The spatial geometry of microporosity influences fluid flow through chalk reservoirs and aquifers, and, hence, numerous geological processes. Analysing porosity is thus often critical in geological studies. Techniques such as mercury injection capillary pressure (MICP), nuclear magnetic resonance (NMR) and X-ray computed tomography (CT) are expensive, and hence often inapplicable to many geological studies, which often necessitate the analysis of large numbers (hundreds) of samples. However, scanning electron microscopes (SEM) have become widely available, and SEM imagery analysis, therefore, is cheaper and faster. However, extracting meaningful porosity descriptors from SEM images can be difficult, in part because of the difficulty in digitally separating pores in laterally continuous pore networks. Moreover, mathematical morphology can be automated to collect porosity parameters from hundreds of images in a short time frame. The technique also quantifies the shape complexity of porosity. Considering the influence of pore geometry on fluid flow, the capacity of image analysis to deconstruct the pore network by pore shapes is crucial when building flow models. This study concludes that mathematical morphology constitutes an alternative to other techniques in geological studies of microporosity. Lithologies dominated by micro- and nanoporosity, such as shales and tight sandstones, could also benefit from this technique.

Summary Fluid flow in sedimentary rocks is controlled mainly by the morphology of pore-connecting throats. Pore throats (PTs) typically exhibit diverse converging/diverging morphologies such as biconic, parabolic, or hyperbolic geometries. These different geometries are defined by variable opening angle, or angularity, between the throat walls from the narrowest point of the throat toward the pore body. Importantly, each of these geometries imposes different constraints on fluid flow. However, current pore-level flow models usually favor simple cylindrical or biconic throat morphologies, in part because of the difficulty to extract the throat angularity from pore-space imagery. An image-analysis technique called mathematical morphology has been used to characterize porosity in laterally continuous pore networks (e.g., in sandstones) from thin-section microphotographs. This method allows the extraction of petrophysical parameters such as pore and throat diameters through successive image alterations—namely, erosion/dilation cycles using an expanding structuring element (SE). This study proposes a novel application of this technique and quantifies PT angularity. Angularity can be measured from the throat toward the pore body so that the true geometry—biconic, parabolic, or hyperbolic—can be recognized. The technique is tested on simple geometries to demonstrate the correctness of the mathematic equations involved. Because all equations assume perfect, nonpixelated geometries while images are composed of square pixels, the accuracy of measurements depends strongly on image resolution. Pixelation causes significant fluctuations of ±2 to 10° around the correct angularity values that decrease in amplitude as image resolution increases. Finally, potential implications of this parameter on fluid-flow modeling are discussed.

Abstract A method for estimating minimum effective pore throat radius from Routine Core Analysis porosity and absolute permeability data is introduced for chalk samples. This method can reduce the need for conducting mercury capillary pressure measurement in the lab to obtain minimum effective throat radius of chalk samples and allow sample screening prior to time consuming core flood. The investigation was based on four sets of chalk porosity and permeability data from Rørdal, Stevns Klint and two North Sea wells from Dan and Tyra SE fields. For each porosity and absolute permeability data point, three new parameters are calculated from the entire data set of porosity and absolute permeability values. Using these parameters, the model estimates capillary pressures at very low mercury saturations. First, the capillary entry pressure is calculated from Røgen and Fabricius’ empirical correlation. Hereafter a line is fitted between capillary pressures and mercury saturations at very low mercury saturations including the mercury entry point. The extrapolated line crosses the capillary pressure curve at a high mercury saturation between 0.91 and 0.99, which represents a minimum affective pore throat radius. The validity of the method is verified using a set of mercury capillary pressure measurements of chalk core samples. In the following, a correlation between ultimate laboratory oil recovery achieved from a water flooding process, and an expression consists of minimum effective pore throat radius and specific surface area is presented. Our analysis shows that higher oil recovery by water flooding is related to lower minimum effective pore throat radiuses and higher average pore throat radiuses. Using this simple relationship, one can screen samples and evaluate ultimate oil recovery performance by water flooding before conducting core-flooding experiments. In addition, an empirical index is developed to estimate wettability of chalk samples from calculated Rmin, Rave and Rmax of chalk samples.

The diagenetic evolution of chalk during burial has previously been established and can be summarized as follows: (1) ooze deposition and dewatering (burial < 300 m), (2) lithification via mechanical compaction and grain-bridging cementation (300–1000 m), (3) complete cementation due to pressure solution, or porosity preservation thanks to pore fluid overpressure and oil invasion (>1000 m). Moreover, chalk particles tend to increase in size as a result of diagenesis, i.e. recrystallization or cementation. As a result of compaction and cementation, the shape, size and connectivity of chalk microporosity evolve during burial. However, if the evolution of bulk porosity during burial is well quantified, actual modifications of pore space topology are less understood.Quantifying pore space properties such as pore and throat sizes, aspect ratio and spatial distribution usually require costly instruments as well as long and complex experimental procedures. Instead, this study documents the application of mathematical morphology to investigate chalk microporosity from two-dimensional (2D) scanning electron microscope (SEM).Chalk samples (n = 105) have been collected from onshore quarries and offshore oil and gas reservoirs. Six chalk lithotypes are defined based on their mineralogical composition, i.e. clay and silica content, as well as the average size of chalk particles, and their apparent diagenetic impact, which appears strongly related to the mean grain size. The latter is used as a proxy for the diagenetic overprint, while the burial-diagenetic model offers a framework for the different lithotypes and their respective pore space properties.During intermediate burial (<1000 m), the effect of mineralogy on pore topology appears more dramatic than after further burial. From the same outcrop previously buried to ca. 700 m, pure chalk yields total porosity of 45–50% whilst clay-rich chalk yields porosity of 35–40%. Moreover, pore and throat dimensions are on average significantly greater in pure chalk (4.15 and 0.73 μm, respectively) than in clay-rich chalk (2.85 and 0.28 μm, respectively). In both lithologies however, particles share many similarities, including their size (1.3 μm), shapes and rare calcite overgrowths, producing a mudstone texture. This suggests that compaction rather than calcite cementation explains the difference in porosity properties. At greater burial depths (>1000 m), pressure solution and cementation become pervasive and produce large clusters of coalescent calcite crystals (3–10 μm; mean = 5.13 μm). Total porosity is strongly reduced as a result (6–11%) while pore body and throat dimensions drop to 1.58 and 0.03 μm, respectively. A high aspect ratio (88.1) and lower proportion of rough porosity relative to total image porosity suggest that throats are proportionally more affected than pore bodies. Cementation leads to less dendritic, more globular and isolated pores. Where processes such as overpressure and oil charge have helped preserve porosity during deep burial (20–30%), pore and throat dimensions were locked to moderately high values (>2.0 and 0.1 μm, respectively), even in silica- and clay-rich chalk.Since the geometry of microporosity exerts a major control on fluid flow, reservoir modelling and recovery predictions could benefit from a better understanding on the geological controls on chalk microporosity. Not only can mathematical morphology quantify pore space properties that are fundamental in pore network and flow modelling, but by being applicable on large datasets, it could provide a new insight into the geological modifications of chalk microporosity during burial.

The geometry of pore space affects the storage and fluid flow capacity of a rock. Pore networks are typically composed of multiple pores of complex shapes connected by minuscule tubes typically showing converging-diverging geometries. Due to computer and software limitations, fluid flow models have commonly been based on simplified pore models. The classical pore-network or capillary tube models consist of spherical pores connected by tubes of constant circular or triangular section.