Calculation Of Relative Permeability Research Articles

Excitation of Odd Harmonics of SH0 Mode Ultrasonic Guided Waves Using Magnetostriction-Based EMAT: Theoretical Modeling

ABSTRACT Magnetostriction-based electromagnetic acoustic transducer (M-EMAT) is a promising tool for generating fundamental shear-horizontal (SH0) mode guided waves in plate. Though the M-EMAT possesses high-order harmonics excitation ability in nature, its conventional way can only generate a fundamental component of SH0 mode. The analytical modeling was performed in this study to releasing the ability of M-EMAT in generating odd harmonics of SH0 mode. First, the inaccurate conditions of magnetic fields for relative permeability calculation in the existing model are corrected in the proposed model. Second, the error of the existing model in predicting the spectrum of the SH0 mode generated in Nickel plate is estimated. Third, numerical solutions are provided by the improved model to examine the key factors governing the ability of M-EMAT in generating odd harmonics of SH0 mode. The conclusions demonstrated that the intensity ratio (H S /H D ) of static and dynamic magnetic fields is adjusted below 1 and the ability of M-EMAT in generating odd harmonics of SH0 mode can be activated. The normalized amplitude of 3rd harmonics decays exponentially with the increase of H S /H D , which is independent of geometrical parameters of M-EMAT. The improved model can effectively optimize excitation parameters of M-EMAT and generate odd harmonics of SH0 mode in plate.

Cluster capillary core model for calculation of relative phase permeability for oil and water filtration

Описана физико-математическая модель стационарного течения водонефтяной смеси в поровом пространстве керна, представляемого в виде совокупности капиллярных кластеров. Разработанная модель позволяет вычислять функции относительных фазовых проницаемостей на основе данных стандартных лабораторных исследований керна и экспериментов по однофазной фильтрации флюидов. В результате регрессионного анализа лабораторных данных по терригенным породам месторождений Западной и Восточной Сибири получены многопараметрические зависимости параметров функции межфазного взаимодействия от фильтрационно-емкостных свойств и параметров капиллярного кластера. Установлено, что результаты расчета относительных фазовых проницаемостей по предложенной модели хорошо согласуются с экспериментальными данными.

Interpretation of Petrophysical Properties in Reservoir Rock Using Capillary Pressure Data of the Mishrif Formation in West Qurna Oilfield, Southern Iraq

In this study, capillary pressure tests for twenty-nine samples acquired from four wells, (Rn-83, WQ-155, WQ286, and WQ-355) were used to estimate pore size distribution, pore-throat sorting, displacement pressure, reservoir grade, oil column, effective porosity, and relative permeability of the Mishrif Formation at West Qurna Oilfield, southern Iraq. Interpretation of capillary pressure data revealed that the formation can be divided into four reservoir facies with different reservoir production performances: very good, good, medium, and poor. The facies with very good performance is characterized by large pore sizes, excellent reservoir grade, low displacement pressure, and high oil saturations. The good facies is characterized by the presence of good pore throat sorting, good reservoir grade, and good porosity. Contrary, Medium-performance reservoir facies are characterized by the presence of medium pore sizes, medium pore throat sorting, and medium reservoir grade. Poorly performing reservoir facies is characterized by small pore size, high displacement pressure, poor throat sorting, and high water saturation levels. Based on the relative permeability calculations some samples are wet with water (water-wet), while others are wet with oil (oil-wet).

Theoretical comparison of two setups for capillary pressure measurement by centrifuge

There are several approaches for the calculation of capillary pressure curves in porous media including the centrifuge method. In this work, a new installation of centrifuge test is introduced and compared with the traditional setup. In the first setup, which is a standard approach in labs, the core face closest to the rotational axis is open to the non-wetting phase, while the farthest face is open to the wetting phase where strictly co-current flow is generated in rotations; labeled Two-Ends-Open (TEO). In the second setup, which is proposed as a new approach, only the outer radius surface is open and is exposed to the light non-wetting phase; labeled One-End-Open (OEO). This setup strictly induces counter-current flow. The two systems and their corresponding boundary conditions are formulated mathematically and solved by a fully implicit numerical solver. The TEO setup is validated by comparison with commercial software. Experimental data from the literature are used to parameterize the models. It is mathematically, and with examples, demonstrated that the same equilibrium is obtained in both systems with the same rotational speed, and changing the installation does not influence the measured capillary pressure. This equilibrium state is only dependent on the rotational speed, rock capillary pressure properties, and fluid densities, not the installation geometry, relative permeabilities, or fluid viscosities. However, the dynamic transition trend and saturation profiles were found to be dependent on the applied installation. It was observed that the OEO setup takes almost identical equilibration time as the TEO setup for mixed-wet states, although it needed much longer time in water-wet states. The presence of threshold capillary pressure significantly increased the time scale of the OEO setup. Also, it was found that in contradiction to the TEO setup, the dynamic saturation profile in OEO was rarely influenced by viscosity ratio. To conclude, the performed history matching analysis demonstrated that the OEO setup can be applied for the calculation of counter-current relative permeability from the production data with reasonable accuracy.

A novel model for oil-water two-phase relative permeability of shale formation during flowback based on fractal method

As an abundant type of unconventional hydrocarbon resources on the earth, shale oil has been widely concerned by scholars across the world. During flowback period, flow-back resistance of fracturing fluids increases because of the existence of shale oil. Therefore, it is of practical significance to study the flow-back capability of fracturing fluid for high well performance. In this paper, fractal method of porous media has been used for calculation of relative permeability of oil-water two phase flow in shale pores. First, we built up flow equation of single nanopore with four layers: boundary layer, bulk wetting phase layer, oil-water two phase layer, and nonwetting phase layer. Furthermore, boundary slip, boundary, viscosity change in boundary layer and threshold pressure gradient is considered for correction flow rate equation. The pores of shale matrix can be simplified into capillary bundle model, and fractal theory is suitable for this model. Aperture fractal dimension and tortuosity fractal dimension is used to expand its scale to porosity media with fractal method. Then the model is verified by experimential results and classic models. Furthermore, serval main factors affecting the relative permeability of water are primarily analyzed, and the more essential factors out of the aforementioned ones are extracted and further studied. The results show that with the increase in the thickness of oil-water two phase layer, the relative permeability of water is affected more seriously; The relative permeability of water is positively correlated with slip length and thickness of boundary layer. This work provides a more convenient approach to calculate relative permeability with no experiments, and provide permeability for numerical simulation in flow back period.

Investigating NMR-based absolute and relative permeability models of sandstone using digital rock techniques

Absolute permeability determines fluid production capacity, and relative permeability determines the produced fluid types, and their accurate calculations are critical for evaluating hydrocarbon-bearing formations. In oil/gas fields, the nuclear magnetic resonance (NMR) logging tool has been widely used due to its unique advantage of directly detecting the rock pores. However, this tool cannot measure absolute permeability or relative permeability directly. There exist many approaches for estimating NMR-based permeabilities, but most of them lack the basic understandings of fluid flow characteristics in micro-pores. To investigate NMR-based absolute and relative permeability models of sandstone , we suggest three types of pores, i.e., non-flowing bound water pores , slow-flowing free water pores, and fast-flowing free water pores, and incorporate them into the permeability calculations. The digital rock technique was utilized to study fluid flow mechanisms. Lattice Boltzmann method (LBM) was applied on two constructed three-dimensional digital rocks to calculate fluid flow velocity field distributions and absolute permeabilities. From the fluid flow simulation results, it was found that bound water exists not only in small pores but also in medium-sized pores and big pores. By comparing the permeability values of digital rocks with various porosities, we demonstrated that fast-flowing free water pores have the highest contribution to absolute permeability. Five relative permeability calculation models were investigated, where we found that the best link between the T 2 spectrum and relative permeability curve was the pore size distribution index. The obtained results indicated that the traditional Coates model combined with the spectral bulk volume irreducible method and the Brooks-Corey model are high-precision models for calculating the NMR-based absolute and relative permeabilities in sandstone reservoirs. • Three fluid flow velocity-based types of pores were investigated. • Fluid flow characteristics and their impacts on permeability were analyzed. • The three-dimensional spatial distribution of bound water was studied. • The accuracies of five relative permeability calculation models were compared.

Influence of gas hydrate saturation and pore habits on gas relative permeability in gas hydrate-bearing sediments: Theory, experiment and case study

Gas relative permeability characterization is of key significance to model the behavior of gas flow in gas hydrate-bearing sediments. The present study proposes a novel model to relate gas relative permeability to gas hydrate saturation based on X-ray micro-CT imaging information of xenon hydrate pore-scale distribution in sand sediments. Lattice Boltzmann method (LBM) was used to obtain permeability values of xenon hydrate-bearing sediments via micro-CT data. The results showed that gas relative permeability (Kr) versus gas hydrate saturation (Sh) data are consistent with the new model and the imitative effect is relatively better than that of the simple Corey model. Besides, we calculated gas relative permeability versus gas hydrate saturation curves for various pore habits via idealized models. Experimental measurements and simulation results showed that the grain-coating gas hydrate exhibits the highest gas relative permeability, while pore-filling gas hydrate exhibits the lowest values of gas relative permeability, and the cementing gas hydrate ranges in between. We validated the new gas relative permeability calculation model by applying it to the well logging data of gas hydrate reservoirs. Our results showed that the novel model is beneficial for permeability characterization of gas hydrate reservoirs and gas relative permeability calculations.

Application of percolation, critical-path, and effective-medium theories for calculation of two-phase relative permeability.

There has been active development of numerical pore-network simulation of two-phase immiscible flows in porous media in recent years. These models allow for generation of capillary pressure and relative permeability curves. However, percolation models provide an efficient alternative, with reduced reliance on numerical techniques. Implementation of effective medium or critical path theory along with the percolation model allows for evaluation of the relative permeability curves. Both approximations failed to match the irreducible water saturation for water relative permeability. While the effective medium approximation poorly matches the pore network simulator, the critical path approximation is shown to match the result of the oil relative permeability. Despite the difference in end points, there is qualitative agreement between critical path approximation and the pore network simulator. Moreover, observed differences are not necessarily a drawback due to important boundary effects as discussed in the paper. Our results indicate that percolation-theory based predictions have the potential to become an efficient tool for upscaling by computing two-phase flow properties for numerous porosity subdomains.

Correction for capillary pressure influence on relative permeability by combining modified black oil model and Genetic Algorithm

The substantial interference of the tight reservoir's capillary pressure on relative permeability measurement can significantly diminish the prediction accuracy of the oilfield production. This study established an innovative method to eliminate the capillary pressure effect on relative permeability calculation by combining the modified numerical simulation model and the Genetic Algorithm. Steady-state measurements were conducted on tight core sample (0.0321mD) to obtain the initial relative permeability curves using Darcy's law. A modified numerical simulation model that considers equivalent phase pressure for water and oil at outlet surface and directly simulates fixed injection-rate boundary conditions without using wells has been proposed. After analysis of water saturation distribution and pressure distribution along the core, absolute permeability, residual water saturation, and the two-phase relative permeability at corresponding saturation need to be optimized by the Genetic Algorithm based on the initial relative permeability curves to match the experimental results. The outcomes show that the optimized absolute permeability is 19.63% higher than the experimentally measured value, and the optimized residual water saturation is 17.46% lower than the experimental residual water saturation. For the other saturations, the differences between the optimized relative permeability and the experimental results range from 25.93% to 10.57%. The whole divergence of the experiment results and the simulation results about average water saturation and inlet pressure using optimized Kr curves is 1.57%, far less than 69.72% of the unoptimized Kr curves. This research is of great significance for accurately obtaining the relative permeability curves of the tight oil reservoir with intense capillary pressure. • A modified black-oil model is built for accurately simulating capillary end effect. • Lower water injection rate affects relative permeability curves more significantly. • The actual residual water saturation is 17.46% lower than the measured one.

A New Model to Calculate Oil-Water Relative Permeability of Shaly Sandstone

Oil-water relative permeability curves are the basis of oil field development. In recent years, the calculation of oil-water relative permeability in sandstone reservoirs by resistivity logging data has received much attention from researchers. This article first analyzed the existing mathematical models of the relationship between relative permeability and resistivity and found that most of them are based on Archie formula, which assumes the reservoir is clean sandstone. However, in view of the fact that sandstone reservoir is commonly mixed with shale contents, this research, based on the dual water conductivity model, Poiseuille’s equation, Darcy’s law, and capillary bundle model, derived a mathematical model (DW relative permeability model) for shaly sandstone reservoir, which calculates the oil-water relative permeability with resistivity. To test and verify the DW relative permeability model, we designed and assembled a multifunctional core displacement apparatus. The experiment of core oil-water relative permeability and resistivity was designed to prove the effectiveness of the DW relative permeability model in shaly sandstone reservoirs. The results show that the modified Li model can well express the transformational relation between resistivity and relative permeability in sandstone reservoir with low clay content. Compared with the modified Li model and the Pairoys model, the DW relative permeability model is more helpful to collect better results of relative permeability in shaly sand. These findings will play a significant role in the calculation of oil-water relative permeability in reservoirs based on resistivity logging data and will provide important data and theory support to the shaly sandstone reservoir characterized oil field development.

A Comprehensive Model for Estimating Stimulated Reservoir Volume Based on Flowback Data in Shale Gas Reservoirs

Stimulated reservoir volume (SRV) which is generated by horizontal drilling with multistage hydraulic fracturing governs the production in the shale gas reservoirs. Although microseismic data has been used to estimate the SRV, it is high-priced and sometimes overestimated. Additionally, the effect of stress sensitivity on SRV is not considered in abnormal overpressure areas. Thus, the objective of this work is to characterize subsurface fracture networks with stress sensitivity of permeability through the shale gas well production data of the early flowback stage. The flowback regions are first identified with the flowback data of two shale gas wells in South China. Then, we measured the permeability stress sensitivity of the core after fracturing, coupled to the dynamic relative permeability (DRP) calculation to obtain an accurate and simple DRP curve. After that, a comprehensive model is built considering dynamic two-phase relative permeability function and stress sensitivity. Finally, we compared the calculated results with the microseismic data. The results show that the proposed model could reasonably predict the SRV using the flowback data after fracturing. Additionally, compared with the microseismic data, the stress sensitivity should be included, especially in the abnormal overpressure block. It is believed that this mathematical model is accurate and useful. The work provides an efficient approach to estimate stimulated reservoir volume in the shale gas reservoirs.

Numerical calculation of relative phase permeabilities for two-phase flow in the channel

Two-phase flow through a channel is considered for different viscosity ratios, surface tension (σ) and types of displacement (drainage or imbibition). The simulation is based on the numerical solution of the incompressible Navier–Stokes equations. Numerical calculation results of the relative phase permeability are compared for different mesh sizes. For calculation of relative phase permeability there is a problem with calculation of the average pressure gradient. Following approaches for calculation of average pressure gradient had been chosen: velocity weighted average of the pressure gradient and velocity weighted average of the viscous force. The approach of velocity weighted average of the viscous force gives more accurate results than the approach of velocity weighted average of the pressure gradient. Fingering instability was observed depending on the viscosity ratio and surface tension. All numerical calculations are performed using OpenFOAM finite volume library.

Relative permeability model of oil-water flow in nanoporous media considering multi-mechanisms

The accurate calculation of relative permeability is of critical importance to clarify the multiphase flow behaviors in nanoporous media. In this paper, the relative permeability model is proposed to investigate the oil-water flow behaviors in water-wetting nanoporous media based on the no-slip Hagen-Poiseuille (HP) equation. The proposed model takes into account the oil-water distribution, slip length, adsorbed water viscosity, viscosity ratio of oil to water and pore size distribution (PSD). The oil-water distribution, slip length and adsorbed water viscosity strongly depend on the wall wettability. The results show that the relative permeability of oil phase increases with an increasing viscosity ratio, and it can be larger than 1 because of the positive slip length caused by ‘lubricating’ effect of water film on oil phase. The relative permeability of oil phase decreases with increase of the contact angle which causes the increasing slip length and decreasing adsorbed water viscosity. As average pore radius and frequency fraction increase, the relative permeability of water phase increases. The reason is that the thickness of water film increases for a specific saturation and then leads to the less resistance by the great adsorbed water viscosity effect. This work focuses on the relative permeability of two-phase flow in water-wetting nanoporous media, which can be used in shale or tight oil production, ground water flow and other aspects of two-phase flow.

Multiphase flow in tight sandstone: An improved application for 3D intermingled fractal model

Abstract Multiphase displacement in tight sandstone is fundamental and critical for tight oil production. Micropores dominate the pore space in tight sandstone. Microscopic mineral components in micropores substantially influence the multiphase displacement behavior. Pore size distribution exhibits a self-similar or fractal property, similar to inorganic mineral grains. Utilizing fractal theory eases the rebuilding of the flowing space and calculation of relative permeability. As an improvement of previous work, we successfully extended the 3D intermingled fractal model (3D IFM). The extended 3D IFM can evaluate multiphase flow behavior in tight sandstone, considering fractal characteristics of pore size distribution and mineral grain distribution. The fractal information of pores and mineral properties are obtained by scalable scanning electron microscopy (SEM) and energy dispersive spectroscopy(EDS) images, respectively. This method is useful and reliable for calculating relative permeability and residual saturation. The method is also successfully used to evaluate the influence of oil-water viscosity ratio, mineral components and formation depth on multiphase displacement behavior, proving its convenience and potential in rapidly evaluating multiphase displacement behavior in tight sandstone.

Determination of relative phase permeabilities in stochastic model of pore channel distribution by diameter

The problem of the pore space description and the calculation of relative phase permeabilities (RPP) for two-phase filtration is considered. A technique for constructing a pore-network structure for constant and variable channel diameters is proposed. A description of the design model of RPP based on the capillary pressure curves is presented taking into account the variability of diameters along the length of pore channels. By the example of the calculation analysis for the core samples of the Urnenskoye and Verkhnechonskoye deposits, the possibilities of calculating RPP are shown when using the stochastic distribution of pores by diameters and medium-flow diameters.

Study on the rock-electric and the relative permeability characteristics in porous rocks based on the curved cylinder-sphere model

Usually, in conventional reservoirs, the rock-electric properties can be explained by Archie's law, and the relative permeability is only considered as a function of fluid saturation. However, as for the complex reservoirs, Archie's law fails to accurately describe the rock-electric properties and the relative permeability is not only affected by saturation, the reason is that both rock-electric and relative permeability characteristics are influenced by multi-factors, including the complex pore structure, fluid distribution, and wettability. Currently, there lacks the theoretical method to comprehensively study the multi-factors effect on rock-electric and relative permeability characteristics. In this paper, the curved cylinder-sphere model is developed to illustrate the complex pore-throat structure, fluid distribution, and wettability in real rocks, which can be characterized by two important parameters: the ratio Cd of the curved cylinder radius to the sphere radius and the tortuosity τ. Based on the curved cylinder-sphere model, and by using Ohm's law, one can carry out the research on the effect of pore geometry, fluid distribution, and wettability on rock-electric characteristics. Moreover, by combining the curved cylinder-sphere model with Li's model, the effect of pore structure, fluid distribution, and wettability can be incorporated into the relative permeability calculation model. By means of the numerical simulation and analysis, it comes to conclusions that pore structure, fluid distribution, and wettability are the principal factors affecting both rock-electric and relative permeability characteristics, which may cause different formation factor, resistivity index, and relative permeability even in those reservoirs with the same porosity and fluid saturation. Besides, the study demonstrates that the complex pore structure, fluid distribution, and wettability may cause the non-Archie phenomenon of rock-electric characteristics, in addition, the complex pore structure can lead to the decrease of water relative permeability and the increase of oil relative permeability, and when the rock wettability changes from water-wet to oil-wet, water relative permeability increases and oil relative permeability decreases. Furthermore, by the comparison of the simulation results and Lab data, the important effect of complex pore structure and fluid saturation is confirmed.

Influence of capillary end effects on steady-state relative permeability estimates from direct pore-scale simulations

We investigate and characterize the influence of capillary end effects on steady-state relative permeabilities obtained in pore-scale numerical simulations of two-phase flows. Our study is motivated by the observation that capillary end effects documented in two-phase laboratory-scale experiments can significantly influence permeability estimates. While numerical simulations of two-phase flows in reconstructed pore-spaces are increasingly employed to characterize relative permeabilities, a phenomenon which is akin to capillary end effects can also arise in such analyses due to the constraints applied at the boundaries of the computational domain. We profile the relative strength of these capillary end effects on the calculation of steady-state relative permeabilities obtained within randomly generated porous micro-structures using a finite volume-based two-phase flow solver. We suggest a procedure to estimate the extent of the regions influenced by these capillary end effects, which in turn allows for the alleviation of bias in the estimation of relative permeabilities.

Multiphase-Flow and Reactive-Transport Validation Studies at the Pore Scale by Use of Lattice Boltzmann Computer Simulations

Summary We describe the recent development of lattice Boltzmann (LB) and particle-tracing computer simulations to study flow and reactive transport in porous media. First, we measure both flow and solute transport directly on pore-space images obtained from micro-computed-tomography (CT) scanning. We consider rocks with increasing degree of heterogeneity: a bead pack, Bentheimer sandstone, and Portland carbonate. We predict probability distributions for molecular displacements and find excellent agreement with pulsed-field-gradient (PFG) -nuclear-magnetic-resonance (NMR) experiments. Second, we validate our LB model for multiphase flow by calculating capillary filling and capillary pressure in model porous media. Then, we extend our models to realistic 3D pore-space images and observe the calculated capillary pressure curve in Bentheimer sandstone to be in agreement with the experiment. A process-based algorithm is introduced to determine the distribution of wetting and nonwetting phases in the pore space, as a starting point for relative permeability calculations. The Bentheimer relative permeability curves for both drainage and imbibition are found to be in good agreement with experimental data. Third, we show the speedup of a graphics-processing-unit (GPU) algorithm for large-scale LB calculations, offering greatly enhanced computing performance in comparison with central-processing-unit (CPU) calculations. Finally, we propose a hybrid method to calculate reactive transport on pore-space images by use of the GPU code. We calculate the dissolution of a porous medium and observe agreement with the experiment. The LB method is a powerful tool for calculating flow and reactive transport directly on pore-space images of rock.

New analytical formulas for prediction of gas–liquid relative permeabilities through fractures – Part I: Incompressible flow

Considering the fact that flow in fractured formations is fracture dominated, relative permeabilities through fractures must be well understood. Contrary to reservoir rocks, there is no standard experimental procedure for measurement of relative permeabilities through fractures. Furthermore, existing techniques are generally inconsistent, time consuming, expensive, complicated, and may fail due to technical difficulties encountered while performing the experiments. Thus, developing an analytical model for accurate prediction of relative permeabilities through fractures is of vital importance for treating one of significant uncertainties associated with characterization and simulation of fractured reservoirs.Historically, the straight-line relative permeability model (X-curve) has been widely used in numerical simulation of fractured reservoirs. However, experimental measurements of gas–liquid relative permeabilities through fractures have revealed high degrees of phase interference which cannot be well represented by the X-model. In this work, idealized flow configurations of stratified and segregated flow are assumed in order to make the analytical derivation tractable without the need of using numerical techniques. Then, basic fluid flow equations are combined to develop simple analytical models for gas–liquid flow in each of the patterns. Combining the models with Darcy's law leads to closed-form analytical expressions for explicit calculation of gas and liquid relative permeabilities through fractures. The relationships simply state that the relative permeabilities depend on several parameters one of which being the saturation, whereas they were considered to be only functions of the saturation in the classic X-model. Afterwards, the formulas are further simplified by adopting a realistic assumption. Eventually, the validity of the derived relative permeability expressions is checked by comparing their predictions with available experimental data. The results show that the ability of the segregated model to accurately predict experimental data is considerably poorer than that of the stratified model. Therefore, the generalized relative permeability expressions proposed for the stratified pattern must be used to describe the dynamics of gas–liquid flow in fractures. It addition to robustness, other advantages of the newly presented formulas such as simplicity, cost effectiveness, and being explicit and analytic make their implementation in numerical simulators straightforward.

Analysis and Evaluation of Oil-water Relative Permeability Curves

Oil-water relative permeability curves are the characteristic curves of evaluating the oil-water infiltrating fluid and also are an important part of reservoir engineering studies. Through a large number of core flooding experiments, based on the establishment of oil-water relative permeability calculation models, the use of the function of the relative permeability curves divided these into the water phase concave, water phase convex and a water phase linear categories. The relationship between different types of relative permeability curves with reservoir characteristics, moisture content, common infiltration points, common permeation range and oil displacement efficiency have been evaluated. Analysis the distribution of the reservoir usable remaining oil and reservoir irreducible oil of different types of relative permeability curves.