scholarly journals Predicting the Relative Permeability of Water Phase Based on Theory of Coupled Electricity-Seepage and Capillary Bundle Model

2015 ◽  
Vol 8 (1) ◽  
pp. 344-349 ◽  
Author(s):  
Xinmin Ge ◽  
Yiren Fan ◽  
Donghui Xing ◽  
Jingying Chen ◽  
Yunhai Cong ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Capillary Pressure ◽  
Relative Permeability ◽  
Water Saturation ◽  
Saturation Index ◽  
Dynamic Parameters ◽  
Empirical Formulas ◽  
Capillary Bundle ◽  
Capillary Walls

An analytical water relative model based on the theory of coupled electricity-seepage and capillary bundle pore structure is described. The model shows that the relative permeability of water is affected by two kinds of parameters, which are depicted as static parameters and dynamic parameters. Revised Kozeny-Carman equation and Archie formulas are introduced to deduce the model, which enhance the characterization ability of pore structure. Two displacing states, where we summarized that oil coats capillary walls and oil occupies capillary centers are also discussed for optimization of the model. In contrast to existing empirical formulas where relative permeability is strongly related to capillary pressure and fractal dimension, we introduce only water saturation and saturation index as input parameters, which make the model simpler to use. Petrophysics and unsteady relative permeability experiments (oil displacing water) are carried out to testify the two models. The fitting results show that for oil displacing experiments presented in this paper, the displacing state where oil coats capillary walls is suitable to predict the relative permeability of water.

FRACTAL MODELS FOR GAS–WATER TRANSPORT IN SHALE POROUS MEDIA CONSIDERING WETTING CHARACTERISTICS

Fractals ◽  
2020 ◽  
Vol 28 (07) ◽  
pp. 2050138
Author(s):  
QI ZHANG ◽  
XINYUE WU ◽  
QINGBANG MENG ◽  
YAN WANG ◽  
JIANCHAO CAI
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Pore Pressure ◽  
Surface Diffusion ◽  
Water Transport ◽  
Relative Permeability ◽  
Fluid Transport ◽  
Water Saturation ◽  
Fractal Theory ◽  
Gas Slippage

Complicated gas–water transport behaviors in nanoporous shale media are known to be influenced by multiple transport mechanisms and pore structure characteristics. More accurate characterization of the fluid transport in shale reservoirs is essential to macroscale modeling for production prediction. This paper develops the analytical relative permeability models for gas–water two-phase in both organic and inorganic matter (OM and IM) of nanoporous shale using the fractal theory. Heterogeneous pore size distribution (PSD) of the shale media is considered instead of the tortuous capillaries with uniform diameters. The gas–water transport models for OM and IM are established, incorporating gas slippage described by second-order slip condition, water film thickness in IM, surface diffusion in OM, and the total organic carbon. Then, the presented model is validated by experimental results. After that, sensitivity analysis of gas–water transport behaviors based on pore structure properties of the shale sample is conducted, and the influence factors of fluid transport behaviors are discussed. The results show that the gas relative permeability is larger than 1 at the low pore pressure and water saturation. The larger pore pressure causes slight effect of gas slippage and surface diffusion on the gas relative permeability. The larger PSD fractal dimension of IM results in larger gas relative permeability and smaller water relative permeability. Besides, the large tortuosity fractal dimension will decrease the gas flux at the same water saturation, and the surface diffusion decreases with the increase of tortuosity fractal dimension of OM and pore pressure. The proposed models can provide an approach for macroscale modeling of the development of shale gas reservoirs.

scholarly journals Identification of Oil Reservoir Meeting Atypical Archie Phenomenon

2015 ◽  
Vol 8 (1) ◽  
pp. 354-357
Author(s):  
Shixiong Yuan ◽  
Haimin Guo ◽  
Yu Ding ◽  
Rui Deng
Keyword(s):  
Pore Structure ◽  
Water Saturation ◽  
Saturation Index ◽  
Oil Reservoir ◽  
Formation Water ◽  
Core Data ◽  
Hydrocarbon Reservoir ◽  
Pore Structures ◽  
Structure Index ◽  
Very High

According to core data, this paper studies variation of resistivity in different pore structures and wettability conditions. The results show that with the increase of pore structure index m, the resistivity will increase significantly when the saturation is constant. Similarly, with increasing saturation index n, the resistivity will also increase even with the same saturation. With fixed m and n, the calculated formation water saturation will be very high, resulting in hydrocarbon reservoir being ignored. This variation characteristic is significant for the identification of hidden reservoir with atypical Archie formula.

A FRACTAL MODEL FOR WATER FLOW THROUGH UNSATURATED POROUS ROCKS

Fractals ◽  
2018 ◽  
Vol 26 (02) ◽  
pp. 1840015 ◽  
Author(s):  
BOQI XIAO ◽  
XIAN ZHANG ◽  
WEI WANG ◽  
GONGBO LONG ◽  
HANXIN CHEN ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Pore Size ◽  
Capillary Pressure ◽  
Water Flow ◽  
Relative Permeability ◽  
Fractal Model ◽  
Water Phase ◽  
Porous Rocks ◽  
Proposed Model ◽  
Flow Through

In this work, considering the effect of porosity, pore size, saturation of water and tortuosity fractal dimension, an analytical model for the capillary pressure and water relative permeability is derived in unsaturated porous rocks. Besides, the formulas of calculating the capillary pressure and water relative permeability are given by taking into account the fractal distribution of pore size and tortuosity of capillaries. It can be seen that the capillary pressure for water phase decreases with the increase of saturation in unsaturated porous rocks. It is found that the capillary pressure for water phase decreases as the tortuosity fractal dimension decreases. It is further seen that the capillary pressure for water phase increases with the decrease of porosity, and at low porosity, the capillary pressure increases sharply with the decrease of porosity. Besides, it can be observed that the water relative permeability increases with the increase of saturation in unsaturated porous rocks. This predicted the capillary pressure and water relative permeability of unsaturated porous rocks based on the proposed models which are in good agreement with the experimental data and model predictions reported in the literature. The proposed model improved the understanding of the physical mechanisms of water flow through unsaturated porous rocks.

scholarly journals Uncertainty span for relative permeability and capillary pressure by varying wettability and spatial flow directions utilizing pore scale modelling

2020 ◽  
Vol 146 ◽  
pp. 01002
Author(s):  
Thomas Ramstad ◽  
Anders Kristoffersen ◽  
Einar Ebeltoft
Keyword(s):  
Continental Shelf ◽  
Pore Structure ◽  
Capillary Pressure ◽  
Relative Permeability ◽  
Phase Flow ◽  
Pore Scale ◽  
Full Field ◽  
Scale Modelling ◽  
Relative Permeability Curves ◽  
Norwegian Continental Shelf

Relative permeability and capillary pressure are key properties within special core analysis and provide crucial information for full field simulation models. These properties are traditionally obtained by multi-phase flow experiments, however pore scale modelling has during the last decade shown to add significant information as well as being less time-consuming to obtain. Pore scale modelling has been performed by using the lattice-Boltzmann method directly on the digital rock models obtained by high resolution micro-CT images on end-trims available when plugs are prepared for traditional SCAL-experiments. These digital rock models map the pore-structure and are used for direct simulations of two-phase flow to relative permeability curves. Various types of wettability conditions are introduced by a wettability map that opens for local variations of wettability on the pore space at the pore level. Focus have been to distribute realistic wettabilities representative for the Norwegian Continental Shelf which is experiencing weakly-wetting conditions and no strong preference neither to water nor oil. Spanning a realistic wettability-map and enabling flow in three directions, a large amount of relative permeability curves is obtained. The resulting relative permeabilities hence estimate the uncertainty of the obtained flow properties on a spatial but specific pore structure with varying, but realistic wettabilities. The obtained relative permeability curves are compared with results obtained by traditional SCAL-analysis on similar core material from the Norwegian Continental Shelf. The results are also compared with the SCAL-model provided for full field simulations for the same field. The results from the pore scale simulations are within the uncertainty span of the SCAL models, mimic the traditional SCAL-experiments and shows that pore scale modelling can provide a time- and cost-effective tool to provide SCAL-models with uncertainties.

A COMPREHENSIVE MODEL FOR OIL–WATER RELATIVE PERMEABILITIES IN LOW-PERMEABILITY RESERVOIRS BY FRACTAL THEORY

Fractals ◽  
2020 ◽  
Vol 28 (03) ◽  
pp. 2050055
Author(s):  
HAIBO SU ◽  
SHIMING ZHANG ◽  
YEHENG SUN ◽  
XIAOHONG WANG ◽  
BOMING YU ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Capillary Pressure ◽  
Relative Permeability ◽  
Fractal Theory ◽  
Low Permeability ◽  
Comprehensive Model ◽  
Relative Permeabilities ◽  
Oil Water ◽  
Seepage Characteristics ◽  
Low Permeability Reservoirs

Oil–water relative permeability curve is an important parameter for analyzing the characters of oil and water seepages in low-permeability reservoirs. The fluid flow in low-permeability reservoirs exhibits distinct nonlinear seepage characteristics with starting pressure gradient. However, the existing theoretical model of oil–water relative permeability only considered few nonlinear seepage characteristics such as capillary pressure and fluid properties. Studying the influences of reservoir pore structures, capillary pressure, driving pressure and boundary layer effect on the morphology of relative permeability curves is of great significance for understanding the seepage properties of low-permeability reservoirs. Based on the fractal theory for porous media, an analytically comprehensive model for the relative permeabilities of oil and water in a low-permeability reservoir is established in this work. The analytical model for oil–water relative permeabilities obtained in this paper is found to be a function of water saturation, fractal dimension for pores, fractal dimension for tortuosity of capillaries, driving pressure gradient and capillary pressure between oil and water phases as well as boundary layer thickness. The present results show that the relative permeabilities of oil and water decrease with the increase of the fractal dimension for tortuosity, whereas the relative permeabilities of oil and water increase with the increase of pore fractal dimension. The nonlinear properties of low-permeability reservoirs have the prominent significances on the relative permeability of the oil phase. With the increase of the seepage resistance coefficient, the relative permeability of oil phase decreases. The proposed theoretical model has been verified by experimental data on oil–water relative permeability and compared with other conventional oil–water relative permeability models. The present results verify the reliability of the oil–water relative permeability model established in this paper.

Proxy models for evaluation of permeability, three-phase relative permeability, and capillary pressure curves from rate-transient data

SIMULATION ◽  
2019 ◽  
pp. 003754971985713 ◽  
Author(s):  
Zhenzihao Zhang ◽  
Turgay Ertekin
Keyword(s):  
Capillary Pressure ◽  
Relative Permeability ◽  
Functional Relationship ◽  
Water Saturation ◽  
Petrophysical Properties ◽  
Laboratory Measurements ◽  
Connate Water ◽  
Three Phase ◽  
Transient Data ◽  
Critical Gas Saturation

This study developed a data-driven forecasting tool that predicts petrophysical properties from rate-transient data. Traditional estimations of petrophysical properties, such as relative permeability (RP) and capillary pressure (CP), strongly rely on coring and laboratory measurements. Coring and laboratory measurements are typically conducted only in a small fraction of wells. To contend with this constraint, in this study, we develop artificial neural network (ANN)-based tools that predict the three-phase RP relationship, CP relationship, and formation permeability in the horizontal and vertical directions using the production rate and pressure data for black-oil reservoirs. Petrophysical properties are related to rate-transient data as they govern the fluid flow in oil/gas reservoirs. An ANN has been proven capable of mimicking any functional relationship with a finite number of discontinuities. To generate an ANN representing the functional relationship between rate-transient data and petrophysical properties, an ANN structure pool is first generated and trained. Cases covering a wide spectrum of properties are then generated and put into training. Training of ANNs in the pool and comparisons among their performance yield the desired ANN structure that performs the most effectively among the ANNs in the pool. The developed tool is validated with blind tests and a synthetic field case. Reasonable predictions for the field cases are obtained. Within a fraction of second, the developed ANNs infer accurate characteristics of RP and CP for three phases as well as residual saturation, critical gas saturation, connate water saturation, and horizontal permeability with a small margin of error. The predicted RP and CP relationship can be generated and applied in history matching and reservoir modeling. Moreover, this tool can spare coring expenses and prolonged experiments in most of the field analysis. The developed ANNs predict the characteristics of three-phase RP and CP data, connate water saturation, residual oil saturation, and critical gas saturation using rate-transient data. For cases fulfilling the requirement of the tool, the proposed technique improves reservoir description while reducing expenses and time associated with coring and laboratory experiments at the same time.

A Water-Gas Relative Permeability Relationship for Tight Gas Sand Reservoirs

1990 ◽  
Vol 112 (4) ◽  
pp. 239-245 ◽  
Author(s):  
S. D. L. Lekia ◽  
R. D. Evans
Keyword(s):  
Capillary Pressure ◽  
Relative Permeability ◽  
Water Saturation ◽  
Gas Permeability ◽  
Tight Gas ◽  
Relative Permeabilities ◽  
The North ◽  
Tight Gas Sands ◽  
Straight Line ◽  
Phase Saturation

This paper presents a new approach for the analyses of laboratory-derived capillary pressure data for tight gas sands. The method uses the fact that a log-log plot of capillary pressure against water saturation is a straight line to derive new expressions for both wetting and nonwetting phase relative permeabilities. The new relative permeability equations are explicit functions of water saturation and the slope of the log-log straight line of capillary pressure plotted against water saturation. Relative permeabilities determined with the new expressions have been successfully used in simulation studies of naturally fractured tight gas sands where those determined with Corey-type expressions which are functions of reduced water saturation have failed. A dependence trend is observed between capillary pressure and gas permeability data from some of the tight gas sands of the North American Continent. The trend suggests that the lower the gas permeability, the higher the capillary pressure values at the same wetting phase saturation—especially for saturations less than 60 percent.

Scale Up of Pore-Network Models into Reservoir Scale: Optimization of Inflow Control Devices Placement

SPE Journal ◽  
2021 ◽  
pp. 1-18
Author(s):  
Farzad Bashtani ◽  
Mazda Irani ◽  
Apostolos Kantzas
Keyword(s):  
Pore Structure ◽  
Capillary Pressure ◽  
Relative Permeability ◽  
Scale Up ◽  
Pore Network ◽  
Flow In Porous Media ◽  
Well Completion ◽  
Control Devices ◽  
Relative Permeability Curves ◽  
Capillary Pressure Curves

Summary Improvements to more advanced tools, such as inflow control devices (ICDs), create a high drawdown regime close to wellbores. Gas liberation within the formation occurs when the drawdown pressure is reduced below the bubblepoint pressure, which in turn reduces oil mobility by reducing its relative permeability, and potentially reducing oil flow. The key input in any reservoir modeling to compare the competition between gas and liquid flow toward ICDs is the relative permeability of different phases. Pore-network modeling (PNM) has been used to compute the relative permeability curves of oil, gas, and water based on the pore structure of the formation. In this paper, we explain the variability of pore structure on its relative permeability, and for a similar formation and identical permeability, we explain how other factors, such as connectivity and throat radius distribution, can vary the characteristic curves. By using a boundary element method, we also incorporate the expected relative permeability and capillary pressure curves into the modeling. The results show that such variability in the pore network has a less than 10% impact on production gas rates, but its effect on oil production can be significant. Another important finding of such modeling is that providing the PNM-created relative permeabilities may provide totally different direction on setting the operational constraints. For example, in the case studied in this paper, PNM-created relative permeability curves suggest that a reduction of flowing bottomhole pressure (FBHP) increases the oil rate, but for the case modeled with a Corey correlation, changes in FBHP will not create any uplift. The results of such work show the importance of PNM in well completion design and probabilistic analysis of the performance, and can be extended based on different factors of the reservoir in future research. Although PNM has been widely used to study the multiphase flow in porous media in academia, the application of such modeling in reservoir and production engineering is quite narrow. In this study, we develop a framework that shows the general user the importance of PNM simulation and its implementation in day-to-day modeling. With this approach, the PNM can be used not just to provide relative permeability or capillary pressure curves on a core or pore- scale, but to preform simulations at the wellbore or reservoir scale as well to optimize the current completions.

Estimation of dynamic petrophysical properties of water-bearing sands invaded with oil-base mud from the interpretation of multiple borehole geophysical measurements

Geophysics ◽  
2012 ◽  
Vol 77 (6) ◽  
pp. D209-D227 ◽  
Author(s):  
Zoya Heidari ◽  
Carlos Torres-Verdín
Keyword(s):  
Capillary Pressure ◽  
Relative Permeability ◽  
Radial Distribution ◽  
Apparent Resistivity ◽  
Water Saturation ◽  
Estimation Method ◽  
Petrophysical Properties ◽  
Fluid Saturation ◽  
Irreducible Water Saturation ◽  
Geophysical Measurements

Nonmiscible fluid displacement without salt exchange takes place when oil-base mud (OBM) invades connate water-saturated rocks. This is a favorable condition for the estimation of dynamic petrophysical properties, including saturation-dependent capillary pressure. We developed and successfully tested a new method to estimate porosity, fluid saturation, permeability, capillary pressure, and relative permeability of water-bearing sands invaded with OBM from multiple borehole geophysical measurements. The estimation method simulates the process of mud-filtrate invasion to calculate the corresponding radial distribution of water saturation. Porosity, permeability, capillary pressure, and relative permeability are iteratively adjusted in the simulation of invasion until density, photoelectric factor, neutron porosity, and apparent resistivity logs are accurately reproduced with numerical simulations that honor the postinvasion radial distribution of water saturation. Examples of application include oil- and gas-bearing reservoirs that exhibit a complete capillary fluid transition between water at the bottom and hydrocarbon at irreducible water saturation at the top. We show that the estimated dynamic petrophysical properties in the water-bearing portion of the reservoir are in agreement with vertical variations of water saturation above the free water-hydrocarbon contact, thereby validating our estimation method. Additionally, it is shown that the radial distribution of water saturation inferred from apparent resistivity and nuclear logs can be used for fluid-substitution analysis of acoustic compressional and shear logs.

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