SPE Gas Slippage in Two-Phase Flow and the Effect of Temperature Kewen Li, SPE, and Roland N. Horne, SPE, Stanford University

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1 PE Gas lippage in To-Phase Flo and the Effect of Temperature Keen Li, PE, and Roland N. Horne, PE, tanford University Copyright 2001, ociety of Petroleum Engineers Inc. This paper as prepared for presentation at the PE Western Regional Meeting held in Bakersfield, California, March This paper as selected for presentation y an PE Program Committee folloing revie of information contained in an astract sumitted y the author(s. Contents of the paper, as presented, have not een revieed y the ociety of Petroleum Engineers and are suject to correction y the author(s. The material, as presented, does not necessarily reflect any position of the ociety of Petroleum Engineers, its officers, or memers. Papers presented at PE meetings are suject to pulication revie y Editorial Committees of the ociety of Petroleum Engineers. Electronic reproduction, distriution, or storage of any part of this paper for commercial purposes ithout the ritten consent of the ociety of Petroleum Engineers is prohiited. Permission to reproduce in print is restricted to an astract of not more than 300 ords; illustrations may not e copied. The astract must contain conspicuous acknoledgment of here and y hom the paper as presented. Write Lirarian, PE, P.O. Box , Richardson, TX , U..A., fax Astract Gas slippage in single-phase gas flo (Klinkenerg Effect has een investigated extensively. Fe papers, hoever, have een pulished on the gas slippage in gas-liquid to-phase flo. The gas relative permeailities at ater saturations close to the residual value have een found to e significantly greater than one in oth nitrogen-ater and steam-ater flo through rocks. These values ecame less than one after the calculation as calirated y taking the to-phase gas slip effect into consideration. The gas relative permeailities have een measured at different mean pore pressures and the values of to-phase gas slip factor have een computed at different ater saturations. The effects of temperature on oth nitrogen and steam slip factors have also een studied and compared. These data have then een used to conduct a caliration in order to otain intrinsic gas relative permeailities that do not vary ith the test pressures. It has een found from the present ork that neglecting the to-phase gas slip effect may overestimate gas relative permeailities. It is the intrinsic gas relative permeailities instead of those measured at lo test pressure that should e utilized in numerical simulation or other reservoir engineering calculation. Introduction Gas-liquid relative permeailities are fundamental properties in reservoir engineering and numerical simulation. There may e significant effect of gas slippage in gas-liquid to-phase flo. Hoever, fe experimental data regarding the gas slip effect in to-phase flo have een pulished. If the slip effect is not considered correctly, the gas relative permeailities ill vary ith test pressures and may e greater than one at some ater saturations. On the other hand, little attention has een paid to the measurements of steam slip factor even in singlephase flo. Reliale data for steam flo is essential to the study of steam injection in heavy oil reservoirs or ater injection in geothermal reservoirs here steam is produced. Rose 1 conducted experimental measurements of gas relative permeailities in oth synthetic cores (Alundum filters and natural sandstone cores. Rose 1 reported that the gas slip factor of the sandstone cores decreased ith the increase of the liquid (ater saturation. Fulton 2 performed experiments on Pyrex cylindrical filters and also found that the gas slip factor decreased ith the increase of the liquid (ater saturation in a range from 0 to aout 30%. These experiments ere not conducted at liquid saturations aove 30%. Therefore, Estes and Fulton 3 extended their experiments to liquid saturations over 30%, ranging from 0 to aout 88% using oltrol oil as the liquid phase; they found a similar phenomenon to that descried y Rose 1 and Fulton 2. Although many researchers 1-3, including ampath and Keighin 4, demonstrated the decrease of gas slip factor ith the increase of liquid saturation, the reason for hich is not readily apparent. Actually, the experimental data presented y these authors are contradictory to the Klinkenerg 5 equation, hich is expressed as follos: 4cO f (1 (1 r here k g is the gas permeaility at a mean pressure, p m, and k gf the intrinsic permeaility of gas at an infinite pressure; c is a proportionality factor ith an apparent value of slightly less than 1; O is the mean free path of the gas and r the average radius of the capillaries. As the mean free path of the gas is inversely proportional to the mean pressure, p m, Klinkenerg 5 reduced Eq. 1 as follos: f (1 (2 here p m is the mean pressure hich is defined y p m = (p i + p o /2; p i and p o are the inlet and outlet pressures of the cores, respectively. is the gas slip factor, hich is defined as: 4c r O p m ince O/p m is a constant, Eq. 3 can e reduced as follos: (3

2 2 K. Li and R.N. Horne PE c (4 r here c is also constant. Eq. 4 implies that the gas slip factor is inversely proportional to the radius of the capillaries. Hoever, the effective radius of the capillaries (for gas phase in porous media must e decreased ith an increase in liquid saturation. Therefore, the gas slip factor should increase ith the increase of the liquid saturation. Rose 1 and Fulton 2 gave different explanations to the contradiction eteen their data and the Klinkenerg theory. In addition, Estes and Fulton 3 found negative values of the gas slip factor at high liquid saturations in the vicinity of 65-75% for all of the natural cores they used. The negative value of means that the apparent gas permeailities measured at lo pressures are smaller than those measured at high pressures. This, of course, is also contradictory to the Klinkenerg theory. The common prolems that existed in the studies of these researchers 1-3 ere the small size of the cores and the methods to estalish the liquid saturations. The end effect due to the capillary discontinuity might have significant effect on the distriution of the liquid saturation in small cores. Rose 1 estalished the liquid saturations y a slo evaporation process. Fulton 2 used to methods to otain the desired ater saturations; one as the same as Rose 1 and the other one as y alloing the cores to imie ater. Estes and Fulton 3 achieved the liquid (oil saturation either y alloing the oil to evaporate sloly from the cores or more frequently y removing the oil in increments ith an asoring tissue. Apparently, the distriutions of the liquid saturations estalished using these methods ould not e uniform. The nonuniform distriution of liquid saturation in the cores may affect the measurements of gas relative permeailities. On the other hand, it is difficult to measure gas relative permeailities at high liquid saturations, for example, aove 50%, y alloing only gas to flo hile keeping ater immoile. Jones and Oens 6 measured the gas permeailities on more than 100 tight gas sand samples ith permeailities ranging from to md and their data yielded a relationship eteen and k gf for single-phase gas flo: 0.33 k gf 0.86 (5 ampath and Keighin 4 thought that a correlation, if it exists, should e eteen and k gf /I rather than eteen and k gf ; they suggested a correlation eteen the gas slip factor and the intrinsic gas permeailities ased on their experimental results using nitrogen: k g f ( (6 I here I is the porosity of the core sample. team-ater relative permeaility is of importance in reservoir engineering for steam injection into oil reservoirs and ater injection into geothermal reservoirs. There are fe measurements of steam-ater relative permeailities reported in the literature, and the values are frequently inconsistent 7-8. The main difficulties in making steam-ater relative permeaility measurements arise from the folloing aspects: (1 significant mass transfer eteen phases makes it difficult to measure or calculate fractional flo; (2 difficulties in measuring heat loss during experiments; (3 unclear mechanisms of gas-liquid flo. For example, the effect of gas slippage on steam relative permeailities in steam-ater flo is not clear; very fe studies related to the gas slip effect in steam-ater flo have een pulished. atik and Horne 7 oserved an unusual phenomenon in that the values of steam relative permeaility (k rg, at some ater saturations sometimes appear to e greater than one. A similar phenomenon as also found in experiments y Mahiya 8. team is suject to a prominent flo characteristic of gas molecules: gas slippage. Gas permeaility k g at a lo mean pressure is greater than the asolute liquid permeaility (k due to the gas slip effect. If the gas slippage is large enough, the gas permeaility at lo ater saturation may still e greater than the asolute permeaility. From the definition of relative permeaility, k g /k, the value of gas relative permeaility may e greater than one. Hence the phenomenon of gas slippage may e the reason. Counsil 9 discussed gas slip effect and shoed that the effect of gas slippage as small hen = 0.2 atm and p m = 10 atm. o the gas (steam slip effect as not considered in the analysis of the gas flo data. Counsil 9 stated that For the case of steam-ater relative permeailities, slip could e reduced y running experiments at very high pressures, and therefore very high temperatures. There are certain difficulties in running experiments at very high pressures and temperatures for measuring steam-ater relative permeailities, for example, hen the X-ray CT method is used to measure the ater saturation in a core (Amusso et al. 10. On the other hand, increasing experimental temperature ill increase the value of significantly as reported y Wel et al. 11 An increasing ill increase the influence of gas slippage on steam flo properties. Geothermal rock often has a very lo intrinsic permeaility of the order of 10-6 md. The value of computed using Eq. 5 ould e aout 82.1 atm for this permeaility. Thus the mean pressure ould need to e aout 1000 atm in order for the gas slip effect to e negligile in single-phase gas flo. Oviously, it is not easy to operate experiments at pressures over 1000 atm. It can e seen from this simple calculation that the effect of gas slippage on steam flo properties may e significant oth in experiments as ell as in actual geothermal reservoirs. Herkelrath et al. 12 recognized the importance of gas slippage and incorporated it into a single-phase steam flo model in order to model steam pressure-transient experimental data. In their study, the steam slip factor as sustituted y the gas slip factor measured using nitrogen. There may e significant differences eteen steam and nitrogen slip factors as e found in this study.

3 PE Gas lippage in To-Phase Flo and the Effect of Temperature 3 In this paper, gas-liquid relative permeailities ere measured at different pressures using an on-line eighing method ith to alances. The effect of ater saturation on the slip factor of nitrogen as investigated. A procedure of measuring and correcting gas relative permeailities as proposed. The slip factors of oth nitrogen and steam ere measured at different temperatures and compared. The experimental values ere used to correct the gas (nitrogen and steam phase relative permeailities. Theory Assuming that Darcys equation is valid for oth nitrogenater and steam-ater to-phase flo and that capillary pressures are neglected, the effective permeaility of gas phase (nitrogen and steam is calculated using the folloing equation: qgp g L po (, (7 A' p here k g (, p m is the effective gas phase permeaility at a ater saturation of and a mean pressure of p m ; q g and P g are the flo rate and viscosity of gas phase; 'p is the differential pressure across the core sample; A and L are the cross-section area and the length of the core sample. In Eq. 7, it is considered that gas permeaility is not only a function of ater saturation ut also a function of mean pressure due to the gas slip effect. The relative permeaility of gas phase is usually calculated ithout the correction of gas slip effect as follos: (, krg (, (8 k here k rg (, p m is the relative permeaility of gas phase at a ater saturation of and a mean pressure of p m ; k is the asolute permeaility of the rock sample measured y liquid injection. With consideration of the gas slip effect, the intrinsic effective permeaility of the gas phase, hich is independent of mean pressure, is calculated using the folloing formula: (, f ( (9 (1 / p m here k gf ( and are the intrinsic effective permeaility and the slip factor of gas phase at a ater saturation of. Hence the relative permeaility of gas phase ith gas slip effect included is calculated using the folloing equation: f ( krgf ( (10 k here k rgf ( is independent of test pressure and is named the intrinsic relative permeaility of gas phase at a ater saturation of. It is seen from Eq. 9 that the essential issue of calculating the intrinsic relative permeaility of gas phase is to measure the value of, the slip factor of gas phase at a ater saturation of. Once the intrinsic gas relative permeailities and the gas slip factors at different ater saturations are availale, the gas relative permeailities at any mean pressure, k rg (, p m, can e computed as follos: krg (, krgf ( (1 (11 Rose 1 defined gas relative permeaility differently as follos: (, k rg (, (12 k ( 0, p g ustituting Eqs. 2 and 9 into Eq. 12: 1 k rg (, krgf ( ( (13 1 p It is knon from Eq. 13 that k (, ould e close to k rgf ( if the slip factor does not change ith ater saturation, as Rose 1 reported. Given that p m =1 atm in Eq. 12, Eq. 13 can e reduced as follos: 1 k rg (, 1 krgf ( ( (14 1 here k rg (, 1 as the gas relative permeaility defined y Estes and Fulton 3. imilarly, Eq. 14 states that k rg (, 1 ould e close to k rgf ( if the slip factor does not vary ith ater saturation, as Estes and Fulton 3 reported. Hoever, this may not e true for other cases. For example, our experimental data in this study shoed that k rgf ( =24.1% = ut k rg ( 24.1%, 1 = Therefore, e defined the gas relative permeaility using the usual ay (see Eq. 8 and deployed k rgf ( as the intrinsic gas relative permeaility hich is independent of mean pressure. A steady-state method as illustrated in Fig. 1 as used to measure the relative permeailities of nitrogen-ater, from hich gas phase relative permeailities ere calculated using the methods descried y Eqs. 8 to 10. Water phase relative permeailities can e calculated directly using Darcys equation. The corresponding ater saturations ere calculated using either of the to alances in the apparatus (see Fig. 1: or, i, i p m rg m ' Mi1 1, i, (using Balance 1 (15 V U ' M 1, i,( using Balance 2 (16 V i2 pu

4 4 K. Li and R.N. Horne PE here V p is the pore volume of the core sample;,i and,i+1 are the ater saturations at i th and i+1 th points, respectively; 'M i1 and 'M i2 are the eight variations recorded y Balances 1 and 2, respectively; U is the ater density. Experiments In this study, experiments to measure nitrogen-ater tophase relative permeailities ere conducted at a room temperature of around 20 o C. The slip factors of nitrogen and steam flo through porous media ere measured at different temperatures up to aout 170 o C. Brine of percent (t NaCl as used as the liquid phase and nitrogen the gas phase in the experiments of measuring nitrogen-ater relative permeailities; the rine specific gravity and viscosity ere 1 and cp at 20 o C. Distilled ater as injected to generate steam in the experiments measuring the steam slip factor. Berea sandstone as used in this study. The Berea core as fired at high temperature to remove the clay. The permeaility and porosity of the rock ere 1.28 darcy and 23.4%; the length and diameter ere 43.2 cm and 5.08 cm respectively. The reason for the use of long core as to reduce the end effect. If the core sample is too short, the end effect may significantly influence the calculation of gas relative permeailities. The schematic of the apparatus used to measure nitrogenater relative permeailities y a steady-state method is shon in Fig. 1. For the ater phase, the system as closed. The decrease (or increase of ater volume in the core as equal to the increase (or decrease of ater volume in the container at the core outlet on Balance 1 (assuming that the ater phase is incompressile. Balance 1 had an accuracy of 0.01 g and a capacity of 1600 g. Water saturations in the core ere then calculated using Eq. 15 ith the data from Balance 1. Another alance (Balance 2 in Fig. 1 as used to eigh the coreholder directly to verify the results otained y Balance 1. Flexile tuings for fluid injection at the inlet and for production at the outlet ere used to connect to the core so that the decrease (or increase of the coreholder eight ould e directly proportional to the decrease (or increase of ater saturations in the core. Therefore, the ater saturations in the core could also e measured y Balance 2; this alance had an accuracy of 0.1 g and a capacity of 6000 g. We found that the ater saturations measured y the to alances ere closely equal to each other. Fig. 2 shos the schematic of the apparatus developed to measure the slip factors of oth the steam and nitrogen at high temperatures. The alance (the same as Balance 2 in Fig. 1 in Fig. 2 as used to monitor the ater saturation in the core sample. The flo rates of steam at oth inlet and outlet of the core can e calculated using the ater injection or production rates, the steam temperature, and pressure measured during the experiments. The steam flo rates at the inlet and outlet ere equal. The purpose in measuring at oth ends as to monitor if there ere prolems such as leakage in the coreholder system. The coreholder and the method to assemle the core sample used in this study ere similar to those of atik and Horne 7. The core sample as first dried y evacuation. The eight of the coreholder as monitored using a alance ith an accuracy of 0.1 g. The core as assumed to e dry hen its eight did not change in eight hours of evacuation at a vacuum of aout 30 millitorr. Then the gas permeailities ere measured at different mean pressures using nitrogen. Folloing that, the core as completely saturated ith 1% (t NaCl rine y evacuation and the asolute liquid permeaility of the core as measured after several pore volumes of rine ere injected. Next, steady-state relative permeaility experiments ere started and varying fractions of nitrogen and ater ere injected into the core. Measurements at each fraction resulted in a single data point on a relative permeaility vs. ater saturation curve. In this study, the experiment commenced from a ater saturation of 100%. The ater saturations ere reduced y increasing the fraction of gas in the injected fluids, hich formed a drainage relative permeaility curve. The nitrogen relative permeailities ere measured at different mean pressures ut at the same saturation. After the relative permeaility experiments ere completed, the core as dried again and the nitrogen slip factors ere measured at temperatures ranging from 20 to 120 o C. Folloing that, the core as evacuated for 24 hours at aout 30 millitorr to get rid of the nitrogen in the core sample. The steam slip factors ere then measured at temperatures ranging from 120 to 170 o C. Results Nitrogen-ater relative permeailities ere measured at amient conditions. It as found that some values of relative permeailities of the gas phase ere greater than one at certain lo ater saturations due to gas slippage. We also conducted experiments at high temperatures to measure the slip factors of oth nitrogen and steam flo in porous media. The results are discussed in this section. Nitrogen-Water Relative Permeaility. Fig. 3 shos the effect of mean pressure in the core on gas (nitrogen relative permeailities calculated ithout considering the gas slip effect in to-phase flo. Gas relative permeailities ere measured at different mean pressures ranging from 5 to 1.40 atm. The ater saturations ere less than 31.8%. The reason for this as the difficulty in keeping ater phase immoile at ater saturations aove 31.8%. The effect of mean pressure on gas relative permeailities as significant (see Fig. 3. Most of the gas relative permeailities measured at these pressures ere greater than one. This as ecause the gas slip effect as not considered in calculating gas relative permeailities hile the asolute permeaility (measured y ater injection as used as the specific permeaility. The relationship eteen the apparent gas permeailities and the reciprocal of mean pressure at different ater saturations ranging from 0 to 31.8% as shon in Fig. 4. A linear correlation eteen the gas permeailities and the

5 PE Gas lippage in To-Phase Flo and the Effect of Temperature 5 reciprocal of mean pressure exists at all the tested ater saturations. The intrinsic gas permeaility at zero ater saturation is calculated y a linear regression on the experimental data. The computed intrinsic gas (nitrogen permeaility, that is, the gas permeaility corresponding to an infinite pressure, k gf, is equal to darcy and close to the asolute liquid permeaility of darcy measured using 1% (t NaCl rine. It can e also seen from Fig. 4 that the ater saturation has a significant effect on the intrinsic effective gas permeaility. Note that the intrinsic effective gas permeaility at the ater saturation of 31.8% is negative if a linear relationship eteen the apparent gas permeaility and the reciprocal of mean pressure is assumed. The reason for this may e due to moility of the ater at such a high ater saturation. If ater flos, the theory of gas slippage may need to e modified. The gas (nitrogen slip factors at different ater saturations ere calculated using the data shon in Fig. 4 and the results are presented in Fig. 5. The data point at the ater saturation of 31.8% as removed due to the unusual value of the intrinsic effective gas permeaility. The gas slip factor increases ith ater saturation although it does not vary much at ater saturations in the range 0 to 18.4%. All the previously mentioned authors 1-4 reported that the gas slip factor decreases ith an increase of ater saturation, hich seems against the Klinkenerg 5 theory. Fig. 6 plots the computed gas slip factors vs. the corresponding intrinsic effective gas permeailities at different ater saturations. Interestingly, a linear relationship eteen the gas slip factor and the intrinsic effective gas permeaility is oserved on a log-log plot. The gas slip factor increases ith the decrease of the intrinsic effective gas permeaility This seems to e reasonale according to Eq. 5 even though Eq. 5 is ased on experimental results for single-phase gas flo. Other authors 1-4 found that the gas slip factor decreased ith the intrinsic effective gas permeaility, hich is in contradiction to Eq. 5. The drainage gas-ater relative permeailities over the hole range of ater saturation are shon in Fig. 7. The open triangles represent the drainage gas relative permeailities at a mean pressure of aout 1.4 atm. The intrinsic gas relative permeailities are calculated using Eq. 10 and plotted in Fig. 7 as solid circles. The corrected intrinsic gas relative permeailities of gas phase are alays less than one. The gas relative permeaility function at any mean pressure, k rg (, p m, can e computed using Eq. 11 once the intrinsic gas relative permeailities and the gas slip factors at different ater saturations are availale. If reservoir pressure is close to or aove the pressure at hich the gas slip effect can e neglected, the gas relative permeailities at reservoir conditions can e represented y the intrinsic gas relative permeailities calculated using Eq. 10. Otherise, the gas relative permeaility function in the reservoir should e computed using Eq. 11. For example, Fort 13 reported that the reservoir pressure near the ellore in the West Panhandle Gas Field had dropped to aout 1 atm due to the area-ide vacuum operations. In such a case, gas slip effect had to e included in reservoir engineering calculations. Another example is the application of thermal vacuum ells in the remediation of deep soil contamination In this case, the reservoir pressure as very lo and the temperature as very high (258 o C. The gas slip effect as not negligile under such reservoir conditions. In geothermal reservoirs, reservoir pressure may not e significantly aove the higher pressure limits here gas slippage can e neglected. Therefore, the gas slip effect may not e neglected due to the lo permeailities and high temperatures. From these examples, it is seen that gas slip effect may e not only an experimental consideration ut also a matter of reservoir engineering in oth single-phase and to-phase flo. Effect of Temperature. Fig. 8 shos the effect of temperature on the apparent nitrogen permeailities measured using the apparatus shon in Fig. 2. The temperature ranged from room temperature to aout 120 o C. The apparent nitrogen permeailities at specific pressures increase ith temperature. The intrinsic permeailities (at infinite mean pressure at different temperatures are equal, around 1.20 darcy. This intrinsic permeaility is close to ut less than the asolute permeaility (1.28 darcy measured y ater flo. Fig. 8 demonstrates that the nitrogen slip factor increases ith temperature. These results are consistent ith those reported y Wel et al. 11 ; their measurements ere made at a loer range of temperature from 0 to 63 o C. The apparent steam permeailities in the Berea sandstone at three different temperatures (120.1, 150.8, and o C ere measured using the apparatus shon in Fig. 2. The results are demonstrated in Fig. 9. The apparent steam permeailities at specific pressures also increase ith temperature. The intrinsic permeailities of steam at the three different temperatures are almost equal to each other and close to the asolute permeaility measured y rine injection. The steam slip factor increases ith temperature, too. Fig. 10 shos the comparison of the relationship eteen the gas permeaility and the reciprocal of mean pressure of nitrogen to steam at a temperature of aout 120 o C. The permeailities and the slip factor of nitrogen are greater than those of steam at specific pressures. Amyx et al. 16 stated that the data otained ith loer molecular eight gas yield a straight line ith greater slope, indicative of a greater slippage effect. The molecular eight of nitrogen is greater than steam ut the nitrogen slip factor is greater than that of steam, as shon in Fig. 10. Actually, this is reasonale, as analyzed in the folloing. The gas slip factor in a circular capillary tue can e expressed as follos (Rose 1 : 32 3 Pc 2 r RT M (17 here P is the gas viscosity, R is the gas constant, T is the asolute temperature, and M the molecular eight of gas. For nitrogen and steam, the folloing equation applies:

6 6 K. Li and R.N. Horne PE P P M M (18 here, P, and M are the slip factor, viscosity, and molecular eight of nitrogen;, P, and M are the slip factor, viscosity, and molecular eight of steam. The viscosities of nitrogen and steam at a temperature of 120 o C are cp and cp respectively. The ratio of nitrogen slip factor to the steam calculated using Eq. 18 ould e aout This shos that the nitrogen slip factor should e greater than that of steam at the same temperature, as shon in Fig. 10. The ratio of nitrogen slip factor to the steam calculated using the data presented in Fig. 10 is aout 1.124, close to the theoretical value in a circular capillary tue. The effects of temperature on oth nitrogen and steam slip factors are plotted in Fig. 11. As e discussed previously, oth nitrogen and steam slip factors increase ith temperature. Nitrogen slip factor is greater than that of steam. Therefore, it may not e appropriate to sustitute steam slip factor using that of nitrogen or other gases. Correction of team Phase Relative Permeaility. teamater relative permeailities are usually measured at high temperatures aove 100 o C. Gas slip effect in steam-ater flo may also e significant due to the high temperature. atik and Horne 7 found that steam relative permeailities at some ater saturations appeared to e greater than unity. Mahiya 8 also oserved a similar phenomenon. This can e attriuted to the gas slip effect in steam-ater flo. The uncorrected steamater relative permeailities measured y Mahiya 8 are shon in Fig. 12 as the open triangles. We measured the steam slip factor using a similar Berea sandstone core hich had almost the same permeaility as the core Mahiya 8 used. The value of the steam slip factor at a temperature of 120 o C, the average temperature at hich steam-ater relative permeailities ere measured, as aout atm. The steam relative permeailities measured at the pressure close to the atmospheric ere corrected using this value of the steam slip factor and the corresponding mean pressure; the corrected intrinsic steam relative permeailities are plotted in Fig. 12 as the solid circles. The steam slip factor as assumed to e constant at all ater saturations due to the lack of data. It can e seen from Fig. 12 that all the corrected steam relative permeailities are less than one. The gas (steam slip effect in steam-ater to-phase flo is significant. Discussion As a matter of experimental practicality, steam-ater or gasater relative permeailities are usually measured at a lo mean pressure. When the gas-liquid relative permeailities are reported to the reservoir engineers, the corresponding experimental mean pressures may not e included ithin the report. It is knon from the analysis reported here that gas relative permeailities may change ith the mean pressure. The reservoir pressure is generally much different from the experimental pressure. o, if reservoir engineers apply the experimental data of relative permeailities in reservoir calculations, significant error may occur. The solution to this prolem is clear. The intrinsic gas relative permeailities independent of test mean pressure should e computed and reported to reservoir engineers together ith the corresponding steam slip factors and the test pressures. Therefore, reservoir engineers can use Eq. 11 to calculate the gas relative permeailities at hatever pressures are required. As discussed previously, gas slip effect is not only an experimental consideration ut also a matter of reservoir engineering if the reservoir pressure is not ell aove the higher pressure limits here gas slippage can e neglected. Examples are the gas reservoirs under vacuum operation 13 and reservoirs ith extremely lo permeailities. Pressure and ater saturation change very much in a reservoir. Therefore, fluid flo calculations for these reservoirs should take account of the gas slip effect as a function of pressure and ater saturation. Ertekin et al 17 developed such a fluid flo model in hich a dynamic slip factor (pressure and saturation dependent as included. This model ould e helpful to modifying numerical simulators in gas reservoirs under vacuum operation and reservoirs ith extremely lo permeailities. Unfortunately, the experimental data of gas slip effect in to-phase flo are fe and inconsistent. There are many issues to e solved in this field. For example, the relationship eteen the gas permeaility and the reciprocal of mean pressure is not yet clear hen the ater phase is moile. On the other hand, little attention has een paid to the effect of capillary pressure on the calculation of gas relative permeailities, hich may e significant hen the core studied is short and very lo permeale. Conclusions The folloing conclusions may e dran ased on the present study: 1. Gas slippage affects gas (oth nitrogen and steam relative permeaility significantly; neglecting the gas slip effect in gas-liquid to-phase flo ill overestimate gas relative permeaility values. 2. The gas slip factor increases ith the ater saturation ut is almost constant at ater saturations elo aout 18%. 3. A linear correlation eteen the gas slip factor and the effective intrinsic gas permeaility as oserved on a loglog plot. 4. Both the nitrogen and steam slip factors increase ith temperature. The steam slip factor is less than that of nitrogen at the same temperature. 5. It may e necessary to calculate the intrinsic gas relative permeailities independent of test pressures ith the gas slip effect in to-phase flo considered. 6. Gas slip effect in oth single- and to-phase flo is not only an experimental consideration ut may also e of consequence in reservoir engineering calculations in some cases.

7 PE Gas lippage in To-Phase Flo and the Effect of Temperature 7 Acknoledgements This ork as supported y the U DOE under grant DE- FG07-99ID13763, the contriution of hich is gratefully acknoledged. The assistance of Huda Nassori and Will Whitted is also acknoledged. Nomenclature A=cross-section area of the core = gas slip factor of single-phase flo =slip factor of nitrogen in single-phase flo =slip factor of steam in single-phase flo = slip factor of gas phase at a ater saturation of c=a proportionality factor c =constant k=asolute permeaility of the core k gf =intrinsic permeaility of gas at an infinite pressure for single-phase flo k gf ( =intrinsic effective permeaility of gas phase at a ater saturation of k g (, p m =effective gas phase permeaility at a ater saturation of and a mean pressure of p m k rgf ( =intrinsic relative permeaility of gas phase at a ater saturation of L=length of the core M=molecular eight of gas M M =molecular eight of nitrogen =molecular eight of steam 'M i1 =eight variation recorded y Balance 1 'M i2 =eight variation recorded y Balance 2 p i = inlet pressure p m = mean pressure p o = outlet pressure 'p = differential pressure across the core sample q g =gas flo rate r = average radius of the capillaries R=gas constant =ater saturation,i = ater saturation at i th point,i+1 = ater saturation at i+1 th point T = temperature V p =pore volume of the core sample U =ater density O =mean free path of gas P g = viscosity of gas phase P =viscosity of nitrogen P =viscosity of steam 3. Estes, R.K. and Fulton, P.F.: Gas lippage and Permeaility Measurements, Trans., AIME, (1956, 207, ampath, K. and Keighin, C.W.: Factors Affecting Gas lippage in Tight andstones of Cretaceous Age in the Uinta Basin, JPT, (Novemer 1982, Klinkenerg, L.J.: The Permeaility of Porous Media to Liquids and Gases, API Drilling And Production Practice (1941, Jones, F.O. and Oens, W.W.: A Laoratory tudy of Lo- Permeaility Gas ands, JPT (eptemer 1980, atik, C. and Horne, R.N.: Measurement of team-water Relative Permeaility, Quarterly report of tanford Geothermal Program (January March 1998, DE-FG07-95ID Mahiya, G.F.: Experimental Measurement of team-water Relative Permeaility, M report, tanford University, tanford, CA, UA, Counsil, J.R.: team-water Relative Permeaility, Ph.D. Dissertation, tanford University ( Amusso, W., atik, C., and Horne, R.N.: Determination of Relative Permeaility for team-water Flo in Porous Media, paper PE 36682, presented at the 1996 Annual Technical Conference and Exhiition, Denver, Colorado, Oct Wel, K.K., Morro, N.R., and Broer, K.R.: Effect of Fluid, Confining Pressure, and Temperature on Asolute Permeailities of Lo-Permeaility andstones, PE Formation Evaluation (August 1986, Herkelrath, W.N., Moench, A.F., and ONeal II, C.F.: Laoratory Investigations of team Flo in a Porous Medium, Water Resources Research (August 1983, 19, No.4, Fort, F.T.: Implementation of West Panhandle Vacuum Operations, paper PE 24297, presented at the 1992 PE Mid- Continent Gas ymposium, Amarillo, Texas, April 13-14, tegemeier, G.L. and Vinegar, H.J.: oil Remediation y urface Heating and Vacuum Extraction, paper PE 29771, presented at the 1992 PE/EPA Exploration & Production Environmental Conference, Houston, Texas, March 27-29, Vinegar, H.J., Menotti, J.L., Coles, J.M., tegemeier, G.L., heldon, R.B., and Edelstein, W.A.: Remediation of Deep oil Contamination Using Thermal Vacuum Wells, paper PE 39291, presented at the 1997 PE Annual Technical Conference and Exhiition, an Antonio, Texas, Oct. 5-8, Amyx, J.W., Bass, D.M., JR., and Whiting, R.L.: Petroleum Reservoir Engineering-Physical Properties, (1960, McGra Hill Book Co., IBN , Ertekin, T., King, G.R., and cherer, F.C.: Dynamic Gas lippage: A Unique Dual-Mechanism Approach to the Flo of Gas in Tight Formation, paper PE 12045, presented at the 1983 Annual Technical Conference and Exhiition, an Francisco, California, Oct. 5-8, References 1. Rose, W.D.: Permeaility and Gas-lippage Phenomena, API Drilling And Production Practice (1948, Fulton, P.F.: The Effect of Gas lippage on Relative Permeaility Measurements, Producers Monthly (Oct., 1951, 15, No. 12, 14.

8 8 K. Li and R.N. Horne PE P regulator Flo rate 'p Core Balance 2 Balance 1 Gas Permeaility (darcy =0.00% =6.54% =10.85% =18.38% =24.13% =31.81% Water Pump Fig. 1 test. chematic of gas-ater relative permeaility steady-state Fig /p (1/atm Gas slippage effect at different ater saturations cale Air Bath T 2 T 1 Core Dp Heat Exchanger team P. Regulator Water lip Factor (atm Water Pump team Generator Water aturation (% Fig. 2 chematic of gas (nitrogen and steam slip factor test. Fig. 5 Effect of ater saturation on Gas slip factor Gas Relative Permeaility =31.8% =24.1% =18.4% =10.9% =6.5% lip Factor (atm Water aturation (% Fig. 3 Effect of gas slippage on gas relative permeailities in nitrogen-ater systems Effective Gas Permeaility (darcy Fig. 6 Relationship eteen gas slip factor and intrinsic effective gas permeailities.

9 Gas PE Gas lippage in To-Phase Flo and the Effect of Temperature Relative Permeaility k rg (at 1.4 atm K rg (calirated k r Gas Permeaility (darcy team Nitrogen Water aturation (% Fig. 7 slippage effect on nitrogen-ater relative permeailities /p (1/atm Fig. 10 Comparison of nitrogen slip effect to steam at a temperature of 120 o C. Gas Permeaility (darcy T=21.2 o C T=63.2 o C T=120.2 o C lip Factor (atm Nitrogen team Fig /p (1/atm Gas (nitrogen slip effect at different temperatures Temperature (C Fig. 11 Effect of temperature on nitrogen and steam slip factor team Permeaility (darcy T=120.1 o C T=150.8 o C T=170.2 o C Relative Permeaility k rs - efore correction k rs - after correction k r Fig /p (1/atm Gas (steam slip effect at different temperatures Water aturation (% Fig. 12 Caliration of steam relative permeailities in steamater flo.