Relationship Between Relative Permeability Ratio (k g /k o ) And Total Liquid Saturation (S l ) For A Reservoir

1985 ◽  
pp. 13-18
Author(s):  
Mihir K. Sinha ◽  
Larry R. Padgett
Keyword(s):  
Relative Permeability ◽  
Permeability Ratio ◽  
Liquid Saturation

scholarly journals Modelling the Molecular Permeation through Mixed-Matrix Membranes Incorporating Tubular Fillers

Membranes ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 58
Author(s):  
Ali Zamani ◽  
F. Handan Tezel ◽  
Jules Thibault
Keyword(s):  
Aspect Ratio ◽  
Relative Permeability ◽  
Polymer Matrix ◽  
Volume Fraction ◽  
Mixed Matrix Membranes ◽  
Analytical Prediction ◽  
Mixed Matrix ◽  
Permeability Ratio ◽  
Filler Volume Fraction ◽  
Matrix Membranes

Membrane-based processes are considered a promising separation method for many chemical and environmental applications such as pervaporation and gas separation. Numerous polymeric membranes have been used for these processes due to their good transport properties, ease of fabrication, and relatively low fabrication cost per unit membrane area. However, these types of membranes are suffering from the trade-off between permeability and selectivity. Mixed-matrix membranes, comprising a filler phase embedded into a polymer matrix, have emerged in an attempt to partly overcome some of the limitations of conventional polymer and inorganic membranes. Among them, membranes incorporating tubular fillers are new nanomaterials having the potential to transcend Robeson’s upper bound. Aligning nanotubes in the host polymer matrix in the permeation direction could lead to a significant improvement in membrane permeability. However, although much effort has been devoted to experimentally evaluating nanotube mixed-matrix membranes, their modelling is mostly based on early theories for mass transport in composite membranes. In this study, the effective permeability of mixed-matrix membranes with tubular fillers was estimated from the steady-state concentration profile within the membrane, calculated by solving the Fick diffusion equation numerically. Using this approach, the effects of various structural parameters, including the tubular filler volume fraction, orientation, length-to-diameter aspect ratio, and permeability ratio were assessed. Enhanced relative permeability was obtained with vertically aligned nanotubes. The relative permeability increased with the filler-polymer permeability ratio, filler volume fraction, and the length-to-diameter aspect ratio. For water-butanol separation, mixed-matrix membranes using polydimethylsiloxane with nanotubes did not lead to performance enhancement in terms of permeability and selectivity. The results were then compared with analytical prediction models such as the Maxwell, Hamilton-Crosser and Kang-Jones-Nair (KJN) models. Overall, this work presents a useful tool for understanding and designing mixed-matrix membranes with tubular fillers.

scholarly journals Novel Treatment for Mitigating Condensate Bank Using a Newly Synthesized Gemini Surfactant

Molecules ◽  
2020 ◽  
Vol 25 (13) ◽  
pp. 3030
Author(s):  
Amjed Hassan ◽  
Mohamed Mahmoud ◽  
Muhammad Shahzad Kamal ◽  
Syed Muhammad Shakil Hussain ◽  
Shirish Patil
Keyword(s):  
Hydraulic Fracturing ◽  
Phase Behavior ◽  
Relative Permeability ◽  
Gemini Surfactant ◽  
Injection Technique ◽  
Rock Surface ◽  
Hydrocarbon Production ◽  
Liquid Saturation ◽  
Salinity Levels ◽  
New Treatment

Condensate accumulation in the vicinity of the gas well is known to curtail hydrocarbon production by up to 80%. Numerous approaches are being employed to mitigate condensate damage and improve gas productivity. Chemical treatment, gas recycling, and hydraulic fracturing are the most effective techniques for combatting the condensate bank. However, the gas injection technique showed temporary condensate recovery and limited improvement in gas productivity. Hydraulic fracturing is considered to be an expensive approach for treating condensate banking problems. In this study, a newly synthesized gemini surfactant (GS) was developed to prevent the formation of condensate blockage in the gas condensate reservoirs. Flushing the near-wellbore area with GS will change the rock wettability and thereby reduce the capillary forces holding the condensate due to the strong adsorption capacity of GS on the rock surface. In this study, several measurements were conducted to assess the performance of GS in mitigating the condensate bank including coreflood, relative permeability, phase behavior, and nuclear magnetic resonance (NMR) measurements. The results show that GS can reduce the capillary pressure by as much as 40%, increase the condensate mobility by more than 80%, and thereby mitigate the condensate bank by up to 84%. Phase behavior measurements indicate that adding GS to the oil–brine system could not induce any emulsions at different salinity levels. Moreover, NMR and permeability measurements reveal that the gemini surfactant has no effect on the pore system and no changes were observed in the T2 relaxation profiles with and without the GS injection. Ultimately, this work introduces a novel and effective treatment for mitigating the condensate bank. The new treatment showed an attractive performance in reducing liquid saturation and increasing the condensate relative permeability.

New Expression of Oil/Water Relative Permeability Ratio vs. Water Saturation and its Application in Water Flooding Curve

2014 ◽  
Vol 32 (5) ◽  
pp. 817-830 ◽  
Author(s):  
Feng Xu ◽  
Longxin Mu ◽  
Xianghong Wu ◽  
Tianjian Sun ◽  
Yutao Ding ◽  
...  
Keyword(s):  
Relative Permeability ◽  
Water Saturation ◽  
Water Flooding ◽  
Permeability Ratio ◽  
Oil Water

Measurements of Relative Permeabilities for Calculating Gas-Condensate Well Deliverability

2000 ◽  
Vol 3 (06) ◽  
pp. 473-479 ◽  
Author(s):  
R.E. Mott ◽  
A.S. Cable ◽  
M.C. Spearing
Keyword(s):  
Relative Permeability ◽  
Capillary Number ◽  
Gas Condensate ◽  
Relative Permeabilities ◽  
Well Productivity ◽  
Gas Condensate Reservoirs ◽  
Liquid Saturation ◽  
Condensate Reservoir ◽  
Deep Reservoir ◽  
The Relationship

Summary Well deliverability in many gas-condensate reservoirs is reduced by condensate banking when the bottomhole pressure falls below the dewpoint, although the impact of condensate banking may be reduced due to improved mobility at high capillary number in the near-well region. This paper presents the results of relative permeability measurements on a sandstone core from a North Sea gas-condensate reservoir, at velocities that are typical of the near-well region. The results show a clear increase in mobility with capillary number, and the paper describes how the data can be modeled with empirical correlations which can be used in reservoir simulators. Introduction Well deliverability is an important issue in the development of many gas-condensate reservoirs, especially where permeability is low. When the well bottomhole flowing pressure falls below the dewpoint, condensate liquid may build up around the wellbore, causing a reduction in gas permeability and well productivity. In extreme cases the liquid saturation may reach values as high as 50 or 60% and the well deliverability may be reduced by up to an order of magnitude. The loss in productivity due to this "condensate banking" effect may be significant, even in very lean gas-condensate reservoirs. For example, in the Arun reservoir,1 the productivity reduced by a factor of about 2 as the pressure fell below the dewpoint, even though the reservoir fluid was very lean with a maximum liquid drop out of only 1% away from the well. Most of the pressure drop from condensate blockage occurs within a few feet of the wellbore, where velocities are very high. There is a growing body of evidence from laboratory coreflood experiments to suggest that gas-condensate relative permeabilities increase at high velocities, and that these changes can be correlated against the capillary number.2–8 The capillary number is a dimensionless number that measures the relative strength of viscous and capillary forces. There are several gas-condensate fields where simulation with conventional relative permeability models has been found to underestimate well productivity.1,9,10 To obtain a good match between simulation results and well-test data, it was necessary to increase the mobility in the near-well region, either empirically or through a model of the increase in relative permeability at high velocity. This effect can increase well productivity significantly, and in some cases may eliminate most of the effect of condensate blockage. Experimental Data Requirements Fevang and Whitson11 have shown that the key parameter in determining well deliverability is the relationship between krg and the ratio krg/ kro. When high-velocity effects are significant, the most important information is the variation of krg with krg/k ro and the capillary number Nc. The relevant values of krg/kro are determined by the pressure/volume/temperature (PVT) properties of the reservoir fluids, but typical values might be 10 to 100 for lean condensates, 1 to 10 for rich condensates, and 0.1 to 10 for near-critical fluids. There are various ways of defining the capillary number, but in this paper we use the definition (1)Nc=vgμgσ, so that the capillary number is proportional to the gas velocity and inversely proportional to interfacial tension (IFT). The capillary numbers that are relevant for well deliverability depend on the flow rate, fluid type, and well bottomhole pressure, but as a general rule, values between 10?6 and 10?3 are most important. Experimental Methods In a gas-condensate reservoir, there are important differences between the flow regimes in the regions close to and far from the well. These different flow regimes are reflected in the requirements for relative permeability data for the deep reservoir and near-well regions. Far from the well, velocities are low, and liquid mobility is usually less important, except in reservoirs containing very rich fluids. In the near-well region, both liquid and gas phases are mobile, velocities are high, and the liquid mobility is important because of its effect on the relationship between krg and krg/kro. Depletion Method. Relative permeabilities for the deep reservoir region are often measured in a coreflood experiment, where the fluids in the core are obtained by a constant volume depletion (CVD) on a reservoir fluid sample. Relative permeabilities are measured at decreasing pressures from the fluid dewpoint, and increasing liquid saturation. In this type of experiment, the liquid saturation cannot exceed the critical condensate saturation or the maximum value in a CVD experiment, so that it is not possible to acquire data at the high liquid saturations that occur in the reservoir near to the well. The "depletion" experiment provides relative permeability data that are relevant to the deep reservoir, but there can be problems in interpreting the results due to the effects of IFT. Changes in liquid saturation are achieved by reducing pressure, which results in a change of IFT. The increase in IFT as pressure falls may cause a large reduction in mobility, and Chen et al.12 describe an example where the condensate liquid relative permeability decreases with increasing liquid saturation. Steady-State Method. The steady-state technique can be used to measure relative permeabilities at the higher liquid saturations that occur in the near-well region. Liquid and gas can be injected into the core from separate vessels, allowing relative permeabilities to be measured for a wide range of saturations. Results of gas-condensate relative permeabilities measured by this technique have been reported by Henderson et al.2,6 and Chen et al.12 .

The Effect of Temperature on Relative and Absolute Permeability of Sandstones

1975 ◽  
Vol 15 (05) ◽  
pp. 376-384 ◽  
Author(s):  
R.M. Weinbrandt ◽  
H.J. Ramey ◽  
F.J. Casse
Keyword(s):  
Relative Permeability ◽  
Temperature Increase ◽  
Absolute Permeability ◽  
Effect Of Temperature ◽  
Residual Oil ◽  
Relative Permeabilities ◽  
Permeability Ratio ◽  
Oil Saturation ◽  
Residual Oil Saturation ◽  
The Individual

MEMBERS SPE-AIME Abstract Equipment was constructed to perform dynamic displacement experiments on small core samples under conditions of elevated temperature. Oil-water flowing fraction and pressure drop were recorded continuously for calculation of both the relative permeability ratio and the individual relative permeability ratio and the individual relative permeabilities. Imbibition relative permeabilities permeabilities. Imbibition relative permeabilities were measured for five samples of Boise sandstone at room temperature and at 175deg.F. The fluids used were distilled water and a white mineral oil. The effect of temperature on absolute permeability was investigated for six Boise sandstone samples and two Berea sandstone samples. Results for all samples were similar. The irreducible water saturation increased significantly, while the residual oil saturation decreased significantly with temperature increase. The individual relative permeability to oil increased for all water saturations below the room-temperature residual oil saturation, but the relative permeability to water at flood-out increased with permeability to water at flood-out increased with temperature increase. Absolute permeability decreased with temperature increase. Introduction Test environment is generally acknowledged to have a significant effect on measurement of relative permeability. The environment consists not only permeability. The environment consists not only of the temperature and pressure, but also of the fluids used and the core condition. Several workers have used the approach of completely simulating the reservoir conditions in the laboratory experiment. Such methods are termed "restored state." Restored state data are generally different from "room condition" data; since several variables are involved, it is difficult to determine the importance of each variable. Another approach used attributes the changes in relative permeability to changes in the rock-fluid interaction or wettability. Wettability, however, depends on many variables. Specifically, wettability depends on the composition of the rock surface, the composition of the fluids, the saturation history of the rock surface, and the temperature and pressure of the system. The purpose of this study is to isolate temperature as a variable in the relative permeability of a given rock-fluid system. Work on isolation of temperature as a variable in relative permeability has been conducted since the early 1960s. Edmondsons established results in 1965 for a Berea sandstone core using both water/refined oil and water/crude oil as fluid pairs. He showed a change in the relative permeability ratio accompanied by a decrease in the residual oil saturation with temperature increase. Edmondson showed no data for water saturations below 40 percent, and his curves show considerable scatter in the middle saturation ranges. Edmondson's work was the only study to use consolidated cores to investigate the effect of temperature on relative permeability measurements. Poston et al. presented waterflood data for sand packs containing 80-, 99-, a nd 600-cp oil, and packs containing 80-, 99-, a nd 600-cp oil, and observed an increase in the individual relative permeabilities with temperature increase. The permeabilities with temperature increase. The increase in the oil and the water permeability was accompanied by an increase in irreducible water saturation and a decrease in the residual oil saturation with temperature increase. Poston et al. was the only work to present individual oil and water permeability. Davidsons presented results for displacement of No. 15 white oil from a sand pack by distilled water, steam, or nitrogen. However, he found little permeability-ratio dependence in the middle permeability-ratio dependence in the middle saturation ranges. Davidson, too, found a decrease in the residual oil saturation with temperature increase, but he did not include data on irreducible water saturation. SPEJ P. 376

Effects of Vaporization and Temperature in Gas/Liquid Relative Permeability Experiments

1982 ◽  
Vol 22 (01) ◽  
pp. 108-116 ◽  
Author(s):  
John R. Counsil ◽  
Henry J. Ramey
Keyword(s):  
Fluid Flow ◽  
Relative Permeability ◽  
Elevated Temperatures ◽  
Gas Mixture ◽  
Relative Permeabilities ◽  
Temperature Dependent ◽  
Liquid Saturation ◽  
Mixture Volume ◽  
Relative Permeability Curves ◽  
Gas Drive

Abstract Liquid vaporization can influence the results of unsteady, external gas-drive relative permeability experiments. At elevated temperatures, liquid vaporization may affectdisplacing gas mixture volume,displacing gas mixture viscosity, andvolumetric liquid saturation calculated from a material balance. Approximate methods are presented to correct laboratory displacement data for the effect of liquid vaporization on displacing gas mixture volume and viscosity. An approximate method also is presented to evaluate the magnitude of liquid saturation reduction caused by liquid vaporization. By use of a modified Jones and Roszelle calculation procedure, equations are developed to describe the dynamic displacement of liquid water by nitrogen gas at elevated temperatures. A conventional analysis of three displacement experiments demonstrated the apparent temperature dependence of gas relative permeability. Use of the proposed method indicated that corrected gas and water relative permeability curves are not strongly temperature dependent for the artificially consolidated sandstone cores used in this study. Introduction Relative permeability curves are required for numerical modelling of multiphase fluid flow through porous media. Although natural reservoir heterogeneity often reduces the utility of laboratory-derived relative permeabilities, laboratory studies are still required to understand basic fluid flow processes. Welge first modified the Buckley-Leverett theory and presented the equations for calculating (relative) permeability ratios from linear displacement data. Johnson et al. later extended this theory, to allow the calculation of individual relative permeabilities. The base permeability was the predrive, displacing-fluid effective permeability at the initial wetting, phase saturation. Jones and Roszelle then presented a simplified graphical technique that yielded individual relative permeabilities with the absolute (brine)permeability as a base. Osoba et al., Geffen et al., Welge, Rapoport and Leas, Stewart et al., Owens et al., Corey and Rathjens. Estes and Fulton. Richardson and Perkins, Craig et al., and others demonstrated the importance of end effects, flow rate, pressure gradient, drainage imbibition hysteresis, viscosity ratio, interfacial tension, contact angle, critical scaling factor, core heterogeneity, gas slippage, and other factors. In addition, temperature-dependent permeability effects were observed by Davidson, Poston et al., Weinbrandt et al., Casse and Ramey, and others. The reasons for the temperature effects were never fully understood or explained. This paper presents a method of eliminating some of the "apparent" gas relative-permeability temperature dependence by correcting approximately for the temperature- and pressure-dependent vapor/liquid phase behavior. Experimental Process and Apparatus The calculation procedure developed in this study models an isothermal, unsteady, linear gas drive. SPEJ P. 108^

A New Diagnostic Analysis Method for Waterflood Performance

2009 ◽  
Vol 12 (02) ◽  
pp. 341-351 ◽  
Author(s):  
Zhengming Yang
Keyword(s):  
Relative Permeability ◽  
Oil Recovery ◽  
Production Performance ◽  
Hydraulic Fractures ◽  
Diagnostic Analysis ◽  
Fractional Flow ◽  
Permeability Ratio ◽  
Sweep Efficiency ◽  
Widespread Application ◽  
Time Plot

Summary Despite the widespread application of reservoir simulation to study waterflood reservoirs, petroleum engineers still need simple predictive tools to forecast production decline, estimate ultimate oil recovery, and diagnose the production performance from the historical field data. On the basis of the Buckley-Leverett equation and the assumption of a semilog relationship between the oil-to-water relative permeability ratio and water saturation, a consistent analytical solution can be derived as:qoD (1 - qoD) = (EV /B)(1 / tD) where qoD is the oil fractional flow, tD is the fraction of cumulative liquid production to related formation volume, B is the relative permeability ratio parameter, and EV is the volumetric sweep efficiency. Two equivalent linear plots can be developed: a log-log plot and a reciprocal time plot. The log-log plot has a slope of -1 and intercept of EV /B. The reciprocal time plot has a slope of EV /B and an intercept value of 0. Both plots can be applied for the diagnostic analysis of waterflood reservoirs. Model and field case studies show the benefits of this technique as a production-decline analysis tool in forecasting the waterflood production decline and the ultimate oil recovery. This method can also be applied as a diagnostic tool to evaluate various aspects of waterflood performance. Examples include assessing waterflood maturity, calculating volumetric sweep efficiency, distinguishing the normal waterflood breakthrough from the premature water breakthrough through hydraulic fractures, and examining the consequences of operational changes. The appropriate use of this analytical method will help to optimize the field waterflood operation.

Sign in / Sign up

Export Citation Format

Share Document