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.

Relative Permeability Characterization for Water-Alternating-Gas Injection in Oil Reservoirs

SPE Journal ◽  
2016 ◽  
Vol 21 (03) ◽  
pp. 0799-0808 ◽  
Author(s):  
H.. Shahverdi ◽  
M.. Sohrabi
Keyword(s):  
Relative Permeability ◽  
Gas Injection ◽  
Hysteresis Effect ◽  
Oil Reservoirs ◽  
Unsteady State ◽  
Two Phase ◽  
Water Alternating Gas ◽  
Three Phase ◽  
Phase Water ◽  
Wag Injection

Summary Large quantities of oil usually remain in oil reservoirs after conventional waterfloods. A significant part of this remaining oil can still be economically recovered by water-alternating-gas (WAG) injection. WAG injection involves drainage and imbibition processes taking place sequentially; therefore, the numerical simulation of the WAG process requires reliable knowledge of three-phase relative permeability (kr) accounting for cyclic-hysteresis effects. In this study, the results of a series of unsteady-state two-phase displacements and WAG coreflood experiments were used to investigate the behavior of three-phase kr and hysteresis effects in the WAG process. The experiments were performed on two different cores with different characteristics and wettability conditions. An in-house coreflood simulator was developed to obtain three-phase relative permeability values directly from unsteady-state WAG experiments by history matching the measured recovery and differential-pressure profiles. The results show that three-phase gas relative permeability is reduced in consecutive gas-injection cycles and consequently the gas mobility and injectivity drop significantly with successive gas injections during the WAG process, under different rock conditions. The trend of hysteresis in the relative permeabilty of gas (krg) partly contradicts the existing hysteresis models available in the literature. The three-phase water relative permeability (krw) of the water-wet (WW) core does not exhibit considerable hysteresis effect during different water injections, whereas the mixed-wet (MW) core shows slight cyclic hysteresis. This may indicate a slight increase of the water injectivity in the subsequent water injections in the WAG process under MW conditions. Insignificant hysteresis is observed in the oil relative permeability (kro) during different gas-injection cycles for both WW and MW rocks. However, a considerable cyclic-hysteresis effect in kro is observed during water-injection cycles of WAG, which is attributed to the reduction of the residual oil saturation (ROS) during successive water injections. The kro of the WW core exhibits much-more cyclic-hysteresis effect than that of the MW core. No models currently exist in reservoir simulators that can capture the observed cyclic-hysteresis effect in oil relative permeability for the WAG process. Investigation of relative permeability data obtained from these displacement tests at different rock conditions revealed that there is a significant discrepancy between two-phase and three-phase relative permeability of all fluids. This highlights that not only the three-phase relative permeability of the intermediate phase (oil), but also the three-phase kr of the wetting phase (water) and nonwetting phase (gas) are functions of two independent saturations.

Simulation of Immiscible WAG Experiments Performed in Carbonate Rocks: The Impact of Heterogeneity on Hysteresis Phenomenon

2021 ◽  
Author(s):  
Latifa Obaid Alnuaimi ◽  
Mehran Sohrabi ◽  
Shokoufeh Aghabozorgi ◽  
Ahmed Alshmakhy
Keyword(s):  
Relative Permeability ◽  
Carbonate Rocks ◽  
Carbonate Rock ◽  
Hysteresis Effect ◽  
Hysteresis Phenomenon ◽  
Hysteresis Model ◽  
Sandstone Rock ◽  
Three Phase ◽  
The Impact ◽  
Permeability Data

Abstract Simulation of Water-Alternating-Gas (WAG) Experiments require precise estimation of hysteresis phenomenon in three-phase relative permeability. Most of the research available in the literature are focused on experiments performed on sandstone rocks and the study of carbonate rocks has attracted less attention. In this paper, a recently published hysteresis model by Heriot-Watt University (HWU) was used for simulation of WAG experiments conducted on mixed-wet homogenous carbonate rock. In this study, we simulated immiscible WAG experiments, which were performed under reservoir conditions on mixed-wet carbonate reservoir rock extracted from Abu Dhabi field by using real reservoir fluids. Experiments are performed with different injection scenarios and at high IFT conditions. Then, the results of the coreflood experiments were history matched using 3RPSim to generate two-phase and three-phase relative permeability data. Finally, the hysteresis model suggested by Heriot-Watt University was used for the estimation of hysteresis in relative permeability data. The performance of the model was compared with the experimental data from sandstones to evaluate the impact of heterogeneity on hysteresis phenomenon. It was shown that the available correlations for estimation of three-phase oil relative permeability fail to simulate the oil production during WAG experiments, while the modified Stone model suggested by HWU provided a better prediction. Overall, HWU hysteresis model improved the match for trapped gas saturation and pressure drop. The results show that the hysteresis effect is less dominant in the carbonate rock compared to the sandstone rock. The tracer test results show that the carbonate rock is more homogenous compared to sandstone rock. Therefore, the conclusion is that the hysteresis effect is negligible in homogenous systems.

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.

Three-Phase Relative Permeabilities from Displacement Experiments with Full Account for Capillary Pressure

1998 ◽  
Vol 1 (02) ◽  
pp. 92-98 ◽  
Author(s):  
H.M. Helset ◽  
J.E. Nordtvedt ◽  
S.M. Skjaeveland ◽  
G.A. Virnovsky
Keyword(s):  
Porous Media ◽  
Multiphase Flow ◽  
Capillary Pressure ◽  
Relative Permeability ◽  
Single Phase ◽  
Flow In Porous Media ◽  
Relative Permeabilities ◽  
The Core ◽  
Three Phase ◽  
Displacement Experiments

Abstract Relative permeabilities are important characteristics of multiphase flow in porous media. Displacement experiments for relative permeabilities are frequently interpreted by the JBN method neglecting capillary pressure. The experiments are therefore conducted at high flooding rates, which tend to be much higher than those experienced during reservoir exploitation. Another disadvantage is that the relative permeabilities only can be determined for the usually small saturation interval outside the shock. We present a method to interpret displacement experiments with the capillary pressure included, using in-situ measurements of saturations and phase pressures. The experiments can then be run at low flow rates, and relative permeabilities can be determined for all saturations. The method is demonstrated by using simulated input data. Finally, experimental scenarios for three-phase displacement experiments are analyzed using experimental three-phase relative permeability data. Introduction Relative permeabilities are important characteristics of multiphase flow in porous media. These quantities arise from a generalization of Darcy's law, originally defined for single phase flow. Relative permeabilities are used as input to simulation studies for predicting the performance of potential strategies for hydrocarbon reservoir exploitation. The relative permeabilities are usually determined from flow experiments performed on core samples. The most direct way to measure the relative permeabilities is by the steady-state method. Each experimental run gives only one point on the relative permeability curve (relative permeability vs. saturation). To make a reasonable determination of the whole curve, the experiment has to be repeated at different flow rate fractions. To cover the saturation plane in a three-phase system, a large number of experiments have to be performed. The method is therefore very time consuming. Relative permeabilities can also be calculated from a displacement experiment. Typically, the core is initially saturated with a single-phase fluid. This phase is then displaced by injecting the other phases into the core. For the two-phase case, Welge showed how to calculate the ratio of the relative permeabilities from a displacement experiment. Efros was the first to calculate individual relative permeabilities from displacement experiments. Later, Johnson et al. presented the calculation procedure in a more rigorous manner, and the method is often referred to as the JBN method. The analysis has also been extended to three phases. In this approach, relative permeabilities are calculated at the outlet end of the core; saturations vs. time at the outlet end is determined from the cumulative volumes produced and time derivatives of the cumulative volumes produced, and relative permeabilities vs. time are calculated from measurements of pressure drop over the core and the time derivative of the pressure drop. Although the JBN method is frequently used for relative permeability determination, it has several drawbacks. The method is based on the Buckley-Leverett theory of multiphase flow in porous media. The main assumption is the neglection of capillary pressure. In homogenous cores capillary effects are most important at the outlet end of the core and over the saturation shock front. To suppress capillary effects, the experiments are performed at a high flow rate. Usually, these rates are significantly higher than those experienced in the underground reservoirs during exploitation.

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

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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