Phase Relative Permeability Research Articles

A novel method for estimating gas and liquid saturation according to the change of temperature field

Nitrogen foam treatment is widely used to control water production in oil wells by selectively reducing water phase relative permeability in oil-water-transition zone. A novel method is proposed to analyze nitrogen gas saturation distribution under varying foam generation pressure drops, which the heat conduction coefficients and heat capacities of nitrogen gas and water are considered. A one-dimensional sand pack model was used to evaluate the impact of gravity on gas saturation distribution, tested in both horizontal and vertical orientations. The gas and water saturation varying along the flow direction of the tube can be calculated according to temperature change. The results indicate that nitrogen injection with pressure drops of 0.9 and 1.2 MPa can generate more evenly gas and water distribution as well as longer foam flow distance comparing to the higher injection pressure drops of 1.5 MPa. Average gas saturation generated in the vertical manner is found to be lower than that of horizontal one due to the higher gas flow resistance in the vertical direction. The simulation result of gas saturation distribution along the tube using Fluent software matches the experimental results well.

Mechanism of Water Control and Gas Augmentation by Fracturing Interface Modifier in Water-bearing Gas Reservoir

Abstract With the development of oil and gas reservoirs, water containing gas reservoirs have gradually received attention. However, problems such as water production during the production process have reduced gas permeability, leading to a decrease in gas well productivity underground. Phase permeability regulators improve productivity by changing the wettability of rocks and enhancing gas permeability. This article tests the interface performance of a phase permeability regulator and evaluates its temperature resistance, formation water salt resistance, and erosion resistance. The pore bound water saturation of the core before and after modification with the phase permeability regulator, as well as the relative permeability of gas and water phases, are tested. The experimental results show that the phase permeation regulator can reduce the surface tension of water to 22.2 mN/m, and the rock contact angle before and after soaking increases from 26.63 ° to 97.69 °, achieving the transition of rock from hydrophilic to hydrophobic. The surface tension of the phase permeation regulator changes significantly before and after aging at 80-120 °C, and its high-temperature resistance is poor. After mixing with formation water with a salinity of 60000 to 100000, the surface tension increases, and at a salinity of 60000, it increases by 5.1 mN/m. The use of phase permeability regulators for matrix core displacement resulted in a slight increase in displacement pressure, while the formation water remained unchanged after approximately 140 hours of erosion. After modification with phase permeability regulators, the irreducible water saturation of the core decreases by about 25%, and the relative permeability of the gas phase increases, resulting in a significant hydrophobic and gas conducting effect. Phase permeability regulators achieve hydrophobic gas conductivity by changing the wettability of rocks, which can alleviate the problem of water production in shallow and low salinity reservoirs.

A coupled fractal model for predicting the relative permeability of rocks considering both irreducible fluid saturation and stress effects

The relative permeability of rocks is an essential parameter for evaluating two-phase flow characteristics and plays an important role in engineering fields such as resource exploitation. To this end, a mathematical model for predicting relative permeability was first developed based on an equivalent capillary model and fractal theory. The proposed model considers the irreducible fluid saturation under stress and quantifies the influence of the pore structure characteristics on the relative permeability. This model was then compared with relevant experimental data and existing theoretical expressions to verify its validity. Finally, the factors affecting the two-phase seepage characteristics were discussed. The results show that the irreducible fluid saturation is intimately connected to the fractal dimensions, pore size, fluid viscosity, pressure drop gradient, and elastic modulus. Fluid properties and pore structure characteristics are the main factors affecting relative permeability. The wetting phase relative permeability is more sensitive to pore structure and irreducible fluids. Increased effective stress increases irreducible fluid saturation, reduces two-phase flow capacity, and significantly decreases the relative permeability of wetting phase fluids. Increased elastic modulus and Poisson's ratio decrease the irreducible fluid content under stress and increase the permeability.

Two-phase flow simulation algorithm for numerical estimation of relative phase permeability curves of porous materials

Abstract The paper presents an algorithm for three-dimensional modelling of two-phase flows on the scale of pore size order for numerical evaluation of relative phase permeability curves of porous materials. Such an evaluation is performed based on the results of numerical simulation of primary drainage with subsequent waterflooding. In this case, models of porous materials based on three-dimensional tomographic images of rocks are used. The simulation of the flow considers the Stokes equation and the Cahn–Hilliard equation for modelling phase transfer, which allows us to determine phases using the concentration function. The combination of the phase field method and finite difference method makes it possible to correctly take into account the contact angle and stably calculate surface tension forces in domains with complex topology.

On the question of comparability of relative phase permeabilities obtained by different methods

The article discusses four methods for obtaining functions of relative phase permeability (RPP): 1) approximation of point laboratory data by known correlations of Corey and LET; 2) calculation of RPP by capillary pressure curves using Burdine, Cory and Cory–Brooks models; 3) calculation of RPP by field data; 4) modification of RPP when setting up a hydrodynamic model. A new method is proposed for obtaining RPP based on field data. In this method, it is assumed that the values of the Buckley–Leverett function are equivalent to the values of the well water-cut, and the water saturation can be determined by the formula linking the accumulated oil production and the initial geological oil reserves. The methods of obtaining RPP have been tested on the example of two real objects. The results of the approbation showed that all pairs of RPPs differ markedly from each other, while different trends take place for the objects considered. The article provides an explanation of the possible reasons for the difference in the RPP. At the same time, it was found that the scale factor is not the most significant. The expediency of the conducted research is due to the need to study the level of correspondence between the functions of the RPP obtained by different methods. This will allow for a more reasoned justification of the functions of the RPP when creating and adapting a hydrodynamic model of an oil deposit.

Cluster Capillary Core Model for the Calculation of the Relative Phase Permeability for Oil and Water Filtration

Cluster Capillary Core Model for the Calculation of the Relative Phase Permeability for Oil and Water Filtration

Steady-state two-phase relative permeability measurements in proppant-packed rough-walled fractures

Understanding multiphase flow in fractures filled with minerals and proppants is vital in various subsurface applications. Limited experimental data have led to reliance on correlations lacking physical basis. We conducted experiments to characterize relative permeability in rough-walled fractures packed with unconsolidated porous media. We tested fractures packed with water-wet 40/70 sand (silica) and surface-coated ceramic proppants. Brine and mineral oil were used as the wetting and non-wetting fluid phases, respectively. Steady-state (SS) drainage (non-wetting-phase displacing wetting-phase) and imbibition (wetting-phase displacing non-wetting-phase) tests were performed under a wide range of saturation histories (full-cycle and scanning-curves) to study relative permeability hysteresis of the propped fractures. Every SS drainage or imbibition test consisted of several discrete points at which fluid saturations and the corresponding relative permeability were measured by varying the fractional flow rates of fluids whilst maintaining a constant total flow rate. We analyzed residual non-wetting phase saturations and relative permeability trends to understand two-phase flow behavior in each proppant pack. High-resolution x-ray microtomography was used to understand the pore-scale topology, wettability, and to provide insights about the pore-scale displacement mechanisms involved in this study. The results showed that commonly used models to estimate relative permeabilities of fractures significantly overestimated the SS brine and oil relative permeabilities (denoted as krw and kro) measured in this study. Further analysis unveiled that the kro values during imbibition exceeded their drainage counterparts in both proppants, the ceramic proppant exhibited a lower initial water saturation and a higher end-point kro permeability at the end of the drainage displacement, as well as higher krw across all flooding processes. Updated fitting parameters for a Brooks-Corey-type relative permeability correlation are introduced. This study presents improved insights, extensive experimentally generated relative permeability data, and an updated relative permeability correlation, which can be collectively utilized to reduce uncertainties associated with continuum-scale forecasts of multiphase flow behavior in fractured subsurface formations.

An integrated approach to the substantiation of the boundary values and the assessment of the character of saturation in the deposits of the Tyumen formation

Background. The Tyumen formation is characterized by the complexity of the structure of deposits and consists of the sediments of different facies groups. To build hydrodynamic models, improve the development system and identify prospective zones, the conditions of sedimentation must be taken into account. Objective. Increasing the reliability of reservoir permeability assessment and clarifying critical resistivities when assessing the nature of saturation, which requires new approaches to petrophysical modeling. Materials and methods. The work uses the results of core studies and interpretation of well-logging data for the JV2 formation considering the facies. Results. The wettability of extracted and nonextracted samples is studied, the dependence of the saturation parameter on the water saturation coefficient is corrected taking into account the wettability of reservoirs, and the relative phase permeabilities are calculated for drainage conditions in the “oil–water” system. Conclusions. An integrated approach makes it possible to clarify the values of permeability, critical resistivities and oil and gas saturation of reservoirs, which can be used to identify prospecting zones when drilling new wells.

On approaches to solving problems when modeling polymer flooding at the Kalamkas oil field

Background: Currently, polymer flooding is one of the most effective methods for increasing reservoir recovery, accordingly and modeling this process is of particular relevance.
 Aim: The purpose of hydrodynamic modeling is to predict the distribution of parameters, technological indicators, and simulate all possible development scenarios. Based on the simulation results, decisions are made on the profitability of projects.
 Materials and methods: There are a number of significant problems in the process of hydrodynamic modeling, one of which is adaptation. Difficulties with adaptation are mainly associated with the incorrect determination of filtration – capacitive properties, which is directly caused by the lack of core research data. The main physical parameters that determine the filtration-capacitive properties of reservoir rocks are porosity, permeability, relative phase permeabilities, and saturation. These properties are critical for accurate fluid flow modeling and production forecasting. However, the lack of core data limits our understanding of these properties and affects the quality of model fit.
 Due to the insufficient data on the oil field in this Vostok site of horizon Ю-1 of the Kalamkas field, the approved initial geological reserves differ from the reserves according to the model by approximately 20%. For a more accurate adaptation of the hydrodynamic model, the availability of current initial geological reserves is significantly insufficient.
 Results: In this article, a number of approaches were applied to solve the above-mentioned problem in the hydrodynamic modeling of polymer flooding in the Kalamkas oil field, and as a result, the results obtained were demonstrated.
 Conclusion: Hydrodynamic modeling allows us to conduct numerical experiments to optimize the parameters of polymer flooding, helps to study their influence and select the optimal ratio to improve the efficiency of the flooding process.

Material balance evaluation method for water-bearing gas reservoirs considering the influence of relative permeability

In this paper, we developed a material balance method based on a two-phase flow equation for evaluating the development efficiency in gas reservoirs. The calculating results show that the theoretical curves of development performance simulated by material balance fit well with early production data and can be used to evaluate the development efficiency of the field. The influence parameters of the theoretical curves were analyzed by simulating a constant production gas reservoir. The results show that the numerical differences between the initial water saturation and the water saturation at the isotonic point of the relative permeability curve greatly influence the theoretical curves. The higher the ratio of water phase relative permeability to gas phase relative permeability, the higher the water-gas ratio in the early and middle periods of well production. It is beneficial to exploit the underground fluid with a large average rock compressibility coefficient which means a strong formation elastic energy. Besides, the value of initial water saturation will also influence the loss of formation elastic energy. This study extends the applicability of material balance and avoids the cost risk of field well testing. Therefore, it has a good practical significance.

Estimating of the boundary values of the relative phase permeability functions of the oil-water system by using empirical correlations

The article describes the results of a search for multiparametric empirical correlations to determine the boundary values of the functions of the relative phase permeability (RPP) of the oil-water system — residual water saturation, residual oil saturation, phase permeability of oil with residual water saturation and phase permeability of water with residual oil saturation. The study was carried out by using a laboratory data on four groups of terrigenous rocks of oil field developed by PJSC Rosneft Oil Company, which differ from each other in characteristic features of the structure of the pore-space and the properties of reservoir fluids. Multiparametric dependencies were searched in a form of a combination of dimensionless influencing parameters in proper degrees. An analysis of the sensitivity of dependencies to the volume of the data sample was carried out. The obtained correlations can be used for a preliminary assessment of the boundary values of the functions of the RPP and can be refined as experimental data accumulate. On the basis of empirical correlations and a previous model of filtration of an oil-water mixture at the core scale, a fully calculated method for determining RPP has been implemented. Method can be used in conditions of shortage or absence of core material, including for reservoir zones in which core sampling has not been carried out.

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.

Experimental investigation of the mutual influence of micro- and macroscale processes on the displacement of viscous oil by water in a two-layer porous medium

This paper presents the results of an experimental and theoretical study of the immissible displacement of high-viscosity model oil from the two-layer porous medium with different layers permeability. The experiments were performed using cylindrical model of the porous medium having the ratio of transverse size to length D/L equals to 0.05 and ratio of layers permeability equals to 0.46 during forced imbibition and drainage. It is shown that the alignment of a displacement front in the layers is caused by macroscale capillarity-driven flow arising from the curvature of the front. The conditions for stabilized motion of the displacement front for this case are determined using the analytical model and proved using experimental data on the recovery of displaced fluid. Microscale processes in pore level caused by the influence of the capillary forces are taken into account throw the relative phase permeability and capillary pressure curves.

Nuclear Magnetic Resonance and High-Speed Centrifugation for Gas-Water Relative Permeability Curve of Low-Permeability and Tight Sandstone

Gas-water relative permeability curve is the foundation of gas reservoir dynamic analysis and numerical simulation. It is generally obtained through gas displacing water experiment. Referring to the existing national standards, gas-water relative permeability test is carried out for low-permeability and tight sandstone. The flow is discontinuous and the curve smoothness is poor, which affects the application of gaswater relative permeability curve. Based on the comparative analysis of a large number of mercury injection and NMR experimental results of low-permeability and tight sandstone, a method to characterize the throat radius distribution of low-permeability tight sandstone based on NMR T2 spectrum is explored. Combined with high-speed centrifugal experiment, the calculation formulas of core water saturation, phase relative permeability of gas-water under different centrifugal force are established. A new method of “nuclear magnetic resonance + high-speed centrifugation” for gas-water relative permeability curve test of lowpermeability and tight sandstone is formed, and the test is carried out on Sulige low-permeability tight sandstone core. The results show that: (1) The shape of cumulative distribution curve of throat radius by mercury injection method is basically consistent with that of T2 relaxation time by NMR, and there is a good corresponding relationship between them. (2) The centrifugation process is similar to the gas displacing water process. With the decrease of water saturation, water centrifugation in rock core becomes more and more difficult until it become irreducible. (3) The core relative permeability curve obtained by the new method is consistent with the curve obtained by the standard method and has good repeatability. The new method can be used for gas-water relative permeability tests of low permeability tight sandstone. (4) The test process of the new method is unified and standard and up to 6 cores can be tested at the same time. The calculation results of water saturation and relative permeability curve are reliable and the integral curve is smooth, which greatly improves the test efficiency of gas-water relative permeability curve in lowpermeability and tight sandstone. The new method can be widely used to study the gas-water two-phase seepage law in low-permeability and tight sandstone gas reservoir.

Adsorbed residual oil saturation and phase permeability relationship for oil in Western Siberia productive formations

Relevance. Relative phase permeabilities determine oil by water displacement mechanism, efficiency of productive formations flooding, dynamics of producing wells flooding. Relative phase permeabilities curves allow us to estimate the inflow nature according to geophysical well studies. Currently, relative phase permeabilities curves are constructed according to core samples laboratory studies. They are used to select a mathematical model describing the nature of the curves for a given productive reservoir. The most optimal option is to justify the individual relative phase permeabilities curve parameters. This option allows transition from the core sample level to the entire productive reservoir characteristics using geophysical well studies data. Aim. To substantiate a choice of a model describing the change in the relative phase permeability curves using field geophysics data based on the adsorbed residual oil saturation and phase permeability to oil relationship. Objects. Productive layers of individual deposits of the West Siberian oil and gas province, confined to the Lower Cretaceous deposits. Methods. Statistical processing of capillarimetric research data, analysis and substantiation of mathematical models describing relative phase permeability. Results. The paper shows that the permeability to oil at residual water saturation (the starting point of the relative phase permeabilities curve to oil) is determined by the adsorbed residual reservoir oil saturation. The authors have obtained the formula, linking the adsorbed residual oil saturation coefficient with the phase permeability to oil with residual water saturation. The adsorbed residual oil saturation is also closely related to the residual reservoir water saturation. Such relation is carried out through the reservoir clay content. The authors proposed the technique that allows residual oil saturation by type structuring and mobility degree. This technique allows as well as finding out the residual reserves of mobile oil distribution to justify the recovery techniques.

Zoning Productivity Calculation Method of Fractured Horizontal Wells in High-Water-Cut Tight Sandstone Gas Reservoirs under Complex Seepage Conditions

Tight sandstone gas reservoirs generally contain water. Studying the impact of water content on the permeability mechanism of tight gas reservoirs is of positive significance for the rational development of gas reservoirs. Selected cores from a tight sandstone gas reservoir in the Ordos Basin were used to establish the variation in its seepage mechanism under different water saturations. The experimental results show that the gas slip factor in tight water-bearing gas reservoirs decreases as the water saturation increases. The stress sensitivity coefficient and the threshold pressure gradient (TPG) increase with increasing water saturation, characterizing the relationships between stress sensitivity coefficients, TPG, permeability, and water saturation. As the water saturation gradually increases, the relative gas phase permeability of tight sandstone gas reservoirs will sharply decrease. When the water saturation exceeds 80%, the gas phase permeability becomes almost zero, resulting in gas almost ceasing to flow. Through the analysis of experimental results, we defined high-water-cut tight sandstone gas reservoirs and analyzed the permeability characteristics of high-water-cut tight sandstone gas reservoirs in different regions. Combining stress sensitivity coefficients and the TPG with permeability and water saturation relationships, we established a zoning productivity calculation method of fractured horizontal wells in high-water-cut tight sandstone gas reservoirs under complex seepage conditions and validated the practicality of the model through example calculations.

Effect of Rock Dissolution on Two-Phase Relative Permeabilities: Pore-Scale Simulations Based on Experimental Data

Relative phase permeability is an important characteristic of multiphase flow in porous media. Its assessment is an urgent issue when the pore structure changes due to rock dissolution. This article examines the effect of carbonate rock dissolution on two-phase flow based on images obtained by X-ray microcomputed tomography with a spatial resolution of ~18 µm. The characteristics of the two-phase flow were calculated through pore network modeling. The studies were conducted on 20 sub-volumes, which were extracted from cylindrical samples A and B with permeabilities of 0.72 and 0.29 D. HCl solutions (12% and 18%) were injected into samples A and B at a rate of 8 and 2 mL/min, respectively. Due to rock dissolution, the porosity and absolute permeability of the sub-volumes increased by 1.1–33% and 44–368%, respectively. Due to dissolution, the residual oil and water saturations decreased by 20–46% and 25–60%, respectively. These results showed that an increase in absolute permeability led to a significant reduction in residual oil and water saturations. These results also demonstrated that rock dissolution resulted in a change in the spatial heterogeneity of the relative phase permeabilities. The spatial heterogeneity increased in sample A after rock dissolution, while in sample B, it decreased.

Performance evaluation of microemulsion acid for integrated acid fracturing in Middle Eastern carbonate reservoirs

Considering the characteristics of carbonate reservoirs in the Middle East, a low-viscosity microemulsion acid that can be prepared on site and has an appropriate retardation ability was developed. It was compared with four conventional acid systems (hydrochloric acid, gelled acid, emulsified acid and surfactant acid) through experiments of rotating disk, multistage acid fracturing and core flooding with CT scanning. The micro-etching characteristics and conductivity of fracture surfaces were clarified, and the variation of saturation field during water invasion and flowback of spent acid and the recovery of oil phase relative permeability were quantitatively evaluated. The study shows that the addition of negatively charged agent to the oil core of microemulsion acid can enhance its adsorption capacity on the limestone surface and significantly reduce the H+ mass transfer rate. Moreover, the negatively charged oil core is immiscible with the Ca2 + salt, so that the microemulsion acid can keep an overall structure not be damaged by Ca2 + salt generated during reaction, with adjustable adsorption capacity and stable microemulsion structure. With high vertical permeability along the fracture walls, the microemulsion acid can penetrate into deep fracture wall to form network etching, which helps greatly improve the permeability of reservoirs around the fractures and keep a high conductivity under a high closure pressure. The spent microemulsion acid is miscible with crude oil to form microemulsion. The microemulsion, oil and water are in a nearly miscible state, with basically no water block and low flowback resistance, the flowback of spent acid and the relative permeability of oil are recovered to a high degree.

Study of the pore structure and calculation of macroscopic characteristics of rocks based on X-ray microcomputed tomography images

Background: Absolute and relative phase permeability and capillary pressure are important parameters in predicting oil and gas production from reservoirs, especially when acidizing the bottomhole zone of a well. They are mainly determined during long and resource-intensive laboratory experiments. Thus, additional approaches are required for the operational determination of the above parameters. The pore-network modeling based on microcomputed tomography data allows, firstly, to study the pore space of rock samples taking into account rock dissolution, secondly, to calculate the main macroscopic properties of rock samples without destroying them, and thirdly, to create a database of digital cores for further research
 Aim: Study of the pore space of two carbonate rock samples and the flow of fluids in them using the General Electric V|tome|X S240 MT and using the Avizo and PNFLOW software package.
 Materials and methods: This article uses microcomputed tomography with a spatial resolution of ~19 m and pore-network modeling of fluid flow in porous media to study the pore space of carbonate rock samples and determine absolute and phase permeabilities, as well as capillary pressure.
 Results: It is shown that an increase in the value of the Marker Extent parameter leads to a decrease in the number of pores and an overestimated absolute permeability due to improper pore separation, while a decrease in the value of this parameter made it possible to identify smaller pores. It is also shown that absolute permeability and porosity have different relationships before and after rock dissolution with high correlation coefficients that range from 0.62 to 0.81. It has been shown that rock dissolution will significantly affect the relative phase permeability of the samples.
 Conclusion: The dissolution of the rock led to a decrease in the residual oil saturation in both samples. In the case of oil displacement by water, as a result of rock dissolution, the residual oil saturation decreased from 38% to 22% and from 53% to 43% for the two samples under study. These results are important for understanding the flow of fluids in carbonate samples.

The Effectiveness of the Introduction of the Water-Alternated-Gas Injection on the example of a Carbonate Field in Kazakhstan

Background: Water-Alternated-Gas Injection (hereinafter referred to as WAG) is considered to be a suitable analogue of gas injection and waterflooding, which increase the efficiency of displacement. With continuous gas injection, the displacement front is unstable due to the low viscosity of the gas, which leads to the formation of gas tongues due to a significant difference in the mobility of gas and oil. Alternate injection of water and gas is considered a suitable option in eliminating this problem and in stabilizing the displacement front.
 Aim: The purpose of this work was to generalize the main factors affecting the efficiency of the process, based on the world experience in applying the WAG technology. The effectiveness of this technology application in a carbonate field was also considered.
 Materials and methods: This article analyzes the efficiency of oil displacement using the WAG method in a carbonate field in Kazakhstan. In order to study the proposed oil production technology, the alternate injection of water and gas into the reservoir was simulated on the ECLIPSE 100 simulator. First of all, the process of optimizing the parameters was carried out based on two injection wells. As a result, it was found that for the studied field, the duration of water and gas cycles of 3 months and the sequence of "gas water" are the optimal conditions for observing the greatest effect from WAG. Further, based on the selected parameters, WAG was scaled to the entire field, for the implementation of which several options were developed with 3, 5, 6 and 12 injection wells.
 Results: As a result of the research, the optimal oil displacement option was selected, which involves 5 injection wells with high injectivity and a large volume of injected gas.
 Conclusion: Due to the hydrophilicity of the reservoir, the effect of alternating WAG turned out to be not as significant as it could be expected, due to the effect of hysteresis of relative phase permeabilities, which can be a topic for future research.