Characterisation of solute transport in heterogeneous porous media by multidimensional imaging and modelling

The study of solute transport in porous media continues to find applications in both traditional and emerging engineering problems, many of which occur in natural environments. Key applications include CO2 sequestration, enhanced oil recovery and soil remediation. Transport is a fundamental component in the analysis of these systems, because it provides the driving force for physical and chemical interactions between the fluid and the solid phase. However, the inherent heterogeneity of the subsurface leads to what is classically referred to as anomalous transport, which challenges classic interpretations of both field and laboratory experiments. In this context, novel laboratory protocols are needed to probe transport in heterogeneous medium by measuring the spatial structure of the concentration field in the medium, rather than relying exclusively on the analysis of breakthrough curves (BTCs). In this thesis, a combined experimental and modelling study of solute transport in a range of porous media has been presented, including sandstone and carbonate rocks, to cover a range of pore structures. At the core of the experimental work is the combination of two imaging methods, X-ray Computed Tomography and Positron Emission Tomography. While the former is used to characterise rock properties spatially, the latter allows visualising the temporal evolution of the full tracer plume within the medium in three dimensions. To this aim, a core-flooding system has been built to carry out pulse-tracer tests over a wide range of Péclet numbers (Pe=15-500) using brine- and radio-tracers. In addition to the experiments on the three rock samples (Bentheimer Sandstone, Ketton Limestone and Edwards Carbonate), control experiments on uniform beadpacks were carried out to verify the accuracy of the in-situ measurements. The experimental BTCs have been analysed in the framework of residence time distribution functions, which revealed mass transfer limitations in the microporous carbonates in the form of a characteristic flow-rate effect. Three transport models: the Advection Dispersion Equation (ADE), the Multi-Rate Mass Transfer (MRMT) and the Continuous Time Random Walk (CTRW) framework have been thoroughly evaluated with both the BTCs and the internal concentration profiles. It is shown that the ADE provides an accurate description of the results on the beadpack and the sandstone. The data on the carbonates are better described by the MRMT, which uses a fraction of stagnant, intra-granular pore space and an external fluid film resistance model to account for mass transfer between the flowing fluid and the porous particles. The CTRW theory, applied here for the first time to carbonate cores, provides a further improvement in describing the BTC, because of its ability to account for unresolved heterogeneities. In the application of the models, a distinction was made between parameters that are rocks-specific (e.g., the dispersivity) and those that depend on the flow rate, by treating the former as global fitting parameters in the optimisation routine. Accordingly, the obtained results provide a more consistent picture than what the current literature may suggest regarding the use of these models to the analysis of BTCs. The dataset obtained from the PET has been used to quantify the extent and rate of mixing in the different porous media. The 3-D images clearly reveal the presence of spreading caused by subcore-scale heterogeneities. To quantify their effects on the core-scale dispersion, various measures has been used, namely the dilution index (Π), the spreading length-scale (K) and the intensity of segregation (I). It was observed that the microporosity has a pronounced effect on mixing, thereby greatly accelerating the time scale to reach the asymptotic regime. Notably, both Π and K scale vary linearly with the square-root of time, indicating the suitability of a Fickian-based model to quantify macrodispersion. This observation suggests that the strength of heterogeneity in the rock samples investigated is moderate and that anomalous transport has evolved to normal behaviour on a length-scale O(l)∼10 cm (∼ length of the samples). In this context, to provide a more comprehensive picture of anomalous transport in laboratory rock samples, future studies should aim at increasing the spatial resolution of the measurement. Non-invasive, imaging tools such as PET are likely to go a long way in addressing this problem and provide significant opportunities to advance our understanding of miscible displacements in consolidated porous media, thus including those involving additional phenomena, such as adsorption and chemical reactions.Open Acces

Description of chemical transport in laboratory rock cores using the continuous random walk formalism

We investigate chemical transport in laboratory rock cores using unidirectional pulse tracer experiments. Breakthrough curves (BTCs) measured at various flow rates in one sandstone and two carbonate samples are interpreted using the one-dimensional Continuous Time Random Walk (CTRW) formulation with a truncated power law (TPL) model. Within the same framework, we evaluate additional memory functions to consider the Advection-Dispersion Equation (ADE) and its extension to describe mass exchange between mobile and immobile solute phases (Single-Rate Mass Transfer model, SRMT). To provide physical constraints to the models, parameters are identified that do not depend on the flow rate. While the ADE fails systematically at describing the effluent profiles for the carbonates, the SRMT and TPL formulations provide excellent fits to the measurements. They both yield a linear correlation between the dispersion coefficient and the Péclet number (DL Pe for 10 < (Pe) < 100), and the longitudinal dispersivity is found to be significantly larger than the equivalent grain diameter, De. The BTCs of the carbonate rocks show clear signs of nonequilibrium effects. While the SRMT model explicitly accounts for the presence of microporous regions (up to 30% of the total pore space), in the TPL formulation the time scales of both advective and diffusive processes (t1 (Pe) and t2) are associated with two characteristic heterogeneity length scales (d and l, respectively). We observed that l 2.5 × De and that anomalous transport arises when ld (1). In this context, the SRMT and TPL formulations provide consistent, yet complementary, insight into the nature of anomalous transport in laboratory rock cores

Estimating Three-Dimensional Permeability Distribution for Modeling Multirate Coreflooding Experiments

Characterizing subsurface reservoirs such as aquifers or oil and gas fields is an important aspect of various environmental engineering technologies. Coreflooding experiments, conducted routinely for characterization, are at the forefront of reservoir modeling. In this work, we present a method to estimate the three-dimensional permeability distribution and characteristic (intrinsic) relative permeability of a core sample in order to construct an accurate model of the coreflooding experiment. The new method improves previous ones by allowing to model experiments with mm-scale accuracy at various injection rates, accounting for variations in capillary–viscous effects associated with changing flow rates. We apply the method to drainage coreflooding experiments of nitrogen and water in two heterogeneous limestone core samples and estimate the subcore scale permeability and relative permeability. We show that the models are able to estimate the saturation distribution and core pressure drop with what is believed to be sufficient accuracy

Estimating Three-Dimensional Permeability Distribution for Modeling Multirate Coreflooding Experiments

Characterizing subsurface reservoirs such as aquifers or oil and gas fields is an important aspect of various environmental engineering technologies. Coreflooding experiments, conducted routinely for characterization, are at the forefront of reservoir modeling. In this work, we present a method to estimate the three-dimensional permeability distribution and characteristic (intrinsic) relative permeability of a core sample in order to construct an accurate model of the coreflooding experiment. The new method improves previous ones by allowing to model experiments with mm-scale accuracy at various injection rates, accounting for variations in capillary&ndash;viscous effects associated with changing flow rates. We apply the method to drainage coreflooding experiments of nitrogen and water in two heterogeneous limestone core samples and estimate the subcore scale permeability and relative permeability. We show that the models are able to estimate the saturation distribution and core pressure drop with what is believed to be sufficient accuracy

Chemo‐Mechanical Coupling in Fractured Shale With Water and Hydrocarbon Flow

The transport of chemically reactive fluids through fractured clay-rich rocks is fundamental to many subsurface engineering technologies. Here, we present results of direct-shear laboratory experiments with simultaneous imaging by X-ray Computed Tomography in Opalinus claystone with subsequent fluid injection to unravel the interplay between mechanical fracture deformation, fluid sorption, and flow. Under constant radial stress (σc = 1.5 MPa), the average mechanical aperture (Formula presented.) increases with shear displacement. Upon brine injection, (Formula presented.) is reduced by 40% relative to initial conditions ((Formula presented.) μm) and fluid-sorption induces a divergent displacement of the two sample halves (Δh = ±50 − 170 μm) quantified by digital image correlation. None of these changes are observed in a control experiment with decane, indicating that creep is subordinate to swelling in sealing the fracture. Swelling-induced changes in permeability within the fracture are heterogeneous and largely affect the fracture flow field, as computed using numerical simulations.ISSN:0094-8276ISSN:1944-800