effects of fractal surface roughness and lithology on single and multiphase flow in a single...

$: Effects of fractal surface roughness and lithology on single and multiphase flow in a single fracture: An experimental investigation$
International Journal of Multiphase Flow 68 (2015) 40–58

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International Journal of Multiphase Flow

journal homepage: www.elsevier .com/locate / i jmulflow

Effects of fractal surface roughness and lithology on single andmultiphase flow in a single fracture: An experimental investigation

http://dx.doi.org/10.1016/j.ijmultiphaseflow.2014.10.0040301-9322/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author at: University of Alberta, Department of Civil and Env.Eng., School of Petroleum Engineering, 3-112 Markin CNRL-NREF, Edmonton, ABT6G 2W2, Canada.

E-mail address: [email protected] (T. Babadagli).

Tayfun Babadagli a,⇑, Xiaojuan Ren b, Kayhan Develi c

a University of Alberta, Dept. of Civil and Environmental Engineering School of Petroleum Engineering, Edmonton, AB, Canadab Xi’an Shiyou University, Xi’an, Chinac Istanbul Technical University, Department of Petroleum and Natural Gas Engineering, Maslak, Istanbul, Turkey

a r t i c l e i n f o

Article history:Received 7 March 2014Received in revised form 4 October 2014Accepted 8 October 2014Available online 17 October 2014

Keywords:Fracture roughnessFractal dimensionSingle phase flowHydraulic conductivityMultiphase flow in single fracturesUnsteady state displacement in fractures

a b s t r a c t

This paper presents qualitative and quantitative analysis of single and multiphase flow in a single fracturebased on experimental results and demonstrates relationships between the roughness and fluidmovement and distribution.

Experiments were conducted on seven perfectly-matching and tightly-closed rough model fracturesreproduced from the single fractures of lithologically different seven rock blocks that were jointedartificially through laboratory indirect tensile tests. Transparent upper and opaque lower walls of thesemodels facilitated the visualization of the flow experiments. Rough surfaces of the model fractures werefirst digitized. Then, using the gathered data in variogram analysis, surface roughness was quantified byfractal dimension. Another roughness quantification parameter was also handled as the ratio betweentotal fracture surface area and planar surface area. Experimental measurements of flow were quantita-tively correlated to surface roughness under different normal loading (aperture) conditions. Also,constant rate immiscible displacement experiments were performed to assess the roughness effectrepresented by seven different lithologies and wettability effect controlled by the material used inmanufacturing the fracture samples on the residual saturation development.

� 2014 Elsevier Ltd. All rights reserved.

Introduction

Flow in single fractures has been of interest over the last fivedecades in many engineering disciplines for different kinds ofapplications including oil and gas production, enhanced oil recov-ery, underground disposal of nuclear waste, groundwater contam-ination, and geothermal energy production. More recently, anincreasing number of hydraulic fracturing applications for oil andgas production from tight reservoirs also entailed research tounderstand the flow in hydraulically developed fractures. Model-ling single and multiphase flow in this type of application requirescorrect description of the hydraulic characteristics of fractures foraccurate performance estimation. Representation of the roughnessof fractures and its effect on these hydraulic properties, such aspermeability and relative permeability, as well as their changesunder normal stress are essential parts of modelling studies.

Laminar flow in porous media is described by Darcy’s law. Yet,fluid flow in a single rock fracture is traditionally approximated bythe cubic law, which is derived from the analogy of laminar flowbetween two perfectly smooth parallel plates separated from eachother by a constant distance.

Q ¼ �DPLl

wb3

12ð1Þ

where DP is the pressure drop in the flow direction, L is the fracturelength over which the pressure drop takes place, w is the fracturewidth perpendicular to the flow direction, and l is the fluid viscos-ity (Zimmerman and Bodvarsson, 1996; Chen et al., 2000;Watanabe et al., 2005). According to this law, volumetric flow rate,Q, is proportional to the cube of the separation distance (aperture),b.

With the parallel plate assumption, the conductivity of a singlefracture is typically based on the cubic law and relative permeabil-ities are defined as straight lines with no irreducible saturations ofboth phases. Attempts were made as to the inclusion of the effectof fracture surface roughness on flow dynamics. For example,Witherspoon et al. (1980) emphasized that ideal cubic law wasderived for modelling flow through planar surfaces of an open par-

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T. Babadagli et al. / International Journal of Multiphase Flow 68 (2015) 40–58 41

allel plate which are not in contact at any point. The validity of thislaw for closed fractures with contacting rough surfaces under nor-mal loading was investigated by Witherspoon et al. (1980) per-forming flow tests on artificially induced tension fractures. Afriction factor ‘‘f’’ was introduced and included the ideal cubiclaw in order to take the roughness effect into consideration. Theyreported that f P 1 in the case of roughness and it varied from1.04 to 1.65 in their study. This friction factor was found very suc-cessful to account for the effects of deviations from the ideal cubiclaw concept due to roughness. Interestingly, this range of ‘‘f’’ isreminiscent of the surface fractal dimension that was measuredin the past (Develi and Babadagli, 1998) and used in the presentstudy.

Further studies were based on stochastic description of theroughness and modelling flow in such fracture systems by griddingthem with assigned fracture apertures (Neuzil and Tracy, 1981;Brown and Scholz, 1985a; Brown, 1987a,b; Tsang, 1984; Tsangand Tsang, 1987; Tsang et al., 1988; Moreno et al., 1988).

Later, it was observed that the fracture surfaces exhibit fractalnature (Mandelbrot et al., 1984; Pande et al., 1987) and detailedanalyses on the fractal nature of the fracture surfaces were per-formed (Dubuc et al., 1989; Miller et al., 1990; Huang et al.,1992; Klinkenberg, 1994; Schmittbuhl et al., 1995; Den Outeret al., 1995; Kwasiniewski and Wang, 1997; Xie et al., 1997;Develi and Babadagli, 1998). An extensive review of fracturecharacterization and their transport properties can be found inBerkowitz (2002).

A group of studies focused on experimental analysis of single(Murata and Saito, 2003; Nowamooz et al., 2009) and – immiscible– multiphase flow (Pruess and Tsang, 1990; Rossen and Kumar,1992; Wong et al., 1996; Amundsen et al., 1999) on rough fracturesurfaces. Two-phase relative permeabilities were measured experi-mentally on smooth fracture surfaces (Romm, 1966; Fourar et al.,1993; Fourar and Bories, 1995; Persoff and Pruess, 1995; Pan et al.,1998; Chen and Horne, 2004; Shad et al., 2010; Shad and Gates,2010). These studies used an analogy to pipe flow and definedtwo-phase flow patterns in two smooth parallel plates (Fouraret al., 1993; Fourar and Bories, 1995; Fourar and Lenormand, 2001).

As seen, a vast amount of experiments for multiphase flow insingle fractures were performed to identify the flow patterns.Channel flow theory in single fractures was investigated primarilyby using theoretical models (Tsang and Tsang, 1987; Shapiro andNicholas, 1989; Kobayashi and Yamashita, 1990; Unger andMase, 1993; Glover et al., 1998). Channelling is controlled by thetortuosity and to accurately define the relationship between thedegree of roughness and channelling behaviour, experimentalstudies are needed. However, most of the experimental studiesare based on parallel plate approximation as mentioned aboveand limited experimental studies exist on immiscible (Radillaet al., 2013) and miscible flooding in rough fractures (Auradouet al., 2001).

Channelling could also be the main reason for the creation ofresidual saturation of the displaced phase, which is a criticalparameter on the relative permeabilities. Auradou et al. (2003)experimentally and numerically studied the effect of roughnesson the phase trapping on a single fracture. Chen and Horne(2006) and Wong et al. (2008) used artificial and uniform roughfracture surfaces and analyzed the effect of the roughness on flowstructures experimentally. More recently, Radilla et al. (2013) usedtransparent replicas of real rough fractures (sandstone and granite)to measure single and multiphase flow characteristics includingrelative permeabilities.

The effect of roughness on the single and multiphase flow is stilla critical question and this paper focuses on this problem using anexperimental approach. There are several issues as to the singlephase, of which the deviation from the cubic law is the most

critical one. Despite remarkable efforts on numerical and analyticalstudies on this (Piggott and Elsworth, 1990; Oron and Berkowitz,1998; Yamatomi et al., 2001; Inoue and Sugita, 2003; Brush andThomson, 2003; Zimmerman et al., 2004), experimental investiga-tions are limited due to the difficulties in preparation and quanti-tative characterization of fracture roughness (Plouraboué et al.,2000; Murata and Saito, 2003).

As widely accepted, the nature of flow of two immisciblephases in a single fracture is not the same as the flow in porousmedia. Capillary forces are not (or cannot be) as strong in singlefractures, and two phase flow (or displacement) can be describedonly by channel flow and is also the reason behind phase trap-ping (residual saturation of the displaced phase). This is especiallycritical in the case of liquid–gas flow due to a high mobility ratio.If this is the case then constant or variable aperture structure dueto roughness will control the whole process during single andmultiphase flow in single fractures. This results in deviation fromcubic law and straight line relative permeabilities for single andmultiphase flow, respectively. Different researchers investigatedthis effect for aperture change (Kostakis et al., 1996; Yeo et al.,1996; van Dam and de Pater, 1999; Chen et al., 2000; Isakovet al., 2001).

In addition to this type of experimental and computationalefforts on the hydraulic behaviour of single fractures, numericaland theoretical studies for modelling fluid flow through 3-D frac-tured porous media were also reported. They include the attemptson modelling two-phase flow using a 3-D discrete fracture descrip-tion (Bogdanov et al., 2003), characterization of the permeabilitybehaviour for isotropic and anisotropic fracture networks(Mourzenko et al., 2011), and an investigation of 3-D steady-stateand 2-D flow through porous medium with intersecting fractures(Vu et al., 2013, 2014, respectively). Even modelling single andmultiphase in fracture networks requires the inclusion of rough-ness and its effects on flow characteristics of a single fracture.

Statement of the problem and solution methodology

Several problems have been identified as remaining questionsbased on the above given literature review:

� Aperture changes (due to fracture opening and closure) andits effect on single (conductivity) and multiphase flow (rel-ative permeability).

� Development of residual saturation of the displaced phaseduring two phase flow in single fractures of different rocktypes.

� Quantification of surface roughness and correlating it to theabove listed single and multiphase flow characteristics.

Smooth parallel plates’ approximation yields no residual satura-tion but different flow patterns for given viscosity ratio of twoimmiscible fluids. However, roughness and aperture change causeschannelling influencing the efficiency of displacement. Thisrequires detailed experimental studies, preferentially visual, onoriginal fracture surfaces of rocks showing different roughnesspatterns.

Many works have been done regarding various aspects of chan-nelling phenomena through fractures caused by roughness. Exper-imental materials representing the single fractures were handledas either natural and synthetically created fractures or replicamodels of both types (Yeo et al., 1998; Chen et al., 2000;Auradou et al., 2001; Zimmerman et al., 2004; Watanabe et al.,2005; Nowamooz et al., 2009; Radilla et al., 2013). Parallel rockplates roughened artificially (Faoro et al., 2009; Schmittbuhlet al., 2008) or idealized fracture models with simulated roughness

42 T. Babadagli et al. / International Journal of Multiphase Flow 68 (2015) 40–58

(Chen et al., 2009) were also used in the experiments. The impor-tance of working with realistic fractures representing complicatedroughness geometry rather than the idealized ones was empha-sized by Qian et al. (2005). These efforts were made as to clarifica-tion of many different aspects of flow through single fractures.However, studies on relating roughness characteristics to hydraulicbehaviour are limited (Lee et al., 2003).

The lack of lithological diversity of fracture samples alsoappears as another missed point in the past efforts. In fact, differ-ent lithologies will reflect different nature of roughness for natu-rally (Develi and Babadagli, 1998) and synthetic (Babadagli andDeveli, 2003) fractures, and thereby hydraulic characteristics. Weare aware of limited number of studies using original fracture rep-licas for visualization purpose (Nowamooz et al., 2009; Radillaet al., 2013; Auradou et al., 2001). Not only quantitative but alsoqualitative (visual) measurements are further needed to describethe physics of this process, especially for a wide range of rock typesfrom different lithologies. Based on the above described problem,we prepared original fracture replicas with a wide range of litho-logical diversity to have a wider spectrum of complex surfacegeometry. As such, seven model fractures reproduced from litho-logical seven different rock types were used as the media for singleand multiphase flow. The surface characteristics of fractures werequantified using different techniques and the hydraulic behaviourof single fractures were related to these characteristics. This type ofresearch will shed light on further development of relative perme-abilities for oil–water, oil–gas, and water–gas systems.

Note that the term lithology was used to emphasize that differ-ent rock samples (limestone, marble, and granite) of different types(two marbles and four limestones with different lithological, min-eralogical, and petrophysical characteristics). However, the word‘‘lithology’’ implies mineralogy and wettability, which are not cap-tured by the replica model surfaces. What is represented on thefracture surfaces is the ‘‘texture’’ that is developed based on themineralogical and petrophysical properties of the rock samples.Hence, the word ‘‘lithology’’ refers to ‘‘texture’’ throughout the text.

Experimental procedure

Material and set-up

Flow experiments were conducted on the model fracturesreproduced from artificially-fractured seven rough rock fracturesof a wide spread of lithological diversity. According to the resultsof thin section inspections under polarized microscope, very briefpetrographic descriptions and average grain sizes of the rock mate-rials are presented in Table 1. The reason for the selection of lith-ologically different rock samples was to be able to obtain a widespectrum of fracture roughness types.

The cubical blocks of seven rock samples in the dimensions of20 � 20 � 20 cm3 were subjected to indirect tensile stresses by

Table 1Model fractures used in the experiments and their roughness characteristics (fractal dime

Model no Rock type

Fr1 fossilized limestoneFr2 Semi-recrystallized micritic pink limestoneFr3 Micro-fossiliferous pisolitic beige limestoneFr4 Coarse grained white marbleFr4s* Coarse grained white marbleFr5 Amphibole graniteFr6 Micritic cemented fossilized beige limestoneFr7 Medium-coarse grained white marbleFlat model –

Dva: Fractal dimension obtained by variogram analysis.At/Ap: Ratio between total fracture surface area (At) and planar surface area (Ap).

* ‘‘s’’ refers to solid, i.e., both sides of fractures are made of solid polyurethane plastic

means of a hydraulic press similar to Brazilian indirect tensile test.Once the tensile failure occurred, each block was fractured andalmost-equally separated into two halves along a rough fractureplane (Fig. 1a). Next, one halve of the fractured blocks was repli-cated to the opaque moulds using white silicone mould-makingrubber. Then, the other halve of the fractures was replicated tocrystal clear transparent plastics by casting polyurethane transpar-ent resin on the silicone rubber moulds under vacuum conditions.Thus, original rock fractures were modelled as white opaque sili-cone rubber lower parts and crystal clear transparent polyurethaneupper parts. Considering the possibility of small deformations ofthe casted resin during its polymerization stage, which could causeunmated adjacent walls of model fractures, the polyurethaneupper parts were remoulded with silicone rubber, as was previ-ously recommended by Auradou et al. (2001). By means of this pro-duction technique, model fractures with perfectly matchingadjacent surfaces, which are the mirror images of each other, wereobtained (Fig. 1b). Fractures with mirror image rough surfaceswere also used in the works by Wang et al. (1988) and Auradouet al. (2001). Three different samples of model fractures are shownin Fig. 2a. A detailed explanation of the model preparation can befound in Develi and Babadagli (submitted for publication).

Flow tests for different investigation purposes have widely beenconducted in literature on various kinds of transparent model frac-tures. The representativeness of the models for the real rock sam-ples can be questioned but the major goal of this paper is toprovide visual evidence (supported by numerical values) and thisentails the use of transparent models. The reason for the usage oftransparent models rather than the originals has usually been theintension of flow visualization for better understanding the physicsand hydromechanics of the process. As our models shown in Figs. 1and 2 are the exact replicas of the fracture surfaces, they presentthe physics of the flow caused by the roughness at the field scale.The works by Yeo et al. (1998), Auradou et al. (2001), Murata et al.(2002) and Zimmerman et al. (2004) provide similar – visual –models to study different aspects of fracture flow.

Note that the upper part of the model is solid/stiff material andthere is no porosity at all. The bottom part is rubber and the poros-ity is minimally low and the material is not permeable. Even theimages shown in Fig. 3b indicate that any fluid just spread onthe materials and there is not fluid take-up. Hence, the injected flu-ids never penetrate into the ‘‘matrix’’ part of fracture model andinstead, flow in the fracture only as the silicone rubber and thetransparent polyurethane resin used for the model productionare purely impermeable materials when cured after casting. Thiswas also observed by earlier studies. The model materials usedby Murata et al. (2002) and Murata and Saito (2003) are very sim-ilar to what we used in our study, i.e., the lower and upper walls ofthe original rough fractures were made using silicone rubber andtransparent acrylic resin, respectively. In fact, Murata et al.(2002) found silicone rubber as helpful to seal the fracture at both

nsion ‘‘Dva’’ and the ratio ‘‘At/Ap’’).

Dva At/Ap Experiment type

1.373 1.145 Single and multiphase1.263 1.079 Single and multiphase1.303 1.061 Single and multiphase1.39 1.098 Single and multiphase1.39 1.098 Multiphase1.299 1.083 Single and multiphase1.290 1.115 Single and multiphase1.326 1.072 Single and multiphase1 – Multiphase

.

Fig. 1. (a) Fractured rock samples and rough fracture surfaces. Fracture sizes are 20 � 20 cm, (b) transparent model fractures casted from the original rock fracture surfaces,(c) 3-D view of the scanned surface of model fracture Fr1.


sides. Similarly, the complementary parts of the models used byAuradou et al. (2001) were silicone rubber and transparent epoxy.

As discussed by Wang et al. (1988), perfectly matching fracturescomposed of mirror image rough surfaces would theoretically notpresent any aperture inside if they are in the closed form (e.g.closed joints in nature). Aperture will theoretically be zero as theadjacent walls will be in contact overall, the fracture and the heightdifference of the contacting walls from a reference plane will bezero at any point throughout the fracture. Yet, they will have con-stant aperture structure if they are opened due to the divergentdisplacement of the adjacent fracture walls along the normal vec-tor of the average fracture plane (e.g. open joints in nature).

Model fractures used in this study exemplify perfectly match-ing, tightly closed rough fractures with mirror image adjacent sur-faces, which can be considered as common case in the deep earthcrust. Note that the term ‘‘fracture’’ refers to ‘‘closed joint with per-fectly matching adjacent walls’’. It is important to emphasize thatno relative displacement was applied to the fracture walls thatmight generate sheared fractures. Thus, any void space or aperturestructure does not occur within our model fractures. In accordancewith this, no visible gaps inside the models were recognized inpractice, at least at the macroscopic scale. In the case of injectionof a fluid into our model fractures, a mechanical aperture structurewas induced by injection pressure, and flow is expected to occurpredominantly through this forced-mechanical aperture. As manyof the fractures in nature are found to be almost closed, the studyof flow through tightly closed rough fractures was indicated byGenabeek and Rothman (1999) as an important issue in solvingthe transport in channel networks.

The main parts of the experimental set-up are composed of aninjection stand, a micro annular gear pump (model mzr� 7205), adigital pressure gauge, an electronic pump control unit and soft-ware, a high resolution camera, and fluorescent black light source(Fig. 3a). The maximum injection rate the pump is able to supply is4.667E�06 m3/s (280 ml/min). Resolution of the digital pressuregauge is 68.95 Pa (0.01 psi).

Quantification of fracture surface roughness

To measure the fractal dimension of each model, we first mappedthe rough surfaces of the polyurethane upper parts of the modelfractures using the fully computer-controlled surface scanningdevice introduced by Develi (2006); Develi et al. (2001). A190 � 190 mm2 square portion, selected in the middle of each sur-face by taking its geometrical centre as a reference point, wasscanned and elevations (z) were automatically digitized with a sam-pling interval of 1 mm in the horizontal (x and y) axes. The measure-ment resolution in vertical (z) axis was 1/10 mm. Following thisprocedure, a 2D data set consisting of 190 � 190 data points wasautomatically obtained for each surface and simultaneously loggedinto a computer. A 3D view for one of the digitized surfaces (e.g. formodel fracture Fr1) plotted using 2D data set is displayed in Fig. 1c.

Once the digitization was completed, the fractal dimensionvalue (Dva) of each surface was calculated using the 2D data setsthrough the variogram analysis. A summary of the mathematicaldescription of this method can be found in Develi and Babadagli(1998) and Babadagli and Develi (2001). In the calculations, 1Dprofile data extracted from the 2D data sets were used. In a 2D data

Fig. 2. (a) Model fractures manufactured after moulding and casting the fracture surfaces seen in Fig. 1. Two sides were sealed and fluid was injected from one side (inlet) inthe direction shown above, (b) variogram fractal dimensions (Dva) of the profiles in the example of the three model fractures, namely Fr1, Fr2 and Fr3.


set, there are 190 lines and 190 columns through x andy-directions, respectively. Thus, the method was applied to all190 profiles in y-direction. This direction is also parallel to theinjection direction in the flow tests. The fractal dimension valueof each profile consisting of 190 data points was computed. Allthe values calculated for each of the 190 profiles ranged between1 and 2, as theoretically expected. The arithmetic mean of the190 fractal dimension values for each model fracture surface wastaken as the surface fractal dimension. Variation of the calculatedfractal dimensions with profile number is exemplified in Fig. 2bfor the model fractures Fr1, Fr2 and Fr3 presented in Fig. 2a.

In addition to the fractal modelling (Dva), another surfaceroughness parameter was also calculated as the ratio between totalfracture surface area (At) and planar surface area (Ap): At/Ap. Themeasured values are listed in Table 1 for seven different models.

Single phase experiments

Before the experiments, the two parallel sides of the squaremodels were sealed by using impermeable silicone leaving theother two parallel sides unsealed (open) for the inlet and outlet

of flow. These two parallel sides were perpendicular to the loadingdirection in the indirect tensile tests. After curing the sealing mate-rial, one centimetre portion of the 20 cm long model along one ofthe unsealed sides was inserted into the reservoir and the gapbetween the model and the surrounding reservoir was sealed usingsilicone (Fig. 3a). These treatments were repeated before the test ofeach model fracture and facilitated the models to be ready for thetests. All experiments were run on the horizontally positionedsamples and no effect of gravity is involved.

To obtain a uniform 2D displacement, the injected water wasfirst filled into the reservoir and then distributed through the drymodel fracture at a constant rate by a computer controlled pump.The flow rates were changed between 1.667E�07 and4.667E�06 m3/s with 1.667E�07 m3/s increments. Pressure mea-surements were taken through a digital pressure gauge attachedto the reservoir. We performed the measurements at a constantrate and continued until the pressure is stabilized. The optimaloperation capacities for the pump and the pressure gauge used inthis study were taken into consideration in the selection of theflow rate range. Qian et al. (2005) applied a wide range of flowrates to observe the transitions between different flow regimes.

Fig. 3a. Experimental set-up used in single and multiphase flow experiments.


They reported that it was not an easy task performing a laboratoryflow test in a fracture at especially low hydraulic gradient and flowrate values due to the requirement of more precise sensors for themeasurements of very small values of these parameters. However,we applied a very wide range of the flow rates, which covers thepossible velocity spectrum at the field scale considering typicalflow/injection rates in the field and fracture apertures.

This process was repeated for each model fracture under fourdifferent normal load (N) conditions applied perpendicularly ontop of the model as well as non-loading condition. We preferredto work with low level normal loads to prevent the silicone rubberlower parts of our model fractures from being deformed. Circularsolid masses (discs) were used for normal loading. These massesactually belong to the normal loading unit of a soil type directshear box machine which is one of the standard test devices com-monly available in many soil mechanics laboratories. The pre-cal-ibrated weights of the masses were N = 2, 4, 8 and 16 kg. As oneside of a square model fracture was 20 cm in length, the corre-sponding normal stress values were rN = 490.3, 980.7, 1961.4 and3923 Pa, respectively. As a result, the criterion in the selection ofthe quantities for the normal loads is not associated with fractureflow problems at specific depths. However, the magnitudes of thenormal loads could be selected by knowing the existing overbur-den pressure as the spectrum of the normal load is rather largeand within the range of possible overburden pressures possiblyencountered in the fields. The reason for normal loading was toobserve its effect on the transport properties of single fracturespresenting roughness. Additionally, experiments were performedin two different – reverse – directions, namely NS (from north tosouth) and SN (from south to north) injection directions. The rea-son for the opposite injection directions on the same model frac-ture was to investigate the effect of anisotropic feature of surfaceroughness on transport properties.

For the model fracture Fr1, the plot of injection pressure (P)against injection rate (Q) under non-loading and four different nor-mal loading conditions for both NS and SN injection directions isgiven in Fig. 4a. In the beginning, for non-loading condition, a rapidincrease is followed in pressure as injection rate increases and therecognized trends of the curves exhibits linear characteristic. Yet,this relationship shows a change after a short while and non-linearbehaviour takes place at an inflection point for the rest due to thegradually bending character of the curves towards x (injectionrate)-axis. The same behaviour was also observed for different nor-mal loading conditions as well as for the opposite injection (NS andSN) directions. It is obvious from the figure that increasing normalload displaces the curves upward. Meanwhile, the slope of the firstlinear part and the local slopes of the non-linear part usually get

steeper, which means the conductivity of the fracture decreasessince the fracture is tighter when more loads are applied. The over-all nature of the P–Q curve described for the model Fr1 was foundto be valid for the other model fractures, too.

By using the data from the boreholes in jointed media, Louisand Maini (1970) drew the characteristic non-linear curves of in-situ water tests in flow rate (Q) versus pressure (P) domain for bothnormal and deformable rocks. For a normal rock, they divided thecurve into four different portions and explained the observed flowbehaviour for each portion:

Zone 1: Laminar flow; at small values of pressure, the curvebehaves as an increasing straight line. For this short lineartrend, flow is laminar and Darcy’s law is valid.Zone 2: Turbulence effect; a deviation from the initial lineartrend occurs just after an inflection point and the curve tendsgradually bending toward the pressure axis for a short durationwhere the turbulence effects are noticed.Zone 3: Turbulence offset by fissure expansion; with a secondinflection point, the curve starts bending upward again wherethe turbulence effect is compensated by fracture opening dueto higher pressure values.Zone 4: Predominance of fissure expansion; the relationshipkeeps gradually curving upward and the influence of the jointdeformation become predominant.

Similar behaviour from the results of in-situ injection tests on afracture were later reported by Rutqvist et al. (1997) and Rutqvistand Stephansson (2003).

It is an important to note that the effects labelled as (Zone 2)and (Zone 3) disappear for deformable rocks. The pressure (P) ver-sus injection rate (Q) curves we obtained (Fig. 4a) are generallyconsistent with what Louis and Maini (1970) observed from in-situwater tests for the fractures of deformable rocks (Fig. 4b). Note thatas the second portion of the curve (ii: turbulence effect), which isintroduced as characteristic for normal rocks, cannot be seen inFig. 4a, our data follows the Zone (3) and Zone (4) portions directlyafter the initial period (Zone 1), which means fracture openingstarts and becomes predominant. A detailed discussion on the flowregimes and their dependency on the roughness and rock types canbe found in Develi and Babadagli (submitted for publication).

Since the silicone sealing material on both parallel sides of ourmodel fractures is able to show expandable behaviour under ten-sile stresses, it allows small displacements of the rigid polyure-thane upper parts of the models upward along the normal vectorof the average fracture plane due to relatively high fluid pressurewithin the model. Moreover, the lower parts of the models may

I II

III IV

=54 =46

=38 =34

I II

III IV

=95 =91

=88 =83

I II

III IV

=27 =24

=21 =21

(1) Water drop on the transparent polyurethane (capturing rate is one image per second)

(2) Water drop on the silicone rubber (capturing rate is one image per second)

(3) Kerosene drop on the silicone rubber (capturing rate is one image per second)

Fig. 3b. Contact angles indicating the wettability of the materials used in the experiments. The kerosene droplet spread on the polyurethane plastic so quickly that imagescould not be taken. This spreading indicates strong oil wetness of the material.


also exhibit very small deformations under relatively high fluidpressure since they are silicone rubber and softer material thanrigid transparent upper parts. The conformity between the resultsof our laboratory flow tests and Louis and Maini (1970) in-situ flowtests for deformable rocks could be attributed to these materialfeatures, which allow our model fractures to behave like the verti-cally-expanding fractures in nature.

The value of the injection rate corresponding to the inflectionpoint after which the initial linearity ends in the curves in Fig. 4ais Q = 5.0E�07 [m3/s]. According to the following equation bySchmittbuhl et al. (2008):

Re ¼ ðq � QÞ=ðL � lÞ ð2Þ

where q is the density of fluid and l is the dynamic viscosity, Q isthe flow rate and L is the lateral extent of fracture, the Reynoldsnumbers corresponding to the injection rates in Fig. 4a rangebetween 0.93 and 26.11. The lateral extent is 0.2 m for our modelfractures. The density and the dynamic viscosity of water in theabove equation were taken at 25 �C as 997.13 kg m�3 and0.000891 kg m�1 s�1, respectively. The value of the Reynolds num-ber for the injection rate of Q = 5.0E�07 [m3/s] is Re = 2.80, accord-ing to the calculations. This value of the Reynolds number (thus the

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65.

0E-0

65.

5E-0

6

Injection Rate, Q [m3/s]

Pres

sure

, P [P

a]

N=0 (NS)

N=2 kg (NS)

N=4 kg (NS)

N=8 kg (NS)

N=16 kg (NS)

N=0 (SN)

N=2 kg (SN)

N=4 kg (SN)

N=8 kg (SN)

N=16 kg (SN)

Model : Fr1

Fig. 4a. Pressure (P)–injection rate (Q) curves of the model fracture Fr1 at differentnormal loads for NS and SN injection directions (NS: injection from north to south,SN: injection from south to north labelled as negative (�) sign in x axis).

Fig. 4b. Characteristic pressure (P) versus injection rate (Q) curves of in-situ watertests (reproduced after Louis and Maini, 1970).

1 Lighter areas (blue color) is water (wetted areas). Darker areas (dark bluecorrespond to dry (unwetted by injected water due to closure) zones also indicatingfracture closure.


corresponding injection rate) where the inflection point occurs andthe non-linearity induced by fracture opening starts is interestinglycharacteristic for all the curves in Fig. 4a. One may infer from thisobservation that the development of the non-linear behaviour dueto fracture opening is independent of fracture – roughness – type.Yet, Develi and Babadagli (submitted for publication) observedthe Reynolds number at which the initial linearity ends asRe = 3.73 for a pair of ‘‘parallel plate’’ model fracture produced fromthe same material as those of the rough model fractures. By takingthe characteristic curve model for deformable rocks (Louis andMaini, 1970) into consideration, it is understood that compensationof turbulence effect by fracture opening starts earlier for rough frac-tures than it does for the parallel plate model. Based on these obser-vations, one may eventually state that the turbulence developsearlier for rough surfaces compared to smooth ones.

Multiphase flow experiments

Four types of displacement experiments were conducted on thefracture samples listed in Table 1: (1) Water displacing gas, (2) gasdisplacing water, (3) oil displacing water, and (4) water displacingoil. As gas, air was used. Oil phase used was kerosene (1.57 cp). Theinterfacial tension between oil and water and gas and water used is40 and 70 dynes/cm, respectively. Water was dyed with bluecolour to distinguish the phases. Injection rate was constant at20 cc/min. Injection was continued after breakthrough for a longperiod of time until no change in the saturation distribution wasobserved. The final images were taken at the stage to estimatethe residual displaced phase saturation. All experiments wererun horizontally situated samples and no effect of gravity wasinvolved.

Also, the wettability of the rubber (bottom) and polyurethane(upper plastic) parts were measured. Fig. 3b shows the water andkerosene droplets on both materials (silicone rubber and polyure-thane plastic and corresponding contact angles. Each image wastaken 1 s apart. As seen, the materials can be described as ‘‘moreoil-wet’’. In fact, the kerosene droplet spread on the polyurethaneplastic so quickly that images could not be even obtained. Thisspreading indicates strong oil wetness of the material.

Results and analysis

Single phase

Qualitative analysisFor qualitative analyses, single phase water injection experi-

ments were conducted at a constant injection rate ofQ = 1.667E�07 m3/s under non-loading condition adding a clearblue reactor tracer to water. This tracer (or dye) is distinguishedby its blue colour1 under fluorescent black light in a dark roomand helped to trace the transport of water. The images of the finalflow fields for zero normal load case taken at equilibrium conditions(the injection pressure is stabilized at constant injection rate) aregiven in Fig. 5a and b. For each fracture sample, these visualizationtests were performed in two opposite but parallel (NS and SN) direc-tions. Injection directions were from right to left in all images givenin Fig. 5a (for NS direction) and Fig. 5b (for SN direction).

In these images, the local zones distinguished by their dark bluecolour represent the dry areas while the wet areas invaded by thewater appear much lighter blue. It is observed that even at zeronormal load conditions, applied injection pressure may not openmodel fractures entirely and model fractures represent a degreeof local dry areas that do not involve any flow. In a visual inspec-tion, it is obviously recognized that differences exist in location,spatial distribution, and shape of these fragmented dry (unwetteddue to closure) areas for the opposite injection direction experi-ments of the same model fracture. For example, for the case ofmodel fracture Fr1; different injection direction experimentsyielded different behaviour qualitatively (see the images of Fr1for NS and Fr1 for SN in Fig. 5a and b, respectively). Interestingly,this sample shows one of the highest fractal dimensions by thevariogram analysis (Dva) and the highest value of the ratio At/Ap.

It should be emphasized at this point that the fracture is filledwith air in the beginning. Then, water is injected at high rates(and pressures) to displace this air and fill the system with 100%water. The visual inspection during the experiments did not revealany existence of air bubble in the lighter (wetted areas). But, the

)

(a) NS injection direction experiments

(b) SN injection direction experiments

(c)

Flow Direc�on

Flow Direc�on

Fig. 5. Visualization of single phase (water) flow tests in the (a) NS and (b) opposite (SN) injection directions. Darker areas correspond to dry (unwetted by injected water dueto closure) zones also indicating fracture closure, (c) comparison of the unwetted area (contacted areas due to closure) for these two different direction experiments.


Fig. 7. Correlations between the ratio hydraulic conductivity and fractal dimensionunder different normal loading conditions for the NS injection direction.


dry areas that correspond to the closure points may contain negli-gible amount of air. But, even if this exists, it will be in the trappedform and will not contribute to the flow. Hence, the flow is still sin-gle phase in the fracture.

Quantitative analysisEffect of surface roughness on the ratio hydraulic conductivity. Weused the ‘‘ratio hydraulic conductivity, (Q/DP)’’ in order to quantifythe transport properties of our model fractures because this ratiois proportional to fracture hydraulic conductivity (Kfr) as it was pre-viously reported and used by Schmittbuhl et al. (2008). The ratiohydraulic conductivity values of each model fracture under non-loading and four different normal loading conditions were calcu-lated using the slopes of the straight best fit lines adjusted to the firstlinear portions of the pressure (P) versus rate (Q) curves (figures notprovided). The values of ‘‘coefficient of determination’’ (R2) in thelinear curve fittings were ranged between 0.90 and 1.00 with amajority quite close to 1.00.

The relationships between the ratio hydraulic conductivitiesand fractal dimensions under non-loading and four different nor-mal loading conditions are shown in Figs. 6 and 7 for the SN andNS direction experiments, respectively. Trends are clearly observedindicating that the ratio hydraulic conductivity decreases as thefracture surface roughness increases and this behaviour of thetrends is independent from the magnitude of any normal load.For the case of SN direction experiments (Fig. 6), the coefficientR2 between the two parameters is 0.42 under the non-loading(N = 0 kg) condition whereas they are 0.85, 0.74, 0.56, and 0.32 atN = 2, 4, 8 and 16 kg normal loads, respectively. As seen, the rela-tionship at the non-loading condition is much more pronounceablefor the intermediate levels (N = 2 and N = 4 kg) of the normal loaddue to higher values of R2. N = 2 kg loading condition presented thebest agreement between the parameters with a R2 value of 0.85showing the strongest correlation.

For the N = 4 and N = 8 kg cases, a similar trend was observedwith a lower R2 values (0.74 and 0.56, respectively. Unexpectedly,the lowest value of R2 (0.32) was obtained for the highest value ofnormal load (16 kg) and the trend changed compared to the otherloading value cases. Low values obtained at the last two stages canbe attributed to the possible small scale deformation of the siliconerubber lower parts of the model fractures under relatively highernormal loads as they are soft when compared to very tough poly-urethane upper parts. Nevertheless, it should be considered thatthe trends are quite obvious in all cases: The rougher fractures tendto have lower conductivities in quite a systematic manner.

Perfectly matching and tightly closed nature of our model frac-tures makes the surface roughness effect critical. While this effectis decreased by the fracture opening due to the fluid pressure,

Fig. 6. Correlations between the ratio hydraulic conductivity and fractal dimensionunder different normal loading conditions for the SN injection direction.

which acts to create an aperture structure, applying normal loadcauses some degree of fracture closure again by restricting fractureopening. Thus, surface roughness begins to be notably more effec-tive on the conductivity, again. These results show that surfaceroughness has critical effect on the fracture hydraulic conductivityand this is less considerable for the fractures with lower aperturesdue to fracture closure as result of normal loads.

The same analysis was also performed for the NS injection direc-tion (Fig. 7). It was observed that the values of R2 for the NS direc-tion showed very similar tendency of variation to those of SNdirection. However, they were lower than the values for SN direc-tion. Develi and Babadagli (submitted for publication) showed thatflow along the two opposite but parallel directions within the samefracture can be different from each other, presenting anisotropicbehaviour as the initiation and continuation of flow are differentalthough the fracture surface data and the resulted variogram arethe same for both reverse directions. This is likely to be the reasonof the differences in R2 values of opposite injection directions. Onthe other hand, the experimental errors may have also been accom-panied. After all, the trend of the experimental data described inthis section is explicit for both injection directions in any loadingcondition, regardless of any determination coefficient.

Relationship between fracture surface geometry and final flowpatterns. By processing the images of final flow patterns throughthe code written in the ‘‘image processing toolbox’’ of MATLAB�,the percentage of dry planar area (contact areas unwetted by theinjected water) for each model fracture was calculated by the ratioof the number of pixels corresponding to the dark zones to the totalnumber of pixels in the images. Detailed description of the algo-rithm used for the calculation can be found in Develi andBabadagli (submitted for publication). Quantitatively, the percent-ages of the dry planar areas obtained from the two opposite (NSand SN) injection directions of a model fracture are close to eachother, as seen in Fig. 5c. These areas were plotted against theroughness parameters, namely At/Ap (the ratio of total fracture sur-face area to planar surface area) and Dva (fractal dimension) inFigs. 8 and 9, respectively.

As seen, the percentage of dry planar area is related to theroughness of the model fractures and, regardless of the rock type(or lithology), an increasing trend was obtained between the per-centage of dry planar area (unwetted by injected water due to clo-sure) and the two roughness characteristics. It is seen that thepercentage of dry planar area increases with the increase of bothAt/Ap and Dva. The trend for the former has much stronger correla-tion. It is interesting to observe that dry planar areas of the modelsvary between 10% and 20%. Higher values of both At/Ap and Dva arethe indication of the rougher surfaces; i.e., the rougher the surface,

0

5

10

15

20

25

1.04 1.06 1.08 1.1 1.12 1.14 1.16

Perc

enta

ge o

f Dry

Are

a (%

)

At/Ap

Injec�on Direc�on: NS

Injec�on Direc�on: SN

Linear (Injec�on Direc�on: NS)

Linear (Injec�on Direc�on: SN)

Fig. 8. Correlations between the percentage of planar dry area (unwetted by theinjected water) and the ratio At/Ap values given in Table 1.

0

5

10

15

20

25

1.24 1.26 1.28 1.3 1.32 1.34 1.36 1.38 1.4

Perc

enta

ge o

f Dry

Are

a (%

)

Variogram Fractal Dimension, DVA

Injec�on Direc�on: NS

Injec�on Direc�on: SN

Linear (Injec�on Direc�on: NS)

Linear (Injec�on Direc�on: SN)

Fig. 9. Correlations between the percentage of planar dry area (unwetted by theinjected water) and Dva values given in Table 1.


the larger the dry planar area within the fracture. This may beinterpreted as a confirmation of a general consensus reached inthe literature that fluid mostly follows the channels through roughfractures. The amount of the channelled fluid flow rises withincreasing level of roughness by causing a larger dry area leftbehind the flow. This kind of flow will eventually affect the trans-port properties of the single fractures and become a critical param-eter, even causing a deviation from the cubic law depending on theinjected fluid type and rate.

Nemoto et al. (2009) and Watanabe et al. (2009) measured thecontact areas experimentally and numerically under differentstresses and with and without shearing. Both studies showed thatpreferential flow paths exist and these are controlled by fractureclosure. The contact area (dry planar area unwetted by the injectedwater) without stress was close to what is observed in the presentstudy (in the range of 10–20%) while increasing under stress.

Multiphase flow – Displacement experiments

As can be inferred from the literature survey given in the ‘‘Intro-duction’’ section, experimental studies on original replicas of rockfractures are very rare. Most of them used smooth-parallel platesor rarely artificial rough fracture surfaces created by systematicallyordered intrusions. In one of the very rare studies, Radilla et al.(2013) prepared replicas of sandstone and granite fracture surfacesand conducted single and multiphase-flow experiments. Theirmultiphase-flow experiments were conducted as the steady stateflow of water and gas. They visually showed that the phase distri-bution was controlled by the roughness, which was determined bythe lithology of the rock. The sandstone cases (example of grainyrock) showed ‘‘thin channels’’ compared to granite (example of

crystalline rock) due to a more rough structure caused by its grainystructure. They did not characterize the fracture surfaces quantita-tively, rather they provided relative permeability data for steady-state flow.

In the present study, we used more variety of rock samples (atotal of seven models from limestone, marble, and granite) andperformed unsteady state (displacement) experiments. We alsodefined the roughness quantitatively as mentioned earlier, whichenabled us to correlate multiphase characteristics to roughnessnumerically as done for the single phase experiments summarizedin the previous sections.

Attention was paid to several specific issues as to the displace-ment process and the effects of the following parameters on thedisplacement process were investigated:

� Fracture roughness.� Lithology.� Normal load (and fracture closure) on the samples.� Model type and material (wettability to some extent) used.

Also considered was the repeatability of the experiments. Fourtypes of experiments were conducted for four different dis-placed-displacing phase scenarios: water–gas, gas–water, oil–water, and water–oil. The observations and results are presentedin the next sections.

Qualitative analysisWater displacing gas. Fig. 10 shows the saturation distributions inthe fractures for eight different samples. Many different and incon-sistent patterns were observed depending on the roughness (orrock type). Channelling is characteristically seen in the limestone(fr2, fr3), granite (fr5) and marble (fr7) samples until breakthrough.At the end of displacement, i.e., no change in the displacement pat-tern has been observed with continuing injection, channelled flowwas still observed for the two carbonate samples fr2 and fr3. Theresidual displaced phase saturation was controlled by the topogra-phy of the fracture surface (or aperture) which was more obviousin the carbonates due to the grainy nature of the rock comparedto crystalline type rocks, i.e., granite (fr5) and marble (fr7).

Obviously, materials used in the preparation of the modelswould affect the process (fr4 and fr4s). As a control case, thedisplacement on a two parallel plexiglass model was included(‘‘flat’’ case in Fig. 10). A perfect displacement is obviously seen.As indicated in the ‘‘Material and set-up’’ section, the two halvesof the fracture were made of different materials to obtain higherquality visual data; the top part being transparent solid materialand the bottom part being elastic (rubber) non-transparentmaterial. In one experiment (fr4s), both sides were used as solidtransparent material. When the two models of different materialswere compared (fr4 and fr4s), similar patterns were observed atbreakthrough and at the end of displacement. Note that these werethe marble samples on which the displacement was very uniformand the residual displaced phase (gas) was in the form of pockets.The same behaviour was observed another carbonate sample (fr6)and granite (fr5).

The rock type impact on the displacement pattern was criticallyimportant in the water–gas displacement cases, whereas the mate-rial type (that could be interpreted as the wettability effect) did notshow any significant effect.

Some experiments were repeated for the sake of reproducibilityof this kind of ‘‘random’’ displacement processes. Fig. 11 shows tworepeated experiments on the same samples. Qualitatively andquantitatively similar patterns were obtained from the twodisplacement tests. Also, a similar type and amount of residualdisplaced phase is seen when the very last images of eachexperiment are compared.

Fig. 10. Water (blue) displacing gas experiments in different fracture models given in Table 1. Injection is from left to right. (For interpretation of the references to colour inthis figure legend, the reader is referred to the web version of this article.)


Another important aspect of displacement in a single fracture isthe stress-flow relationship. As seen in Fig. 12, when an extra –normal – load is applied to the model that eventually reducedthe aperture and yielded a certain degree of closure, a more uni-form distribution was observed in the lateral direction and the dis-placement was more ‘‘frontal’’ (the lower images named fr5) thanthe no-load case (the upper images named fr5-clamp). However,the very last images of each case demonstrate that the displace-ment pattern at the end and the residual oil saturation type andamount are very similar.

Gas displacing water. A very unstable displacement case was testedby injecting gas into the fracture upon the completion of the waterinjection experiments (Fig. 13). As seen in the images, however, theinstability is not in the form of viscous fingering reminiscent ofTaylor–Saffman type displacement but it is governed by the

Fig. 11. Water (blue) displacing gas experiments. Repeatability of the test on the same mleft to right. (For interpretation of the references to colour in this figure legend, the rea

roughness of the fracture. Except fr3 (limestone) and fr7 (marble)cases, gas channels (white colour) were obvious in all cases atbreakthrough and end of the displacement. In these five cases(fr2, fr5, fr6, fr4, and fr4s), the channels were developed until break-through establishing the main flow path and the displacement pat-tern did not grow in any other direction.

Note the gas displacing water experiments were started uponcompletion of the previous water displacing gas case. Therefore,this ‘‘history’’ (i.e., the saturation distribution obtained in the pre-vious – water displacing gas – case) could be critical on the follow-ing gas injection process. However, when fr3 and fr7 cases arecompared, one observes similar gas injection patterns andrelatively better sweep by gas compared to the other channel typedisplacement cases. The history of fr3 and fr7 are very much differ-ent but the patterns, especially at the end of displacement, are verymuch similar.

odel (fr1) with two different experiments indicated by (1) and (2). Injection is fromder is referred to the web version of this article.)

Fig. 12. Water (blue) displacing gas experiments. The effect of normal load on the same model (fr5) with two different experiment indicated by ‘‘fr5’’ and ‘‘fr5-clamp’’.Injection is from left to right. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 13. Gas displacing water (blue) in different fracture models given in Table 1. Injection is from left to right. (For interpretation of the references to colour in this figurelegend, the reader is referred to the web version of this article.)


In the ‘‘both sides transparent’’ case (fr4s), the channelling tookplace through the edge of the model whereas in several cases (fr2,fr5, fr4), channels in the middle were observed. Note that thesethree samples (fr2, fr5, fr4) are of three different origins (limestone,granite, and marble). The patterns seen in the fr4s case indicatesthe importance of material type as no displacement in the middleportion of the sample was observed, unlike other samples. This canbe interpreted as wettability effect and similar patterns wereobserved by Naderi and Babadagli (2011) on 2-D displacement inoil-wet sandpacks (Figs. 9 and 10 of this reference).

In the case of fr6 (limestone), more dispersed gas phase isobserved. One may conclude from these observations that thelithology effect may not be as critical as in the more stable dis-placement cases (water displacing gas).

It should be emphasized that this type of flow (gas displacingwater) is critically important in hydraulically fractured – tight –gas reservoirs. Gas in the porous rock should initially displacethe water-based fracturing liquid in the fractures and replace itfor efficient flow towards the production well through thefractured developed. Our observations indicate the importance of

Fig. 15. Oil (white) displacing water (blue) experiments in different fracturemodels given in Table 1: The progress of the front. Injection is from left to right.Injection is from left to right. (For interpretation of the references to colour in thisfigure legend, the reader is referred to the web version of this article.)


wettability and less pronounced effect of lithology compared to amore stable (water displacing gas) displacement on this process.

Oil displacing water. All cases except the ‘‘both sides transparent’’model (fr4s) showed a similar lithology/roughness controlleddisplacement patterns (Fig. 14) to the ones observed for waterdisplacing gas cases (Fig. 10). Fr4 and fr4s, on the other hand,displayed a similar pattern to the gas displacing water case. Thetransparent model (fr4s) yielded channelling at the lower part ofthe image for both the gas displacing water and oil displacingwater cases. This can be another implication of the wettabilityeffect. It is expected that the system shows water-wet nature whengas and oil are injected into water saturated medium. Having bothhalves of the fracture made of solid transparent – plexiglass-likepolymeric material, the wettability is expected to be different fromthe ones with one side of rubber-like material. In this case, thesweep of gas and oil during displacing water is not very efficient.This is also justified by the different displacement patternsobserved for fr4 and fr4s. The injected oil phase followed a similarchannelling behaviour to the one in fr4s at the breakthrough buteventually fr4 yielded more uniformly distributed oil phase inthe fracture with a better displacement at the end of the displace-ment. The rubber is expected to show a more oil-wet nature com-pared to the solid polymeric material used in the fr4s as a bottomhalf of the fracture.

The residual water development is in the form of smaller ‘‘pock-ets’’ for the cases of fr5, fr6, and fr4. These are relatively‘‘smoother’’ surface samples (at least at the microscale) due tothe crystalline nature of the rock compared to more grainy lime-stone cases used in fr2 and fr3.

To have a clearer idea about the displacement patterns andresidual water saturation development, the images taken atdifferent stages of the displacement for three distinct samples(limestone, fr1, granite, fr5, and marble, fr4) are given in Fig. 15.Although the fronts progressed in a similar matter (no severe chan-nelling), the residual water developed a different structure at theend of the experiments. The limestone case (fr1) showed largerresidual water pockets in larger quantity than the marble (fr4)and granite (fr5) cases. The lowest residual water was observed inthe case of granite (fr5). The surface was relatively homogeneousas also indicated by lower fractal dimensions and At/Ap values

Fig. 14. Oil displacing water (blue) in different fracture models given in Table 1. Injectilegend, the reader is referred to the web version of this article.)

(Table 1) for the sample fr5. This yielded no channelling and bettersweep. In the limestone and marble cases, larger residual water sat-uration pockets were observed at the edge of the models.

Water displacing oil. Finally, oil saturated fracture models were dis-placed by water mimicking enhanced oil recovery processes.Fig. 16 shows the patterns for different samples. Severe waterchannelling was very obvious for the fr3 case as similar to all threeother displacement patterns observed on this model. The othersamples (fr2, fr5, fr6, and fr7) showed similar patterns of displace-ment but remarkable residual oil saturation, implying that the

on is from left to right. (For interpretation of the references to colour in this figure

Fig. 16. Water (blue) displacing oil in different fracture models given in Table 1. Injection is from left to right. Injection is from left to right. (For interpretation of thereferences to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 17. Water (blue) displacing oil experiments in different fracture models given


amount and type of residual oil saturation has to do with lithology.For example, fr2 (semi crystalline micritic pink limestone) showedchannelling as well as bigger residual oil pockets than those of fr6and fr7. This could be attributed to larger scale roughness ratherthan microscale roughness. The larger scale (cm scale) type ofroughness can be observed as big humps or big channels in Figs. 1and 2a.

The model fr4 showed larger residual oil pockets compared tothe samples fr2, fr5, fr6, and fr7. Although it is a coarse crystallinemarble, it is not as grainy as the limestone samples. Its ‘‘both sidestransparent’’ version model (fr4s) showed much better sweep withmore frontal displacement (see the image for breakthrough) andlower residual oil saturation at the end of displacement. This alsoimplies the importance of wettability on the displacement; fr4sis expected to be more water-wet as the bottom half of the modelis made of solid polymeric material rather than rubber.

As similar to the previous case, the progress of displacement isgiven in Fig. 17 for three different lithologically distinct samples:fr2 (limestone), fr5 (granite), fr7 (marble). The patterns are of sim-ilar kind and no significant effect of lithology was observed. On theother hand, the residual oil saturation types were slightly different.The limestone case (fr2) showed bigger pockets than the marble(fr7) and granite (fr5) samples, which has to do with the roughnessand thereby the lithology. However, the wettability of the sampleswas quite similar due to the material used in the model prepara-tion and this yielded similar patterns and residual oil saturation.

in Table 1: The progress of the front. Injection is from left to right. Injection is fromleft to right. (For interpretation of the references to colour in this figure legend, thereader is referred to the web version of this article.)
Quantitative analysis
In a final attempt, the residual displaced phase saturationsobtained were analyzed quantitatively. Fig. 18 illustrates the resid-ual saturations reached at the end of the experiments for four dif-ferent displacement cases. This is of critical importance indeveloping relative permeabilities for simulation studies in whichthe end points (initial wetting phase and residual non-wettingphase saturations) are typically assumed to be zero in practice.

The recovery of the displaced phase varied between 10% (fr4s)and 53% (fr3) for the gas displacing water cases (shaded bars inFig. 18a). Note that fr4s is a different model in which no rubbermaterial was used for the lower half of the sample. This wouldyield a different wettability characteristic than the other samples

with the lower half of the fracture made of rubber. Interestingly,significant difference in the water recovery (25%) was observedbetween fr4 and fr4s (the two identical models of which the lowerpart was made of difference material). Hence, one may concludethat when gas displaces water (unfavourable mobility), wettabilityinfluences the displacement. Interestingly, no remarkable differ-ence was observed when fr4 was compared to fr4s for water dis-placing gas; they showed 95% and 90% recoveries, respectively.This implies that when water displaces gas (very favourable mobil-ity ratio), the wettability effect is not critical and mobility controlsthe process.

Fig. 18. Final recoveries of the displaced phase for different fracture samples: (a)Gas–water and water–gas, and (b) oil–water and water–oil displacement tests.

Fig. 19. Correlation between the final recovery of the displaced phase and the fractal dimWater displacing gas, (b) gas displacing water, (c) oil displacing water, and (d) water di


The roughness effect was observed to be critical for the lime-stone samples. Marbles (fr4 and fr7), granite (fr5), and – fine –crystalline limestone (fr6) cases showed high recoveries for thewater displacing gas cases (between 80% and 95%). This indicatesthat roughness, which was more observable in grainy or coarselycrystalized limestone samples, played a role in displacement evenif the mobility and wettability were highly favourable (water dis-placing gas).

In case of water–oil systems, the identical models of fr4 and fr4sdid not show a significant difference in the recoveries. This indicatesthat the wettability did not play a critical role (affinity of the mate-rial used is similar to water and oil) but roughness controlled the dis-placement process. The difference in the recoveries for the waterdisplacing oil and oil displacing water cases, however, is quiteremarkable for the fr5 and fr7 cases. Note that these were crystallinerocks (granite, fr5 and marble, fr7). Overall, in oil displacing watercases, the grainy rocks (limestones) showed lower recoveries thancrystalline rocks (fr4, fr5, fr7). The water displacing oil cases yieldedmore uniform displacement and the recoveries varied between 50%and 75% whereas this interval was observed between 45% (fr1) and85% (fr5 and fr7) for the oil displacing water cases.

This kind of data (as presented in Fig. 18) will be useful in prac-tical applications as to the development of relative permeabilitycorrelations for different fluid pairs considering the roughnesseffect. Recently, Babadagli et al. (submitted for publication)reported such correlations using the residual saturation measure-ment through these tests. They also related the residual saturationsto the fractal or statistical characteristics of the fracture surfacesgiven in Table 1 using linear and non-linear regression.

Finally, the images given in Figs. 10, 13, 14 and 6 were pro-cessed and converted into black and white. Then the fractal dimen-sion of the front at breakthrough was calculated using the box

ension (box-counting) of the displacement frat obtained at breakthrough time: (a)splacing oil.


counting method. This was achieved through public softwareknown as Image-J (Karperien, A., FracLac for Image-J, 1999–2013). Linear correlations were observed between the fractaldimension of the displacement front at breakthrough and therecovery of the displacing phase (Fig. 19). The strongest relation-ship was obtained for the water displacing gas (Fig. 19a) whilegas displacing water (Fig. 19b) and water displacing oil (Fig. 19d)showed a similar trend with lower correlation coefficients. Theoil displacing water case did not exhibit any trend and correlation(Fig. 19c).

Conclusions

Single phase flow

� Pressure versus injection rate curves present a short lineartrend in the beginning at low flow rates. But this is replacedwith a non-linear trend at higher flow rates developing as thegradually bending behaviour of the initial linear curve towardinjection rate axis. The non-linearity is caused by the fractureopening due to the pressure of the flowing fluid inside. This flowbehaviour was found to be in accordance with the Louis andMaini (1970)’s characteristic nonlinear flow curve of in-situwater tests through deformable fractures, where fissure expan-sion starts to become predominant after the initial linear trend,which compensates the turbulence effect. The Reynolds numberat the end of the initial linear trend was calculated as Re = 2.80in our study. This value is interestingly characteristic for thecurves of all model fractures, regardless of the normal loadand injection direction.� Increasing normal load displaces the pressure versus injection

rate curves upward by making the slopes of the linear partsand the local slopes of the non-linear parts steeper. This meansconductivity decreases as the fracture is tighter when moreloads are applied.� Surface roughness of adjacent fracture walls has a critical effect

on the hydraulic conductivity of a fracture. The ratio hydraulicconductivity shows decreasing trend with increasing fracturesurface roughness. The rougher fractures tend to have lowerconductivities. This effect is more considerable for the fractureswith lower aperture due to normal loading.� Even at zero normal load conditions, model fractures may not

be opened entirely by the injection pressure and they exhibita degree of local dry areas that do not involve any flow. Loca-tions, spatial distributions and shapes of these fragmented dry(unwetted) areas within the same fracture are qualitatively dif-ferent from each other in the case of opposite direction experi-ments. Yet, the percentages of them are quantitatively close toeach other.� Fractures with different surface morphologies represent similar

resistance to fluid flow under high normal load conditions.Beyond a certain degree of normal load (it is around 16 kg inour experiments), the roughness is no longer critical on theconductivity.� The percentage of the dry planar area increases with the

increase of both roughness parameters, namely At/Ap andDva, regardless of the lithology, and could be as high as 20%.The trend for the former has much stronger correlation. Sincehigher values for the parameters At/Ap and Dva means roughersurfaces, this relationship may be considered as an indicationof the general agreement in the literature on fracture flowthat fluid mostly follows the channels through rough rockfractures. The amount of the channelled fluid flow rises dueto increasing level of the roughness leaving larger dry areabehind the flow.

Multiphase flow

Water displacing gas

� The residual gas was developed in the form of pockets in themarble, coarse grain limestone (fr6) and granite cases. The rocktype impact on the displacement pattern is critically importantin water–gas displacement cases. The material type (that couldbe interpreted as the wettability effect as well) did not showany critical effect.� When an extra load is applied to the model that eventually

reduced the aperture and yielded a certain degree of closure,a more uniform distribution is observed in the lateral directionand the displacement is more ‘‘frontal’’ (the lower images) thanthe no-load case (the upper images). However, the displace-ment pattern at the end and the residual gas saturation typeand the amounts are very similar.

Gas displacing water

� The lithology effect may not be as critical as in the more stabledisplacement cases (water displacing gas). Overall, the residualwater saturation was observed to be below 50% when gas dis-placed water.� A combined effect of wettability and roughness was observed to

be critical on the development residual saturation of the dis-placed phase. Roughness effect caused more channelling typeflow and big pockets of residual displaced phase saturation.Residual saturations were controlled by the wettability effectand therefore more critical in relatively smoother samples likenon-grainy or finely crystallized rock types (granites and mar-bles or fine crystalline limestone).� All the cases presented have favourable viscosity ratio except

the gas displacing oil case. However, expected instability isnot in the form of viscous fingering reminiscent of Taylor Saff-man-type displacement, but it is governed by the roughnessof the fracture and appeared as channel flow. Further investiga-tions are needed on displacement at different rates and differ-ent roughness/aperture characteristics to clarify theboundaries of viscous fingering and channelling due toroughness.

Oil displacing water

� Although the fronts progressed in a similar matter (no severechannelling), the residual water developed different structureat the end of the experiments. The limestone case (fr1) showedlarger residual water pockets in larger quantity than the marble(fr4) and granite (fr5) cases.� The lowest residual water was observed in the case of granite

(fr5). The surface was relatively homogeneous as also indicatedby lower fractal dimensions and At/Ap values for the samples fr5.This yielded no channelling and better sweep.� The residual water development is in the form of smaller ‘‘pock-

ets’’ for the relatively ‘‘smoother’’ surface samples (fr5, fr6, andfr4) due to crystalline nature of the rock compared to moregrainy limestone cases (fr2 and fr3). In the limestone and mar-ble cases, larger residual water saturation pockets wereobserved at the edge of the models.

Water displacing oil

� Severe water channelling was very obvious for the fr3 case assimilar to the all other three displacement patterns observedon this model. The other samples (fr2, fr5, fr6, and fr7) showed


similar patterns of displacement but remarkable residual oilsaturation implying that the amount and type of residual oilsaturation has to do with lithology. Sample fr2 (semi crystallinemicritic pink limestone) showed challenging as well as biggerresidual oil pockets than fr6 and fr7. This could be attributedto the larger scale roughness (big humps or big channels).� Although the displacement patterns of similar kind were

observed for different lithologies, the residual oil saturationtypes were slightly different. The limestone case (fr2) showedbigger pockets than the marble (fr7) and granite (fr5) samples,which has to do with the roughness and thereby the lithology.

In closing, it should be reiterated that the residual displacedphase saturations are strongly affected by the roughness regardlessof the mobility ratio and wettability. Even under very favourablemobility and wettability conditions, i.e., water displacing gas,residual displaced phase saturations varying between 35% (fr3)and 5% (fr4 and fr6) were observed. The difference in the residualdisplaced phase saturation for oil displacing water and water dis-placing oil was between 55% (fr1) and 85% (fr7) and 48% (fr3)and 75% (fr4), respectively. These values are critically below theones considered in modelling studies of immiscible displacementin fractured reservoirs.

Acknowledgements

This research was conducted under the first author’s (TB)NSERC Industrial Research Chair in Unconventional Oil Recovery(industrial partners are Schlumberger, CNRL, SUNCOR, Petrobank,Sherritt Oil, APEX Eng., PEMEX, Statoil, and Husky Energy) and anNSERC Discovery Grant (No: RES0011227). The third author (KD)is also thankful to the Scientific and Technological Research Coun-cil of Turkey (TÜB_ITAK) for his postdoctoral scholarship throughthe BIDEP program. We gratefully acknowledge these supports.

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