Effect of positive rate sensitivity and inertia on gas condensate relative permeability at high velocity

Transcription

1 Effect of positive rate sensitivity and inertia on gas condensate relative permeability at high velocity G. D. Henderson, A. Danesh and D. H. Tehrani Department of Petroleum Engineering, Heriot-Watt University, Riccarton, Edinburgh, UK ABSTRACT: The authors have previously reported that gas condensate relative permeability will increase with increasing velocity when conducting steady-state measurements. The increase in relative permeability was referred to as positive rate sensitivity or the positive coupling effect. A systematic series of core tests has since been conducted, generating data at IFT values ranging from to 0.78 mn m 1, using core types ranging in permeability from 11 to 350 md. The results confirmed that the positive coupling effect existed in low permeability cores and different lithologies at low and high IFT. The maximum tested velocity was in the region of 75 m per day, which was estimated to be at the boundary above which inertia would be significant. To investigate the competition between inertia and the positive coupling effect, subsequent core tests have been conducted at velocities ranging from 7 to 700 m per day, with the higher velocity being in the region of fractions of a metre from the wellbore. The maximum test velocity was one order of magnitude above the velocity boundary with significant inertia. The test programme has generated previously unpublished data, showing that the positive coupling effect initially reduces the effect of inertia before becoming dominant in the core tests conducted using gas condensate fluids. Such unique data provide valuable information on the forces governing production at the wellbore to reservoir engineers. KEYWORDS: gas condensate, relative permeability, interfacial tension, non-darcy flow INTRODUCTION During the production of gas condensate reservoirs the highest velocities will occur in the wellbore region of producing wells. When below the dew-point, the local condensate saturation near the wellbore can increase due to condensate being deposited by inflowing gas and by the flow of condensate from the regions around the wellbore, resulting in a reduction in gas relative permeability. The effect this local flow regime and condensate accumulation will have on the near wellbore gas and condensate mobility is one of the main areas of interest for reservoir engineers. Relative permeability data generated from core tests in the laboratory can be used to assess the impact of gas permeability reduction with increasing condensate saturation in the wellbore region. By conducting tests at increasing values of IFT (interfacial tension) the effect of increasing capillary forces on mobility can be investigated, and by increasing the velocity the effect of viscous forces can also be studied. In June 1994, a new phenomenon named the positive coupling effect was reported for the first time by Danesh et al. (Danesh et al. 1994). This described the increase in relative permeability of gas condensate fluids associated with increasing velocity in long cores; it was subsequently confirmed by Henderson et al. (Henderson et al. 1995, 1996). Since this phenomenon was reported, research in gas condensate relative permeability has increased significantly (Bourbiaux & Limborg Presented at the EAGE 10th European Symposium on Improved Oil Recovery, Brighton, UK, August Petroleum Geoscience, Vol , pp ; Boom et al. 1995; Chen et al. 1995; Fevang & Whitson 1995; Munkerud & Torsaeter 1995; Ali et al. 1997; Blom et al. 1997). Although the relevant literature confirms the findings of Danesh and Henderson (Boom et al. 1995; Chen et al. 1995; Blom et al. 1997) in some of the studies the techniques used are contradictory (Boom et al. 1995; Blom et al. 1997). The positive rate sensitivity data reported by the authors to date has been limited to tests conducted using Berea sandstone core samples. As an extension to previously reported data, the initial part of this paper presents data from core tests conducted using cores of different lithology (carbonate and sandstone), containing connate water, ranging in permeability from 11 to 350 md, covering a range of IFT values from to 0.78 mn m 1. The objective was to investigate whether the positive coupling effect would still be evident in cores of different lithology. The highest flow rates used in the tests corresponded to a superficial velocity in the region of 75 m per day, with the calculated Reynolds number from the test data indicating that inertia was still insignificant. It has been hypothesized by subsequent investigators that if the velocity was increased into the region of inertial flow, the reported positive coupling effect at high IFT would be cancelled by dominant inertial forces and the relative permeability would reduce (Fevang & Whitson 1995). To investigate the competition between inertial forces and the positive coupling effect in the flow regime conventionally perceived as being dominated by inertia, the second part of this paper reports data generated from core tests which have been conducted at velocities ranging from approximately 7 to 700 m /01/$ EAGE/Geological Society of London

2 46 G. D. Henderson et al. Table 1. Core properties Core Length (cm) Diameter (cm) Porosity % Absolute k (md) S wi % Effective k at S wi (md) Clashach Texas Cream Clashach per day. The higher velocity represents flow in the region of fractions of a metre from the wellbore of a typical North Sea producer. The maximum test velocity was one order of magnitude above the velocity with significant inertia. The test programme has generated previously unpublished gas condensate relative permeability data, relevant to flow regimes where the effect of inertia would conventionally be expected to reduce the relative permeability. For the first time in literature, the dominance of the positive coupling effect over inertia at high velocity is demonstrated, even at the highest tested velocities and values of IFT. The positive coupling effect associated with gas condensate flow had not been appreciated by industry before It was generally thought that gas condensate relative permeability would reduce, due to the inertial effect, at high velocity. It has been demonstrated that the positive coupling effect at high velocities reduces the negative inertial effect at low to medium condensate saturations, and at medium to high condensate saturations becomes dominant and improves the relative permeability. The findings contradict the conventional view that relative permeability would be insensitive to velocity or reduce with increasing velocity due to inertia. This highlights the need for appropriate experimental procedures to generate accurate gas condensate relative permeability data at high velocities. The unique data generated provide valuable information on the forces governing production at the wellbore and highlight the need to include the positive coupling effect in simulations to prevent underestimating the rate of production from gas condensate reservoirs (Danesh et al. 1998). EXPERIMENTAL PROCEDURE High pressure core facility A high pressure core facility was developed to allow steadystate relative permeability tests to be conducted. Within the core facility, fixed volumes of gas and condensate were circulated in a closed loop around the flow system, which increased the accuracy of fluid saturation measurements. The pumps used to circulate the gas phase have a range in flow rate from 1 to cm 3 h 1, with the volumes of fluid displaced into the core being measured with a resolution of 0.01 cm 3. The equilibrium condensate was circulated using pumps with a range in flow rate from 1 to 1000 cm 3 h 1, which limited the measurement of steady-state points at higher CGRs (condensate gas ratio, volume of condensate/volume of gas, at test pressure). Fluid production from the core was measured in a sightglass situated at the core outlet to within an accuracy of 0.05 cm 3. The differential pressure was measured using two high accuracy Quartzdyne quartz crystal transducers located at the inlet and outlet of the core, which provided stable differential pressure data to an accuracy of 0.01 psi, during the course of the tests. Core properties The characteristics of the water-wet cores used in the tests are shown in Table 1. All cores were mounted horizontally and continually rotated through 360 for the duration of the tests to minimize the influence of gravitational forces on the fluid distribution. Tracer analysis of the cores prior to the tests had indicated that they were homogeneous. The connate water saturation is believed to have remained constant during the course of the tests, as the core effective permeability remained unchanged and no water production was observed. Test fluid The gas condensate fluid used in the tests was a mixture of methane and normal butane, with a dew-point of 1870 psia at a temperature of 37 C. The liquid drop-out curve of the fluid can be seen in Figure 1, and was measured in a PVT cell by constant composition expansion. A fluid with an initial high rate of liquid drop-out was selected, allowing a condensate saturation of up to 31% to be established in the core prior to the injection of gas and condensate. This was considered to be an important aspect of the tests, as previous studies had shown that it was necessary to establish the condensate saturation by condensation as opposed to injection (Henderson et al. 1995, 1996). An added attraction of the use of a binary fluid is that the physical properties of the gas and condensate phases would be constant at a given pressure and fixed temperature below the dew-point, regardless of the total fluid composition. Both gas and condensate fluids were kept in equilibrium with water. Measurement of single phase β-factor The core was initially saturated with single phase equilibrium gas which had been equilibrated with condensate at the required test pressure. The gas was then injected through the core covering the same velocity range as used in the steady-state tests, with the gas permeability being measured at each velocity. The gas permeability reduction associated with increasing velocity due to inertial forces was then plotted and the Fig. 1. Liquid drop-out by constant composition expansion.

3 Gas condensate relative permeability 47 Fig. 2. Gas relative permeability curves Clashach-1 core. beta factor calculated using equation (1). This procedure was followed for all tests. The Reynolds number (Re β ), which is obtained from the Forchheimer equation, is given by; Relative permeability measurement procedure The core was initially saturated with gas condensate fluid at a pressure well above its dew-point prior to each suite of tests. The pressure was then reduced to below the dew-point to the selected test pressure, allowing an initial condensate saturation varying between 31% and 28.5%, depending on the test pressure, to be established by condensation. It has been calculated that the value of the initial condensate saturation in the core is accurate within 0.24% of the pore volume of the core. Gas and condensate were then continually injected into the core at a selected CGR until steady-state conditions were established, i.e. the CGR at the outlet was the same as that of the inlet. The test was then halted and the core isolated from the flow system. The condensate saturation in the core was then calculated from the change in the total volume of condensate in the flow system (final condensate volume relative to initial condensate volume), excluding the core. The measurement accuracy of the condensate saturation relative to the volume by depletion after each steady-state point was estimated at 0.22% of the pore volume. The total error in the measurement of the condensate saturation in the core for each steady-state relative permeability point is estimated at 0.32%. Steady-state relative permeability points were measured at selected CGRs ranging from the lowest CGR used in the tests of up to a maximum of At each CGR, the gas and condensate steady-state relative permeability was measured at a maximum of 11 velocities, ranging from approximately 7 to 700 m per day. At higher CGRs of 0.4, and when the oil relative permeability end-points were being measured, it was not possible to measure points over the complete range of velocities due to the flow rate limitations of the pumps injecting condensate. Flow regimes All flow rates used were converted to superficial pore velocities (m per day), calculated using, The flow regime during injection is defined in terms of the capillary number for the gas phase, using RESULTS EFFECT OF CORE TYPE AND S WI ON THE POSITIVE COUPLING EFFECT Tests were conducted using the Clashach-1 core where the relative permeability was measured at three values of IFT and at four velocities, with the resultant gas relative permeability curves shown in Figure 2. It can be seen from Figure 2 that the positive coupling effect was present over the range of velocities and values of IFT. At the lowest IFT of mn m 1, the increase in velocity resulted in the gas relative permeability curves approaching the 45 diagonal, previously only associated with miscible conditions where the IFT approaches zero (Bardon & Longeron 1980; Assar & Handy 1988; Hannif & Ali 1990). When the associated condensate relative permeability curves are examined, as shown in Figure 3, the effect of the positive coupling effect is seen to be minimal, with little variation in condensate relative permeability with changing IFT. It has been reported previously in literature that condensate relative permeability increased and the curves approached 45 diagonals as IFT reduced (Bardon & Longeron 1980; Assar & Handy 1988; Hannif & Ali 1990). However, such tests did not use condensing fluids and interstitial water, as used in this study. Tests conducted using the Texas Cream limestone core also exhibited rate sensitivity, as shown in Figure 4. The core contained a connate water saturation of 22%, with the effective permeability being approximately 8 md, and was the lowest permeability core used in the study. As with the Clashach core, rate sensitivity was most evident for the gas phase. COMBINED EFFECTS OF INERTIA AND POSITIVE COUPLING The tests reported were conducted using the Clashach-2 sandstone core, the properties of which are given in Table 1. Beta-factor measurement When the core was initially saturated with single phase equilibrium gas and the velocity was increased above approximately 70 m per day, the inertial effect appeared and the gas permeability reduced with increasing velocity, as

4 48 G. D. Henderson et al. Fig. 3. Condensate relative permeability curves Clashach-1 core. Fig. 4. Gas and condensate relative permeability curves Texas Cream (0.14 mn m 1 ). Fig. 5. Gas permeability reduction with increasing velocity. shown in Figure 5. Using these data the single phase beta factor was calculated to be m 1. The data generated were used as the gas permeability end-points at zero condensate saturation for the subsequent relative permeability measurements. Steady-state relative permeability at high velocity IFT 0.78 mn m 1. The relative permeability curves measured at an IFT of 0.78 mn m 1 are shown in Figure 6, where the velocity ranges from 7.3 to m per day. At a condensate saturation of zero, the gas permeability continually reduced as Fig. 6. Gas relative permeability curves at high velocity IFT 0.78 mn m 1. velocity increased, as previously discussed. At the initial CGR of 0.005, corresponding to an average condensate saturation of 20%, inertial forces were still dominant; however, the effect of inertia had reduced considerably. This is shown by the overall gas relative permeability reduction being 0.07 between the lowest and highest velocities at a CGR of 0.005, compared to a reduction of 0.35 when gas only was flowing. The steady-state points were then measured at a CGR of 0.01, where the condensate saturation in the core had increased to approximately 30%. At these conditions the effect of inertia had been balanced by the positive coupling

5 Gas condensate relative permeability 49 Fig. 7. Condensate relative permeability curves at high velocity IFT 0.78 mn m 1. Fig. 8. Gas relative permeability IFT mn m 1. effect, as the relative permeability curves appeared to converge at this CGR and saturation. As the CGR increased above 0.01 there was a crossover in the trend of the relative permeability curves, as positive coupling was now dominant and relative permeability increased with increasing velocity. Relative permeability continued to increase with increasing velocity up to the maximum velocity of 698 m per day. For the velocities reported at the test conditions, the capillary number ranged from approximately to , with the corresponding Reynolds number (Re β ) ranging from to The associated condensate relative permeability curves are shown in Figure 7, where a degree of rate sensitivity can also be seen for the condensate phase. IFT mn m 1. Gas and condensate relative permeabilities were measured at velocities ranging from 7.3 to a maximum of m per day, and for a range of CGRs covering to 0.40, with the resultant gas relative permeability plot shown in Figure 8. The range of velocities used in this test was limited to avoid significant phase changes encountered at higher differential pressures. When the core was saturated with 100% gas, inertia was again present with the single phase gas permeability continuing to reduce with increasing velocity. At the initial CGR of 0.005, where the average core saturation increased to approximately 6%, inertia was still dominant; however, the reduction in gas relative permeability was less compared to the associated reduction measured when gas only was flowing. When relative permeability was measured at the subsequent CGRs of 0.03, 0.1 and 0.4, covering a saturation range from Fig. 9. Gas and condensate relative permeability IFT mn m 1. 30% to 60%, the positive relative permeability rate sensitivity associated with increasing velocity for condensing fluids was greater than the reduction due to inertia over the entire velocity range. At velocities ranging from 7.3 to m per day, the relative permeability increased with increasing velocity. As the velocity increased from to m per day there was no further increase in relative permeability, with both curves being similar. The relative permeability did, however, reduce as the velocity was increased to m per day. It is important to note, however, that the positive coupling effect was always greater than the relative permeability reduction caused by inertial forces over the CGR range from 0.03 to This is shown by the curves generated at higher velocities being well above the base curve measured at the lowest velocity of 7.3 m per day. The positive coupling effect increased the gas relative permeability curves towards the 45 diagonal, which is regarded as the maximum relative permeability as IFT approaches zero, but occurs at this IFT at velocities ranging from 58.1 and m per day. At the higher velocities of and m per day, sections of the gas curves also approached the 45 diagonal; however, inertia had reduced the relative permeability at lower condensate saturations below 30% at these velocities. The condensate relative permeability curves shown in Figure 9 follow the same trend in terms of rate sensitivity as the gas relative permeability curves. Although the gas curves approached the 45 diagonal the condensate relative permeability curves did not, and only increased rapidly when the condensate saturation exceeded 30%. For the velocities reported at the test conditions, the capillary number for the gas phase ranged from approximately to , with the corresponding Reynolds number Re β ranging from to DISCUSSION The data reported have shown that the negative effects of high velocities were greatest when 100% gas was present in the core tests. However, as the condensate saturation increased, the effect of inertia, compared to that of positive coupling was reduced until balanced by positive coupling, and then was overtaken by it. The positive coupling effect was, therefore, evident over the entire condensate saturation range in the core, as it initially reduced the drop in relative permeability due to inertia, before becoming dominant and increasing relative permeability with increasing velocity. The saturation at which the positive coupling effect became dominant over that of inertia has been shown to vary with

6 50 G. D. Henderson et al. IFT. At an IFT of mn m 1, the saturation at which the positive coupling effect exceeded that of inertia can be estimated to occur at a condensate saturation of approximately 20%. At the higher IFT of 0.78 mn m 1, the corresponding relative permeability crossover occurred at a condensate saturation of approximately 30%. Although it has been previously hypothesized that the combined rate effect would reduce as IFT and velocity increased, the opposite has been shown to be the case, with the effect of positive coupling being reduced by inertia at low IFT, but not at high IFT. At an IFT of mn m 1, the combined rate effect reached a maximum at a velocity of m per day, with the relative permeability reducing at the higher velocity of m per day. The gas relative permeability curves were already at the 45 diagonal maximum, and would not be expected to increase significantly with increasing velocity. At the higher IFT of 0.78 mn m 1 the gas relative permeability was significantly lower than the values measured at mn m 1, and the relative permeability continued to increase with increasing velocity up to the maximum tested velocity of approximately 700 m per day. The combined rate effect could, therefore, be more prevalent at higher values of IFT over a greater range in velocity compared to low IFT conditions. The findings have shed new light on the impact of inertial forces on high velocity flow in gas condensate systems. The data generated from single phase gas beta factor measurements have been shown to significantly under-predict the relative permeability of gas condensate fluids, when the effects of positive coupling are neglected. CONCLUSIONS The positive coupling effect was measured in cores of different lithology with and without the presence of connate water. The effect of positive coupling was evident over the entire condensate saturation range in the cores at high velocity. The presence of condensate initially reduced the permeability reduction due to inertia, before the positive coupling effect became dominant and increased relative permeability with increasing velocity. Crossover relative permeability curves have been reported which show a transition from inertia-dominated relative permeability curves with increasing velocity, to conditions where the positive coupling effect was dominant, at low and high IFT. The positive coupling effect continued to increase the relative permeability up to the highest tested velocity of almost 700 m per day at the higher IFT of 0.78 mn m 1. At the lower IFT of mn m 1 the increase in relative permeability with velocity reached a maximum between 116 and 232 m per day. SYMBOLS A Area β Beta factor, the coefficient defining the inertial effect (Equation 1) CGR Condensate gas ratio (volume/volume at test conditions) ϕ Porosity k Permeability L Length M Molecular weight of the gas µ Viscosity P Pressure q Volumetric flow rate R ρ S wi σ T υ s W z Subscripts c Condensate g Gas w Water Gas constant Density Interstitial water saturation Interfacial tension Temperature Superficial fluid velocity Mass flow rate Compressibility factor This study was sponsored by: The UK Department of Trade and Industry, British Gas plc, BP Exploration Operating Company Ltd, Chevron Petroleum (UK) Ltd, Conoco (UK) Ltd, Elf Exploration UK plc, Marathon International (GB) Ltd, Mobil (North Sea) Ltd, Norsk Hydro a.s, Phillips Petroleum Co. (UK) Ltd, Shell UK Exploration and Production Ltd, and Total Oil Marine plc, which is gratefully acknowledged. REFERENCES Ali, J., McGauley, P. J. & Wilson, C. 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