Electrical transport properties of saturated porous media, such as soils, rocks and fractured networks, typically composed of a non-conductive solid matrix and a conductive brine in the pore space, ...have numerous applications in reservoir engineering and petrophysics. One of the widely used electrical conductivity models is the empirical Archie's law that has a practical application in well-log interpretation of reservoir rocks. The Archie equation does not take into account the contributions of clay minerals, isolated porosity, heterogeneity in grains and pores and their distributions, as well as anisotropy. In the literature, either some modifications were presented to apply Archie's law to tight and clay-rich reservoirs or more modern models were developed to describe electrical conductivity in such reservoirs. In the former, a number of empirically derived parameters were proposed, which typically vary from one reservoir to another. In the latter, theoretical improvements by including detailed characteristics of pore space morphology led to developing more complex electrical conductivity models. Such models enabled us to address the electrical properties in a wider range of potential reservoir rocks through theoretical parameters related to key reservoir-defining petrophysical properties. This paper presents a review of the electrical conductivity models developed using fractal, percolation and effective medium theories. Key results obtained by comparing experiential and theoretical models with experiments/simulations, as well as advantages and drawbacks of each model are analyzed. Approaches to obtaining more reasonable electrical conductivity models are discussed. Experiments suggest more complex relationships between electrical conductivity and porosity than experiential models, particularly in low-porosity formations. However, the available theoretical models combined with simulations do provide insight to how microscale physics affects macroscale electrical conductivity in porous media.
In the past decades, there was considerable controversy over the Lucas–Washburn (LW) equation widely applied in capillary imbibition kinetics. Many experimental results showed that the time exponent ...of the LW equation is less than 0.5. Based on the tortuous capillary model and fractal geometry, the effect of tortuosity on the capillary imbibition in wetting porous media is discussed in this article. The average height growth of wetting liquid in porous media driven by capillary force following the
law is obtained (here
D
T
is the fractal dimension for tortuosity, which represents the heterogeneity of flow in porous media). The LW law turns out to be the special case when the straight capillary tube (
D
T
= 1) is assumed. The predictions by the present model for the time exponent for capillary imbibition in porous media are compared with available experimental data, and the present model can reproduce approximately the global trend of variation of the time exponent with porosity changing.
•IOR in shale by using fractures in the same well as injection and production zones.•Compared injection of water, immiscible CO2, and surfactant as IOR fluids.•IOR did not work when average ...heterogeneous matrix permeability was below 0.01mD.•Unswept oil is inaccessible due to low permeability and not capillary pressure.
Tight-oil reservoirs exhibit two characteristic behaviors that limit potential for improved recovery: (i) limited fluid movement from the unfractured matrix limits the potential to sweep additional oil towards the production wells with injection of a displacing fluid, (ii) the wettability of these reservoirs tend to be oil-wet which holds oil in relatively smaller pores, as compared to gas or water, making it difficult to mobilize that trapped oil. Primary oil production from these formations can decline to half of initial rates in the first year due to low permeability in the unfractured reservoir matrix, and a large amount of unrecovered oil remains in smaller pores that is not able to move out. To address these challenges, this study investigates the potential to improve oil recovery from tight-oil reservoirs by a method that includes injecting a fluid into the fractured reservoir to produce hydrocarbons from adjacent fractures intersecting the same wellbore. The injection and production through fractures has a potential economic advantage over huff-n-puff scheme such that there is no lag-period between injection and production. We compare the estimates of incremental oil recovery obtained by injecting water, immiscible CO2, and surfactant over the oil recovered by primary depletion (with no injection). The results suggest that injection of fluids may not always improve recovery from tight-oil reservoirs, especially in a heterogeneous reservoir (having different rock types) whose average matrix permeability is lower than 0.01mD. In cases where recovery is improved over primary depletion, water flood and surfactant flood perform almost equally well with no noticeable difference between the two. Although, surfactant results in favorable fluid properties to mobilize oil, the reason surfactant did not perform well in tight-oil formation studied here is because the unswept oil is inaccessible due to small permeability, and not because of high capillary pressure.
Archie's equation is an empirical electrical conductivity‐porosity model that has been used to predict the formation factor of porous rock for more than 70 years. However, the physical interpretation ...of its parameters, e.g., the cementation exponent m, remains questionable. In this study, a theoretical electrical conductivity equation is derived based on the fractal characteristics of porous media. The proposed model is expressed in terms of the tortuosity fractal dimension (DT), the pore fractal dimension (Df), the electrical conductivity of the pore liquid, and the porosity. The empirical parameter m is then determined from physically based parameters, such as DT and Df. Furthermore, a distinct interrelationship between DT and Df is obtained. We find a reasonably good match between the predicted formation factor by our model and experimental data.
Key Points
An electrical conductivity model is derived based on fractal geometry
Physical definitions of empirical parameters in Archie's equation are presented
Predictions of proposed model show good correspondence with experimental data
•Gradient boosting regression and random forest are combined to analyse net ecosystem carbon exchange.•The model considers 22 environmental variables, more than other similar works.•The extremums are ...employed to analyse the corresponding variables’ importance.
Carbon balance is essential to keep ecosystems sustainable and healthy. Net ecosystem carbon exchange (NEE), which is affected by a bunch of meteorological variables to different extent, helps to gauge the balance of the carbon cycle between biological organisms and atmosphere. In this study, the NEE data is collected from two flux measuring sites. Gradient boosting regression algorithm is employed to predict NEE based on the meteorology and flux data from site UK-Gri. During the training process, KFold cross-validation algorithm is implemented to avoid overfitting, and random forest algorithm is implemented to identify the important variables influencing NEE mostly. The four most important variables are found to be global radiation, photosynthetic active radiation, minimum soil temperature, and latent heat. The regression model was compared with three state-of-the-art prediction models: support vector machine, stochastic gradient descent, and bayesian ridge to verify its performance. The experimental results show that this regression model outperforms the other three models, and gives higher value of R-squared, lower values of mean absolute error and root mean squared error. To verify the regression model’s generalization ability, the data from the second flux site, NL-Loo, was employed, and the hybrid data of the two sites was used. The results show that this model performs well on the hybrid data, too. In practical terms, the gradient boosting regression model provides many tunable hypterparameters and loss functions, which make it more flexible and accurate compared to the other three models. This study has conclusively demonstrated for the first time that the combination of gradient boosting regression and random forest models should be considered as valuable tools to make effective prediction for NEE and acquire reliable important variables influencing NEE mostly. The methodologies could be useful in the research fields of ecosystem stability evaluation, environmental restoration, trend analysis of climate change, and global warming monitoring.
Magnetic field effects are encountered in many engineering applications which include but are not limited to metal casting, nuclear reactor coolers, and geothermal energy extraction. On the other ...hand, due to their outstanding thermal performance, nanofluids have been successful in obtaining acceptability as per the new generation of heat transfer fluids in automotive cooling devices, in heat exchangers, and building heating. Therefore, this research is carried out to understand how the nanofluid flow in a cavity is affected by a magnetic field (due to a dipole placed nearby). The single-phase model is employed for modeling the nanofluid, whereas the governing partial differential equations are solved numerically. The dipole may give rise to the new vortices in the flow near its location while enhancing Nusselt number. The Reynolds number reduces Nusselt number along the lower wall while affecting the strength of vortices near the dipole location. Increasing the strength of the dipole results in distorting the symmetry of streamlines by first enhancing the size of the lower vortex; some vortices near dipole also join and merge. Further, the magnetic field makes the temperature field nonsymmetric and shifts the zone of higher temperature gradient around the location of a dipole. The presence of dipole is more effective for skin friction compared with the Nusselt number.
Estimate of permeability plays a crucial role in flow-based studies of fractured tight-rocks. It is well known that most of the flow through tight-rocks (e.g., shales) is controlled by permeable ...features (e.g., fractures, laminations, etc.), and there is negligible flow through the matrix. However, current approaches in the literature to model permeability of tight-rocks do not account for such features present within the rock ranging from micro-scale to field-scale. Current permeability modeling approach assumes a single continuum without considering the presence of permeable features within the matrix (e.g., micro-fractures) or outside the matrix (e.g., natural fractures). Although the laboratory-measured permeability implicitly captures discrete features present in that sample (e.g., fractures, laminations, micro-fractures), most of the permeability models proposed for shale do not account for these features. Fracture permeability in the literature is typically modeled using an ideal slit assumption; however, this highly overestimates its permeability because fractures in real medium are non-ideal in terms of their porosity and tortuosity, which affect their permeability. Additionally, the transition zone between fracture and matrix also affects the permeability of fracture. In this study, part of a two-part series, a new method to predict permeability of fractured shale by discretizing the medium into matrix (inorganic and organic) and fractures is presented. New analytical expressions of permeability are derived to account for non-ideal nature of porous medium and two-phase flow in fractures. Rock feature in each cell of the grid is identified as one of the three elements (organic matter, inorganic matter, or fracture), and permeability of that cell is estimated using a suitable analytical expression. This method allows estimating permeability at any scale of interest and more robustly than by a pure analytical approach. The proposed method is validated against local and global-scale measurements on three fractured samples from laboratory. Finally, the method is used to predict two-phase flow permeability of supercritical CO
2
displacing water within a fracture in a Utica shale sample. The proposed two-phase flow permeability equations can be used as a quick analytical tool to predict relative permeability estimates of two-phase flow in fractured shale samples. In Part 2, the proposed method is used to estimate field-scale permeability through an optimization process that uses field-scale production and other readily available information.
A model for gas transport in shale is proposed by accounting for three major fluid flow mechanisms in shale stratum, which is modeled as a 3D fractal media. The proposed apparent permeability of ...shale is an analytical expression that also accounts for heterogeneous pore sizes in shale stratum, and is verified using experimental datasets for methane and helium flow in shale. Results of sensitivity analysis indicate that surface diffusion of adsorbed gas plays an important role, specifically in smaller pores, while surface diffusion would be negligible in larger pores. Further, the proposed model shows that flow due to surface diffusion decreases moderately with the increase of isosteric adsorption heat, while it increases significantly with the increase of the maximum adsorption capacity. One of the key novelties of the proposed permeability model is that it accounts for pore size distribution to reveal novel insights on gas transport in shale that can be used to optimize gas production by operational controls (e.g. controlling reservoir pressure) as flow regimes change with time.
•A new model for gas transport in shale media by means of a 3D fractal porous media with variable pore sizes is proposed.•Model reveals that permeability due to surface diffusion is not affected by the maximum pore diameter.•We find that the permeability of surface diffusion decreases moderately with the increase of isosteric adsorption heat.•Theoretical understanding of transport mechanisms can be used to optimally exploit shale by operational controls.
The successful pilot testing of depressurization production for natural gas hydrate reservoir was conducted at Shenhu Area in the South China Sea. However, pressure changes due to depressurization ...production cause shrinkage of creeping pore and throat space for fluid flow, ultimately resulting in permeability damage in this reservoir. To optimize gas recovery for natural gas hydrate reservoir, it is important to understand the substantial variations of the pore structure and physical properties under different pressure conditions. In this study, by integrating computed tomography imaging with water flow experiments on Clay-silt sediment sample, we analyze how pore scale structural parameters (such as average pore and throat radius, pore and throat median radius, maximum pore and throat radius, and fractal dimension) change under different axial stresses by using fractal geometry approach. It is found that there is a negative relationship between axial stress and structural parameters. Meanwhile, with the axial stress increases, the range of pore and throat radius distribution located on the right of center distribution decreases. On the basis of fractal geometry theory, a fractal model is then proposed to explain the effects of axial stress and creeping microstructure on permeability for natural gas hydrate reservoir. Results show that the model provides good match with experimental data when the axial stress is larger, while poor agreements with experimental results at low pressure. This study helps us understand fundamental mechanism for permeability changes during the depressurization of gas hydrate reservoir.
•The creeping microstructural images of gas hydrate reservoir sediment are obtained by micro-CT.•The quantitive microstructure parameters under different axial stresss are simulated.•A creeping permeability fractal model is proposed and tested by experiments.
Spontaneous capillary imbibition is an important fundamental phenomenon existing extensively in a variety of processes such as polymer composite manufacturing, oil recovery, soil science and ...hydrology, etc. In this work, analytical expressions for characterizing a spontaneous co-current imbibition process of wetting fluid into gas-saturated porous media are proposed based on the fractal characters of porous media. The mass of imbibed liquid is expressed as a function of the fractal dimensions for pores and for tortuous capillaries, the minimum and maximum hydraulic diameter of pores, and the ratio for minimum to maximum hydraulic diameters, porosity, and fluid properties, as well as the fluid−solid interaction. The imbibed weight predicted by the present model is in good agreement with the available experimental data.
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