Relative Permeability Curves Research Articles

Displacement Efficiency in Tight Sandstone Based on Fractional Flow Curve Using Relative Permeability Data

In tight gas sandstone, relative permeability is an essential special core analysis dynamic test that can be used to estimate injectivity, secondary recovery, production rate, reservoir simulation, residual gas saturation, and effective water management. Having about 65% of hydraulic fracturing fluid not to flow back and stay in the reservoir results in having the tight sandstone gas reservoir to involve multi-phase flow, namely water and gas. During the hydraulic fracturing job both imbibition and forcibly imbibition processes take place while during fracturing fluid cleanup and gas production drainage flow becomes dominant.
 The steady state flooding process was used to measure the relative permeability curves for tight sandstone core sample collected from Travis Peak Formation at a depth of 8707 ft. The measurement process involved the performance of a series of steady state experiments with different gas-water injection ratio. The fractional flow curve has been plotted, based on the measured relative permeability, and used to calculate the displacement efficiency for the flow through such type of tight porous media. The measurement showed relatively high irreducible water saturation (31%) and low residual gas saturation (6%). The measured gas relative permeability decreased slowly at a constant rate with increased wetting fluid saturation. The obtained fractional flow curve does not follow the s-shape behavior observed in conventional reservoir. The obtained results showed that displacement efficiency can be enhanced by increasing water viscosity.

Effect of temperature on two-phase gas/oil relative permeability in unconsolidated sands

Thermal Enhanced Oil Recovery (TEOR) for heavy oil reservoirs involves the simultaneous flow of oil and steam, mimicking the gaseous phase with an elevation in the temperature. While implementing the TEOR process, reservoir performance prediction tools require the water/oil and gas/oil relative permeability data. Many studies reported the temperature effect on two-phase water/oil relative permeability despite knowing that steam or vapor is conventionally injected, mimicking the gaseous phase during heavy oil recovery. Thus, this requires the knowledge of temperature effect on two-phase gas/liquid relative permeability as well. However, limited studies are reported in the literature regarding the temperature dependency of relative permeability in gas/liquid systems; offer no census about its effects. The scarcity of such studies in the literature is due to the lack of systematic experimental studies and complications observed while conducting the higher temperature tests to mimic the thermal EOR. Hence, the objective of this study was to examine the temperature effect on two-phase gas/liquid relative permeability at varying temperatures from 64 to 132 °C using a systematic and reliable experimental process.In this study, Poly Alpha Olefin (PAO-100) was used as the oleic phase, deionized water as the immobile phase, and nitrogen gas as the displacing phase in a clean unconsolidated sandpack under the confining pressure around 1000 psi. Furthermore, Johnson-Neumann-Bossler (JBN) method was opted to interpret the two-phase gas/liquid relative permeability curves from the displacement data, i.e., cumulative oil production and pressure drop measured across the sandpack. The experimental observation suggests that irreducible water saturation and endpoint oil relative permeability are temperature independent. The residual oil saturation decreased with the increase in temperature and led to a higher endpoint relative permeability to gas. On the other hand, the oil relative permeability at equal saturation uplifted, suggesting the enhanced mobility of oil through pores with increasing temperature. On the other side, the gas relative permeability at equal saturation was temperature-insensitive other than at residual oil saturation. Also, the two-phase flow region increased with the rise in temperature as both the relative permeability curves shifted upwards, and the broader curve was observed. Hence, this study strongly suggests that the reservoir engineers or commercial reservoir simulators should account for the temperature effects on two-phase gas/oil relative permeability to efficiently predict heavy oil reservoir performance and management during the thermal enhanced oil recovery process (TEOR).

Silica nanofluid in low salinity seawater containing surfactant and polymer: Oil recovery efficiency, wettability alteration and adsorption studies

Production of crude oil from a matured oil reservoir is challenging due to the low recovery factor. Hybrid methods have demonstrated potential in oil recovery from the matured crude oil reservoir. In recent years, the low salinity water with chemicals (viz., surfactant, polymer) and nanoparticles have brought the attention of the researchers due to their ability in altering the interfacial properties of the rock-oil-water systems favorable for crude oil recovery. The current interest by industries in injection fluid (i.e., low salinity water injection) has prompted the invention of a hybrid oil recovery agent for matured crude oil reservoirs. In the current study, a novel silica-based hybrid nanofluids (NFs) of variable silica nanoparticles (NPs) concentration in low salinity seawater with anionic surfactant (AOT: dioctyl sodium sulfosuccinate) and polymer (PVP–K30: polyvinylpyrrolidone) (sometimes referred to as SMART LowSal) are used as an injection fluid in a sand-pack reactor. Oil recovery from oil saturated sand-pack reactor is observed to enhance due to NFs (hybrid) injection after secondary recovery. The characteristic study of relative permeability curves discloses that sand surface was initially water-wet and converted to strongly water-wet in the presence of NFs. A nuclear magnetic resonance (1H NMR) study reveals that adsorption of the chemical appeared on the sand surfaces, which could be the reason for wettability alteration, and thereby enhanced oil recovery. Similarly, the scanning electron microscopy (SEM) and energy dispersive X-ray analysis (EDXA) of the sand samples before and after injection disclosed desorption of hydrocarbon from the sand surfaces after NFs injection. An additional 5–10% oil recovery is achieved after chemical flooding due to the injection of NFs. Adsorption isotherm study well agreed with the monolayer adsorption of surfactant on the sand surface.

Research on the Relationship between Electrical Parameters and Relative Permeability of Tight Sandstone

The relationship between the electrical properties and relative permeability of tight sandstones with complex pore-throat structures is still unclear. In this study, a relationship model between the electrical parameters and pore-throat structure and the relative permeability of tight sandstone based on experimental data was established by combining theoretical derivation and experimental comparison. The model has typical three-terminal element characteristics. Porosity had little effect on relative permeability, whereas saturation index had a significant control effect on relative permeability. The relative permeability curve deduced based on the electrical parameters was quite different from the experimental fitting curve. Because irreducible water could conduct electricity but not flow, the relative permeability of the gas phase derived from the theory was higher than the experimental one, while the relative permeability of the water phase was lower. The isotonic point saturation of the phase permeability curve derived from the rock electrical parameter theory was larger than that obtained from the experiment. This research could help us obtain accurate relative permeability curves through electrical parameters and provide a basis for the fine evaluation of tight sandstone two-phase flow.

A Method for Calculating Oil Field Relative Permeability Curve by Using Water Drive Characteristic Curve in High Water Cut Stage

With the production of strong bottom water reservoir, it will soon enter the ultra-high water cut stage. After entering the ultra-high water cut period, the main means of stable production is liquid extraction. Large liquid volume has a certain impact on the physical property distribution and fluid seepage law of the oilfield. The relative permeability curve measured according to the industry standard is not used for the prediction of development indicators and the understanding of the dynamic law of the oilfield. In order to understand the characteristics of water drive law in high water cut stage of water drive oilfield, starting from the water drive characteristic curve in high water cut stage, the method for calculating the relative permeability curve is deduced. Through numerical simulation verification and fitting the actual production data, it is confirmed that the obtained relative permeability curve is in line with the reality of the oilfield, It can provide some guiding significance for understanding the production law and water drive law of strong bottom water reservoir in ultra-high water cut stage.

Prediction of Relative Permeability Curve Based on Machine Learning Driven by Logging Data

Prediction of Relative Permeability Curve Based on Machine Learning Driven by Logging Data

Performance Evaluation of Ionic Liquids Using Numerical Simulation

Given the rise in oil productivity from conventional and unconventional resources in Canada using Enhanced Oil Recovery (EOR), the need to understand and characterize these techniques, for the purpose of recovery optimization, has taken a prominent role in resource management. Chemical flooding has proved to be one of the most efficient EOR techniques. This study investigated the potential of employing Ionic Liquids (ILs) as alternative chemical agents for improving oil recovery. There is very little attention paid to employing this technique as well as few experimental and simulation studies. Consequently, very limited data are available. Since pilot and field studies are relatively expensive and time consuming, a numerical simulation study using CMG-STARS simulator was utilized to explore the efficiency of employing 1-Ethyl-3-Methyl-Imidazolium Acetate ([EMIM][Ac]) and 1-Benzyl-3-meth- limidazolium chloride ([BenzMIM][Cl]) with respect to improving medium oil recovery. Eight different lab-scale sandpack flooding experiments were selected to develop a numerical model to obtain the history matching of the experimental flooding results using CMG-CMOST. We observed that the main challenge was tuning the relative permeability curves to achieve a successful match for the oil recovery factor. Finally, a sensitivity study was performed to examine the effect of the chemical injection rate, the chemical concentration, the slug size, and the initiation time on oil recovery. The results showed a noticeable increase in the oil RF when injecting IL compared to conventional waterflooding.

A new approach to measure wettability by relative permeability measurements

Wettability is a key factor controlling the flow of fluids, solutes, heat and electrical current in porous media, and therefore it is important in studies of various processes including CO2 storage, secondary and tertiary oil recovery, as well as the displacement of water and nonaqueous phase liquid (NAPL). Although Amott-Harvey and USBM are conventional industry-standard techniques for measuring average wettability, they have some limitations. In this paper, we show that, in a plot of the relative permeability of a fluid, the area below the curve is closely related to the wettability. By using the areas below the water and oil relative permeability curves, we derive a new wettability index (called modified Lak). To demonstrate the applicability of this new index and testing other indices, we performed primary imbibition relative permeability, and primary imbibition and secondary drainage capillary pressure measurements on twenty carbonate reservoir samples. In general, all indices predicted oil-wet character of the tested rocks. USBM was associated with the broadest range of variation, whereas the new index corresponded to the smallest range of variation. Amott-Harvey and Lak, however, fell between USBM and the new index, with fairly similar ranges of variation. In addition, we report the correlations between different indices, and the change of wettability indices vs. reservoir depth. Advantages and limitations of different wettability indices are also discussed. Since each wettability index has some limitations in revealing the true state of wettability, none of these indices can be considered as an absolute measurement. Therefore, different indices should be regarded as complementary to each other, and determination of wettability should not be limited to only one method.

Forecasting the impact of formation damage on relative permeability during low-salinity waterflooding

Low-salinity waterflooding is considered to be an advanced oil recovery method, but the main mechanism behind the increase in oil recovery factor is still under investigation. Fines migration has been recognized to be one of the mechanisms responsible for the increase in oil production. In this case, the increase in oil recovery happens as a result of increased sweep efficiency and consequent reduction of residual oil. The release of particles due to reduction of electrostatic forces results in flux diversion to previously unswept areas in the reservoir, increasing oil recovery. This paper provides a better understanding of the effects of formation damage during low-salinity water injection in Berea sandstones and proposes a methodology to forecast its effects on water relative permeability. We have performed one- and two-phase flow coreflood experiments with varying salinity of the injected solution. The effluent was analysed for salinity, pH and particle concentration. The laboratory data was treated using a mathematical model that accounts for permeability impairment during low-salinity waterflooding due to fines detachment, migration and capture in small pore throats. The parameters of the model were used to predict the impact of formation damage on the water relative permeability during two-phase flow. The mathematical model matched the laboratory data for pressure drop and particle concentration in the outlet with great accuracy. A methodology to predict the impact of formation damage in two-phase flow using one-phase flow data was proposed. A good agreement between the predicted and the measured water relative permeabilities was obtained. The forecasted water relative permeability curve was able to reproduce the non-monotonic behaviour of water relative permeability due to low-salinity water injection.

How Does Capillary Pressure Affect the Relative Permeability Curves of Heterogeneous Carbonate Rocks?

How Does Capillary Pressure Affect the Relative Permeability Curves of Heterogeneous Carbonate Rocks?

Effects of the laminated-structure and mixed wettability on the oil/water relative permeabilities and oil productions in shale oil formations

Shale oil formations are highly heterogeneous laminated systems containing organic matter (OM). In this study, oil/water flow in laminated shale oil formations are investigated from the pore-scale perspective using the lattice Boltzmann method (LBM). The effects of the pore size and wettability heterogeneities including different pore sizes, contents of OM, wettabilities of OM, and OM distributions on oil/water flow are analyzed. The relative permeability curves of water and oil are calculated and then substituted into the model of numerical simulations to analyze the variations of oil production for each case. Results showed that the relative permeabilities of the mudstone and sandstone laminae are different, and that using the average relative permeabilities of the two laminae can lead to significant errors in the calculation of oil production. With the content and the hydrophobicity of OM increasing and with OM locating in the middle of the mudstone, more oil occupies the pore space around OM and thereby increases the relative permeability of oil (kro) in the mudstone, but conversely decreases kro in the sandstone, which in turn affects the proportions of oil production through the mudstone and sandstone.

An Algorithm to Determine the Truncated Weibull Parameters for Distribution of Throats and Pores in Random Network Models

In random network models, sizes for pores and throats are distributed according to a truncated Weibull distribution. As a result, parameters defining the shape of the distribution are critical for the characteristic of the network. In this paper, an algorithm to distribute pores and throats in random network was established to more representatively describe the topology of porous media. First, relations between Weibull parameters and the distribution of dimensionless throat sizes were studied and a series of standard curves were obtained. Then, by analyzing the capillary pressure curve of the core sample, frequency distribution histogram of throat sizes was obtained. All the sizes were transformed to dimensionless numbers ranged from 0 to 1. Curves of the core were compared to the standard curves, and truncated Weibull parameters could be determined according an inverse algorithm. Finally, aspect ratio and average length of throats were adjusted to simultaneously fit the porosity and the capillary pressure curves and the whole network was established. The predicted relative permeability curves were in good agreement with the experimental data of cores, indicating the validity of the algorithm.

A New Method for Quantitative Analysis of Water Flooding Characteristics by Fitting Relative Permeability Curve and T2 Spectrum Based on Nmr Technology

A New Method for Quantitative Analysis of Water Flooding Characteristics by Fitting Relative Permeability Curve and T2 Spectrum Based on Nmr Technology

Integrated characterization of wormhole network by use of a modified pressure-gradient-based (PGB) sand failure criterion and ensemble-based history matching during CHOPS processes

In this paper, a damped iterative ensemble Kalman filter (IEnKF) technique has been developed and integrated with a recently modified pressure-gradient-based (PGB) sand failure criterion to implicitly and inversely characterize the dynamic wormhole network during cold heavy oil production with sand (CHOPS) processes. With an improved upscaling process, not only has a microscopic PGB sand failure criterion been properly upscaled to the grid-scale simulation, but also it can be dynamically, implicitly, and inversely determined. Then, such a sand failure model together with three-phase relative permeability is validated and applied to reproduce wormhole network in a laboratory experiment conditioned to its sand production profile. Good agreements between the observed and simulated cumulative production profiles including oil, gas, and sand have been achieved with satisfactory convergence by integrating the ensemble-based history matching method. The simulated wormhole network has shown its great similarity to the experimental observations, while the convergence of the ensemble-based history matching algorithm is greatly improved with a widespread of initial ensembles in each grid. Furthermore, deviations between the observed and updated production profiles can be significantly minimized by dividing the entire production period into three sequential stages, each of which has its distinct relative permeability curves due to the major effect (i.e., foamy oil flow, sand failure, and slurry flow) on its multiphase flow behaviours, respectively. By integrating the ensemble-based sand failure model with the damped-IEnKF method, the dynamic wormhole network during a CHOPS process can be accurately characterized with satisfactory convergence, demonstrating its robustness and practicality of dynamically and inversely simulating the preferential wormhole network. Such an ensemble-based sand failure model can be seamlessly incorporated with any commercial reservoir simulators under various conditions. • A hybrid IEnKF-PGB technique is developed to characterize wormhole network for CHOPS wells. • Good agreements between the observed and simulated cumulative production profiles are achieved. • Simulated wormhole network shows its great similarity to the experimental observations. • Dividing the production period into three stages minimizes deviations between observed and updated production profiles. • This hybrid technique is robust and can be seamlessly coupled with any reservoir simulators.

A new computational approach to predict hot-water flooding (HWF) performance in unconsolidated heavy oil reservoirs

In this study, a new computational approach for predicting the performance of hot-water flooding in unconsolidated heavy oil reservoirs is presented. The proposed model predicts the changes in the oil–water viscosity ratio (μo/μw) by estimating the reservoir temperature distribution through porous media. Then, the dimensionless and normalized variables were redefined to forecast water fractional flow as a function of temperature and water saturation. Moreover, the proposed approach predicts the cumulative heavy oil production and recovery factor more accurately and with less required input data and runtime compared to commercial simulators such as CMG-STARS (computer modeling group), etc.Estimated results were validated using laboratory experimental data and numerical simulation outputs. A total of 4 core-flooding experiments were conducted at injection temperatures of 20–80 °C. Numerical simulation models based on the laboratory HWF tests were developed in CMG-STARS. The water–oil relative permeability curves were tuned to history match simulation results with those obtained from experiments.Finally, the predicted cumulative heavy oil productions, recovery factors (RF) and production rates by the proposed approach were compared to the results from the laboratory sandpacked tests and simulation runs for three scenarios. The relative errors between heavy oil recovery factors obtained from computational approach and experimental data were measured to be 11.01%, 14.51% and 13.69% for injection temperatures of 40, 60 and 80 °C, respectively.

Research on Boundary Layer Effect in Fractured Reservoirs Based on Pore-Scale Models

It is of great significance to study the seepage characteristics of heavy oil reservoirs, which are conducive to the efficient development of resources. Boundary layer effect (BLE) exists in the pore-scale flow process of macromolecular fluid media, which is different from the flow law of conventional fluid in the pore, yet the influence of BLE is ignored in the previous pore-scale simulation. Conventional porous media simulations have difficulty analyzing the mass transfer law of small-scale models under the influence of microfractures. Based on the CT scanning data and thin section data of the real core in the target area, the rock skeleton and flow space were extracted according to the maximum ball algorithm, and the pore network model representing the complex structure was constructed. The microscale effect of macromolecules in the flow process in the pores was characterized by modifying the effective flow. The effects of the BLE on the effective connectivity, displacement process, and oil distribution law were analyzed. The seepage characteristics of different wettability conditions and different water cut stages were compared. The results show that BLE reduces the effective flow space and leads to deviations in the relative permeability curve and capillary curve. For fractured porous media, the irregular shape of porous media was characterized by the morphological method, and the mass transfer process was analyzed by the equivalent flux method. The influence of the porous media shape on the macromass transfer process was compared. This study provides a solution to the problem of BLE in pore-scale simulation.

Calculation Model of Relative Permeability in Tight Sandstone Gas Reservoir with Stress Sensitivity

During the development of tight gas reservoir, the irreducible water saturation, rock permeability, and relative permeability change with formation pressure, which has a significant impact on well production. Based on capillary bundle model and fractal theory, the irreducible water saturation model, permeability model, and relative permeability model are constructed considering the influence of water film and stress sensitivity at the same time. The accuracy of this model is verified by results of nuclear magnetic experiment and comparison with previous models. The effects of some factors on irreducible water saturation, permeability, and relative permeability curves are discussed. The results show that the stress sensitivity will obviously reduce the formation permeability and increase the irreducible water saturation, and the existence of water film will reduce the permeability of gas phase. The increase of elastic modulus weakens the stress sensitivity of reservoir. The irreducible water saturation increases, and the relative permeability curve changes little with the increase of effective stress. When the minimum pore radius is constant, the ratio of maximum pore radius to minimum pore radius increases, the permeability increases, the irreducible water saturation decreases obviously, and the two-phase flow interval of relative permeability curve increases. When the displacement pressure increases, the irreducible water saturation decreases, and the interval of two-phase flow increases. These models can calculate the irreducible water saturation, permeability and relative permeability curves under any pressure in the development of tight gas reservoir. The findings of this study can help for better understanding of the productivity evaluation and performance prediction of tight sandstone gas reservoirs.

Two‐Phase Relative Permeability of Rough‐Walled Fractures: A Dynamic Pore‐Scale Modeling of the Effects of Aperture Geometry

AbstractAn accurate description of the relative permeability–saturation function is crucial for reliable predictions of multi‐phase flow behavior in subsurface applications. Although extensive efforts have been put forth to investigate the relative permeability behavior in different types of porous media, only few studies have focused on rough‐walled fractures. In this work, we present an entirely new, cost‐effective, heavily‐parallelized, dynamic pore‐network modeling framework that is employed to conduct a systematic study of relative permeability curves under two‐phase flow conditions in rough‐walled fractures. We first build a two‐dimensional (101.42 × 24.86 mm2) equivalent pore network of a Berea sandstone fracture from its x‐ray images. Subsequently, dynamic primary drainage and imbibition simulations are conducted in the fracture. We show that the two‐phase fluid occupancy maps predicted from the simulations agree well with the fracture fluid configurations obtained via X‐ray computed tomography. Afterward, the validated model is used to probe two‐phase flow properties in a series of synthetic aperture fields generated with a broad range of geometric characteristics including aperture spatial correlation length (normalized correlation length varying from 0.05 to 0.95), anisotropy factor (0.25–4), surface roughness (normalized fracture roughness varying from 0.05 to 0.4), and mean aperture size (50–800 μm). The generated results provide novel insights into the effects of these features on two‐phase flow properties such as fluid–fluid interfacial area, phase interference, and relative permeability. Moreover, based on the simulation results we propose two new correlations to describe the relative permeability curves for primary drainage and imbibition processes in rough‐walled fractures.

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.

The relevance of the linear stability theory to the simulation of unstable immiscible viscous-dominated displacements in porous media

The 2D governing equations for the immiscible two-phase flow admissible to linear stability analysis are inspected. The identification of the term vwsDδsiD in the generalized Saffman–Taylor criterion is key to the analysis. It can be regarded as a predictor that correlates with observed immiscible instability in terms of the rate of advancement of the viscous pattern, the number of small protrusions, and their roughness in a given heterogeneous domain described by a correlated random field. The predictor is extended, heuristically, for polymer flooding shock-wise and used to characterize the instability of the two shocks. The extension is validated by simulation. The instability of the primary shock is essential when considering the breakthrough recovery. In light of the instability predictor, the geometric interpretations of the fractional flow are essential to understand the stability enhancement of the primary shock over the Buckley–Leverett shock in water flooding. It is also concluded that the end-point mobility ratio does not directly control the immiscible instability. This conclusion was arrived at by fixing the end-point mobility ratios for three sets of relative permeability curves, and yet noticeably different instabilities occur, both in transverse and correlated random fields. The criterion can predict the viscous instability in the laboratory experiments under certain flooding conditions and sample configurations. Concerning the instability in a field scale, the predictor is applicable if the field is regarded as a prototype of a given model experiment.