New insights on fracture roughness and wall mismatch in carbonate reservoir rocks

Fracture roughness refers to the degree to which undulations occur along fracture surfaces (e.g., Barton and Choubey, 1977; see also Figs. 1A, 1B). Mismatch of fracture walls refers to the degree of deviation from perfectly interlocking (matching) walls (e.g., Zhao, 1997; see Figs. 1C, 1D). Roughness and mismatch of fracture walls are key hydromechanical properties in the rock shear strength and hydraulic conductivity (permeability) of rock masses (e.g., Barton et al., 1985; Olsson and Barton, 2001). Measurement of rock strength and permeability is an important topic in a wide range of scientific research and industrial applications. Relevant fields include geotechnical, hydrological, and petroleum reservoir sciences as well as geophysical imaging of subsurface fractures.

Roughness measurements have been extensively and almost exclusively reported from numerical simulations, laboratory experiments on artificial fractures, and fractures and faults in near-surface rocks (e.g., Barton and Choubey, 1977; Maerz et al., 1990; Brown, 1987; Tatone and Grasselli, 2010; Candela et al., 2009; Sagy et al., 2007; Schmittbuhl et al., 1993). Roughness measurements on deep reservoir fractures are rare, possibly due to inadequacy of direct data on roughness and/or lack of efficient measuring techniques. Rationally, direct roughness measurements are unattainable using the various subsurface data sources other than core—assuming it is in good quality and from boreholes that were geometrically ideal to intersect with reservoir rock fractures.

Here, we present new measurements and insights on the nature of roughness and wall mismatch of carbonate reservoir fractures. The fractures are described from outstanding data sets of directional core combined with high-resolution electrical borehole imaging. The data sets were obtained from extended-reach drilling into the Arab carbonate reservoirs, the world’s most prolific and producing hydrocarbon-bearing rocks. The drilling site is a well-studied hydrocarbon field of a dome structure that is located within the tectonically active region of Eastern Arabia (e.g., Al-Fahmi et al., 2016; Ameen, 2014; see also Fig. 2). Roughness measurements were obtained by applying new quantitative nondestructive techniques on fracture profiles digitized from high-definition optical scans of the core. The results from core data were correlated with the detection levels of fractures and aperture measurements from corresponding borehole images. The results bear implications on the modeling of fracture permeability and sliding potential in subsurface carbonate reservoirs.

The data sets were obtained from two directional boreholes (X-01 and X-03) that were drilled into the Upper Jurassic Arab carbonate reservoirs (A, B, C, and D). The drilling targeted the reservoirs located at ∼1.4 km below surface in a hydrocarbon field of a low-relief dome in Eastern Arabia (Al-Fahmi et al., 2016, 2014). Each reservoir consists of a shallowing-upward marine sequence of a variety of lithofacies, including mudstones, wackestones, packstones, skeletal grainstones, ooid grainstones, and dolomites (e.g., Mitchell et al., 1988). The porosity averages ∼15%, ranging in type from interparticle to intraparticle to moldic to vugular (e.g., Mitchell et al., 1988).

Carbonate reservoir fractures in Eastern Arabia were interpreted from borehole images of the directional boreholes that were drilled for oil and gas extractions from the Arab, Hanifa, Khuff, and other reservoirs (Ameen, 2014; Ameen et al., 2010; MacPherson and Ameen, 2014; Luthy and Grover, 1995; Thagafy et al., 2017). The fractures are generally grouped based on their strikes into east-west (E-W), northeast-southwest (NE-SW), and northwest-southeast (NW-SE) regional systems (e.g., Ameen et al., 2010; Ameen, 2014). The NE-SW and E-W systems are optimally oriented to the present-day maximum horizontal principal stress (S_Hmax) in Eastern Arabia (Ameen et al., 2010; Ameen, 2014). The S_Hmax has an estimated ∼60° and 100° azimuth from analyses of breakouts and wall-tensile fractures in boreholes in the Arab, Hanifa, and Khuff reservoirs (e.g., Ameen et al., 2010; Alghamdi et al., 2016; Thagafy et al., 2017). The S_Hmax is recognized to be higher than the vertical stress (S_v) of the sediment load, generating a strike-slip stress regime in the region, due to the active tectonic compression of the Arabian-Eurasian plate collision (e.g., Ameen, 2014).

The data sets in this study show that the Arab reservoir fractures exist in two systems: 80% unfilled fractures, and 20% calcite-filled fractures (Figs. S1 and S2 in the Supplemental File¹). The two systems are opening-mode fractures with normal dips to the nearly flat strata. After comparing observations from the core and borehole images, 80% of unfilled fractures are missing from the borehole images in X-01 and 45% are missing in X-03 (Al-Fahmi and Cartwright, 2015). The boreholes (X-01 and X-03) intersected a NW-SE system, and X-03 additionally intersected E-W and NW-SE systems (Fig. 2). Fracture strikes indicate that the boreholes missed the fractures that are nearly parallel to the boreholes, but the fracture strikes from all drilled boreholes in this region resemble the NW-SE, E-W, and NE-SW fracture systems that were previously recognized in the carbonate reservoirs in Eastern Arabia (Fig. S1 in the Supplemental File [^{footnote 1}]).

Fracture roughness has long been described using various empirical, statistical, and fractal methods (e.g., Tatone and Grasselli, 2010; Weissbach, 1978; Lee et al., 1990; Barton and Choubey, 1977; Schmittbuhl et al., 1993; Haneberg, 2007). Among these methods, roughness is widely described by visually comparing two-dimensional (2-D) profiles of fracture surfaces to 10 typical profiles using joint roughness coefficients (JRCs; Fig. 1A; Barton and Choubey, 1977). The values of the JRCs range on a scale from 0 (very smooth) to 20 (very rough; Barton, 2013). Roughness has been also described numerically using statistical parameters that were proposed to overcome the simple and subjective nature of the visual techniques (e.g., Tatone and Grasselli, 2010; Li and Zhang, 2015). Nevertheless, the visual and statistical techniques cannot be used to measure roughness and wall mismatch of filled and unfilled fractures in a cylindrical directional core. The visual techniques are limited in use to the unfilled fractures. Walls of filled fractures are not accessible, and breaking core or dissolving mineral fills to precisely expose the host rock walls is unfeasible. Furthermore, the available statistical techniques require presenting core fractures in a digital format of flattened profiles from their actual different elliptical traces around the core circumference.

To overcome these challenges, we used a novel combination of efficient and nondestructive techniques to describe roughness and wall mismatch of fractures. The techniques provide a solution that allows both types of filled and unfilled fractures from geometrical core to be described. The core was scanned using an industrial scanner, which produced 360° optical images of core circumference in true color with a resolution of up to 10 pixel/mm, and details up to 40 pixel/mm. Calcite-filled and unfilled fractures were then digitized from the optical scans up to 0.1 mm (measuring resolution) of core dimensions using a computer-aided design (CAD)–based commercial software (Fig. 3). It was not possible to extract precise profiles for the core fractures using image-processing techniques such as pattern recognition and edge detection, so the fracture digitization was done manually.

The shape of a digitized fracture profile resembles a sine wave produced by the intersection plane of the fracture with the drill-core cylinder (Fig. 3B). The shapes of digitized profiles encompass information about fracture geometry (strikes, dips, amplitude, and roughness) and intersection with the core geometry (strike, dip, height, and diameter; Fig. 3). The lengths of fracture profiles vary according to their elliptical intersection perimeters and mostly range between 25 cm and 35 cm.

JRC values are preferred here because values of typical JRC profiles provide visual references that can be correlated to the rock hydromechanics using empirical relationships (e.g., Barton, 2013).

The wall mismatch was analyzed using three different methods and analyzing top and bottom profiles (profile pair) of each fracture (Fig. 3B). The first method estimates the difference in JRCs between profile pairs. The second method calculates the standard deviations of apertures (STDEV-A) between profile pairs after flattening and resampling the profile pairs (Fig. 3C) to be at the same x-y coordinates. The third method uses the flattened and resampled profiles for a quantitative correlation, from which we can relate mismatch coefficients (MCs) ranging between 0 and 1, where 0 indicates perfectly matching fracture walls.

The obtained measurements on roughness were correlated with the host-rock lithology, which was described in detail (∼5 cm interval) from core and thin sections following a modified version of Dunham’s classification (Dunham, 1962). In addition, the measurements were correlated to the results obtained from borehole imaging of unfilled fractures using two different methods: (1) calculations of mechanical and hydraulic apertures, and (2) correlations between apertures and fracture strikes. These measurements were performed to evaluate if fracture apertures were sensitive to the stress field and stress-dependent permeability in the subsurface.

i.e., the cubic mean of the mean of the cubes of mechanical aperture. This calculation method is provided by the imaging tool manufacturer based on production data, and as such, the hydraulic aperture is equal to, or greater than, mechanical apertures if fracture walls are not perfectly matching. This calculation differs from the rock mechanical methods, in which hydraulic aperture is expected to be either equal to or smaller than the mechanical aperture if fracture walls are mismatching (e.g., Barton et al., 1985).

Fracture roughness measurements are summarized in Figure 4A. About 95% of the Z₂ measured values range between 0.08 and 0.24. The Z₂ values are normally distributed, with equal JRCs ranging between 5 and 15 for both filled and unfilled fractures (Fig. 4A). Measurements of wall mismatch are presented in Figure 4B. Most fractures exhibit mismatch coefficients less than 0.1. A few fractures have noticeable degrees of mismatch. Results from calculating the standard deviation (SD) of apertures show that about two thirds of fractures have less than 0.15 SD. The remaining third ranges between 0.15 and 0.4 SD. The limited occurrences of wall mismatch resulted in weak relationships between the JRCs and correlation coefficients as well as the standard deviations of apertures.

The unfilled fractures in coarse-grained lithofacies exhibited profiles rougher than the fractures in fine-grained lithofacies (Fig. 4C). These observations were similar for the calcite-filled fractures (Fig. 4C). This relationship between roughness and lithology was more obvious in the limestone fractures than in the dolomite fractures (Fig. S3 in the Supplemental File [^{footnote 1}]). The roughness generally increased with the increasing grain size of host limestone. The probability of finding wall mismatch, although limited, seemed to increase with increasing grain and pore size of host limestone rocks.

The aperture measurements from borehole images displayed separation between mechanical and hydraulic apertures (Fig. 4D). In addition, the size of apertures varied along the profiles of unfilled fractures in borehole images (Fig. S4 in the Supplemental File [^{footnote 1}]). In addition, the mean apertures displayed comparable trends from both boreholes, with increasing apertures toward the fractures striking E-W and NE-SW (∼60°–100°), and decreasing toward the fractures striking NW-SE (∼120°–180°).

The fractures exhibited a moderate to high range of roughness magnitudes on the JRC scale between 5 and 15. The range of roughness measurements was comparable for unfilled and calcite-filled fractures, despite the fact that the two fracture systems differ in their diagenesis history. The roughness is apparently independent of the fracture mineralization process. Mineral fills are well-preserved casts for paleofracture roughness of fracture walls. The fractures (smooth and rough) have generally matching walls, and only a minority of the rough fractures exhibited an obvious wall mismatch. Therefore, the parallel-plate approach (the cubic law) is practical for estimating fluid flow in these reservoir fractures.

The roughness and mismatch of fracture walls are clearly products of the variations in sizes and shapes of the matrix, grains, crystals, and pores of host carbonates (Fig. 5A). The limestones and dolomites of the Arab carbonate reservoirs exhibit both primary and diagenetic fabrics (e.g., Mitchell et al., 1988). The statistical distributions (Figs. 4A and 4B) reveal the probability of sampling different lithological beds from fine-grained to coarse-grained beds. High values of roughness and wall mismatch are more common from coarse-grained rock than from fine-grained rock of small sizes of pores (Fig. 4C). The observed wall mismatch can be noted here as fabric-dependent, to make a distinction from the wall mismatch occurring due to wall slips in sheared fractures (faults; Barton et al., 1995). Fabric-dependent roughness and wall mismatch are potentially predictable from limestone lithological descriptions. The Arab reservoir rocks exhibit a wide range of limestone lithofacies, such as mudstone, wackestone, packstones, grainstones, floatstone, and rudstone (e.g., Mitchell et al., 1988). Some, if not all, of these lithofacies exist in other carbonate reservoirs. Nonetheless, the prediction of roughness magnitudes from lithological fabrics involves some assumptions about fracture heights. The prediction is possible for multi-lithofacies carbonates, where the mechanical stratigraphy typically bounds fracture heights (Fig. 5C). The through-going fractures (that cut through various lithological layers) are expected to display a roughness stratification (i.e., roughness anisotropy with the vertical direction normal to the strata horizontal planes). The measured magnitudes of fracture roughness are considered static, which means that the core-based measurements are representative of the magnitudes of reservoir fracture roughness. Two reasons can be listed here to support this consideration. First, the texture, porosity, mineralogy, and mechanical properties of the Arab reservoir rocks are not stress-sensitive, (i.e., these properties do not change under the reservoir stress conditions; Ameen et al., 2009). Second, the core did not exhibit distortions in the pore-scale architecture, such as the breakages of grain bonds, or cracks that can be considered signs for the confining stress removal (unloading).

The effects of fracture roughness and wall mismatch on aperture of unfilled fractures are apparent from analyses of borehole images. There are two important results supporting these interrelated effects on apertures. First, wall mismatches of fractures are obvious from the variation in aperture size along the profiles of detected fractures in borehole images. The sum of these aperture variations is visible from the separations between the mean mechanical and mean hydraulic apertures (Fig. 4D). Second, the mean apertures (hydraulic and mechanical) generally increase toward the fractures optimally oriented to the S_Hmax (∼60°–100°), and they decrease toward the fractures striking NW-SE (∼120°–180°), as their walls (oblique and perpendicular to the S_Hmax) are closed under the compressive stress in Eastern Arabia. The fracture apertures are dynamic under the stress field due to the fact that tensile strengths of barren fractures are typically zero (i.e., the fracture walls are not bonded by minerals). Because the S_Hmax and the dominance of fractures with matching walls, ∼80% of the core unfilled fractures could not be detected in the corresponding borehole images of X-01. The majority of these NW-SE fractures are closed under the compressive stress. The minority of fractures (∼20%) that were detected from X-01 had wall mismatches preserving apertures between fracture walls under this compressive tectonic regime. The unfilled fractures were detected because their apertures (and hence permeability) were susceptible to the infiltrated drilling mud. Calcite-filled fractures exhibited high resistivity in borehole images, indicating they are impermeable to the infiltrating drilling fluid. These observations indicate that in situ permeability of fractures is ineffective if fractures are mechanically closed along complete (matching) wall contacts, or sealed completely with impermeable minerals like calcite cements (Figs. 5B and 5C). Dissolving calcite, however, by acid fracking can potentially make the calcite-filled fractures with wall mismatch as permeable as unfilled fractures (Fig. 5B).

It is not possible to describe the effects of fracture roughness on reservoir rock strength (i.e., the strength of the intact rock blocks and freedom of block movement) for deeply buried rocks. In the absence of observations, we can only relate the possible effects of roughness from previous empirical studies. Rock strength is an important factor in planning, drilling, and completing boreholes, especially the directional drilling boreholes that cost millions of dollars. In general, lower JRCs bear the highest potential of sliding (e.g., Barton, 2013) and hence may risk the stability of directional boreholes (Fig. 5C). The sliding potential can be correlated to slope instabilities; the rougher the fracture surface, the lower is the sliding potential (e.g., Younessi and Rasouli, 2010). The drilled boreholes (X-01 and X-03) did not have any signs of instability issues such as collapse or tight holes. However, some fractures may slip in critically stressed environments and under the dynamics of reservoir production and injection (Zoback, 2007; Fig. 5B). Some considerations must be given, besides roughness, to the shapes and sizes of fractured rocks (blocks). Fractured blocks that are smaller than borehole sizes can slide and fall into the borehole (Fig. 5C). The blocks that are larger than the borehole size cannot be displaced into the boreholes, and their movement can only happen tectonically on moving faults. Some considerations must also be given to internal friction angles, bonding strengths of calcite filling, and the setting with regard to the effective stress field and borehole geometry (Fig. 5C).

The effect of fracture roughness and wall mismatch on geophysical detection methods of subsurface fractures can be related from borehole images. Borehole imaging is the mostly utilized geophysical method for measuring fracture orientation, abundance, and apertures in subsurface reservoir rocks. Fracture roughness and wall mismatch are among the major factors influencing the borehole imaging capability used to detect or miss carbonate reservoir fractures (Al-Fahmi and Cartwright, 2015). The sizes of unfilled fracture apertures are dynamic, depending on the roughness and wall mismatch of fracture walls as well as the compressive stress field. The wall mismatch, especially of rough fractures, contributed to the relatively large fracture sizes and preserved apertures in the fractures in Eastern Arabia, which are under stress in the current tectonic compression. Accordingly, these fractures are easily detected and measured in borehole images. Wall-matching fractures that are closed under the compressive stress field (i.e., lack apertures for infiltrating drilling mud) are undetected in borehole images. This situation contributed to the inconsistency and reduction in estimating fracture abundance by borehole images. The variations in fracture aperture sizes due to wall mismatch and stress field contribute to the reservoir rock anisotropy, which affect geophysical measurements for reservoir electrical, acoustic (seismic), and fluid-flow properties.

We presented new insights about roughness and wall mismatch of opening-mode fractures in viable reservoir rocks using a combination of new measuring techniques. The main results are summarized as follows:

• • The opening-mode (calcite-filled and unfilled) fractures of the Arab carbonate reservoirs exhibit moderate to high roughness between 5 and 15 on the JRC scale. The smooth and rough fractures have matching walls, and only a minority of the rough fractures exhibit an obvious wall mismatch.

• • The roughness and mismatch of the fracture walls reflect the lithology of the host carbonates and therefore are considered “fabric-dependent,” to be distinguished from the roughness produced by rock sliding and friction. The values of roughness are higher in coarse-grained rock and lower in fine-grained rock and can accordingly be predicted from describing the carbonate lithofacies such as mudstones, packstones, grainstones, and rudstones.

• • Wall mismatch measurements of unfilled fractures from core are correlated with the aperture measurements from the borehole images. The results indicate that most of the NW-SE fractures (that are normal to the S_Hmax) are mechanically closed. The pressurized drilling fluids could not enter into the fractures (no apertures), and hence the fractures were undetected in borehole images. Nevertheless, a minority of the NW-SE fractures were detected in borehole images and found to have mismatching walls from aperture measurements. This indicates that these fractures preserved some apertures under the tectonic compression in Eastern Arabia that closed the wall-matching fractures.

We thank Saudi Aramco, especially the Reservoir Characterization Department, for funding this project, and for giving us the data and permission to publish this paper. This work is part of Fahmi’s Ph.D. project at Oxford University. Support from Oxford’s Department of Earth Sciences is highly appreciated. Many thanks go to previous reviewers, including Nick Barton, whose insightful comments improved this manuscript.