The impact of porous media heterogeneity on non-Darcy flow behaviour from pore-scale simulation

The effect of pore-scale heterogeneity on non-Darcy flow behaviour is investigated by means of direct flow simulations on 3-D images of a beadpack, Bentheimer sandstone and Estaillades carbonate. The critical Reynolds number indicating the cessation of the creeping Darcy flow regime in Estaillades carbonate is two orders of magnitude smaller than in Bentheimer sandstone, and is three orders of magnitude smaller than in the beadpack. It is inferred from the examination of flow field features that the emergence of steady eddies in pore space of Estaillades at elevated fluid velocities accounts for the early transition away from the Darcy flow regime. The non-Darcy coefficient β, the onset of non-Darcy flow, and the Darcy permeability for all samples are obtained and compared to available experimental data demonstrating the predictive capability of our approach. X-ray imaging along with direct pore-scale simulation of flow provides a viable alternative to experiments and empirical correlations for predicting non-Darcy flow parameters such as the β factor, and the onset of non-Darcy flow

A spatially resolved fluid-solid interaction model for dense granular packs/Soft-Sand.

Fluid flow through dense granular packs or soft sands can be described as a Darcy’ s flow for low injection rates, as the friction between grain-grain and grain-walls dominate the solid system behaviour. For high injection rates, fluid forces can generate grain displacement forming flow channels or “fractures”, which in turn modify local properties within the system, such as permeability and stress distribution. Due to this kind of “self organized” behaviour, a spatially resolved model for these interactions is required to capture the dynamics of these systems. In this work, we present a resolved model based on the approach taken by the CFDEM open source project which uses LIGGGHTS – a discrete elements method (DEM)– to model the granular behaviour and OpenFoam finite volume library for computational fluid dynamics (CFD), to simulate the fluid behaviour. The capabilities provided by the DEM engine allows the properties of the solid phase, such as inter-grain cohesion and solid confinement stress to be controlled. In this work the original solver provided by the CFDEM project was modified so as to deal with dense granular packs more effectively. Advantages of the approach presented are that it does not require external “scaling parameters” to reproduce well known properties of porous materials and that it inherits the performance provided by the CFDEM project. The model is validated by reproducing the well-known properties of static porous materials, such as its permeability as a function of the system porosity, and by calculating the drag coefficient for a sphere resting inside a uniform flow. Finally, we present fracture patterns obtained when modelling water injection into a Hele-Shaw cell, filled with a dense granular pack

Pore-scale mechanisms of CO2 storage in oilfields

Rapid implementation of global scale carbon capture and storage is required to limit temperature rises to 1.5 °C this century. Depleted oilfields provide an immediate option for storage, since injection infrastructure is in place and there is an economic benefit from enhanced oil recovery. To design secure storage, we need to understand how the fluids are configured in the microscopic pore spaces of the reservoir rock. We use high-resolution X-ray imaging to study the flow of oil, water and CO2 in an oil-wet rock at subsurface conditions of high temperature and pressure. We show that contrary to conventional understanding, CO2 does not reside in the largest pores, which would facilitate its escape, but instead occupies smaller pores or is present in layers in the corners of the pore space. The CO2 flow is restricted by a factor of ten, compared to if it occupied the larger pores. This shows that CO2 injection in oilfields provides secure storage with limited recycling of gas; the injection of large amounts of water to capillary trap the CO2 is unnecessary

Automatic measurement of contact angle in pore-space images

A new approach is presented to measure the in-situ contact angle (θ) between immiscible fluids, applied to segmented pore-scale X-ray images. We first identify and mesh the fluid/fluid and fluid/solid interfaces. A Gaussian smoothing is applied to this mesh to eliminate artifacts associated with the voxelized nature of the image, while preserving large-scale features of the rock surface. Then, for the fluid/fluid interface we apply an additional smoothing and adjustment of the mesh to impose a constant curvature. We then track the three-phase contact line, and the two vectors that have a direction perpendicular to both surfaces: the contact angle is found from the dot product of these vectors where they meet at the contact line. This calculation can be applied at every point on the mesh at the contact line. We automatically generate contact angle values representing each invaded pore-element in the image with high accuracy. To validate the approach, we first study synthetic three-dimensional images of a spherical droplet of oil residing on a tilted flat solid surface surrounded by brine and show that our results are accurate to within 3° if the sphere diameter is 2 or more voxels. We then apply this method to oil/brine systems imaged at ambient temperature and reservoir pressure (10MPa) using X-ray microtomography (Singh et al., 2016). We analyse an image volume of diameter approximately 4.6  mm and 10.7  mm long, obtaining hundreds of thousands of values from a dataset with around 700 million voxels. We show that in a system of altered wettability, contact angles both less than and greater than 90° can be observed. This work provides a rapid method to provide an accurate characterization of pore-scale wettability, which is important for the design and assessment of hydrocarbon recovery and carbon dioxide storage

Representation of fully three‐dimensional interfacial curvature in pore‐network models

Quasi two-dimensional approximations of interfacial curvature, present in current network models of multiphase flow in porous media, are extended to three dimensions. The new expressions for threshold capillary pressure are validated and calibrated using high-resolution direct numerical simulations on synthetic geometries. The effects of pore-space expansion and sagittal interface curvature on displacement are quantified, and are shown to be a key step in improving the physical accuracy of network models. Finally, the calibrated network model is used to obtain predictions for relative permeability and capillary pressure in a water-wet Bentheimer sandstone. The predictions are compared to experimental measurements, revealing that the inclusion of three-dimensional interfacial curvature leads to more accurate predictions

Preferential Paths of Air-water Two-phase Flow in Porous Structures with Special Consideration of Channel Thickness Effects.

Accurate understanding and predicting the flow paths of immiscible two-phase flow in rocky porous structures are of critical importance for the evaluation of oil or gas recovery and prediction of rock slides caused by gas-liquid flow. A 2D phase field model was established for compressible air-water two-phase flow in heterogenous porous structures. The dynamic characteristics of air-water two-phase interface and preferential paths in porous structures were simulated. The factors affecting the path selection of two-phase flow in porous structures were analyzed. Transparent physical models of complex porous structures were prepared using 3D printing technology. Tracer dye was used to visually observe the flow characteristics and path selection in air-water two-phase displacement experiments. The experimental observations agree with the numerical results used to validate the accuracy of phase field model. The effects of channel thickness on the air-water two-phase flow behavior and paths in porous structures were also analyzed. The results indicate that thick channels can induce secondary air flow paths due to the increase in flow resistance; consequently, the flow distribution is different from that in narrow channels. This study provides a new reference for quantitatively analyzing multi-phase flow and predicting the preferential paths of immiscible fluids in porous structures

Determination of Appropriate Irrigation Depth of Sante Cultivar and New Potato Clones in Deficit Irrigation condition

Water is the most important factor in agricultural products, water shortage and low irrigation efficiencies in Iran necessitates research in deficit irrigation. This Study to estimate the production function, calculate the depth and optimal index and effect of deficit irrigation on yield was done in Agriculture and Natural Resources Research Center of Hamadan. Test was performed in Split Plot Design based on Randomized Complete Block in three replications with two factors, containing 1: water deficit irrigation treatment namely, 50, 60, 70, 80, 90 and 100% of basically potato irrigation requirement. 2: Two clones accompanied with Sante Cultivar. The results indicated the effect of different treatment on yield and water use efficiency was significant at the 1% level. Also with increasing water depth until maximum depth, gross income was increased. Also results showed that the net benefit was the same for the equivalent depth under earth limitation and the maximum water depth by 414761192, 84952553 and 91034463 rails for santeh, 397001-13 and 397008-2 clones. The maximum saved water relative complete irrigation belongs to irrigation equal depth under water limitation. It can be concluded that with the savings of water under deficit irrigation practices, the planting area would increase by 21, 27 and 14% for santeh, 397001-13 and 397008-2 clone. The maximum earning return (Rails per m3 of water) under water limitation will be 6080, 12096 and 14185 rails for santeh, 397001-13 and 397008-2 clones. According to 397008-2 clone relative to other cultivars has the highest earning return, so cultivar of this clone than other varieties is recommended

Pore occupancy, relative permeability and flow intermittency measurements using X-ray micro-tomography in a complex carbonate

We imaged the steady-state flow of brine and decane (oil) at different fractional flows during dual injection in a micro-porous limestone, Estaillades, using X-ray micro-tomography. We applied differential imaging to: (a) distinguish micro-porous regions from macro-pores, and (b) determine fluid pore occupancy in both regions, and relative permeability at a capillary number, Ca = 7.3 × 10 −6 . The sample porosity was approximately 28%, with 7% in macro-pores and 21% in pores that could not be directly resolved (micro-porosity). Fluid occupancy in micro-porosity was classified into three sub-phases: micro-pore space with oil, micro-pore space with brine, and micro-pores partially filled with oil and brine. Our method indicated an initially higher oil recovery from micro-porosity, consistent with waterflooding in a water-wet rock. The fractional flow and relative permeabilities of the two fluids were obtained from measurements of the pressure differential across the sample and the saturation calculated from the images. The brine saturation and relative permeabilities are impacted by the presence of water-wet micro-porosity which provides additional connectivity to the phases. Furthermore, we find that in addition to brine and decane, a fraction of the macroscopic pore space contains an intermittent phase, which is occupied either by brine or decane during the hour-long scan time. Pore and throat occupancy of oil, brine and intermittent phase were obtained from images at different fractional flows using the generalized pore network extracted from the image of macro-pores. The intermittent phase, where the occupancy fluctuated between oil-filled and brine-filled, was predominantly located in the small and intermediate size pores and throats. Overall, we establish a new experimental methodology to: (i) quantify initial and recovered oil in micro-pores, (ii) characterise intermittent flow, and (iii) measure steady-state relative permeability in carbonates, which is shown to be greatly influenced by micro-porosity