An Integrated Imaging Study of the Pore Structure of the Cobourg Limestone—A Potential Nuclear Waste Host Rock in Canada

With the development of imaging technology, tools to quantitatively describe pore structure, morphology, and connectivity have been widely applied on low permeable rocks; however, it is still questionable to what extent this information can be used to predict permeability. Applicability and comparability of different techniques are discussed here for the Middle Ordovician Cobourg limestone (Canada), a rock dominated by calcite grains of variable sizes (µm–cm) and heterogeneously distributed quartz, dolomite, pyrite, and meshy clay minerals. Absolute porosities determined by helium pycnometry (HP) in literature are approximately 1.6% (±0.9%), and gas permeabilities range from 10−20 to 10−19 m2. Porosities obtained from BIB-SEM are much smaller compared to those from HP (16–69% of HP). Pores found in clays are smaller, slit-shaped, and more densely spaced when compared to those in calcite minerals. Connectivity between pores could not be resolved with 3D micro-CT or FIB-SEM reconstructions, which have a resolution limit of 8 µm and 10 nm, respectively. However, assuming the pores to be connected, laboratory-derived permeability data could be fitted using a simple capillary bundle model, including information about the visible pore size distributions obtained from BIB-SEM images and a tortuosity range of 8 to 15.

Spontaneous Imbibition in a Fractal Network Model with Different Wettabilities

In this work, we derived a mathematical model for spontaneous imbibition in a Y-shaped branching network model. The classic Lucas–Washburn equation was used for modeling the imbibition process occurring in the Y-shape model. Then, a mathematical model for the Newtonian fluid’s imbibition was derived to reveal the relationship between dimensionless imbibition time and length ratio, radius ratio, and wetting strength. The dimensionless imbibition time in the model was adopted to compare with that of the capillary bundle model. Different length and radius ratios were considered in the adjacent two-stage channels, and different wettabilities were considered in the different branches. The optimal radius ratio, length ratio, and wetting strength were calculated under the condition of the shortest imbibition time. In addition, the shortest dimensionless imbibition time of the three-stage Y-shaped branching network model was calculated when the wettability changes randomly. The results indicate that the imbibition time changed mostly when the wettability of the second branch changed, and the second branch was the most sensitive to wettability in the model.

Role of Pore-Size Distribution on Effective Rheology of Two-Phase Flow in Porous Media

Immiscible two-phase flow of Newtonian fluids in porous media exhibits a power law relationship between flow rate and pressure drop when the pressure drop is such that the viscous forces compete with the capillary forces. When the pressure drop is large enough for the viscous forces to dominate, there is a crossover to a linear relation between flow rate and pressure drop. Different values for the exponent relating the flow rate and pressure drop in the regime where the two forces compete have been reported in different experimental and numerical studies. We investigate the power law and its exponent in immiscible steady-state two-phase flow for different pore size distributions. We measure the values of the exponent and the crossover pressure drop for different fluid saturations while changing the shape and the span of the distribution. We consider two approaches, analytical calculations using a capillary bundle model and numerical simulations using dynamic pore-network modeling. In case of the capillary bundle when the pores do not interact to each other, we find that the exponent is always equal to 3/2 irrespective of the distribution type. For the dynamical pore network model on the other hand, the exponent varies continuously within a range when changing the shape of the distribution whereas the width of the distribution controls the crossover point.

An improved saturation evaluation method of Chang 8 tight sandstone reservoir in Longdong West area of Ordos Basin, China

This study focus on saturation evaluation of Chang 8 tight sandstone reservoir in Longdong West area of Ordos Basin, China. An improved saturation calculation method was proposed based on the equivalent rock capillary bundle theory. Firstly, according to characteristics of reservoir pore structure and rock conductivity, the conductive space of reservoir rock is equivalent to the parallel conductive of micro capillary bundle representing the micro pores and the coarse capillary bundle representing the macro pores. Then, the variable cementation index(m) saturation model was deduced by using Poiseuille flow equation and Darcy's law. During the calculation of model parameters, the T2 spectrum data of nuclear magnetic resonance (NMR) was used to calculate the equivalent radius of reservoir micro pores and macro pores, which ensured the ability of model popularization and application. Finally, the proposed saturation calculation method is applied to reservoir evaluation of the study area, and compared with the classical Archie saturation model. The application effect shows that the calculated saturation from the proposed variable m model is much closer to the sealed coring data than that from classical Archie model, and the average relative error of saturation calculated by the variable m model is within 7%, which proves that the proposed saturation calculation method is applicable and effective.

On the applicability of viscosity-based capillary bundle concepts to predict the penetration behaviour of polymer solutions into sand

The increasing use of polymer solutions as support fluids in pile drilling, diaphragm walling or tunnelling applications demands a more detailed discussion of their penetration behaviour and prediction thereof. In this context, the capillary bundle approach can be a useful tool. However, while it is widely discussed in the oil and gas application, the subject is currently addressed only scarcely with regard to support fluid penetration targeting stagnation, where small flow velocities and non-cohesive soil environments are of relevance. In these boundary conditions, the applicability of capillary bundle approaches is not yet sufficiently confirmed and substantiated. The current paper thus reviews current capillary bundle models based on Hagen–Poiseuille in combination with a power-law rheological model and discusses their applicability with respect to support fluid application in the context of experimental soil permeation tests for small gradients ($$i\le 10$$ i ≤ 10 ). Two granular materials of similar grain size, but different angularity (glass beads and sand), and four polymer solutions varying in polymer chain length and concentration are investigated, and the impact of model assumptions and bulk material input variables is systematically discussed. The experimental results show that the theoretical models are generally able to predict the filter velocity qualitatively for values above $${\bar{v}}=5\times 10^{-7}$$ v ¯ = 5 × 10 - 7 m/s and also quantitatively, when an empirical shift factor $$\alpha ^*$$ α ∗ is introduced and water permeability values are determined experimentally. With respect to the influence of soil parameters, it was found that the soil particle roughness decreases the flow velocity of the polymer solution despite similar hydraulic conductivity in water. Polymer chain length and concentration were observed to control the degree of possible dilution ($$\alpha ^*<1$$ α ∗ < 1 ) in the porous system compared to bulk rheological characteristics. It can therefore be concluded that capillary bundle models can indeed be applied in the targeted fields even though they are unable to predict a complete stagnation for $$i>0$$ i > 0 . However, rather than specific model assumptions for tortuosity, taking into account the specific soil-polymer interaction has shown to be of primary importance to ensure no under- or over-prediction of penetration velocities solely based on bulk rheology.

A Simplified Capillary Bundle Model for CO2-Alternating-Water Injection Using an Equivalent Resistance Method

CO2-alternating-water injection is an effective way of enhancing recovery for low-permeability oil reservoirs. The injection process is one of the essential issues that are facing severe challenges because of the low permeability and poor pore space connectivity. Previous researchers mentioned that water injection ability could be decreased by around 20% after the CO2-flooding; hence, it is necessary to quantify the water injectivity variation during an alternated injection process. In this paper, a CO2 convection-diffusion model is established based on the seepage law of CO2 and dissipation effect. The relationship between the width of miscible flooding and injection time is defined. Besides, an equivalent resistance method is introduced for developing a capillary bundle model for featuring an unequal diameter for CO2 water vapor alternate flooding. CO2-oil and CO2-water interactions are analyzed using the new model. The effects of oil viscosity, pore throat ratio, CO2 slug size, and equivalent permeability of the capillary bundle on water injection are analyzed. The result indicates that water injection ability increases with the rise of CO2 slug size and equivalent permeability of the capillary bundle and decreases with the increase of viscosity and pore throat ratio.