Corresponding author: S. A. Hall, Division of Solid Mechanics, Lund University, Lund 22100, Sweden. (firstname.lastname@example.org)
 The challenge of understanding how localized deformation modifies fluid flow in porous rock is addressed. New approaches are presented, based on neutron radiography and digital image analyses, to track fluid flow in rock specimens and to calculate flow velocity fields providing local flow measurements. The results show that neutron radiography, backed up by appropriate image analysis, is a very powerful tool in this context, being far more sensitive to the fluids in the rock than X-ray radiography. Analysis of neutron radiography images of water imbibition into a laboratory-deformed sandstone specimen has provided new measurements of local fluid flow velocities within a shear band, indicating that flow is faster and water storage is higher in the band (attributed to higher capillary forces associated with damage).
 Fluid flow during subsurface resource engineering operations (e.g., hydrocarbon production from and CO2 sequestration into subsurface geologic reservoirs) can be significantly modified (increased or decreased) by deformation and in particular by localized deformation (fractures, shear bands, and compaction bands). However, how such deformation alters fluid flow is not well characterized experimentally. Standard laboratory approaches only provide some average measure for whole specimens, but to fully understand in detail the effect of (localized) deformation on fluid flow, it is necessary to measure fluid flow locally within a test specimen in a full-field sense. Such measurements could allow understanding of how flow properties are modified within different regions of a sample, including within localized zones, that likely have strong control over the alterations in overall permeability.
 X-ray imaging has been used previously to follow flow through localized rock samples [e.g., David et al., 2008; Pons et al., 2011]. However, X-rays are sensitive primarily to density changes (X-ray attenuation varies roughly linearly with atomic number). Therefore, there needs to be significant density change, i.e., significant contrast between the porosity before and after fluid enters, to detect the passage of the fluid. Thus, a propagating fluid front may not standout from the background in an X-ray image or will only do so when there is a significant saturation change. An alternative method is neutron imaging, as has been demonstrated for fluid flow into rocks by Dierick et al. , Cnudde et al. , and Hall et al. , for example. Neutron imaging is similar in concept to X-ray imaging except that the attenuation is by no means a linear function of atomic number. The key benefits, which make neutron imaging particularly adapted to tracking fluid in rocks, are that neutrons are extremely sensitive to the presence of hydrogen, which exists in many of the fluids that are of interest (i.e., water, oil) and rocks are generally less absorbing than water.
 Results from neutron radiography monitoring of water imbibition into a sample of a sandstone with localized deformation features (shear bands) are presented. The fluid flow through the sandstone sample is quantified through image processing-based fluid-front tracking to provide measurements of the local flow velocities inside the shear bands. Furthermore, 3-D tensor strain fields are determined by 3-D volumetric digital image correlation (DIC) analysis of X-ray tomography images of the sample before and after the triaxial compression that led to the formation of the localized deformation. Observations are also presented on the imbibition of the water into an oil invaded region of the sample.
2 Experimental Method
2.1 Study Material and Triaxial Compression
 The studied material is a sandstone from the Vosges mountains in France (average porosity 22% and mean grain diameter 300 μm; see Bésuelle et al.  for details). A cylindrical specimen (diameter 40 mm and height 80 mm) was cored perpendicular to bedding. Two opposing sides of this cylinder were flattened (the distance between these faces and the width of the images presented are 35 mm) and notches were cut at well-defined positions relating to the expected shear band inclination angle [Charalampidou, 2011]; see Figure 1a. This geometry encourages a quasi-plane deformation behavior and focusing of the expected strain localization in the center of the sample. The sample was deformed dry under triaxial compression at 50 MPa confining pressure (at Laboratoire 3SR in Grenoble) until just after the macroscopic failure, as indicated by a peak in the axial stress (at about 170 MPa). At this confining pressure, strain localization is expected in the form of a shear band, and indeed the external surface of the specimen suggested this to be the case; confirmation is provided through the DIC analysis presented later. (See Bésuelle et al.  and Charalampidou  for full details on the mechanical behavior of this rock.)
 At the end of the triaxial compression test, whilst dismounting the specimen, a small amount of the confining oil entered into the specimen and was imbibed into the dry sample; this oil can be clearly seen in the neutron radiography (Figure 1b). The oil only entered one end of the sample and so the subsequent flow test was performed with water imbibition into the opposite end. Furthermore, the presence of the oil added an extra aspect to the analysis in that the neutron imaging of both the water and oil phases could be assessed and, most interestingly, the imbibition of the water into both dry (air saturated) and oil-invaded rock could be characterized. Note that whilst the oil shows up clearly in the neutron radiography, it does not show up in the X-ray radiography, Figure 2c (or tomography, Figure 2d), which indicates the greater sensitivity of the neutrons to the fluid than the X-rays.
2.2 X-ray Imaging and 3-D Strain Field Measurements
 X-ray tomography of the sample was performed (at Laboratoire 3SR, Grenoble) before and after the triaxial deformation to provide comparable 3-D images (voxels were cubes with sides of 100 μm; see Figures 1c and 1d). 3-D volumetric DIC was performed on these images to provide 3-D tensor strain fields describing the triaxial test-induced deformation. DIC is a method for determining the image transformation (in this case 3-D displacement fields) that maps one image onto another and the tensor strain fields are derived by differentiation of the 3-D vector displacement fields; see Hall et al.  for details on the approach used. Figures 1e and 1f present the first and second invariants of the DIC-derived strain tensors (i.e., the volumetric (εv=ε1+ε2+ε3, where ε1,2,3 are the principal strain values) and shear strains ()) as the median projection through the 3-D images parallel to the strike of the shear band, which gives a representative field for comparison to the 2-D neutron radiography data.
 The 3-D volumetric DIC reveals a main strain localization zone traversing the sample between the two notches and a smaller zone below the lower side notch (Figures 2e–2g). Comparison of the shear and volumetric strain fields indicates a strong shear component to the localized deformation and that the band has undergone compaction; this can thus be considered to be a compactant shear band. The strains are close to zero outside of the localized deformation zone, although a slightly dilated zone exists around the peripheries of the band. The 3-D, thresholded rendering of the shear-strain field in Figure 1g indicates that the shear band has an almost planar, disc-like geometry. Also, whilst the zone is quite continuous, there are two bands in the central part, one band extending into the middle of the sample from each of the notches that meet about two thirds of the way up from the lower notch.
2.3 Imbibition Experiments, Neutron Imaging, and Fluid Velocity Measurements
 Neutron radiography was performed during the imbibition experiment, at the Neutrograph station of the Institut Laue Langevin (ILL) in Grenoble, using a high-speed digital camera with a scintillator to convert the transmitted neutron radiation to visible light. The neutron radiography setup was similar to that described in Dierick et al. . Each radiography image is 480×640 pixels and each (square) pixel has a dimension of about 120 μm; an example radiograph is presented in Figure 1b (note that only about 7/8 of the sample was imaged due to the camera field-of-view).
 The flow-experiment setup involved a small reservoir, in which the sample was placed on aluminium feet. This reservoir was filled with water to the bottom of the sample and the water passed into the sample by imbibition. The sample was air saturated before the water imbibition (except the oil-invaded zone). The reservoir was filled through a pipe from outside the experimental area to allow neutron imaging from the first instance of imbibition (the experimental area must be fully sealed before opening the neutron beam). These radiography images represent a 2-D picture of the attenuation of the neutrons through the specimen. The change in neutron attenuation as the water enters the rock is used as a proxy for the water saturation. Images were acquired with an exposure time of 0.1 s at 10–15 s intervals in the initial stages of the tests (the extremely high neutron flux of the Neutrograph (about 3×109N/cm2/s) allows for fast measurements) to provide a good time resolution of the advancing fluid front; later in the tests, as the flow slowed, the intervals were longer. An example neutron radiograph is shown in Figure 1b, only removal of (high and low) outliers has been applied, i.e., the data quality is very high. Furthermore, the rock/water contrast is very strong (see Figure 2). Therefore, very little pre-processing was required before implementing the imbibition front tracking.
 Full-field measurements of the fluid flow velocities through the test specimen require that the advancing fluid front is identified in the radiographs at each time step and that points along the front are tracked from one step to the next to give time-lapse traces of the front positions and “streamlines” that connect the points on the front at each time. This image processing challenge is essentially an evolving (deformable) contour issue, but with the additional aspect of handling the highly convex and concave regions of the advancing front. The processing flow for the front tracking is described in detail in the supporting information and the outputs are a set of fluid fronts for each time step and the streamlines that connect them, from which, knowing the time interval between the images, a flow velocity map over the whole sample can be calculated.
 Figure 2 presents the time-lapse neutron radiography of the water imbibition (animations can be found in the supporting information); 270 images were acquired, all of which were analyzed in the front tracking, but only every fifth image is presented here. Figure 3 shows the tracked flow fronts at each time step and the corresponding calculated fluid advance velocities. Velocities are higher at the beginning of the imbibition (bottom of the sample) and decrease with height, as is expected since velocity should decrease with distance from the source during imbibition due to the reduction in the driving force [David et al., 2008]. Also, it is noted that the measured velocities are of the same order of magnitude as observed by Pons et al. . The observations can be summarized into five stages:
 Rise of curved front (homogeneous material);
 Acceleration up lower branch of shear-band (faster velocities in band);
 Acceleration up main shear band, increased saturation and velocity in band;
 Water front pushes into oil zone;
 Lower neutron image intensity in oil-water zone and also reduced intensities (increased saturation) below.
 Figure 4 shows a comparison of the neutron radiography intensity profiles before and after the water imbibition, which highlights five main zones:
 Oil zone; no change after imbibition test as water does not invade this region. The image gradient prior to the water imbibition test, which continues into zone 2, indicates the decreasing saturation profile of the oil up to the oil front where there is a sharp gradient in image intensity (zone 3) before the water imbibition test.
 Water-invaded oil zone indicating a reducing oil saturation downward before the water imbibition test, which is replaced by a reduced gradient after water invasion (see also Figure 5); the fact that the oil zone is still noticeable after water invasion indicates that the oil is not replaced.
 The strong intensity gradient in this zone before water imbibition indicates the oil front.
 This region shows a slightly higher image intensity reduction with water invasion, suggesting a pooling of water in a layer of different porosity or that the oil has prevented the inflow of water (so there is a buildup of water in the region before).
 Almost constant intensity profile after water imbibition, indicating a uniform water saturation (except the elevated saturation in the localized zone).
4 Discussion and Conclusions
 The full-field time-lapse neutron radiography measurements of water imbibition into a sandstone specimen with localized deformation (shear bands) represent new data on local fluid flow velocities within and around a shear band. The first key result is that neutron radiography, backed up by appropriate image analysis, is a very powerful tool in this context, being far more sensitive to the fluids in the rock than X-ray radiography. In fact, the time-lapse neutron radiography images show remarkable clarity on the advancing fluid front, even before any image processing, due to the large neutron attenuation contrast between the water and the rock. Furthermore, an oil-invaded zone can be clearly identified in the neutron radiography acquired before the water imbibition, whereas it cannot be easily seen in the corresponding X-ray radiography (see also Figure 5). Thus, whilst X-ray imaging can be used to observe fluid distributions in rocks, neutron imaging is a far more sensitive technique.
 The measurements show that in this case, the water imbibition velocities and the subsequent water saturation are higher in the shear band than outwith, which might seem contrary to the observation that this is a compactant shear band (from the DIC) where porosity is reduced. However, it is likely that the localized deformation is associated with localized damage, i.e., increased microcrack density, that will have a higher capillary effect giving increased imbibition and thus faster fluid velocities, than in the less deformed matrix. Breakdown in cements, which otherwise fill the potential fluid pathways, might also contribute. Furthermore, outwith the band the rock will have undergone some compaction with little damage, which could reduce the flow potential by closing down fluid pathways. Therefore, whilst the compaction is greater in the shear band, it would appear that the damage enhances imbibition and storage potential. Further studies will be needed to confirm this observation, including analysis of samples deformed under different confining pressures and taken to different levels of deformation.
 The approaches presented have the potential to provide enhanced understanding of how localized deformation modifies fluid flow in rocks, which is essential to properly calibrate material models (standard approaches provide whole sample permeability values and thus neglect or, at best, average out, localized effects). However, this is just a first step and further studies are required. For example, it is difficult to determine the permeability from imbibition experiments, as the measured flow velocities depend on both permeability and fluid pressure, the latter being a function of, amongst other parameters, the pore size. Local permeabilities might be calculated based on some simplifying assumptions, e.g., Darcy flow [see David et al., 2008; Pons et al., 2011], but this is likely to just provide some nominal values. A more effective method would be to use numerical simulations of the flow and inverse methods to constrain the local parameters (e.g., permeability, pore size). Furthermore, fluid-pressure controlled tests, instead of imbibition, would enable permeability-dominated flow to be studied more directly. It is also noted that radiography imaging provides a 2-D image of the accumulated neutron intensity reduction across the sample. Whilst the DIC shows the deformation is quite planar, it has a 3-D (disc-like) shape and, furthermore, the imbibition front curvature seen in the less deformed part of the sample will also exist in the third dimension. These effects might be overcome with 3-D imaging, but this would involve slower acquisition and issues with turning the sample at speed (which initial tests have suggested can induce a centrifugal effect on the fluid). Therefore, future work will focus on producing “more 2-D” samples (e.g., from plane-strain deformation, Bésuelle and Hall ) and also on comparison of the data to predictions of projected 2-D images from 3-D numerical flow simulations.
 Andrew Harrison (ILL) is thanked for the special access to the Neutrograph station and D. Hughes and S. Rowe (ILL) are gratefully acknowledged for their help with the experiments. Colleagues at Laboratoire 3SR (Grenoble, France) are acknowledged for their support and access to the triaxial device and X-ray tomograph and, in particular, thank you to Pascal Charrier for his support in using these equipments and in the sample preparation.
 The Editor thanks Chris Wibberley and an anonymous reviewer for their assistance in evaluating this paper.