Simulating stress-dependent fluid flow in a fractured core sample using real-time X-ray CT data

Abstract

Abstract. Various geoscientific applications require a fast prediction of fracture permeability for an optimal workflow. Hence, the objective of the current study is to introduce and validate a practical method to characterize and approximate single flow in fractures under different stress conditions by using a core-flooding apparatus, in situ X-ray computed tomography (CT) scans and a finite-volume method solving the Navier-Stokes-Brinkman equations. The permeability of the fractured sandstone sample was measured stepwise during a loading-unloading cycle (0.7 to 22.1 MPa and back) to validate the numerical results. Simultaneously, the pressurized core sample was imaged with a medical X-ray CT scanner with a voxel dimension of 0.5 × 0.5 × 1.0 mm 3 . Fracture geometries were obtained by CT images based on a modification of the simplified missing attenuation (MSMA) approach. Simulation results revealed both qualitative plausibility and a quantitative approximation of the experimentally derived permeabilities. The qualitative results indicate flow channeling along several preferential flow paths with less pronounced tortuosity. Significant changes in permeability can be assigned to temporal and permanent changes within the fracture due to applied stresses. The deviations of the quantitative results appear to be mainly caused by both local underestimation of hydraulic properties due to compositional matrix heterogeneities and the low CT resolution affecting the accurate capturing of sub-grid-scale features. Both affect the proper reproduction of the actual connectivity and therefore also the depiction of the expected permeability hysteresis. Furthermore, the threshold value CT mat (1862.6 HU) depicting the matrix material represents the most sensitive input parameter of the simulations. Small variations of CT mat can cause enormous changes in simulated permeability by up to a factor of 2.6 ± 0.1 and, thus, have to be defined with caution. Nevertheless, comparison with further CT-based flow simulations indicates that the proposed method represents a valuable method to approximate actual permeabilities, particularly for smooth fractures (< 35 µm). However, further systematic investigations concerning the applicability of the method are essential for future studies. Thus, some recommendations are compiled by also including suggestions of comparable studies.

Measuring hydraulic fracture apertures: a comparison of methods

“…In contrast, the mechanical aperture is defined as the arithmetic average distance between the adjacent fracture walls measured perpendicular to a reference plane (Barton et al, 1985;Hakami and Larsson, 1996;Renshaw et al, 2000). Previously, the relative roughness expressed by the ratio of the standard deviation of the measured mechanical aperture and the mean mechanical aperture was used to estimate hydraulic fracture aperture (Zimmerman et al, 1991;Renshaw, 1995;Barton and de Quadros, 1997;Xiong et al, 2011;Kling et al, 2017). In addition, a correlation between hydraulic and mechanical aperture was established introducing the contact area ratio, defined as the ratio of the true contact area of fracture asperities and the apparent total fracture surface area of a single fracture (Walsh, 1981).…”

“…Furthermore, the hydraulic aperture of a fractured rock can also be characterized indirectly by statistical measurements of mechanical aperture such as image analysis of fracture profiles performed by progressively grinding an epoxy resin-fixed sample in predefined intervals (e.g., Snow, 1970;Hakami and Larsson, 1996;Konzuk and Kueper, 2004), fracture topography determination using profilometry (e.g., Brown and Scholz, 1985a, b;Matsuki, 1999), X-ray computer tomography (e.g., Kling et al, 2016), structure from motion photogrammetry (e.g., Corradetti et al, 2017;Zambrano et al, 2019), magnetic resonance imaging (e.g., Renshaw et al, 2000), and optical methods applied to rock replicas (e.g., Isakov et al, 2001;Ogilvie et al, 2003;Ogilvie et al, 2006). With known fracture surface topographies and fracture aperture patterns, flow-through properties or hydraulic apertures can be evaluated by numerical fluid flow simulations (e.g., Nemoto et al, 2009;Zambrano et al, 2019) or empirical correlations (e.g., Renshaw, 1995;Kling et al, 2017). All these methods have certain limitations, such as being only applicable within the laboratory scale or requiring open fracture surfaces.…”

Integrated Research as Key to the Development of a Sustainable Geothermal Energy Technology

“…Examples representI)aphase field model (PFM) of fracture sealing; [20] II) as ynthetic model [21] of atypical self-affine,rough fracture surface (fractal dimension = 2.2 [22] ); III) alocal cubic law visualization of typicalf low channelsbased on aperture distributions; [23] IV) amedical X-ray computed tomography (CT) scan of af racturedc ore sample; [24] V) lineament interpretationsb ased on remote sensing; [25] and VI) arandom stochasticD FN model. [26] Fracture or DFN studies provide improved permeability predictions of single fractures(analytical, [27] numerical [24,28] )and fracturedg eothermalreservoirs (analytical, [29] numerical [24,25,30] availability of outcrops and subsurface data;this is often provided, for example,b yf ield measurements,t errestrial laser scanning, [39] and remote sensing [40] (Figure6V), as well as aa pplied samplingm ethod, such as scanline or window sampling. [38] In conclusion, the evaluation of fluid flow in fractured reservoirs is am atter of scales,r angingf rom single fracture scales (mmt oc ms cale,m echanically and chemically induced geometries)t ot he field scale (cm to km scale,t ransferability of DFN geometries), the interactions of which have to be better understood to provide more reliable geothermal reservoir models.…”

“…Typically, hydraulic properties underlie coupled mechanical, chemical, temperature‐dependent processes. Examples represent I) a phase field model (PFM) of fracture sealing; II) a synthetic model of a typical self‐affine, rough fracture surface (fractal dimension=2.2 [22] ); III) a local cubic law visualization of typical flow channels based on aperture distributions; IV) a medical X‐ray computed tomography (CT) scan of a fractured core sample; V) lineament interpretations based on remote sensing; and VI) a random stochastic DFN model . Fracture or DFN studies provide improved permeability predictions of single fractures (analytical, numerical) and fractured geothermal reservoirs (analytical, numerical).…”

“…used μCT scanning of an unaffected natural fracture to prove the significance of fracture heterogeneity on flow behavior. On the other hand, Kling et al . introduced a useful method to transfer in situ medical CT data of fracture flow under loading–unloading condition into flow simulations (Figure IV).…”