scholarly journals An Analytical Equation to Predict Oil-Gas-Water Three-Phase Relative Permeability Curves in Fractures

2017 ◽  
Keyword(s):  
Relative Permeability ◽  
Analytical Equation ◽  
Three Phase ◽  
Relative Permeability Curves ◽  
Oil Gas

Simultaneous Interpretation of Three-Phase Relative Permeability and Capillary Pressure for a Tight Carbonate Reservoir From Wireline Formation Testing

2019 ◽  
Vol 142 (6) ◽  
Author(s):  
Xiangnan Liu ◽  
Daoyong Yang
Keyword(s):  
Capillary Pressure ◽  
Relative Permeability ◽  
History Matching ◽  
Carbonate Reservoir ◽  
Reservoir Rock ◽  
Fluid Saturation ◽  
Three Phase ◽  
Tight Carbonate ◽  
Wet Condition ◽  
Oil Gas

Abstract In this paper, techniques have been developed to interpret three-phase relative permeability and water–oil capillary pressure simultaneously in a tight carbonate reservoir from numerically simulating wireline formation tester (WFT) measurements. A high-resolution cylindrical near-wellbore model is built based on a set of pressures and flow rates collected by dual packer WFT in a tight carbonate reservoir. The grid quality is validated, the effective thickness of the WFT measurements is examined, and the effectiveness of the techniques is confirmed prior to performing history matching for both the measured pressure drawdown and buildup profiles. Water–oil relative permeability, oil–gas relative permeability, and water–oil capillary pressure are interpreted based on power-law functions and under the assumption of a water-wet reservoir and an oil-wet reservoir, respectively. Subsequently, three-phase relative permeability for the oil phase is determined using the modified Stone II model. Both the relative permeability and the capillary pressure of a water–oil system interpreted under an oil-wet condition match well with the measured relative permeability and capillary pressure of a similar reservoir rock type collected from the literature, while the relative permeability of an oil–gas system and the three-phase relative permeability bear a relatively high uncertainty. Not only is the reservoir determined as oil-wet but also the initial oil saturation is found to impose an impact on the interpreted water relative permeability under an oil-wet condition. Changes in water and oil viscosities and mud filtrate invasion depth affect the range of the movable fluid saturation of the interpreted water–oil relative permeabilities.

A Semianalytical Approach for Analysis of Wells Exhibiting Multiphase Transient Linear Flow: Application to Field Data

SPE Journal ◽  
2020 ◽  
Vol 25 (06) ◽  
pp. 3265-3279
Author(s):  
Hamidreza Hamdi ◽  
Hamid Behmanesh ◽  
Christopher R. Clarkson
Keyword(s):  
Numerical Model ◽  
Relative Permeability ◽  
History Matching ◽  
Volatile Oil ◽  
Low Permeability ◽  
Two Phase ◽  
Linear Flow ◽  
Field Case ◽  
Three Phase ◽  
Relative Permeability Curves

Summary Rate-transient analysis (RTA) is a useful reservoir/hydraulic fracture characterization method that can be applied to multifractured horizontal wells (MFHWs) producing from low-permeability (tight) and shale reservoirs. In this paper, we applied a recently developed three-phase RTA technique to the analysis of production data from an MFHW completed in a low-permeability volatile oil reservoir in the Western Canadian Sedimentary Basin. This RTA technique is used to analyze the transient linear flow regime for wells operated under constant flowing bottomhole pressure (BHP) conditions. With this method, the slope of the square-root-of-time plot applied to any of the producing phases can be used to directly calculate the linear flow parameter xfk without defining pseudovariables. The method requires a set of input pressure/volume/temperature (PVT) data and an estimate of two-phase relative permeability curves. For the field case studied herein, the PVT model is constructed by tuning an equation of state (EOS) from a set of PVT experiments, while the relative permeability curves are estimated from numerical model history-matchingresults. The subject well, an MFHW completed in 15 stages, produces oil, water, and gas at a nearly constant (measured downhole) flowing BHP. This well is completed in a low-permeability,near-critical volatile oil system. For this field case, application of the recently proposed RTA method leads to an estimate of xfk that is in close agreement (within 7%) with the results of a numerical model history match performed in parallel. The RTA method also provides pressure–saturation (P–S) relationships for all three phases that are within 2% of those derived from the numerical model. The derived P–S relationships are central to the use of other RTA methods that require calculation of multiphase pseudovariables. The three-phase RTA technique developed herein is a simple-yet-rigorous and accurate alternative to numerical model history matching for estimating xfk when fluid properties and relative permeability data are available.

A New Analytical Equation to Predict Gas-Water Two-Phase Relative Permeability Curves in Fractures

2014 ◽  
Author(s):  
Gang Lei ◽  
Pingchuan Dong ◽  
Shu Yang ◽  
Yuansheng Li ◽  
Shaoyuan Mo ◽  
...  
Keyword(s):  
Relative Permeability ◽  
Analytical Equation ◽  
Two Phase ◽  
Relative Permeability Curves

A New Analytical Equation to Predict Gas-Water Two-Phase Relative Permeability Curves in Fractures

2014 ◽  
Author(s):  
Gang Lei ◽  
Pingchuan Dong ◽  
Shu Yang ◽  
Yuansheng Li ◽  
Shaoyuan Mo ◽  
...  
Keyword(s):  
Relative Permeability ◽  
Analytical Equation ◽  
Two Phase ◽  
Relative Permeability Curves

Issue with Stone-II Three Phase Permeability Model, and A Novel Robust Fundamentals-Based Alternative to It

2021 ◽  
Author(s):  
Subodh Gupta
Keyword(s):  
Relative Permeability ◽  
Phase Flow ◽  
Residual Oil ◽  
Relative Permeabilities ◽  
Phase Permeability ◽  
Permeability Model ◽  
Oil Saturation ◽  
Three Phase ◽  
Three Phase Flow ◽  
Relative Permeability Curves

Abstract The objective of this paper is to present a fundamentals-based, consistent with observation, three-phase flow model that avoids the pitfalls of conventional models such as Stone-II or Baker's three-phase permeability models. While investigating the myth of residual oil saturation in SAGD with comparing model generated results against field data, Gupta et al. (2020) highlighted the difficulty in matching observed residual oil saturation in steamed reservoir with Stone-II and Baker's linear models. Though the use of Stone-II model is very popular for three-phase flow across the industry, one issue in the context of gravity drainage is how it appears to counter-intuitively limit the flow of oil when water is present near its irreducible saturation. The current work begins with describing the problem with existing combinatorial methods such as Stone-II, which in turn combine the water-oil, and gas-oil relative permeability curves to yield the oil relative permeability curve in presence of water and gas. Then starting with the fundamentals of laminar flow in capillaries and with successive analogical formulations, it develops expressions that directly yield the relative permeabilities for all three phases. In this it assumes a pore size distribution approximated by functions used earlier in the literature for deriving two-phase relative permeability curves. The outlined approach by-passes the need for having combinatorial functions such as prescribed by Stone or Baker. The model so developed is simple to use, and it avoids the unnatural phenomenon or discrepancy due to a mathematical artefact described in the context of Stone-II above. The model also explains why in the past some researchers have found relative permeability to be a function of temperature. The new model is also amenable to be determined experimentally, instead of being based on an assumed pore-size distribution. In that context it serves as a set of skeletal functions of known dependencies on various saturations, leaving constants to be determined experimentally. The novelty of the work is in development of a three-phase relative permeability model that is based on fundamentals of flow in fine channels and which explains the observed results in the context of flow in porous media better. The significance of the work includes, aside from predicting results more in line with expectations and an explanation of temperature dependent relative permeabilities of oil, a more reliable time dependent residual oleic-phase saturation in the context of gravity-based oil recovery methods.

Calculation of Imbibition Relative Permeability for Two- and Three-Phase Flow From Rock Properties

1968 ◽  
Vol 8 (02) ◽  
pp. 149-156 ◽  
Author(s):  
Carlon S. Land
Keyword(s):  
Pore Size Distribution ◽  
Pore Size ◽  
Size Distribution ◽  
Relative Permeability ◽  
Empirical Relation ◽  
Phase Flow ◽  
Three Phase ◽  
Phase Saturation ◽  
Phase Systems ◽  
Relative Permeability Curves

Abstract Relative permeability functions are developed for both two- and three-phase systems with the saturation changes in the imbibition direction. An empirical relation between residual nonwetting-phase saturation after water imbibition and initial nonwetting-phase saturations is found from published data. From this empirical relation, expressions are obtained for trapped and mobile nonwetting-phase saturations which are used in connection with established theory relating relative permeability to pore-size distribution. The resulting equations yield relative permeability as a function of saturation having characteristics believed to be representative of real systems. The relative permeability of water-wet rocks for both two- and three-phase systems, with the saturation change in the imbibition direction, may be obtained by this method after properly selecting two rock properties: the residual nonwetting-phase saturation after the complete imbibition cycle, and the capillary pressure curve. Introduction Relative permeability is a function of saturation history as well as of saturation. This fact was first pointed out for two-phase flow by Geffen et al. and by Osaba et al. Hysteresis in the relative permeability-saturation relation also has been reported for three-phase systems. Since saturations may change simultaneously in two directions in a three-phase system, four possible relationships arise between relative permeability and saturation for a water-wet system. The four saturation histories of this system were given by Snell as II, ID, DI and DD. I refer to the direction of saturation change (imbibition and drainage), with the first letter of the symbol indicating the direction of change of the water phase. As used in this paper, the second letter of the symbol refers to the direction of saturation change of the gas phase, i.e., D and I indicate an increase and decrease, respectively, in gas saturation. Only a few three-phase relative permeability curves have been published. Leverett and Lewis published three-phase curves for unconsolidated sand, and Snell reported results of several English authors for both drainage and imbibition three-phase relative permeability of unconsolidated sands. Three-phase relative permeability curves for a consolidated sand were published by Caudle et al. for increasing water and gas saturations (ID). Corey et al. reported drainage (DD) three-phase relative permeability for consolidated sands. Recently, Donaldson and Dean and Sarem calculated three- phase relative permeability curves from displacement data on consolidated sands, also for saturation changes in the drainage direction. The only published three - phase relative permeability curves for consolidated sands with saturation changes in the imbibition direction (II) are those of Naar and Wygal. These curves are based on at theoretical study of the model of Wyllie and Gardner as modified by Naar and Henderson. Interest in three-phase relative permeability has increased recently due to the introduction of new recovery methods and refinements in calculation procedures brought about by the use of large-scale digital computers. The scarcity of empirical relations for three-phase flow, and the experimental difficulty encountered in obtaining such data, have made the theoretical approach to this problem attractive. RELATIVE PERMEABILITY AS A FUNCTION OF PORE-SIZE DISTRIBUTION Purcell used pore sizes obtained from mercury-injection capillary pressure data to calculate the permeability of porous solids. Burdine extended the theory by developing a relative permeability-pore size distribution relation containing the correct tortuosity term. SPEJ P. 149ˆ

Measurement of Three-Phase Relative Permeability with IFT Variation

2005 ◽  
Vol 8 (01) ◽  
pp. 33-43 ◽  
Author(s):  
Yildiray Cinar ◽  
Franklin M. Orr
Keyword(s):  
Experimental Data ◽  
Relative Permeability ◽  
Oil And Gas ◽  
Gas Injection ◽  
Relative Permeabilities ◽  
Two Phase ◽  
Rich Phase ◽  
Injection Process ◽  
Three Phase ◽  
Relative Permeability Curves

Summary In this paper, we present results of an experimental investigation of the effects of variations in interfacial tension (IFT) on three-phase relative permeability. We report results that demonstrate the effect of low IFT between two of three phases on the three-phase relative permeabilities. To create three-phase systems in which IFT can be con-trolled systematically, we used a quaternary liquid system composed of hexadecane(C16), n-butanol (NBA), water (H2O), and isopropanol (IPA). Measured equilibrium phase compositions and IFTs are reported. The reported phase behavior of the quaternary system shows that the H2O-rich phase should represent the "gas" phase, the NBA-rich phase should represent the "oil" phase, and the C16-rich phase should represent the "aqueous" phase. Therefore, we used oil-wet Teflon (PTFE) bead packs to simulate the fluid flow in a water-wet oil reservoir. We determined phase saturations and three-phase relative permeabilities from recovery and pressure-drop data using an extension of the combined Welge/Johnson-Bossler-Naumann (JBN) method to three-phase flow. Measured three-phase relative permeabilities are reported. The experimental results indicate that the wetting-phase relative permeability was not affected by IFT variation, whereas the other two-phase relative permeabilities were clearly affected. As IFT decreases, the oil and gas phases become more mobile at the same phase saturations. For gas/oil IFTs in the range of 0.03 to 2.3 mN/m, we observed an approximately 10-fold increase in the oil and gas relative permeabilities against an approximately 100-fold decrease in the IFT. Introduction Variations in gas and oil relative permeabilities as a function of IFT are of particular importance in the area of compositional processes such as high-pressure gas injection, where oil and gas compositions can vary significantly both spatially and temporally. Because gas-injection processes routinely include three-phase flow (either because the reservoir has been water-flooded previously or because water is injected alternately with gas to improve overall reservoir sweep efficiency), the effect of IFT variations on three-phase relative permeabilities must be delineated if the performance of the gas-injection process is to be predicted accurately. The development of multicontact miscibility in a gas-injection process will create zones of low IFT between gas and oil phases in the presence of water. Although there have been studies of the effect of low IFT on two-phase relative permeability,1–14 there are limited experimental data published so far analyzing the effect of low IFT on three-phase relative permeabilities.15,16 Most authors have focused on the effect of IFT on oil and solvent relative permeabilities.17 Experimental results show that residual oil saturation and relative permeability are strongly affected by IFT, especially when the IFT is lower than approximately 0.1 mN/m (corresponding to a range of capillary number of 10–2 to 10–3). Bardon and Longeron3 observed that oil relative permeability increased linearly as IFT was reduced from approximately 12.5 mN/m to 0.04 mN/m and that for IFT below 0.04, the oil relative permeability curves shifted more rapidly with further reductions in IFT. Later, Asar and Handy6 showed that oil relative permeability curves began to shift as IFT was reduced below 0.18 mN/m for a gas/condensate system near the critical point. Delshad et al.15 presented experimental data for low-IFT three-phase relative permeabilities in Berea sandstone cores. They used a brine/oil/surfactant/alcohol mixture that included a microemulsion and excess oil and brine. The measurements were done at steady-state conditions with a constant capillary number of 10–2 between the microemulsion and other phases. The IFTs of microemulsion/oil and microemulsion/brine were low, whereas the IFT between oil and brine was high. They concluded that low-IFT three-phase relative permeabilities are functions of their own saturations only. Amin and Smith18 recently have published experimental data showing that the IFTs for each binary mixture of brine, oil, and gas phases vary as pressure increases(Fig. 1). Fig. 1 shows that the IFT of a gas/oil pair decreases as the pressure increases, whereas the IFTs of the gas/brine and oil/brine pairs approach each other.

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