Evaluation of Normalized Stone's Methods for Estimating Three-Phase Relative Permeabilities

1984 ◽  
Vol 24 (02) ◽  
pp. 224-232 ◽  
Author(s):  
F.J. Fayers ◽  
J.D. Matthews
Keyword(s):  
Relative Permeability ◽  
Gas Oil ◽  
Residual Oil ◽  
Relative Permeabilities ◽  
Two Phase ◽  
Mobile Water ◽  
Oil Displacement ◽  
Three Phase ◽  
Phase Data ◽  
Definition Of

Abstract This paper examines normalized forms of Stone's two methods for predicting three-phase relative permeabilities. Recommendations are made on selection of the residual oil parameter, S om, in Method I. The methods are tested against selected published three-phase experimental data, using the plotting program called CPS-1 to infer improved data fitting. It is concluded that the normalized Method I with the recommended form for S om, is superior to Method II. Introduction Stone has produced two methods for estimating three-phase relative permeability from two-phase data. Both models assume a dominant wetting phase (usually water), a dominant nonwetting phase (gas), and an intermediate wetting phase (usually oil). The relative permeabilities for the water and gas are assumed to permeabilities for the water and gas are assumed to depend entirely on their individual saturations because they occupy the smallest and largest pores, respectively. The oil occupies the intermediate-size pores so that the oil relative permeability is an unknown function of water and gas saturation. For his first method, Stone proposed a formula for oil relative, permeability that was a product of oil relative permeability in the absence of gas, oil relative permeability in the absence of gas, oil relative permeability in the absence of mobile water, and some permeability in the absence of mobile water, and some variable scaling factors. He compared this formula with the experimental results of Corey et al., Dalton et al., and Saraf and Fatt. The formula is likely to be most in error at low oil relative permeability where more data are needed that show the behavior of residual oil saturation as a function of mixed gas and water saturations. In particular, the best value for the parameter S om that occurs in the model is not well resolved. In his second method, Stone developed a new formula and compared it against the data of Corey et al., Dalton et al., Saraf And Fatt, and some residual oil data from Holmgren and Morse. Stone suggested that his second method gave reasonable agreement with experiments without the need to include the parameter S om. If in the absence of residual oil data, S om = 0 is used in the first method, the second method is then better than the first method, although it tends to under predict relative permeability. Dietrich and Bondor later showed that Stone's second method did not adequately approximate the two-phase data unless the oil relative permeability at connate water saturation, k rocw, was close to unity. Dietrich and Bondor suggested a normalization that achieved consistency with the two-phase data when k rocw, was not unity. This normalization can be unsatisfactory because k roc an exceed unity in some saturation ranges if k rocw is small. More recently this objection has been overcome by the normalization of Method II introduced by Aziz and Settari. Aziz and Settari also pointed out a similar normalization problem with Stone's first method and suggested an alternative to overcome the deficiency. However, no attempt was made to investigate the accuracy of these normalized formulas with respect to experimental data. In the next section of the paper we review the principal forms of Stone's formulas, and introduce some new ideas on the use and choice of the parameter S om. Later we examine the first of Stone's assumptions that water and gas relative permeabilities are functions only of their respective saturations for a water-wet system. This involves a critical review of all the published experimental measurements. Earlier reviews did not take into account some of the available data. Last, we examine the predictions of normalized Stone's methods for oil relative permeability against the more reliable experimental results. It is concluded that the normalized Stone's Method I with the improved definition of S om is more accurate than the normalized Method II. Mathematical Definition of Three-Phase Relative Permeabilities We briefly review the principal forms of the Stone's formulas that use the two-phase relative permeabilities defined by water/oil displacement in the absence of gas, k rw = k rw (S w) and k row = k row (S w) and gas/oil displacement in the presence of connate water, k rg = k rg (S g) and k rog = k rog (S g). SPEJ p. 224

Experimental Study and History-Match of Near-Miscible WAG Coreflood Experiments on Mixed-Wet Carbonate Rocks

2021 ◽  
Author(s):  
Mohamed Mehdi El Faidouzi
Keyword(s):  
Relative Permeability ◽  
Carbonate Rocks ◽  
Hysteresis Model ◽  
Relative Permeabilities ◽  
Two Phase ◽  
Recovery Method ◽  
Phase Displacement ◽  
Three Phase ◽  
Displacement Experiments ◽  
Phase Water

Abstract Water-alternating-gas (WAG) injection, both miscible and immiscible, is a widely used enhanced oil recovery method with over 80 field cases. Despite its prevalence, the numerical modeling of the physical processes involved remains poorly understood, and existing models often lack predictability. Part of the complexity stems from the component exchange between gas and oil and the hysteretic relative permeability effects. Thus, improving the reliability of numerical models requires the calibration of the equation of state (EOS) against phase behavior data from swelling/extraction and slim-tube tests, and the calibration of the three-phase relative permeability model against WAG coreflood experiments. This paper presents the results and interpretation of a complete set of two-phase and thee-phase displacement experiments on mixed-wet carbonate rocks. The three-phase WAG experiments were conducted on the same composite core at near-miscible reservoir condition; experiments differ in the injection order and length of their injection cycles. First, the two-phase water/oil and gas/oil displacement experiments and first cycles of WAG were used to estimate the two-phase relative permeabilities. Then, a synchronized history-matching procedure over the full set of WAG experiments and cycles was carried out to tune Larsen ans Skauge WAG hysteresis model—namely the Land gas traping parameter, the gas reduction exponent, the residual oil reduction factor and three-phase water relative permeability. The second part of this paper deals with the multiphase upscaling of microscopic displacement properties from plug to coarse grid reservoir scale. The two-phase relative permeability curves and three-phase WAG parameters were upscaled using a sector model to preserve the displacement process and reservoir performance. The result of the coreflood calibration indicate that the two-phase displacement and first cycles of WAG yield a consistent set of two-phase relative permeabilities. Including the full set of WAG experiments allowed a robust calibration of the hysteresis model.

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.

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.

The Effect of Interfacial Tensions on Relative Oil/Water Permeabilities of Consolidated Porous Media

1982 ◽  
Vol 22 (03) ◽  
pp. 371-381 ◽  
Author(s):  
Jude O. Amaefule ◽  
Lyman L. Handy
Keyword(s):  
Porous Media ◽  
Interfacial Tension ◽  
Relative Permeability ◽  
Residual Oil ◽  
Relative Permeabilities ◽  
Interfacial Tensions ◽  
Oil Displacement ◽  
Oil Water ◽  
Relative Permeability Curves ◽  
Low Tension

Abstract Relative permeabilities of systems containing low- tension additives are needed to develop mechanistic insights as to how injected aqueous chemicals affect fluid distribution and flow behavior. This paper presents results of an experimental investigation of the effect of low interfacial tensions (IFT's) on relative oil/water permeabilities of consolidated porous media. The steady- and unsteady-state displacement methods were used to generate relative permeability curves. Aqueous low-concentration surfactant systems were used to vary IFT levels. Empirical correlations were developed that relate the imbibition relative permeabilities, apparent viscosity, residual oil, and water saturations to the interfacial tension through the capillary number (Nc=v mu / sigma). They require two empirical, experimentally generated coefficients. The experimental results show that the relative oil/water permeabilities at any given saturation are affected substantially by IFT values lower than 10-1 mN/m. Relative oil/water permeabilities increased with decreasing IFT (increasing N ). The residual oil and residual water saturations (S, and S) decreased, while the total relative mobilities increased with decreasing IFT. The correlations predict values of relative oil/water permeability ratios, fractional flow, and residual saturations that agree with our experimental data. Apparent mobility design viscosities decreased exponentially with the capillary number. The results of this study can be used with simulators to predict process performance and efficiency for enhanced oil-recovery projects in which chemicals are considered for use either as waterflood or steamflood additives. However, the combined effect of decreased interfacial tension and increased temperature on relative permeabilities has not yet been studied. Introduction Oil displacement with an aqueous low-concentration surfactant solution is primarily dependent on the effectiveness of the solutions in reducing the IFT between the aqueous phase and the reservoir oil. With the attainment of ultralow IFT's (10 mN/m) and with adequate mobility controls, all the oil contacted can conceivably be displaced. When the interfacial tension is reduced to near zero values, the process tends to approach miscible displacement. However, most high-concentration soluble oil systems revert to immiscible displacement processes as the injected chemical traverses the reservoir. This is a result of the continual depletion of the surfactant by adsorption on the rock and by precipitation with divalent cations in the reservoir brine. The mechanism by which residual oil is mobilized by low-tension displacing fluids cannot be explained solely by the application of Darcy's law to both the aqueous and the oleic phases. On the other hand, in those reservoir regions in which water and oil are flowing concurrently as continuous phases, Darcy's law would be expected to apply and the relative permeability concept would be valid. If a low-tension aqueous phase were to invade a region in which the oil had not as yet been reduced to a discontinuous irreducible saturation, one would expect, also, that the relative permeability concept would be applicable. Under circumstances for which these conditions apply, relative permeabilities at low interfacial tensions would be required, The effect of IFT's on relative permeability curves has received limited treatment in the petroleum literature. Leverett reported a small but definite tendency for a water/oil system in unconsolidated rocks to exhibit 20 to 30% higher relative permeabilities if the IFT was decreased from 24 to 5 mN/m. Mungan studied interfacial effects on oil displacement in Teflons cores. The interfacial tension values varied from 5 to 40 mN/m. SPEJ P. 371^

Effect of Temperature on Oil/Water Relative Permeabilities of Unconsolidated and Consolidated Sands

1985 ◽  
Vol 25 (06) ◽  
pp. 945-953 ◽  
Author(s):  
Mark A. Miller ◽  
H.J. Ramey
Keyword(s):  
Relative Permeability ◽  
Room Temperature ◽  
Water Saturation ◽  
High Water ◽  
Distilled Water ◽  
Relative Permeabilities ◽  
Two Phase ◽  
Dynamic Displacement ◽  
Irreducible Water Saturation ◽  
Increasing Temperature

Abstract Over the past 20 years, a number of studies have reported temperature effects on two-phase relative permeabilities in porous media. Some of the reported results, however, have been contradictory. Also, observed effects have not been explained in terms of fundamental properties known to govern two-phase flow. The purpose of this study was to attempt to isolate the fundamental properties affecting two-phase relative permeabilities at elevated temperatures. Laboratory dynamic-displacement relative permeability measurements were made on unconsolidated and consolidated sand cores with water and a refined white mineral oil. Experiments were run on 2-in. [5.1-cm] -diameter, 20-in. [52.-cm] -long cores from room temperature to 300F [149C]. Unlike previous researchers, we observed essentially no changes with temperature in either residual saturations or relative permeability relationships. We concluded that previous results may have been affected by viscous previous results may have been affected by viscous instabilities, capillary end effects, and/or difficulties in maintaining material balances. Introduction Interest in measuring relative permeabilities at elevated temperatures began in the 1960's with petroleum industry interest in thermal oil recovery. Early thermal oil recovery field operations (well heaters, steam injection, in-situ combustion) indicated oil flow rate increases far in excess of what was predicted by viscosity reductions resulting from heating. This suggested that temperature affects relative permeabilities. One of the early studies of temperature effects on relative permeabilities was presented by Edmondson, who performed dynamic displacement measurements with crude performed dynamic displacement measurements with crude and white oils and distilled water in Berea sandstone cores. Edmondson reported that residual oil saturations (ROS's) (at the end of 10 PV's of water injected) decreased with increasing temperature. Relative permeability ratios decreased with temperature at high water saturations but increased with temperature at low water saturations. A series of elevated-temperature, dynamic-displacement relative permeability measurements on clean quartz and "natural" unconsolidated sands were reported by Poston et al. Like Edmondson, Poston et al. reported a decrease in the "practical" ROS (at less than 1 % oil cut) as temperature increased. Poston et al. also reported an increase in irreducible water saturation. Although irreducible water saturations decreased with decreasing temperature, they did not revert to the original room temperature values. It was assumed that the cores became increasingly water-wet with an increase in both temperature and time; measured changes of the IFT and the contact angle with temperature increase, however, were not sufficient to explain observed effects. Davidson measured dynamic-displacement relative permeability ratios on a coarse sand and gravel core with permeability ratios on a coarse sand and gravel core with white oil displaced by distilled water, nitrogen, and superheated steam at temperatures up to 540F [282C]. Starting from irreducible water saturation, relative permeability ratio curves were similar to Edmondson's. permeability ratio curves were similar to Edmondson's. Starting from 100% oil saturation, however, the curves changed significantly only at low water saturations. A troublesome aspect of Davidson's work was that he used a hydrocarbon solvent to clean the core between experiments. No mention was made of any consideration of wettability changes, which could explain large increases in irreducible water saturations observed in some runs. Sinnokrot et al. followed Poston et al.'s suggestion of increasing water-wetness and performed water/oil capillary pressure measurements on consolidated sandstone and limestone cores from room temperature up to 325F [163C]. Sinnokrot et al confirmed that, for sandstones, irreducible water saturation appeared to increase with temperature. Capillary pressures increased with temperature, and the hysteresis between drainage and imbibition curves reduced to essentially zero at 300F [149C]. With limestone cores, however, irreducible water saturations remained constant with increase in temperature, as did capillary pressure curves. Weinbrandt et al. performed dynamic displacement experiments on small (0.24 to 0.49 cu in. [4 to 8 cm3] PV) consolidated Boise sandstone cores to 175F [75C] PV) consolidated Boise sandstone cores to 175F [75C] with distilled water and white oil. Oil relative permeabilities shifted toward high water saturations with permeabilities shifted toward high water saturations with increasing temperature, while water relative permeabilities exhibited little change. Weinbrandt et al. confirmed the findings of previous studies that irreducible water saturation increases and ROS decreases with increasing temperature. SPEJ P. 945

Distribution of the Oil Phase Obtained Upon Imbibition of Water

1964 ◽  
Vol 4 (01) ◽  
pp. 49-55 ◽  
Author(s):  
Pietro Raimondi ◽  
Michael A. Torcaso
Keyword(s):  
Primary Production ◽  
Relative Permeability ◽  
Water Saturation ◽  
Initial Conditions ◽  
Flow Behavior ◽  
Phase System ◽  
Residual Oil ◽  
Two Phase ◽  
Connate Water ◽  
Phase Water

Abstract The distribution of the oil phase in Berea sandstone resulting from increasing and decreasing the water saturation by imbibition was investigated Three types of distribution were recognized: trapped, normal and lagging. The amount of oil in each of these distributions was determined as a function of saturation by carrying out a miscible displacement in the oil phase under steady-state conditions of saturation. These conditions were maintained by flowing water and oil simultaneously in given ratios and by using a displacing solvent having essentially the same density and viscosity as the oil.A correlation shows the amount of trapped oil at any saturation to be directly proportional to the conventional residual oil saturation Sir The factor of proportionality is related to the fractional permeability to the water phase. Part of the oil which was not trapped was displaced in a piston- like manner (normal part) and part was eluted gradually (lagging part). The observed phenomena are more than of mere academic importance. Oil which is trapped may well provide the fuel essential for forward combustion and thus be beneficial. On the contrary, in tertiary recovery operations, it is this trapped oil which seems to make current techniques uneconomic. Introduction A typical oilfield may initially contain connate water and oil. After a period of primary production water often enters the field either from surrounding aquifers or from surface injection. During primary production evolution and establishment of a free gas saturation usually occurs. The effect and importance of this third phase is fully recognized. However, this investigation is limited to a two- phase system, one wetting phase (water) and one non-wetting phase (oil). The increase in water content of a water-wet system is termed imbibition. In a relative permeability-saturation diagram such as the one shown in Fig. 1, the initial conditions of the field would he represented by a point below a water saturation of about 35 per cent, i.e., where the imbibition and the drainage curves to the non-wetting phase nearly coincide. When water enters the field the relative permeability to oil decreases along the imbibition curve. At watered-out conditions the relative permeability to the oil becomes zero. At this point a considerable amount of oil, called residual oil, (about 35 per cent in Fig. 1) remains unrecovered. Any attempt to produce this oil will require that its saturation be increased. In Fig. 1 this would mean retracing the imbibition curve upwards. In addition, processes like alcohol and fire flooding, which can be employed at any stage of production, involve the complete displacement of connate water and an increase, or imbibition, of water saturation ahead of the displacing front. Thus, in several types of oil production it is the imbibition-relative permeability curve which rules the flow behavior. For this reason a knowledge of the distribution of the non-wetting phase, as obtained through imbibition, whether "coming down" or "going up" on the imbibition curve, is important. SPEJ P. 49^

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