGURE 11 SELECTING THE THRESHOLDING FOR FRACTURES. THE ‘’SELECTION’’ BUTTON WAS USED, THEN “INTERPOLATE” IN ORDER TO VIEW THE ENTIRE FRACTURE. ------25 FIGURE 12 THE ORIENTATION ANGLES MEASURED IN AVIZO FIRE. THE CORE IS ORIENTATED PARALLEL TO THE Z-AXIS. ------29 FIGURE 14 IN THESE THREE FIGURES A,B AND C THE DIFFERENT FRACTURE GEOMETRIES WILL BE SIMULATED. IN FIGURE A SMALLER CROSS FRACTURE IS ORIENTATED OBLIQUELY TO TWO LARGE FRACTURES. IN FIGURE B THE TWO LARGE FRACTURES ARE SEEN. 0 THE LARGEST FRACTURE IS ACCOMMODATED BY A SMALLER FRACTURE AT AN ANGLE OF 30 . IN FIGURE C TWO LARGE FRACTURES ARE SEEN THAT ARE SLIGHTLY OFFSET AND ARE NOT ACCOMMODATED BY SMALLER FRACTURES. ------32 FIGURE 15 COMPARISON OF MICRO-CT FRACTURED SHALE CORE WITH DIFFERENT LAYERING ORIENTATIONS. SAMPLE 49C IS VERTICALLY LAYERED. SAMPLE 49E IS DIAGONALLY LAYERED AND SAMPLE 53B IS HORIZONTALLY LAYERED. THESE THREE SAMPLES WERE TAKEN FROM A 2D SLICE THROUGH A 3D MICRO-CT DATA SET. THE VOXEL RESOLUTION IS GIVEN IN THE GREY BOXES ON TOP OF EACH FIGURE. ------34 FIGURE 16 A 3D VIEW OF THE CORE FROM SAMPLE 49C. THE DEVELOPMENT OF THE FRACTURES THROUGHOUT THE CORE CAN BE OBSERVED. IT IS CLEARLY SEEN THAT THE NUMBER OF FRACTURES IN THE CORE IN SCANS 1 THROUGH 5 INCREASES. IN THE LOWER RIGHT HAND SIDE PICTURE, A CROSS SECTION IS SEEN OF THE CORE FROM SCAN 5. THE FRACTURES CAN BE VIEWED IN 3D. ------35 FIGURE 17 THIS CORE PRESENTS THE AXIAL LOADING UNITL FAILURE IS REACHED. ------36

FIGURE 18 A LIMESTONE SAMPLE. THE IMAGE IS UNCLEAR DUE TO POOR SCAN RESOLUTION. THE FRACTURE PATTERN SEEN IN THE LIMESTONE IS DIFFERENT TO THAT OBSERVED IN THE SHALE CORE. THE PATTERN LOOKS LIKE ONE LARGER CIRCULAR FRACTURE CONNECTED BY MANY SMALLER FRACTURES AT THE EDGES. ------37 FIGURE 19 A HORIZONTALLY-LAYERED SHALE SAMPLE THAT HAS BEEN ACCOMMODATED WITH AXIAL PRESSURE UNTIL FAILURE IS REACHED. THE FRACTURES SHOW LARGE APERTURES. ------37 FIGURE 20 A VERTICALLY-ORIENTED CORE WITH FRACTURE COALESCENCE THROUGHOUT THE CORE. THESE 2D SLICES WERE TAKEN FROM ONE CORE AND ONE SCAN. THE BLUE CIRCLE INDICATES IN 2D HOW THE COALESCENCE OF TWO FRACTURES CONNECT TO EACH OTHER AND GROW FURTHER INTO ONE FRACTURE. THE GREEN CIRCLE ILLUSTRATES A LARGE CROSS FRACTURE THAT DEVELOPED AND CONNECTED TO THE LARGER FRACTURE AT THE EDGE OF THE CORE. THE YELLOW CIRCLE INDICATES THE GROWTH OF A THIN FRACTURE INTO A FRACTURE THAT SEEMS TO HAVE A LARGER APERTURE. ------39 FIGURE 21 COALESCENCE OF A FRACTURE THROUGHOUT A HORIZONTALLY-LAYERED SAMPLE. THE SLICES WERE TAKEN FROM DIFFERENT LOCATIONS WITHIN THE CORE. ------40 FIGURE 22 THE FRACTURE PATTERN FREQUENTLY OBSERVED IN HORIZONTAL LAYERS ------40 FIGURE 23 A SLICE FROM A VERTICALLY-LAYERED SHALE CORE. THE PATTERNS OBSERVED CAN BEEN SEEN ON THE RIGHT SIDE OF THE IMAGE, AND ARE HIGHLIGHTED WITH BLUE AND YELLOW DOTTED LINES. ------41 FIGURE 24 COMMON FRACTURE PATTERNS SEEN IN DIAGONALLY-LAYERED SHALE SAMPLES. ------41 FIGURE 25 FROM THIS FIGURE IS CLEARLY SEEN THE DIFFERENCE IN INVESTIGATING FRACTURES. IN FIGURE A1 AND B1 REPRESENT THE A 2D SLICE AT THE EXACT LOCATION. IN FIGURE A2 THE FRACTURES HAVE BEEN ANALYSED BY A WORKFLOW THAT RECOGNISES FRACTURES AS A ‘FAMILY’ OF FRACTURE. IN FIGURE B2 THE WORKFLOW, DESCRIBED IN THIS REPORT IS USED. THE CURRENT WORKFLOW IS USEFUL TO INVESTIGATE EACH FRACTURE INDIVIDUALLY. MIND THAT ANALYSING EACH FRACTURE CAN BE A TIME CONSUMING OPERATION. ------43 FIGURE 26 MICRO FRACTURES IN THE SHALE SAMPLES ARE OFTEN NOT QUANTIFIED, BECAUSE THE LACK OF RESOLUTION, AS INDICATED BY THE RES ARROWS. OFTEN ALL FRACTURES ARE QUANTIFIED FOR SAMPLES WITH ONLY LARGE FRACTURES. SMALLER (MICRO) FRACTURES, AS SEEN IN THIS FIGURE, ARE DIFFICULT TO QUANTIFY. ------44 FIGURE 27 THIS FREQUENCY-LENGTH HISTOGRAM ILLUSTRATE THE AREAS OF WHICH FRACTURES WILL BE ANALYSED QUANTITATIVELY. THE RED BOX INDICATED THAT LARGER FRACTURES ARE IDENTIFIED IN THE SHALE AND THE MICRO-FRACTURES, THE LEFT SIDE AREA OF THE RED BOX, ARE NOT QUANTIFIED. ALBEIT FOR THE SANDSTONE CORE, WITH LARGER FRACTURES, THE FREQUENCY- LENGTH HISTOGRAM, IS APPLICABLE FOR THE WHOLE SET OF FRACTURES IN THE SANDSTONE CORE. (SOURCE: (VERMILYE & SCHOLZ, 1995)) ------45 FIGURE 28 THE NUMBER OF FRACTURES IDENTIFIED IN THE SHALE SAMPLE THAT HAD BEEN SCANNED FIVE TIMES ------46 FIGURE 29 THE FRACTURES WHICH WERE IDENTIFIED IN THE TWO SHALE, ONE LIMESTONE AND ONE SANDSTONE SAMPLES. THE MAJORITY OF FRACTURES WERE IN THE SHALE_JV SAMPLE, AND THE FEWEST FRACTURES WERE FOUND IN THE SANDSTONE SAMPLE.------46 FIGURE 30 FRACTURES IN A SANDSTONE CORE WITH HORIZONTAL LAYERING AND A VOXEL SIZE OF 0.03 X 0.03 X 0.03 MM. FOUR FRACTURES WERE IDENTIFIED. THE GREEN-COLOURED FRACTURE, FRACTURE 1, IS THE LARGEST FRACTURE. THE PURPLE- COLOURED FRACTURE, FRACTURE 4, IS THE SMALLEST FRACTURE. ALL FRACTURES ARE CONNECTED TO EACH OTHER. THE APERTURE, VOLUME, AREA AND WIDTH ARE PROVIDED IN THE GRAPHS BELOW. THE COLOURS OF THE CORE AND THE 2D SLICES DIFFER, BECAUSE THE COLORMAP OF THE CORE WAS LOWERED TO GIVE BETTER INSIGHT INTO HOW THE IDENTIFIED FRACTURES ARE ORIENTED WITHIN THE CORE. ------47 FIGURE 31 THE QUANTIFIED MEASUREMENTS OF THE FOUR IDENTIFIED FRACTURES IN THE SANDSTONE SAMPLE. THE COLOR OF EACH FRACTURE CORRESPONDS TO THE FRACTURES SEEN IN ERROR! REFERENCE SOURCE NOT FOUND.. ------48 FIGURE 32 THE CORRESPONDING LENGTH AND APERTURE OF EACH FRACTURE. THE LENGTH CAN BE FOUND ON THE X-AXIS AND THE APERTURE ON THE Y-AXIS. THE SMALLEST FRACTURE, FRACTURE 4, HAD THE SMALLEST APERTURE. THE LARGEST APERTURE WAS SEEN IN FRACTURE 3.------48 FIGURE 33 FRACTURE 1 HAD THE GREATEST AREA, AND FRACTURE 3 HAD THE GREATEST VOLUME. ------49 FIGURE 34 THE FRACTURES WITHIN THE INDIANA LIMESTONE SAMPLE WITH A VOXEL SIZE OF 0.04 X 0.04 X 0.04 MM. ------49 FIGURE 35 FROM THE DIFFERENT SCANS, IT CAN BE SEEN HOW THE FRACTURES DEVELOPED. IN SCAN 1, ONLY ONE FRACTURE WAS IDENTIFIED. IN SCANS 2, 3, 4 AND 5 IT WAS CLEARLY SEEN THAT THE NUMBER OF FRACTURES HAD INCREASED. ------50 FIGURE 36 THE APERTURES OF THE INDIVIDUAL FRACTURES IN EACH SCAN CLEARLY SHOW THAT THE LARGEST APERTURE WAS MEASURED IN SCAN 5. IN SCANS 3 AND 4, THE APERTURE OF FRACTURES 1, 2 AND 4 SHOWED A SLIGHT INCREASE. ------51 FIGURE 37 A SHALE SAMPLE BROUGHT IN ONE LOADING STAGE TO FAILURE, BY AXIAL LOADING. ------52 FIGURE 38 THE IDENTIFIED FRACTURES IN A SHALE CORE. THE SURFACES OF THE FRACTURES WERE DIFFERENT FROM THE OTHER SURFACES DUE TO THRESHOLDING DIFFICULTIES. THE MAJORITY OF THE FRACTURES WERE ORIENTED ALONG THE Z-AXIS.

OBLIQUE-ORIENTED FRACTURES WERE OBSERVED FOR EXAMPLE IN THE FIRST PICTURE, WHERE THE LIGHT YELLOW FRACTURE IS OBLIQUE TO THE DARK YELLOW FRACTURE .THE HIGHEST CONCENTRATION OF FRACTURES WAS SEEN ON THE EDGES, CLOSE TO THE Z-AXIS. ------53 FIGURE 39 THE APERTURES OF ALL THE ANALYSED FRACTURES FOR EACH INDIVIDUAL SMAPLE. THE APERTURES FOR SHALE CORE 53B ARE AVERAGED VALUES. ------54 FIGURE 40 THE RELATIONSHIP BETWEEN THE LENGTH OF THE FRACTURES AND THE APERTURES FOR EACH SAMPLE. ------54 FIGURE 41 LENGTH DISTRIBUTION BETWEEN THE DIFFERENT CORES. NOTE THAT IN SAMPLE TR_53B THE FRACTURE LENGTHS ARE AVERAGED. ------55 FIGURE 42 THE CALCULATED ORIENTATION NUMBER OF THE IDENTIFIED FRACTURES IN ALL THE SHALE CORES. ------55 FIGURE 43 ALL SAMPLES WITH THEIR FRACTURES AND ORIENTATION NUMBERS. THE HIGHEST CONCENTRATION OF NUMBERS IS ILLUSTRATED BY THE CIRCLES.------56 0 FIGURE 44 THE FRACTURE GEOMETRY MODELLED IN ABAQUS. THE ANGLE OF THE SMALLER FRACTURE IS 30 TOWARDS THE LARGER FRACTURE. THE RED ARROW INDICATES THE RESULT OF THE SMALLER FRACTURE ON THE LARGER FRACTURE. THE HIGHEST 0 CONCENTRATION OF STRESS IS INDICATED IN BY THE RED AREAS AT THE TIP OF THE SMALLER 30 FRACTURE. ------57 FIGURE 45 IN FIGURE A THE MAXIMUM IN INPLANE PRINCIPAL STRESS IS INDICATED AND IN FIGURE B THE MINIMUM INPLANE PRINCIPAL STRESS. THE MAXIMUM INPLANE PRINCIPAL STRESS IS IN GEOLOGY KNOWN AS THE SIGMA 3, THE MINIMUM STRESS. THE MINIMUM INPLANE PRINCIPLE STRESS IS KNOWN AS THE SIGMA, MAXIMUM STRESS. THE FRACTURE OPENING SHOULD BE IN THE DIRECTION OF THE MINIMUM STRESS. IN FIGURE B THIS IS THE CASE. THE BLEU COLOURS INDICATE THE SMALLEST STRESS AND THE FRACTURE OPENING PROPAGATES TOWARDS THE MINIMUM STRESS. ------57 FIGURE 46 ONE OF THE SETBACKS EXPERIENCED IN THIS INVESTIGATION. SOMETIMES THE THRESHOLDING DID NOT TAKE THE ENTIRE FRACTURE INTO ACCOUNT. THEREFORE, USING THE BRUSH TOOL (RED ARROW), THE FRACTURE NEEDED TO BE ‘’BRUSHED’’ FOR EACH FIVE SLICES AND THEN BE INTERPOLATED. THE CHOICE OF FIVE SLICES WAS MADE AS THIS MEANT THAT THE INTERPOLATION WOULD NOT DEVIATE FROM THE FRACTURE. ------60 FIGURE 47 FIGURE A SHOWS THE OBSERVED FRACTURE PATTERNS IN THE WHITBY MUDSTONE, WHICH ARE INDICATED BY THE RED LINES. IN FIGURE B PARALLEL FRACTURES ARE SEEN WITH ORTHOGONAL FRACTURES CONNECTING THE LARGER PARALLEL FRACTURES. THE OTHROGONAL FRACTURE IS INDICATED BY THE RED ARROW. SOURCE: (BOERSMA, 2015) ------61 FIGURE 48 THE CROSS-PLOT BETWEEN THE AVERAGE FRACTURE LENGTH AND THE AVERAGE APERTURE. A POWER FIT IS APPLIED THROUGH THE DATA POINTS. ------62 FIGURE 49 THE CROSS-PLOT SHOWING THE AVERAGE FRACTURE LENGTH VS THE WIDTH. A LINEAR FIT IS APPLIED THROUGH THE DATA POINTS. ------63 FIGURE 50 THIS FLOWCHART REPRESENTS THE DIFFERENT OPERATIONS WHICH WERE NECESSARY TO OBTAIN THE DATA. ------67 FIGURE 51 THE WORKFLOW IN AVIZO. AFTER CLOSING, THE ‘’EDIT NEW LABEL FIELD‘’ OPERATION WAS APPLIED. ------68 FIGURE 52 THE APERTURE FOR EACH FRACTURE ------69 FIGURE 53 THE AREA OF EACH FRACTURE ------69 FIGURE 54 THE VOLUME OF EACH FRACTURE ------70 FIGURE 55 THE FRACTURE LENGTH OF EACH FRACTURE ------70 FIGURE 56 THE WIDTH OF EACH FRACTURE ------71 FIGURE 57 THE FRACTURE APERTURE FOR EACH FRACTURE. ------71 FIGURE 58 THE AREA OF EACH FRACTURE. ------72 FIGURE 59 THE VOLUME OF EACH FRACTURE. ------72 FIGURE 60 THE LENGTH OF EACH FRACTURE. ------73 FIGURE 61 THE WIDTH OF EACH FRACTURE. ------73 FIGURE 62 THE FRACTURE POROSITY FOR SAMPLE 36A. ------74 FIGURE 63 THE APERTURES OF EACH FRACTURE IN THE LIMESTONE CORE. ------74 FIGURE 64 THE AREA OF EACH FRACTURE IN THE LIMESTONE SAMPLE. ------75 FIGURE 65 THE VOLUME OF EACH FRACTURE IN THE LIMESTONE SAMPLE. ------75 FIGURE 66 THE LENGTH OF EACH FRACTURE IN THE LIMESTONE SAMPLE. ------76 FIGURE 67 THE WIDTH OF EACH FRACTURE IN THE LIMESTONE SAMPLE. ------76 FIGURE 68 THE AREA, VOLUME, LENGTH AND WIDTH OF EACH FRACTURE IN THE FIVE MICRO-CT SCANS. ------77

List of tables

TABLE 1 THE RESULTS OF TAKING SHALE GAS INTO ACCOUNT IN THE LONG TERM, AS PRESENTED BY ROYAL HASKONING DHV. SOURCE:

HTTP://WWW.RLI.NL ...... 13

TABLE 2 AN OVERVIEW OF THE ANALYZED SAMPLES WITH LAYER ORIENTATION, WEIGHT, HEIGHT, DIAMETER, BULK VOLUME AND

MATRIX DENSITY, WHICH WERE LATER USED FOR QUANTITATIVE ANALYSES. ALL DATA WERE CREATED BY A FORMER MASTER’S

STUDENT...... 16

TABLE 4 THE FUNCTIONS OF ALL THE TOOLS USED TO ANALYZE THE FRACTURES. THE NUMBERS ARE SHOWN IN FIGURE 9...... 26

TABLE 5 THE OBSERVED COALESCENCE TYPES AND COMPARISONS WITH THE LITERATURE ...... 39

1. Motivation

The extraction of oil and gas in the Netherlands has been a successful business for more than half a century. Taking a closer look at the production of natural gas, the Netherlands is one of the dominant countries for gas production in the EU, producing a large amount of gas. The largest natural gas producing field in the Netherlands is the Groningen gas field. The Groningen field is expected to produce, according to statistics, approximately 40 billion cubic meters (BCM) of natural gas during the next four years (Figure 1). However, a decline in gas production is expected. The Dutch government, through the minister of economic affairs, has recently exerted pressure to reduce the production of natural gas to 30 BCM. This decision was made due to the subsidence of the subsurface, which has resulted in earthquakes and damage to the houses of people living in Groningen. Subsidence in the Groningen gas field is caused by the declining reservoir pressure. Due to the decline of the reservoir pressure the overburden pressure becomes too large for the sandstone particles to provide support, which cause these to collapse and initiate subsidence. In the future, the gas demand will increase and the production of the Groningen gas field will decline. In the long term, the Netherlands needs to identify new resources to compensate for the declining gas production. Therefore, the question which arises is: how will the Dutch government maintain the supply of natural gas to the local market if the demand is increasing and production is declining?

Figure 1 This chart shows the production of natural gas from the Groningen gas field. The x-axis indicates the years; the y- axis indicates the billion cubic meters. The green bars indicate gas production, and the blue bars indicate the expected natural gas production from the Groningen gas field (Source: http://www.nlog.nl).

In order to maintain the supply, alternative resources must be found. The first of these alternative resources is producing natural gas from smaller fields in the north of the Netherlands, where the

Groningen gas field is also located. A second alternative is to import gas from, for example, Russia, and the third option is to produce gas from shale reservoirs, which occur in the subsurface of the Netherlands. The third alternative is currently under ongoing discussion. The production of hydrocarbon from shale reservoirs is already occurring in the USA. In May 2015, a report was published about the role of gas in the Netherlands until 2040, which takes into account the production of shale gas. These results are presented in Table 1. However, the minister of economic affairs has decided to postpone the drilling of an exploration well, which was planned for 2020.

Shales are fine-grained sedimentary rocks that can be rich resources of petroleum and natural gas. In the Netherlands, two types of shale formations have been identified in the subsurface; the Posidonia Shale formation and the Geverik Laagpakket. A map of the occurrence of shale layers in the

Netherlands is given in Figure 2.

Shale reservoirs are ‘’tight’’ reservoirs, which means that the flow of hydrocarbons needs to be stimulated. In technical terms, shale reservoirs have a low permeability. To improve their permeability, artificial fracture patterns are created; this process is called fracking. By fracking the shale formations, certain fracture patterns and fracture networks are created. Understanding these fracture patterns and networks is essential for the flow of hydrocarbons. The presence of (micro) fractures in the development of new reservoirs is often neglected or not carefully accounted for.

To date, extensive research has been done into shale formation especially; however, the majority of scientists have only touched on the subject when dealing with fractures in shales. In this thesis, the emphasis is on understanding the different fracture patterns, not only in shales, but also in other available reservoir rocks, such as sandstone and limestone. The cores on which this research is done were drawn from the Posidonia shale formation.

Figure 2 A map of the Netherlands showing the shale formations. The light blue sections indicate the Posidonia shale formation, and the light green indicates the Geverik Laagpakket. Source: http://aardgas-in-nederland.nl/

Table 1 The results of taking shale gas into account in the long term, as presented by Royal Haskoning DHV. Source: http://www.rli.nl

Gas production Shale gas Gas Gas import Profit (Billion $) Decline climate

Groningen production import until 2040 footprint (CO2- from (BCM) eq) (year) 25 BCM 0 BCM 2031 69 181 0 70 BCM 2035 9 197 2 Mton/year 200 BCM 0 225 5 > 2040 Mton/year 40 BCM 0 BCM 2026 153 184 0 70 BCM 2027 75 199 2 Mton/year 200 BCM 0 228 5 > 2040 Mton/year

2 Research question

This study was conducted as often the presence of fractures in reservoirs are oversimplified or even ignored in the interpretation and development of a new reservoir, which leads to incorrect decisions being made in exploration and decision plans. This study was also conducted in order to enable (micro) fractures configurations to be simulated to understand the stress regime. There is a possibility that these micro-fractures or fracture networks may contain a significant volume of hydrocarbon. Therefore, it is vital to understand the complexity of fractures and fracture networks. The third important point is that the micro fracture horizons are not seen in seismic, which makes it difficult to identify how fractures the reservoir really is. In this thesis, these two subjects are investigated in order to solve the problem mentioned in the above section. In order to obtain quantitative and qualitative data of fractures of the different cores, a commercial fracture analyses software, Avizo® Fire 8.1.1, was used. The cores had already been scanned into the micro-CT scanner present at the Technical University of Delft (TUD). Further information regarding how the samples were made and the fractures follows in chapter 3. A simulation model was built in Abaqus using the qualitative analyses with different fracture configurations. Abaqus is a commercial software which makes it possible to create fracture geometries and angles of any kind. Using Abaqus, only a two dimensional simulation routine was built. In this thesis, the author used only a shale fracture configuration as models. In chapter 5. Results presents the results of the qualitative and quantitative analysis which was done on the fractures present in the shale, sandstone and limestone cores. Another important field of interest is the development of numerical simulators to mimic the flow in these reservoirs. In order to run simulators for the new developments or existing fields, the fracture patterns or networks are important to take into account. The upscaling of fractures is important in flow simulations, as the connectivity between micro-fractures and larger fractures are particularly important. This forms the motivation for the performance of this research into the modelling of different fractures geometries. In order to determine the behavior of fractures, the geometry and dimensions of the fractures are essential.

In order to address the stated problem, the following research question was formulated:

“3D FRACTURE ANALYSES OF VARIOUS ROCK SAMPLES THROUGH X-RAY MICRO-TOMOGRAPHY”

3 Methodology

In this chapter, a brief explanation is given about the samples used for fracture analysis and how the fractures were obtained. Different cores were used for the fracture analysis, these were: three shale cores, a sandstone core and a limestone core. In order to recognize the shale samples, they were named using the prefixes of the former master students. How the cores were prepared and how the fractures were created are explained in the following paragraphs.

Table 2 An overview of the analyzed samples with layer orientation, weight, height, diameter, bulk volume and matrix density, which were later used for quantitative analyses. All data were created by a former master’s student1.

Sample Layer Weight Height Diameter Porosity Bulk Matrix Orientation (g) (mm) (mm) (%) Volume density (mm3) (g/mm3) TR53B Horizontal 22.26 21.68 23.45 4.14 9.36 2.48 36A Horizontal Shale_JV Horizontal 27±0.5 to 40±0.5 0.5-2.5 2.25-2.55 41±0.5 Limestone Horizontal 32±0.5 40±0.5 19 2.69

Sandstone Horizontal TR49C Vertical 22.23 22.93 5.15 2.46 TR49E Diagonal 25.16 23.77 4.30 2.53

§ 3.1 shales cores As mentioned above, three shale cores were used. These cores were obtained from previous master students2. The shale samples were cored from the Posidonia shale formation. All three shale cores had the same layering orientation, and the fractures of all three cores were made by unconfined pressure experiments. The unconfined pressure experiment apparatus used was available in the TU Delft laboratory in the faculty of Civil Engineering and Geoscience. Fracture initiation in the samples was done by placing the sample in a pressure bench and exposing it to axial forces. Displacement control was applied to the pressure bench, working by pumping hot oil underneath the bottom plate and lifting it upwards, while applying some forces to the sample (see the (Ravestein, 2014) report for details). The shale sample 53B was fractured by applying axial pressure in phases, i.e., the sample was first exposed to some axial pressure, and the sample was then scanned in the micro-CT scanner. This process of exposing the shale core to cyclic axial pressure was done until maximum failure was reached. The sample used in this report was scanned five times. The method of cyclic loading and scanning gave the fractures the ability to ‘’grow,’’ and the phenomenon of observing fracture

1 (Verheij, 2015) (Ravestein, 2014) (Primarini, 2015)(Janmahomed,2016) 2 Ravestein.T,Primarini.M,Verheij.J

16 coalescence was made possible. The shale cores 36A and shale_JV were placed under axial pressure until failure was reached, without cyclic loading. In this report, a comparison will be made between the results of these two fracturing methods.

§ 3.2 Sandstone sample The next core used for fracture analysis was the sandstone sample. This sample was made by a master’s student, Faroek Janmahomed; the research of this sample is ongoing. This sample was cored from the Bentheimer Formation. It was a sandstone sample, which was also fractured in the unconfined pressure bench apparatus. Axial pressure was applied to the sample. At each stage, the axial pressure was loaded and unloaded onto the sample. A 2.0 MPa of axial pressure was added to the new loading stage. This process continued until failure was reached. Having reached the failure point, the sample was scanned in the micro-CT scanner. In Figure 3 the sandstone core is illustrated.

Figure 3 The sandstone core on which fracture analysis was done using the Avizo® Fire software.

§ 3.4 Indiana limestone sample The limestone sample for fracture analyses was a calcite-cemented grainstone formed from fossil fragments and oolites, also known as the Salem limestone. The limestone was assumed to be homogenous, and was ordered from Kocurek Industries (Verheij, 2015). Fractures were initiated by axial loading until failure was reached.

4. Fracture analysis in Avizo® Fire and modelling in Abaqus

In this chapter, the workflow for fracture analysis in Avizo® Fire 8.1.1 will be explained. Image processing, segmentation and characterization were the three most important stages in the obtaining of quantitative information from fractures within the cores. In the next three paragraphs,

the image processing, segmentation and characterization will be described. In essence, an image was obtained, and each voxel was evaluated in a fixed space. A formula was then applied and the voxel was replaced.

§4.1.0 Image processing and segmentation The stage of image processing involved de-noising the image as much as possible. A three- dimensional (3D) image was built using cubes, called voxels. A voxel is a unit of graphic information that defines a point in 3D space. In 3D space, each of the coordinates was defined in terms of its position, color and density. Sometimes the voxels in an image did not have the same value as their neighboring voxels. This resulted in noise in the image. In order to remove noise from an image, certain filters were used. These filters helped to smooth and sharpen the image, which was important for thresholding during a later stage. The choice was made to use the median filter to remove outlying voxels. As a result, the median filter smoothed the image and replaced the voxel with the outlying value, using mathematical formulas. The operation of median filtering is shown in Figure 4.

Figure 4 An explanation of the median filter. This filter replaced the voxel value of 10 to 4 by taking the median value of the neighboring voxel sizes.

Figure 5 A micro-CT scan of a shale core from the Posidonia Shale Formation, detailing the different processing steps used to obtain fracture analysis for quantitative analysis. A. Raw image. B. Result of the median filter; the effect of the filter is not seen clearly in this image. C. Deblur operator used to sharpen the image. D. Erosion. E. Opening and F. Closing. The red boxes are enlarged images, which can be seen in Figure 6. The next step is image segmentation and fracture characterization. This sample is horizontally layered shale. Voxel size: 0.04x0.04x0.040 mm. View: xy.

Figure 6 A. Raw data. B. Median filter operation. C. Deblur image. D. Erosion. E. Opening. F. Closing.

After applying the median filter, the image appeared hazy. In order to sharpen the image, a ‘deblur’ operation was applied to the filtered image. After sharpening the image, the binary morphological operators were used: these included ‘erosion,’ ’opening’ and ‘closing.’

The ‘’erosion’’ operation changes the output pixel, which is the minimum value if all the input pixels neighborhood. If for examples the minimum value was 0, then the pixel value is changed to 0 after erosion. The same principle is used for the three dimensional pixels, called voxels. In Avizo Fire the neighborhoods can be chosen, in which the common face, edge or vertex is considered to be connected. The neighborhoods are chosen by the number 6, 18 or 26. The number 6 applies to voxels with a common face were considered to be connected. The number 18 applies to voxel neighborhoods where at least one common edge is considered to be connected and number 26 means that at least one common vertex was considered to be connected. Analyses in this report are performed using number 26.

The ‘’opening’’ operation is applied to the grey image after the ‘’erosion’’ operator has been applied. Opening will help to operation cleaned up small local protrusions after the image had been eroded. This filter removes small objects that cannot contain the structured element defined by the neighborhood.

After having applied the two mentioned operations a third operations is than applied, which is ’closing’. The ‘closing’ operation is used to remove small holes that cannot contain the structured

21 element defined by the neighborhood and the size. This filter is usually used after a dilation or opening operation.

The functions of these mentioned morphological operations are explained in Figure 7,Figure 8 and Figure 9. These operations are usually used for binary images; however, in Avizo, these operators also apply to grey images.

A B C

Figure 7. Erosion. This image is a binary image, figure A has not been eroded. The image in the figure B illustrates the erosion operation, and figure C is the result of applying erosion. The value of the output pixel was the minimum value of all the pixels in the input pixel's neighborhood. If the minimum value was 0, then the pixel value was changed to 0 after erosion (Figure B &Figure C). In Avizo, the same was done for the voxels. The neighborhoods were chosen to be 6, 18, or 26. The 6 means that the voxels with a common face were considered to be connected. The 18 voxels means that at least one common edge was considered to be connected, and the 26 means that at least one common vertex was considered to be connected. This analysis was performed with 26 voxels.

A B C

Figure 8 Opening. This morphological operation cleaned up small local protrusions after the image had been eroded. This filter removes small objects that cannot contain the structured element defined by the neighborhood. This can be seen in the binary image in figure A; after the applying the filter, the result is seen in the binary image in figure C.

A B C

Figure 9 Closing. This morphological filter was used to remove small holes that cannot contain the structured element defined by the neighborhood and the size. This filter is usually used after a dilation operation. In this case, this was after using the Opening filter. Figure A, a binary image is dilated; after applying the closing filter, the result can be seen in Figure C.

§ 4.1.1 Fracture characterization Having applied the three above mentioned morphological operators to the grey image, the final step that of fracture characterization, began. Fracture characterization was done by using the Edit New Label Field operation. This was the most important and time consuming step. During this stage, a binary image was made by thresholding the observed fractures. There were several possibilities available to threshold and label each observed fracture. This workflow was also applied to the sandstone and limestone images. Although it worked very well on the shales, it had a less optimal result for the limestone and sandstone cores used in this report. A possible cause for having poorer binary images for the fracture analyses of the limestone and sandstone cores is the lack of resolution. In addition, the composition of the rock being analyzed is important. When using the Edit New Label Field operation for the fracture characterization, different possibilities were available regarding how to identify and create binaries from the grey images. In Figure 10, the screenshot of the Edit New Label Field window provides the functions and possibilities. The numbers 11, 12, 13 and 14 are the operators for making the binaries of the fractures. The detail of each function is also given in Table 3.The most frequently used tools for separately identifying the fractures are number 13. This tool is called the magic want tool, which helps to identify only the interested areas of the fractures. While using this tool a red line will appear in the area of number 15. This redline indicate the threshold value is of the fracture. Albeit not all parts of a fracture has the same threshold value. Using the sliders, indicated by the black arrows, the parts of the fracture with different threshold values are partially taken into account. Often this tool is not sufficient for identifying the whole fracture. While using the sliders fractures, unnecessary parts are also identified and added to the

23 fracture. To help remove these unnecessary added parts form the fracture the Lasso tool, number 12 in Figure 10, is used. This tools cuts and adds unwanted and missed parts to fractures. This tool has the power to operate in 2D as well in 3D. The operation in 3D is only possible after having selected an area in 2D. After having selected several area in 2D for example after every 5 slices, then the several 2D areas are interpolated. This interpolation is done clicking on ‘’selection’’ in the menu and then ‘’interpolate’’, see Figure 11 for the details. Having performed this operation then number 10 in used to remove the unwanted parts. Be aware that the distance between the interpolations is within then slices range. The brush tool is used to paint the missing pieces of a fracture, indicated by number 11. This is only used when the threshold value is one particular fracture in a wide range. The blow tool is also a tool for thresholding fractures, indicated by number 14 in Figure 10. This tool is often used to add missing parts to the fracture. Using the volume rendering, the fractures can be viewed in the core. Volume rendering provides a 3D view of the core.

Figure 10 A overview of the tools used for fracture analysis.

Figure 11 Selecting the thresholding for fractures. The ‘’selection’’ button was used, then “interpolate” in order to view the entire fracture.

Table 3 The functions of all the tools used to analyze the fractures. The numbers are shown in Figure 10.

Number Function 1 Create new label, e.g., a new fracture is created. 2 Delete a created label, e.g., deleting a fracture. 3 Locate a fracture in the viewing window. 4 In the material window, the new material can be viewed. By clicking in material, different options were available, e.g., to change the color or name of the material. 4.1 The ‘’eye-function’’ was used to view the fractures in 2D or 3D. The ‘’lock’’ was useful when the interpretation of a particular fracture was finished; it is then advisable to ‘’lock’’ this particular material. 5 and 6 Zoom in and out of the sample for different orientations. 7 The eraser can clear the errors when using the magic want, blow or brush tools. 8 Replace the current material selected. 9 Add button. When adding missing pieces to the fractures. The lock button must be unthicken. 10 Subtraction of wrongly interpreted parts from a fracture. 11 The brush tool. This tool is used to paint the missing pieces of a fracture. This is only used when the threshold value is one particular fracture in a wide range. 12 Lasso tool. This tool is used to remove parts of a fracture which are invalidly identified. First, the area of interest was selected. If parts of the fracture need to be removed on more than one slice, the next five slides can be selected. It is desirable to use intervals of five slices for the interpolation. Then ‘’selection’’ and then ‘’interpolate’’ were chosen. Avizo interpolates the areas between these the slices (Figure 10). 13 The magic wand tool is used for thresholding the area of interest. For example, a fracture. The entire fracture can be selected by checking the “all slices” box. It can sometimes be difficult to use this tool with the all slices box checked on. This is because the voxels can have other threshold values in the next slices. 14 Blow tool. This tool is used as an alternative for the magic wand tool. As mentioned in number 5, the blow tool can also help add missing parts to the fracture. 15 In this viewer, the threshold values are given. When using the magic wand tool, a vertical redline will indicate the threshold value for selected area. A range can then be decided which represents the fracture at its best. 16 In some cases, the “all slices” box can be checked. This gives the possibility to interpret the fracture in the entire volume at one time, instead of going through all the slices. Often, this option does not work very well. Unnecessary parts are also selected. Instead of deleting these parts, it is faster to use intervals of five slices each time and then to interpolate these.

Thresholding can sometimes be incorrect when working with one of these tools. Using the Ctrl + Z shortcut and the undo button, one can go back to the previous step. Having identified all of the

27 fractures in the core, the next step was to create the surfaces. In order to do this, the generate surfaces option was clicked. Avizo gave a warning for a set which contained a voxel size which was too large; in this case, continue was clicked. After generating the surface, surface view was chosen. The surfaces were now visible. The results were obtained by going to individual measurements, followed by clicking on label analysis. The measurements in the label analysis window were set to default and two-dimensional (2D) measurement. A separate group was made to measure parameters, such as volume3d, area3d, width3d, lenght3d, orientationTheta and orientationPhi. The group entitled “Thomas group” was used in the workstation in room 3.190. All of the above- measured parameters had already been made in this group. It was easy to make an own group with the preferred parameters. These results were output as a spreadsheet, and were then able to be exported as a CSV-format for further processing in Microsoft Excel.

After label analysis, the aperture of each fracture was measured. The measurements for the aperture were set by using the surface thickness option (Voorn, Exner, Barnhoorn, Baud, & Reuschle, 2015), and were applied to the segmented data; however, this operation involved biases in the segmentation routine. Each fracture was individually selected and the thickness of each fracture was measured. This was a time-consuming process, due to the segmentation routine. After the measurement of the surface thickness was completed, a histogram was plotted with the frequency on the y-axis and the thicknesses on the x-axis. The data were saved as a CSV-format for later use in Excel, in order to create normalized aperture distributions. This process of measuring the surface thickness was applied to each fracture. This module was useful for computing the thickness of flat regions from surface objects. To do so, at each vertex, the module computed the distance along the vertex normal to the normal intersection, with the closest triangle of the same material. In order to obtain a reasonably reliable thickness estimate, the surface was smoothed and opposing triangles were approximately parallel. The result was exported as a surface scalar field with a distance measure per vertex. For surfaces composed of multiple materials, the field values were set only for the vertices belonging to the selected material. All other vertices were set to 0. Distances were negative for triangles with an incorrect orientation. In order to correctly adjust the range of the colormap, these negative distances were set as undefined values.

§4.1.3 Quantification of orientation The orientation number obtained in Avizo® Fire was measured in spherical coordinates and described the position of the fracture on the x, y and z -axes. Two angles, theta and phi, were measured for the orientation. The angle for orientationTheta was the rotation angle around the z-

28 axis, which was between -180° and 180°. The Phi angle was the elevation angle between the fracture and the positive z-axis, which is between 0° and 90°.

Figure 12 The orientation angles measured in Avizo Fire. The core is orientated parallel to the z-axis.

As the angles measured were in spherical coordinates, the angles needed to be converted to the proper angle between the fracture and the x and y-axes. The elevation angle3, ф, was in the range of 0° and 90°. Therefore, no conversion needed to be applied. However, the rotational angle was in the range of -180° and 180°. The angle containing negative degrees was converted to positive angles. This was done using Equation 1.0.

′ θ for θ ≥ 0° θ = { (1.0) θ + 180 for θ < 0°

Where:

θ: rotation angle measured in degrees ( 휃 ∈ −180,180)

θ′: transformed angle in degrees

The angles were now transformed to positive angles. The following step was to determine the angles between the fractures and the x, and y-axes (Equation 1.1).

3 (Hicks, 2015)

휃′ 푓표푟 휃′ ≤ 90 휃 = { (1.1) 푥 180 − 휃′ 푓표푟 90° < 휃′ ≤ 180

Where:

휃′ : is the tranformed angle calculated in equation 1.0

휃푥: ∶ is the angle between the x − axis and the fracture in degrees (0°, 90°)

The angle between the y-axis and the fracture was calculated in a similar way (Equation 1.2).

90 − 휃′ 푓표푟 휃′ ≤ 90 휃 = { (1.2) 푦 휃′ − 90° 푓표푟 90° < 휃′ ≤ 180

Where:

휃′ : the tranformed angle calculated in equation 1.0

휃푦 ∶ the angle between the y − axis and the fracture in degrees (0°, 90°)

After the angles were calculated with respect to each axis, the orientation number was calculated. The calculations for the orientation number were performed using formula 1.3.

1 휂 = ∑푁 푐표푠휃 (1.3) 푖 푁 푖=1 푖

Where:

η푖 ∶ orientation number with respect to the i − axis

N: total number of fractures

° ° cos θi: the angle of the fracture with respect and the i axis (0 , 90 )

The orientation number values ranged from 0 to 1. The numbers close to 0 indicated fractures which were almost parallel to the z-axis; fractures which were close to a value of 1 were perpendicular to the x-axis.

Further data are found in chapter 5. In the final step, the local axis and scale bars were added, which were useful for the snapshots. In order to measure all thicknesses in a faster way, the Avizo software was opened in several windows. Each project was run simultaneously. The software crashed several times.

§4.2 Modeling in Abaqus In this paragraph a model is built in Abaqus. The model is a representation of the fracture geometries, which are observed in a fractured core. Further in this chapter a brief explanation will be provided why and how modelling is essential.

§4.2.1 Objective for modelling? From the cores that were analysed qualitatively, certain fracture configurations are recognised. These patterns are classified in two large parallel fractures accompanied by smaller micro cracks, two fractures that are slightly offset or a small cross fracture oblique to two larger fractures. Especially the fractures in the shale cores with shear-type fracture patterns will be investigated. These fracture patterns often show coalescence. These three kind of geometries are illustrated in Figure 13.

The first observed fracture geometry in Figure 13A, shows the presence of a smaller cross fracture that is orientated orthogonally between two larger fractures.

The second geometry is seen in Figure 13B, where two large fractures are seen that will coalescence to a one larger fracture. These two fractures intersect at an angle of approximately 300 . These two fractures are companied by smaller fractures.

In the third geometry Figure 13C two large fractures are slightly offset from each other and these two fractures coalescence to one larger fracture. These two fractures are not companied by smaller fractures.

The aim is to model one of these shear type of fracture geometries and investigate the interaction between the larger fractures and the smaller neighbouring fractures. How do these fractures effect the local stress perturbation? How is the interaction between the larger and smaller fractures?

Different interaction properties can be assigned in Abaqus for the modelled fractures. These properties can be changed in ‘frictionless’, ‘rough’ and ’penalty’. These results can be exported to a excel file. The results should provide insight on the how the Mohr-circles change when the interaction properties are different. In this thesis only the effects of the smaller fracture on the larger(master) fracture will be investigated.

A B C

Figure 13 in these three figures A,B and C the different fracture geometries will be simulated. In figure A smaller cross fracture is orientated obliquely to two large fractures. In figure B the two large fractures are seen. The largest fracture is accommodated by a smaller fracture at an angle of 300. In figure C two large fractures are seen that are slightly offset and are not accommodated by smaller fractures.

§4.2.2 Building a 2D-model in Abaqus The model is built in the following steps:

1. The model is created as a standard/ explicit model 2. Draw the 2D sketch and create the Parts 3. Assign the material properties and Section properties 4. Assemble the model and give the interaction 5. Mesh the frame 6. Apply the Boundary conditions and apply Load 7. Create a Job 8. Submit the job 9. View the results for analyses

The detailed steps can be found in the report of Quinten Boersma, who did some great research on how to build two- and three dimensional models in Abaqus.

Properties applied assigned4

Table 1 the youngs modulus and the poison ratio.

Properties Young Modulus 67.109 (Mpa) Poison ratio 0.22

4 (Ravestein, 2014)

5. Results

In this chapter, the qualitative and quantitative results are presented. First, the qualitative description of three shale samples with different layering orientations, a limestone and sandstone sample, are described. 2D slices were taken from 3D data, which were scanned in the micro-CT scanner. The qualitative observations were based on commonly-seen fracture patterns, relations between larger and smaller fractures, fracture coalescence, and the observed angle of the fractures throughout the 2D and 3D images.

§5.1 Qualitative analyses In order to quantify fracture morphologies, their geometrical characteristics were determined from micro-CT images. The fracture morphologies of three shale samples with different orientations were quantified and compared with the fracture patterns of sandstone, limestone and two horizontally- layered shale samples to which axial pressure was applied until failure was reached.

Sample: 49C Sample: 49E Sample: 53B

Layering: Vertical Layering: Diagonal Layering: Horizontal

Voxel size: 0.02x0.02x0.020 Voxel size: 0.02x0.02x0.020 Voxel size: 0.02x0.02x0.020 3D-View 3D-View 3D-View

xy-view xy-view xy-view

xz-view xz-view xz-view

yz-view yz-view yz-view

Figure 14 Comparison of micro-CT fractured shale core with different layering orientations. Sample 49C is vertically layered. Sample 49E is diagonally layered and sample 53B is horizontally layered. These three samples were taken from a 2D slice through a 3D micro-CT data set. The voxel resolution is given in the grey boxes on top of each figure.

A more detailed explanation of Figure 14 will now be provided. First, these samples were all shale samples with different layering orientations. The samples shown in Figure 14 are the fractures which were formed at maximum failure. From the vertically-layered sample, seen in 2D, the larger fractures were parallel to each other and were fairly homogeneous throughout the sample. Also, small intersecting cross fractures were observed, which were important for connecting the larger fractures to form a complete connective network in the core. The larger fractures were characterized by the minor clustering of smaller fractures surrounding them locally. In 3D, it could be seen that these cross fractures and smaller fracture networks were connected to the larger fractures. The orientation of the smaller fractures did not differ to as great an extent as that seen in the larger fractures. From the diagonally-layered core, it was seen in 2D that the majority of the fractures were located at the edge of the core, and one large fracture went through the core. In the horizontally-layered core, one large fracture was seen that crossed the core. These fractures were oriented differently in comparison to the other layered core. Fractures in the diagonally-layered shale sample had developed a clustered parallel pattern. The majority of these fractures were seen at the edges of the 2D slice. The smaller observed fractures are also connected to the larger fractures. Smaller fractures that connected to the larger fractures had different orientations and were discontinuous. In the last sample, 53B, which was horizontally layered, one continuous large fracture was seen throughout the image. Smaller fractures were connected to larger fractures and were orientated differently. Each crack differed in orientation from the previously-formed crack. In the xz-view, oblique secondary cracks5, indicated by the red arrows, were seen. These were oblique secondary cracks to the larger pre-existing crack (blue arrow) and wing crack (green arrow).

5 (Tentler & Amcoff, 2010)

Figure 15 A 3D view of the core from sample 49C. The development of the fractures throughout the core can be observed. It is clearly seen that the number of fractures in the core in scans 1 through 5 increases. In the lower right hand side picture, a cross section is seen of the core from scan 5. The fractures can be viewed in 3D. Illustrates how the development of fractures in a horizontally- orientated shale core occurs. The first top left hand side figure, scan 1, shows the core with one large fracture. Scan 2 shows that the fracture had developed two parallel fractures, with one fracture crossing these two fractures. In scan 3, it can be seen that more fractures have developed and that the fractures seemed to have larger apertures when observed with the naked eye. In scans 4 and 5, the fractures had developed throughout the entire core. On top of the core, fractures were seen. In scan 5, a cross section is provided in order to show in 3D how the fractures had developed.

Figure 16 This core presents the axial loading unitl failure is reached.

In Figure 16, it can be observed that the majority of the fractures developed at the edges of the core. One fracture was seen which crossed through the core (indicated by the green arrow). The fractures were orientated in different directions. Two fractures were oblique (indicated by the red arrow) to the parent fracture.

Figure 18 A horizontally-layered shale sample that has been accommodated with axial pressure until failure is reached. The fractures show large apertures.

Limestone View: slice through the core

Figure 17 A limestone sample. The image is unclear due to poor scan resolution. The fracture pattern seen in the limestone is different to that observed in the shale core. The pattern looks like one larger circular fracture connected by many smaller fractures at the edges.

§5.1.0 Comparison of fracture patterns with different layering orientations The vertical layered core showed that the fractures developed to be almost parallel to each other. The fracture spacing was observed to be almost consistent. In the 45° layered sample, fewer parallel fractures were observed. The majority of the fractures were seen at the edges of the core. The occurrence of fractures at the edges of the core may be explained by the rock being weaker at the edges. The first micro-fractures grow from the edges and continue the center of the core. In sample 53B, only one large sample was observed, and this was connected by smaller fractures. It is clear that in all of these three samples, the larger fractures developed by a process of coalescence of the smaller fractures. The main differences seen in fracturing between the horizontal, diagonal and vertical layered cores is the location where the fractures occurs. From the vertical layered sample, fractures occur on the almost in the whole core, while in the diagonal and horizontal core fractures occur at the edges with fewer larger fractures accompanied by smaller fractures. The second difference observed in the 2D slice from the horizontal core, is seen that the oblique orientated fractures are larger to the parent fracture than the cross fractures seen in the vertical layered core. Meanwhile in the diagonal orientated core is seen in 2D that there are no cross or oblique orientated fractures that connect to the larger fractures. These smaller fractures are connected to the larger fracture at a gentle angle.

The next comparison was made between the fractures seen in the different layer shale cores with the fractures seen in the two shale cores, in which the fractures were induced by one-time axial loading. The main difference was qualitatively seen in the aperture of the fractures. Fewer micro- fractures were seen and larger fractures were observed. Therefore, the dimensions of the fractures were larger in the shale cores that were fractured by one-time loading. The fractures in the horizontally-layered core were concentrated at the edges. This is illustrated in Figure 14 and Figure 16.

The final comparison led to the observation that the least number of fractures was seen in the sandstone and the highest number of fractures were counted in the limestone sample.

§5.1.1 Fracture interaction (coalescence) In this section, the interaction between parent fractures and smaller, daughter fractures is highlighted. By looking at the scans from the vertically-orientated and horizontally-orientated cores, the different micro-CT-scans showed the development of fracture coalescence. This is an important topic in order to understand connectivity in hydrocarbon reservoirs. Coalescence will be described by type, initiation position and mode of coalescence (Bobet A, 1998).

Figure 19 A vertically-oriented core with fracture coalescence throughout the core. These 2D slices were taken from one core and one scan. The blue circle indicates in 2D how the coalescence of two fractures connect to each other and grow further into one fracture. The green circle illustrates a large cross fracture that developed and connected to the larger fracture at the edge of the core. The yellow circle indicates the growth of a thin fracture into a fracture that seems to have a larger aperture.

The type of coalescence seen in Figure 19 was correlated to what has been investigated in the literature for gypsum. The coalescence types are given below (Table 4).

Table 4 the observed coalescence types and comparisons with the literature

Schematic path of Type of coalescing Mode of coalescence coalescence fracture Wing crack. The wing Tension cracks are indicated by green arrows Secondary crack Shear

Figure 20 Coalescence of a fracture throughout a horizontally-layered sample. The slices were taken from different locations within the core.

§5.1.2 Frequently observed fracture patterns During the investigation into the fractures, common fracture patters were frequently observed. The commonly-seen fracture patterns are indicated in Figure 21,Figure 22 and Figure 23.

Figure 21 The fracture pattern frequently observed in horizontal layers

Figure 22 A slice from a vertically-layered shale core. The patterns observed can been seen on the right side of the image, and are highlighted with blue and yellow dotted lines.

Figure 23 Common fracture patterns seen in diagonally-layered shale samples.

In the figures above (Figure 21, Figure 22 and Figure 23), it can be seen that the yellow pattern in Figure 22 and Figure 23 occurs in the diagonally as well as in the vertically-layered slices. In Figure 21 and Figure 22, it can be seen that the shear type of fracturing pattern is seen in the horizontally as well as in the diagonally-layered slice.

The fractures in the shale, limestone and sandstone cores are further investigated qualitatively. In the sandstone core it is easier to qualify the fractures in 3D then the shale or limestone core. The reason why it is easier to qualify this fractures have two reasons. The first reason is the aperture difference between the fractures in the sandstone core are much larger than in the shale core. The shale core has larger apertures and contain no micro-fractures that connect to the larger fracture. Albeit in the shale core the fractures with large apertures are accommodated by micro-fractures. The second reason is the number of fractures present in the sandstone core is far less than the number of fractures present in the shale core. When analyzing the fractures in the different cores by the generated workflow, each fracture is identified separately. In previous reports the characteristics of fractures where described by one whole ‘’family’’ of fractures. In this report these same fractures are identified individually. In Figure 24 a clear image is given on what the improvement is based on fracture analyses from previous reports.

Figure 24 from this figure is clearly seen the difference in investigating fractures. In figure A1 and B1 represent the a 2D slice at the exact location. In figure A2 the fractures have been analysed by a workflow that recognises fractures as a ‘family’ of fracture. In figure B2 the workflow, described in this report is used. The current workflow is useful to investigate each fracture individually. Mind that analysing each fracture can be a time consuming operation.

Shale

Figure 25 micro fractures in the shale samples are often not quantified, because the lack of resolution, as indicated by the res arrows. Often all fractures are quantified for samples with only large fractures. Smaller (micro) fractures, as seen in this figure, are difficult to quantify.

The results of the quantified analyses are based on the fractures that have good apertures and are observed clearly in the shale core. Especially the micro-fractures are difficult to quantify and are often not even taken into account. A reason for this is that the aperture is so small, that when the filters are applied the voxels are not clearly seen and making it hard to identify these micro- fractures. In the sandstone core all fractures where analyzed, because these fractures are clearly visible. When plotting the fracture length against the frequency in a histogram the area of fracture investigation will differ. An example is given from a fracture length –frequency graph is provided in Figure 26 and is taken from (Vermilye & Scholz, 1995).

Figure 26 This frequency-length histogram illustrate the areas of which fractures will be analysed quantitatively. The red box indicated that larger fractures are identified in shales and the micro-fractures, the left side area of the red box, are not quantified. Albeit for the sandstone core, with larger fractures, the frequency-length histogram, is applicable for the whole set of fractures in the sandstone core. (Source: (Vermilye & Scholz, 1995))

§5.2Quantitative analyses For the quantitative analyses, five samples were analyzed. These samples were three shale samples, a limestone sample and a sandstone sample. In this paragraph, a comparison will be made between the aperture distributions, volume and angles between the fractures for each sample. In chapter 6, the discrepancies observed will be commented upon. The measurements for the quantitative analyses were in 3D, and the parameters measured were: area, length, volume, aperture and width. The fracture porosity was calculated by volume of the fracture divided by the total volume of the core. The measurement data for all samples can be found in §8.2 Analyzed data in order to maintain the clarity of this paragraph for the reader. A shale core example is used in this paragraph to illustrate the measurement data.

Figure 27 The number of fractures identified in the shale sample that had been scanned five times

Figure 28 The fractures which were identified in the two shale, one limestone and one sandstone samples. The majority of fractures were in the shale_JV sample, and the fewest fractures were found in the sandstone sample.

§5.2.1 Sandstone sample

Figure 29 Fractures in a sandstone core with horizontal layering and a voxel size of 0.03 x 0.03 x 0.03 mm. Four fractures were identified. The green-coloured fracture, fracture 1, is the largest fracture. The purple-coloured fracture, fracture 4, is the smallest fracture. All fractures are connected to each other. The aperture, volume, area and width are provided in the graphs below. The colours of the core and the 2D slices differ, because the colormap of the core was lowered to give better insight into how the identified fractures are oriented within the core.

Figure 30 The quantified measurements of the four identified fractures in the sandstone sample. The color of each fracture corresponds to the fractures seen in Figure 29.

Figure 31 The corresponding length and aperture of each fracture. The length can be found on the x-axis and the aperture on the y-axis. The smallest fracture, fracture 4, had the smallest aperture. The largest aperture was seen in fracture 3.

Figure 32 Fracture 1 had the greatest area, and fracture 3 had the greatest volume.

From the quantified data, it was seen that the largest fracture was that represented in green, the second largest fracture was the blue fracture, the yellow fracture was third largest and the smallest fracture was the purple-colored fracture. The largest aperture was measured within fracture 3, the yellow fracture. Upon closer examination of the fractures, it was confirmed that the aperture of the third fracture was indeed the fracture with the largest aperture.

§5.2.2 Limestone sample

Figure 33 The fractures within the Indiana limestone sample with a voxel size of 0.04 x 0.04 x 0.04 mm.

§5.2.3 Shale sample 53B

Figure 34 From the different scans, it can be seen how the fractures developed. In scan 1, only one fracture was identified. In scans 2, 3, 4 and 5 it was clearly seen that the number of fractures had increased.

Aperture for each scan with their corresponding fracture 0,45 0,40

0,35

0,30 Scan 1 0,25 Scan 2 0,20 Scan 3

0,15 Aperture (mm) 0,10 Scan 4 0,05 Scan 5 0,00 0 1 2 3 4 5 6 7 8 9 10 11 12 Number of fracture

Figure 35 The apertures of the individual fractures in each scan clearly show that the largest aperture was measured in scan 5. In scans 3 and 4, the aperture of fractures 1, 2 and 4 showed a slight increase.

§5.2.4 Shale sample 36A

Figure 36 A shale sample brought in one loading stage to failure, by axial loading.

§5.2.5 Shale_JV The fractures in this shale sample were difficult to threshold. The surfaces that were identified are illustrated in Figure 37.

Figure 37 The identified fractures in a shale core. The surfaces of the fractures were different from the other surfaces due to thresholding difficulties. The majority of the fractures were oriented along the z-axis. Oblique-oriented fractures were observed for example in the first picture, where the light yellow fracture is oblique to the dark yellow fracture .The highest concentration of fractures was seen on the edges, close to the z-axis.

§5.2.4 Comparison of the quantified results

Figure 38 The apertures of all the analysed fractures for each individual smaple. The apertures for shale core 53B are averaged values.

Figure 39 The relationship between the length of the fractures and the apertures for each sample.

Figure 40 length distribution between the different cores. Note that in sample TR_53B the fracture lengths are averaged.

Orientation number vs fracture number 1

0,9

0,8

) 0,7 -

0,6

0,5

0,4

Orientation ( number Orientation 0,3

0,2

0,1

0 0 2 4 6 8 10 12 14 16 18 20 Fracture# (-)

Scan 1 Scan 2 Scan 3 Scan 4 Scan 5 Shale_JV 36A

Figure 41 The calculated orientation number of the identified fractures in all the shale cores.

Orientation number vs fracture number 1

0,9

0,8

) 0,7 -

0,6

0,5

0,4

Orientation ( number Orientation 0,3

0,2

0,1

0 0 2 4 6 8 10 12 14 16 18 20 Fracture# (-)

Scan 1 Scan 2 Scan 3 Scan 4 Scan 5 Shale_JV 36A Limestone Sandstone

Figure 42 All samples with their fractures and orientation numbers. The highest concentration of numbers is illustrated by the circles.

§5.3 Modeling fracture geometry The simple 2D model that has been simulated in Abaqus shows how the stress regime. From the model is seen that the smaller fracture causes the larger fracture to open. The smaller fracture is oriented at an angle of 300 towards the larger fracture.

Figure 43 the fracture geometry modelled in Abaqus. The angle of the smaller fracture is 300 towards the larger fracture. The red arrow indicates the result of the smaller fracture on the larger fracture. The highest concentration of stress is indicated in by the red areas at the tip of the smaller 300 fracture.

Figure 44 in figure A the maximum in inplane principal stress is indicated and in figure B the minimum inplane principal stress. The maximum inplane principal stress is in geology known as the sigma 3, the minimum stress. The minimum inplane principle stress is known as the sigma, maximum stress. The fracture opening should be in the direction of the minimum stress. In figure B this is the case. The bleu colours indicate the smallest stress and the fracture opening propagates towards the minimum stress.

The results of the modeled fracture geometry is illustrated in Figure 44. In figure A the maximum in inplane principal stress is indicated and in figure B the minimum inplane principal stress. The maximum inplane principal stress is in geology known as the sigma 3, the minimum stress. The minimum inplane principle stress is known as the sigma, maximum stress. The fracture opening

57 should be in the direction of the minimum stress. In figure B this is the case. The bleu colours indicate the smallest stress and the fracture opening propagates towards the minimum stress.

6. Discussion

In this chapter, a discussion is made about the measured parameters and the setbacks that were encountered in analyzing the fractures.

§6.1 Aperture First, the aperture of the different shale samples will be discussed, and then the discussion will continue with a comparison of all the apertures in the analyzed samples. Comparing the apertures found in sample 53B, it can be seen that the aperture increased in the scans from 1 to 5 for each fracture. The lowest apertures were measured in scans 2 and 3. The highest measurement for an aperture was seen in scan 5. Why was this? During the axial loading and unloading, the fractures did not reach failure point, causing these fracture to behave elastic. Another cause of having a lower aperture, as seen in scans 2 and 3, is that the defect of analyzing these smaller fractures. Fractures with larger apertures are easier to analyze than the smaller apertures. Comparing the two other shale samples, 36A and Shale_JV, it can be concluded that the largest aperture is seen in Shale_JV. These two shale samples fractured in a different way than shale sample 53B, as has already been mentioned. The apertures in the sandstone were between 0.3 and 0.5 mm. One small fracture was also identified with an aperture of 0.05 mm. The majority of the limestone fractures showed an aperture in the range of 0.2 to 0.3 mm.

§6.2 Fracture length Regarding the length of the fractures, it can be seen in Figure 40 that the highest density of measured length was between 10 mm and 25 mm for all samples. The shortest length was seen for shale sample 53B, and the longest fracture length was seen in the limestone sample. The correlation between the aperture and the fracture width are discussed in §6.8 Comparison of the quantified data

§6.3 Fracture angle The angle of the fractures were oriented to the angle in the sandstone. Regarding the angles of the fractures, it can be seen that the relevant data points that are closer to the xy-axis are closer to the z-axis, and that data further away from the xy-axis, and closer to 1.0, are located further away from the z-axis. The reason to analyse the values with respect to the z-axis is that the core is orientated along the z-axis. As can be seen in Figure 41 and Figure 42, the majority of the orientation numbers

58 are in the range of 0.1 – 0.4. This range indicates that the majority of all of the analysed fractures are not close the z-axis.

§6.4 Comparison of the quantitative and qualitative analyses In comparing the qualitative and quantitative results, it was observed that not all fractures could be analyzed quantitatively. In the vertically-layered shale, a larger number of fractures and micro- fractures were counted than when trying to analyze the fractures. In the sandstone sample, three clear large fractures were seen, and the small fracture was not clearly seen. It was often difficult to analyze the fourth fracture, due to the wide range of threshold values. These encountered difficulties will be further explained in section 6.6.

§6.5 Contribution to flow Also important in this research was to determine how these analyzed fractures contributed to the flow. In order to answer this question, it was important to first analyze the apertures of the fractures. The largest apertures were seen in sample Shale_JV. This shale sample would provide good permeability. The smallest apertures were seen the horizontal sample, which was subjected to axial loading in stages.

§6.6 Setbacks Three setbacks were encountered. The first setback involved thresholding the micro-fractures. The second setback concerned thresholding the samples with poor scan resolution. As seen in Figure 45, below, other tools needed to be used to threshold the entire fracture. This may have resulted in inaccurate measurement parameters. The third setback was that It can be challenging to trace back or recognize the fractures identified in the previous scan. A solution to this problem could be to place the cores in the scanner in the same position for each scan or making micro-CT scans while doing loading experiments in the core, if possible.

Figure 45 One of the setbacks experienced in this investigation. Sometimes the thresholding did not take the entire fracture into account. Therefore, using the brush tool (red arrow), the fracture needed to be ‘’brushed’’ for each five slices and then be interpolated. The choice of five slices was made as this meant that the interpolation would not deviate from the fracture.

§6.7 Comparison of fracture patterns on field scale

In this paragraph a comparison is made between the fracture patterns seen in the shale outcrops and the patterns seen in the cores. It is good to remember that the fracture patterns in outcrops are subjected to stresses from various direction. The stresses in the cores are only axial.

Figure 46 figure a shows the observed fracture patterns in the Whitby Mudstone, which are indicated by the red lines. In figure b parallel fractures are seen with orthogonal fractures connecting the larger parallel fractures. The orthogonal fracture is indicated by the red arrow. Source: (Boersma, 2015)

From the figure above shows that a few recognisable fracture patterns from the field are also observed in the core. In Figure 14 sample 49C shows the same pattern of parallel layered fracture. The second comparison between Figure 19 and Figure 46 is the existence of cross fractures, which are indicated by the red arrow. The third comparison between Figure 21 and the outcrop show the existence of shear type fracture, which is indicated by the yellow dashed circle.

§6.8 Comparison of the quantified data

In this paragraph a comparison of the quantified data is made with two scientific papers and with the results of two other thesis. To have a good and consistent comparison between the data of the other two theses is made using the average data.

Figure 47 the cross-plot between the average fracture length and the average aperture. A power fit is applied through the data points.

Figure 48 the cross-plot showing the average fracture length vs the width. A linear fit is applied through the data points.

From Figure 47 and Figure 48 is seen that the fit for the average fracture length and the average fracture aperture is 0.3158. According to literature (Klimczak, Parashar, Schutz, & Reeves, 2010) the aperture- length ratio for confined and unconfined experiments can be compared. The power-law exponents in Klimczak paper range between 0.2191 and 0.6915. According to the analyzed data in this report the ratio of aperture and length is in the range of Klimczak paper, which is 0.3158. A second paper (Olson, 2003) mentions that fractures have driving stresses that vary inversely with the square root of fracture length, producing fracture apertures that scale with length to the power 0.5. From the data set in this report, the scale power is 0.3158, which is significantly lower than the number mentioned by Olson. The reason for a lower scale power number from this data set is much smaller in scale then the results which are mentioned by Olson.

The third comparison of the results is with two other reports (Primarini, 2015) and (Ravestein, 2014) it is seen that ratio for aperture and length is approximately 0.6604 and 0.27, which differs significantly from Primarini report and is close to the one of Ravenstein. The reason for the large difference between 0.3158 and 0.6604, can be explained by two reasons. The first reason is the different workflow of analyzing fractures. Secondly the data in this report contains not only the data of shale fracture analyses, but also sandstone and limestone. The comparison from this data 0.3158 with 0.27 shows that there is no large difference, why this small difference? This small difference can be explained by the fact that in the report of Ravenstein the same sample has been used for analyses, which is shale sample 53B. The majority of the fractures in his report are identified as a

63 whole ‘’family’’ of fractures, which results in les data in contrast to this report , where the fractures in the shale core are analyzed as individual fractures resulting is more measure data on the same scale.

7. Conclusions and recommendations

In this chapter the findings to the research question will be given based on the workflow, qualified, quantified and Abaqus model. Secondly some recommendations based on fracture analyses and modeling of fracture configurations will be provided, which are useful for further investigation.

§7.1 Conclusion

The first conclusion drawn is that the software and the applied workflow is sufficient to qualify and quantify the data. The workflow used in this thesis works best for large fractures in the shale cores.

The second conclusion is drawn from the results obtained is seen in a qualitative matter that there are fracture patterns, which do occur in the field as in the shale cores. Especially cross fractures and shear fractures are observed in the field as well in the cores. Also the larger fractures accommodated by smaller micro fractures is clearly seen on field scale as well in the cores. The best comparison between the field observations and the shale core is seen in Figure 14 for the vertical layered shale core. The second conclusion drawn from qualitative results are that layering of shale cores do have an effect on the way fractures develop, meaning that for horizontally layered shale core the majority of fractures develop on the edges of the cores as seen in Figure 16, Figure 17 , Figure 20 and Figure 21. From the vertically layered shale cores can be concluded that fractures are developed parallel to each other and over the whole core. This result is seen in Figure 16, Figure 19 and Figure 22. The diagonally layered shale cores results in few large fractures that develop at the edges and are accommodated by a lot of micro fractures as seen in Figure 16 and Figure 23. For the sandstone core and the limestone core the only conclusion that can be drawn ,in qualitative matter, is that the fracture patterns in limestone show a large circular fracture at the center of the core accommodated by smaller vertical fractures originated from the edges of the core, see Figure 18. The sandstone sample show one diagonal fracture almost throughout the core. The quantified data is not enough for the sandstone and limestone to conclude if these fracture patterns are typical for limestone and sandstone, because only one core for the limestone and sandstone is analyzed. In terms of flow the best core for connectivity is the one with the most micro fractures connected to the larger fractures. This is seen in the diagonally layered shale core.

The third conclusion is based on the quantified data, conclusion will be drawn on a criteria which is import for the flow of hydrocarbons. For the flow of hydrocarbon the aperture and length of fractures are important. The largest measured apertures and length of fractures are seen in the

65 horizontal layered shales where fractures where created by axial loading until failure is reached. The Figure 38 and Figure 39 show the results. The results of the shale cores where fractures where initiated by axial loading in stages, result in the lowest number in aperture and length for the fractures.

Based on the models made in Abaqus is seen that the fracture configuration does show the expected fracture opening with the highest concentration of stress located at tips of the fractures .

The final conclusion from the results indicate that the occurrence of fracture patterns in 2D as in 3D are dependent on the type of layering. The apertures of the shale sample, which are fractured in stages clearly show much lower apertures in contrast to the samples fractured without stages. Fracture patterns recognized in the shale core can be found in the field. The modelled fracture geometry do indicate the expected stress regime and opening of fracture.

§7.2 Recommendations

Suggestions for further research first a higher resolution when making micro-CT scans to improve scan detail. Secondly model different fracture configurations in Abaqus. Perhaps a 3D model could be built containing a fracture configuration seen in the sandstone or shale cores, which could be used in a simulation to read the stresses. The model used in this report is too simplistic. Run simulations with various loading directions and not only mimic for experimental setup like axial loading. In essence try to simulate field conditions. A third recommendation is to investigate the roughness of the fractures surfaces and other fracture interaction to take into account in to the models.

8. Appendix

§8.1 Flow chart Avizo Fire

Figure 49 This flowchart represents the different operations which were necessary to obtain the data.

Figure 50 The workflow in Avizo. After closing, the ‘’Edit New Label Field‘’ operation was applied.

§8.2 Analyzed data

§8.2.1 shale_JV

Figure 51 The aperture for each fracture

Figure 52 The area of each fracture

Figure 53 The volume of each fracture

Figure 54 The fracture length of each fracture

Figure 55 The width of each fracture

§8.2.2 Sample 36A

Figure 56 The fracture aperture for each fracture.

Figure 57 The area of each fracture.

Figure 58 The volume of each fracture.

Figure 59 The length of each fracture.

Figure 60 The width of each fracture.

Figure 61 The fracture porosity for sample 36A.

§8.2.3 Limestone

Figure 62 The apertures of each fracture in the limestone core.

Figure 63 The area of each fracture in the limestone sample.

Figure 64 The volume of each fracture in the limestone sample.

Figure 65 The length of each fracture in the limestone sample.

Figure 66 The width of each fracture in the limestone sample.

§8.2.4 Sample 53B

Figure 67 The area, volume, length and width of each fracture in the five micro-CT scans.

9. Bibliography

Bobet A, E. H. (1998). Fracture coalescence in rock-type materials under uniaxial and biaxial compression. Elsevier, 863-888.

Boersma, Q. D. (2015). Role of regional stress and pre-existing fractures on local stress and network development . Delft.

Bonneau, F., Caumon, G., Renard, P., & Sausse, J. (2012). Stochastic sequential simulation of genetic- like discrete fracture networks. 1-18.

Bonnet, E., Bour, O., Odling, N., Davy, P., Main, I., Cowie, P., & Berkowitz, B. (2001). SCALING OF FRACTURE SYSTEMS IN GEOLOGICAL MEDIA. American geophysical union, 347-383.

Cao, P., Liu, T., Pu, C., & Lin, H. (2015). Crack propagation and coalescence of brittle rock-like specimens with pre-excisting cracks in compression. elsevir, 113-121.

Correia, M. G., Maschio, C., & Schiozer, D. ,. (2014). Upscaling approach for meso-scale heterogeneities in natural fractured carbonate reservoirs. Elsevier, 90-101.

Gabor F, G. B. (2007). An imperative workflow for modeling of naturally fractured reservoirs on different scales. SPE Europe/EAGE Annual Conference and Exhibition . London: SPE International.

Hicks, N. (2015). Fiber Orientation in Ultra-High-Performance Concrete (UHPC) Shear Connections in . Ohio.

Jung, A., Darryl, H., Fenwick, & Caers, F. (2013). Training image-based scenario modeling of fractures reservoirs for flow uncertainty quantification. Comput Geosci, 1015-1017.

Klimczak, C., Parashar, R., Schutz, R., & Reeves, D. (2010). Cubic law with aperture-length correlation: implications for network scale ﬂuid ﬂow. Hydrogeology Journal , 851-862.

Lei, Q., Latham, J.-P., Tsang, C.-F., Xiang, J., & and Lang, P. (2015). A new approach to upscaling fracture network models while perserving geostatistical and geomechannical characteristics. American geophysical union.

Olson, J. (2003, September 5). Sublinear scaling of fracture aperture versus length: An exception or the rule? Journal of Geophysical Research .

Ouenes, A., & Hartley, L. J. (2000). Integrated Fractured reservoir modeling using both discrete and continuum approaches. 2000 SPE Annual Technical Conference and Exhibition. Dallas, Texas: SPE.

Primarini, M. I. (2015). Fracture Mode Analysis, Geomechanics, Petrophysics and Fracture Characterization. A n Experimental Investigation on Whitby Shales and Various Other Rock Types . Delft.

Ravestein, T. (2014). Fraccability determination of a Posidonia Shale Formation analogue through geomechanical experiments and micro-CT fracture propagation analysis. Delft.

Renard, F., Bernard, D., Desrues, J., & Ougier-Simonin, A. (2009). 3D image of fracture propagation using synchroton X-ray microtomography. Elsevier, 285-291.

Shen, B., Stephansson, O., Einstein, H. ,., & Ghahreman, B. (April 10 ,1995). Coalescence of fractures under shear stresses in experiments. Journal of geophysical research, 5975-5990.

Shipton, Z., & Cowie, P. (2001). Damage zone and slip-surface evolution over microm to km scales in high-porosity Navajo sandstone, Utah. Journal of structural geology, 1825-1824.

Tentler, T., & Amcoff, O. (2010). Interaction of microfractures: the mechanics of network building. Elsevier, 215-230.

Verheij, J. (2015). Seismic attenuation analyses of fracturing in reservoir rocks. Delft.

Vermilye, J., & Scholz, C. (1995). Relation between vein lenght and aperture. Journal of structural geology, 423-434.

Voorn, M., Exner, U., Barnhoorn, A., Baud, P., & Reuschle, T. (2015). Porosity, Permeability and 3D fracture network characterisation of dolomite reservoir rock samples. Elesevier, 270-285.

Warren, J., & Root, P. (1962). The behavior of naturally fractures reservoirs. SPE, 245-255.

Willemse, E., & Pollard, D. ,. (February 10, 1998). On the orientation and patterns of wing cracks and solution surfaces at the tips of a sliding flaw of fualt. Journal of geophysical research, 2427- 2438.