Prediction of Wettability Variation Within an Oil/Water Transition Zone and Its Impact on Production

Transcription

1 Prediction of Wettability Variation Within an Oil/Water Transition Zone and Its Impact on Production Matthew D. Jackson, SPE, Per H. Valvatne,* SPE, and Martin J. Blunt, SPE, Imperial College Summary We use a pore-scale network model in conjunction with conventional reservoir-scale simulations to investigate wettability variation within an oil/water transition zone. If the initial water saturation within the transition zone is controlled by primary drainage, we predict that initial production behavior is the same regardless of wettability. However, if the initial water saturation has been modified by movement of the free water level (FWL) following reservoir filling, then both the initial water saturation and production behavior are different depending upon wettability. In this case, the wettability of the reservoir may be estimated using in-situ measurements. Moreover, wettability variation may yield anomalous dry oil production from the transition zone. Over longer production timescales, wettability variation can result in high displacement efficiency during waterflooding. Assuming that the reservoir is uniformly water-wet or oil-wet, or using empirical hysteresis models, leads to a significant underestimate of recovery. Introduction Many oil reservoirs contain a significant transition zone, in which fluid saturations and production characteristics vary with depth. 1 5 Typically, the top of the transition zone contains oil in the presence of connate (immobile) water, while the base of the transition zone is fully water saturated. Within the transition zone, both oil and water are usually mobile. The transition zone may vary from a few meters to several hundred meters in thickness and contain a significant proportion of the oil in place. The transition zone often exhibits variable wettability, with the most water-wet conditions found at the base and the most oil-wet conditions at the top. 4 9 The wettability of a crude oil/water/rock system depends upon factors such as the mineralogy of the rock, the composition of the oil and water, the temperature, and the initial water saturation Wettability variations within a transition zone are principally controlled by the increase in water saturation with depth. 4 9 At the top of the transition zone the oil saturation is high, so more pores and throats are contacted by oil. These pores and throats can become oil-wet if surface-active components such as asphaltenes within the oil are adsorbed onto the mineral surfaces At the base of the transition zone the pores and throats are not contacted by oil, so they remain water-wet. The reservoir is least water-wet (most oil- or mixed-wet) at the top of the transition zone, becoming progressively more water-wet with depth as the water saturation increases. 4 9 Wettability can have a significant impact on flow during oil recovery, and upon the volume and distribution of the residual oil However, the impact of wettability variation associated with an oil/water transition zone is poorly understood. Masalmeh 4 measured oil relative permeability in cores that had been aged at different initial water saturations. He found that the oil relative permeability at a given water saturation increased with initial water saturation (increasingly water-wet conditions). Based on these * Now at Shell Intl. Exploration and Production B.V. Copyright 2005 Society of Petroleum Engineers This paper (SPE 77543) was first presented at the 2002 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 29 September 2 October. Original manuscript received for review 9 January Revised manuscript received 10 March Manuscript peer approved 3 April findings, he suggested that oil may be more mobile toward the base of a transition zone, yielding higher oil recoveries than conventionally predicted. However, he did not measure the variation in water relative permeability with initial water saturation (and therefore wettability), which is much more significant and can have a profound influence on waterflood efficiency. 20 Parker and Rudd 5 suggested that wettability alteration may yield anomalous dry oil production from a transition zone, but provided only a qualitative explanation of the pore-scale mechanisms responsible. The aim of this study is to investigate and predict the effect on production of wettability variation associated with an oil/water transition zone, using a pore-scale network model in conjunction with conventional reservoir-scale simulations. We use a 3D network model, which combines a physically based pore-scale model of wettability alteration 21 with a network representation of a Berea sandstone. 22,23 The network is reconstructed directly from a sample of the sandstone, so the pore-size distribution and coordination number are fixed and are not tuned to match experimental data. We demonstrate that this network model can successfully predict experimental relative permeability data for water-wet Berea sandstone 24 and waterflood recoveries for mixed-wet Berea. 19 We therefore have confidence in its ability to capture and predict the effect of wettability alteration on relative permeability and capillary pressure. The network model is a tool that allows us to investigate wettability variations much more quickly and efficiently than laboratory experiments. We begin with a detailed analysis of initial production behavior from a transition zone. We find that, if the initial water saturation is governed by the balance of gravity and drainage capillary forces, wettability variation makes no difference to production behavior, because this is dictated by the drainage relative permeability curves. These are the same irrespective of wettability alteration following oil migration into the reservoir. However, if the FWL migrates upward following wettability alteration (for example, because of leakage of hydrocarbons from the reservoir), then the initial water saturation is governed by the balance of gravity and waterflood capillary forces, and production behavior is dictated by the waterflood relative permeability curves. These depend upon the wettability of the reservoir. Consequently, the initial water saturation and production behavior is different depending on whether wettability alteration has occurred. In this case, the wettability of the reservoir may be determined from in-situ measurements. Moreover, wettability alteration may yield anomalous dry oil production from the transition zone. We then perform a simulation study to investigate longer production timescales and find that wettability variation can result in high displacement efficiency during waterflooding. Assuming that the reservoir is uniformly water-wet or oil-wet, or using empirical hysteresis models, leads to a significant underestimate of recovery. Network Model The 3D network model used in this study has been described in detail elsewhere, 25 so we provide only a brief summary. The model is derived from a cube of volume 27 mm 3 reconstructed to represent a sample of Berea sandstone. A topologically equivalent network of 12,349 pores and 26,146 throats is then generated. 22,23 Each pore and throat is represented as a duct with a triangular, square, or circular cross-section, characterized by an inscribed radius which controls the threshold capillary entry pressure, effective 184 June 2005 SPE Journal

2 corner angles which control the amount of fluid held in wetting layers, and an effective volume which controls the mobile (nonclay-bound) saturation. 21,23,26 31 A clay volume is associated with the network which represents the volume that remains watersaturated. Empirical formulae are used to compute the hydraulic conductance of each pore and throat. 29 Two-phase flow is simulated for primary drainage and waterflooding assuming that capillary forces dominate, so the pores and throats are filled in order of increasing capillary entry pressure. This is a reasonable approximation for low capillary number flow. 26,32 The drainage cycle begins with the network fully saturated with water and strongly water-wet, with the receding contact angle r 0. Oil then enters the network, and as the capillary pressure is increased step by step, it invades the pore or throat with the lowest capillary entry pressure in an invasion percolation process. At each step, water and oil saturations, relative permeabilities, and the capillary pressure are calculated subject to pressure boundary conditions at the inlet and outlet faces, and periodic boundaries on the other faces. To avoid end effects, only a subset of the network model is included. Drainage is complete when a target capillary pressure or saturation has been reached, or when all pores and throats have been invaded by oil. Wettability variations are modeled by changing the advancing contact angle a assigned to each oil-filled pore after primary drainage. 26,27 Different pores may have different contact angles. Depending upon the number of pores and throats invaded by oil, and the range of advancing contact angles, this approach allows us to model a mixed-wet system, in which only those pores invaded by oil become oil-wet; a fractionally-wet system, in which a fraction of the pores and throats invaded by oil become oil-wet; and a system that remains water-wet. Water injection (waterflooding) is then simulated. The three distinct types of water invasion are represented: piston type, porebody filling, and snap-off. Pore-body filling is a cooperative process 33,34 favored when many surrounding throats contain water and suppressed when few surrounding throats contain water. Pistonlike advance leaves the center of the pore or throat filled with water, but if the advancing contact angle is large enough, water also remains in the corners with a layer of oil sandwiched in between. Oil can flow through these layers 16,29 which are stable until the two oil/water interfaces meet. 16 During water injection, water and oil saturations, relative permeabilities, and the capillary pressure are calculated in the same way as for drainage. Injection is complete when a target capillary pressure or saturation has been reached, or when all available pores and throats have been invaded by water. Predictive Capability of the Network Model We have used the network model to successfully predict experimental oil/water relative permeability data for both water-wet and mixed-wet cases. 20,25 Fig. 1 shows the match between network model and experimental data for primary drainage in water-wet Berea cores. 24 During drainage, the receding contact angle is assumed to be 0 ; there are no other parameters to adjust. The match is good whether plotted on linear (Fig. 1a) or logarithmic (Fig. 1b) axes, although there is a slight tendency to overestimate the oil relative permeability at low water saturations. Fig. 2 shows the match for waterflooding (imbibition) in the same water-wet Berea cores. The network model data were obtained using advancing contact angles drawn at random from a uniform distribution with a minimum of 50 and a maximum of The match is good for both the water and oil relative permeabilities, whether plotted on linear (Fig. 2a) or logarithmic (Fig. 2b) axes. Small changes in the contact angle distribution do not adversely affect the match. 20,25 Given that the data were obtained from water-wet cores, it is perhaps surprising that the advancing contact angles that best match the data are quite large. However, it should be remembered that contact angles measured at a smooth flat surface may not resemble those found within the pore space of a typical reservoir rock, because of the additional complexities introduced by converging and diverging pore and throat geometries, surface roughness, and heterogeneous mineralogy Jadhunandan and Morrow 19 waterflooded Berea cores that had been aged in the same crude oil and brine but with different initial water saturation S wi. This is analogous to the situation in a transition zone, where S wi varies with height. In their experiments, S wi was varied from 7.8 (most oil-wet) to 31.1% (most water-wet; see Fig. 7 in Jadhunandan and Morrow 19 ). We used the network model to simulate primary drainage to the different values of S wi, followed by wettability alteration and then waterflooding. Wettability alteration was captured by assigning contact angles varying uniformly between 110 and 180 to the oil-filled pores. 20 The network model predicted relative permeability curves and we used these in a semianalytic Buckley-Leverett analysis, ignoring capillary pressure, to predict waterflood recovery. Fig. 3 shows predicted and experimental results. The reference water-wet case (a core flood without wettability alteration) was simulated assuming a uniform contact angle distribution in the range of 35 to 85. This is similar to the distribution used to match the Oak data 24 shown in Fig. 2. The agreement between experiment and prediction is good, bearing in mind that the Berea network that we have used in the modeling studies has a larger permeability than the cores used in the experiments. 19 Also, while the experimental results were gen- Fig. 1 Drainage relative permeability predicted from the network model (lines) and measured on a water-wet Berea core (crosses; data from Oak 24 ). Plotted on linear scale (a) and on logarithmic scale (b). June 2005 SPE Journal 185

3 Fig. 2 Waterflood (imbibition) relative permeability predicted from the network model (lines) and measured on a water-wet Berea core (crosses; data from Oak 24 ). Plotted on linear scale (a) and on logarithmic scale (b). Fig. 3 Predictions of oil recovery (solid lines) using pore-scale modeling compared with experimental results from Jadhunandan and Morrow 19 (points). In the network model we assumed that the pores contacted by oil had a uniform distribution of contact angles from 110 to 180, regardless of the initial water saturation S wi. The water-wet reference case was simulated assuming a uniform distribution of contact angles from 35 to 85. erally reproducible, similar cores with similar values of S wi gave recoveries that varied by 0.1 or more, within the range of mismatch of our predictions. The significant feature is that the trend in recovery is correctly predicted: the water-wet case gives a high recovery at breakthrough, but there is significant trapping of oil. With wettability alteration, recovery is higher with significant production of oil post-breakthrough. The most favorable recovery is found for an intermediate value of S wi of approximately 20%, and the recovery is lower for both higher and lower values of S wi. There are some differences between prediction and experiment, and we tend to underestimate the impact of varying S wi on waterflood recovery. These differences have been discussed in more detail elsewhere; our key assumption is that the distribution of contact angles in oil-filled pores is independent of S wi (and therefore capillary pressure). 20,25 However, the key conclusion of this section is that the network model can predict waterflood recovery for different values of S wi in mixed-wet systems within the range of experimental variation. We can now use the model with confidence to predict recovery in a reservoir with a wettability trend associated with varying S wi through the transition zone. Relative Permeability Hysteresis Through the Transition Zone We used the network model to investigate the effect on relative permeability and capillary pressure of varying the water saturation obtained after drainage, reproducing the effect of variations in S wi observed in a transition zone above the oil/water contact (OWC). We drained the network to water saturations ranging from connate (S wi S wc 0.25) to close to 1, and then injected water until all the available pores and throats had been invaded. This yielded a suite of waterflood curves, each of which originates on the drainage curve at a different S wi. We term these scanning curves, following the convention of empirical hysteresis models, 38,39 although in our case they have been generated using the network model rather than interpolation or remapping. The drainage curves, and waterflood curves originating from connate water saturation (S wi S wc ), are termed bounding curves. Initially, we assumed that pores and throats invaded by oil remain water-wet, with the same distribution of advancing contact angles as used to match the Oak data 24 (Fig. 4). We then assumed that pores and throats invaded by oil become oil-wet, with the same range of advancing contact angles as used to match the Jadhunandan and Morrow 19 data in Fig. 4 (Fig. 5). For convenience, we refer to this system as oil-wet. For the water-wet case (Fig. 4), there is little difference between the oil relative permeability curves regardless of S wi. There is some hysteresis in the water curves, but the scanning curves lie between the bounding drainage and waterflood curves, so this behavior could be captured using conventional empirical hysteresis models. 38,39 However, for the oil-wet case there is hysteresis in both the oil and water relative permeability curves. Moreover, the bounding waterflood curve for water lies above the drainage curve, while the scanning curves lie below the drainage curve (Fig. 5). This behavior could not be captured using conventional empirical models. 20 The bounding curve represents the most oil-wet conditions at the top of the transition zone, whereas the scanning curves reflect progressively less oil-wet conditions as S wi increases and the OWC is approached. As S wi increases, we observe an increase in oil relative permeability for a given S w. This agrees with the experimental results of Masalmeh. 4 However, we predict that hysteresis in the water relative permeability is much more pronounced. The scanning curves are very low for low S wi (between S wi 0.26 and S wi 0.4) compared to the bounding waterflood curve, and also compared to the water-wet case; they also 186 June 2005 SPE Journal

4 Fig. 4 (a) Relative permeability and (b) capillary pressure curves obtained from the network model. Crosses denote drainage curves (water saturation decreasing); lines denote waterflood (imbibition) curves (water saturation increasing). The waterflood curves were calculated for initial water saturations ranging from connate (S wi =S wc =0.25) to close to 1. During waterflooding the advancing contact angle of pores and throats invaded by oil ranged from 50 to 80. The inset (c) shows a close-up of the water relative permeability curves at small values. yield lower residual oil saturations (S or ) compared to the waterwet case. The water relative permeabilities can be explained by considering the displacement sequence at the pore scale. During waterflooding, water invades the largest oil-wet pores first. This results in a rapid increase in water saturation. However, the water relative permeability remains low until these pores form a connected network that spans the model. The water relative permeability then increases rapidly (Fig. 5; notice the shape of the curves originating at low S wi ). This behavior is not captured by empirical hysteresis models. It is also very different from the water-wet case (Fig. 4). It is clear that the relative permeability (and capillary pressure) curves vary significantly with S wi if the oil-filled pores become oil-wet, suggesting that wettability variations within a transition zone above the OWC yield variations in relative permeability with height. These variations cannot be captured using empirical hysteresis models. 20 However, it is not clear whether the differences are significant enough to affect production at the reservoir scale. We address this issue in the next two sections. Impact of Wettability Variation on Initial Production Behavior We considered initial production from a vertical well completed within the transition zone. By initial production, we mean production from a well in a virgin reservoir, over a time period too short to cause significant saturation changes. A typical example would be a drillstem test. We characterized production by calculating the water cut (water fractional flow) as a function of depth (and therefore as a function of S wi ). This has been measured by wells tested over short completion intervals. 40 Wells tested over larger completion intervals would record a composite water cut. The water cut was calculated using an oil viscosity of 0.8 cp and a water viscosity of 0.4 cp (viscosity ratio o / w 2). These values were chosen to be consistent with the Maureen Field simulation model used in a subsequent section. Our predicted water-cut behavior will clearly be sensitive to the viscosity ratio; as the viscosity ratio increases, the water cut increases for a given water saturation. However, the results we present are not significantly different for viscosity ratios up to 8, and the contrast between water-wet and oil-wet reservoir behavior remains the same. The initial water saturation as a function of depth through the transition zone (S wi ) is dictated by the balance of capillary and gravity forces. 1,2 In most situations, capillary forces are governed by the primary drainage process by which the reservoir first fills with oil. 2,3,41 We considered this case first, using the drainage capillary pressure curve derived from the network model (Figs. 4 and 5) to determine S wi (Fig. 6). The density contrast was chosen to yield a transition zone approximately 100 m high above the FWL. We then used the network model to generate, for both waterwet and oil-wet cases (represented by the advancing contact angles described in the previous section), a suite of 500 waterflood relative permeability curves, each of which corresponds to a different S wi (and therefore depth). A subset of these is shown in Figs. 4 and 5. We found that the initial production behavior is the same irrespective of wettability alteration (Fig. 6a). The explanation is simple. The scanning waterflood curve corresponding to a given S wi originates at the same point on the drainage curve regardless of the local wettability (Figs. 4 and 5). Consequently, the initial water-cut is dictated by the drainage relative permeability curves, so initial production behavior is not affected by wettability alteration following drainage. We then investigated the situation in which capillary forces are modified by movement of the FWL following initial reservoir filling and wettability alteration. This situation has been reported in several fields Upward movement of the FWL results in a June 2005 SPE Journal 187

5 Fig. 5 (a) Relative permeability and (b) capillary pressure curves obtained from the network model. Crosses denote drainage curves (water saturation decreasing); lines denote waterflood curves (water saturation increasing). The waterflood curves were calculated for initial water saturations ranging from connate (S wi =S wc =0.25) to close to 1. During waterflooding the advancing contact angle of pores and throats invaded by oil ranged from 110 to 180. The inset (c) shows a close-up of the water relative permeability curves at small values. paleo-owc. Several mechanisms, such as leakage of hydrocarbons from the trap, or tectonic movements, have been invoked to explain the phenomenon. The initial saturation distribution is still dictated by the balance of capillary and gravity forces, but capillary forces are now governed by the natural waterflood process associated with movement of the FWL. 41 We reproduced this numerically, assuming that capillary and gravity forces dominate. The initial condition was that described previously following drainage (Fig. 6a). Movement of the FWL was simulated over 100 years using Eclipse 100, with a further period of equilibration of 300 years, in a 1D model with 500 gridblocks in the vertical direction using the suite of relative permeability curves described previously. Increasing the equilibration period did not modify the saturation distribution, so we were confident that we had achieved capillary-gravity equilibrium. This gave us our new S wi, following movement of the FWL but prior to production. We then predicted the production water cut at this S wi using the appropriate waterflood relative permeabilities. We began by considering a case in which the FWL has moved upward approximately 28 m from its original position (Fig. 6b). In the water-wet case, S wi below the new FWL is at its maximum value (1 S or ) and there is no mobile oil (water cut of 100%). Above the new FWL, S wi is governed by the waterflood (imbibition) capillary pressure curve, so it is different from the drainage case. The water-cut curve is also different from the drainage case. In the oil-wet case, S wi below the new FWL is governed by the waterflood capillary pressure curve, so some oil has imbibed downward into this region. This oil is mobile, so the water cut is less than 100%. Above the new FWL, S wi is essentially governed by the drainage capillary pressure curve, but some water has been displaced upward by the downward imbibition of oil, causing an increase in water saturation relative to the drainage curve. This slightly increases the water cut compared to the drainage case. We next considered a case in which the FWL has moved upward approximately 56 m from its original position (Fig. 6c), approximately halfway through the original (drainage-controlled) transition zone. Below the new FWL, there is again no mobile oil in the water-wet case, but in the oil-wet case, significant volumes of mobile oil have imbibed downward. This yields essentially dry oil production (with a very low or zero water cut) immediately below the FWL. Moreover, there is a pronounced difference in S wi. In the oil-wet case, S wi initially increases with depth below the FWL but then decreases until close to the paleo-owc, whereas in the water-wet case, S wi is approximately constant (1 S or ) with depth until close to the paleo-owc (although it is not exactly constant; there are slight increases in S or with depth, which reflects the increase in S or of the scanning curves originating at higher S wi in Fig. 4a). In general, S wi below the new FWL is higher in the oil-wet case than in the water-wet case. Finally, we considered a case in which the FWL has moved upward approximately 84 m from its original position (Fig. 6d), close to the top of the original (drainage-controlled) transition zone. Below the new FWL, there is a significant interval (approximately 10 m) over which dry oil would be produced in the oil-wet case, whereas only water would be produced in the water-wet case. S wi is also very different, with an increase followed by decrease with depth observed in the oil-wet case. If S wi is controlled by drainage capillary forces, then the initial production behavior is the same regardless of wettability. However, if S wi has been modified by movement of the FWL, then both S wi and the initial production are different depending upon wettability. In the water-wet case, there is no mobile oil and only water is produced below the FWL. S wi is approximately constant (1 S or ) with depth until close to the paleo-owc. In the oil-wet case, there is a significant interval of mobile oil, and dry oil may be produced below the FWL. S wi initially increases with depth, but then de- 188 June 2005 SPE Journal

6 Fig. 6 Initial water saturation and production watercut (water fractional flow) as a function of height through the transition zone for cases in which (a) the initial configuration is dictated by the balance of gravity and drainage capillary forces following reservoir filling; (b) the initial configuration is dictated by the balance of gravity and waterflood capillary forces following upward migration of the FWL by approximately 28 m from its original position after reservoir filling; (c) following upward migration of the FWL by approximately 56 m; (d) following upward migration of the FWL by approximately 84 m. In each plot, points record water saturation and should be read from the lower abscissa axis; lines record watercut and should be read from the upper abscissa axis. creases until close to the paleo-owc. The increase in S wi with depth occurs because capillary forces cause oil to imbibe downward; S wi is therefore lowest close to the FWL. As the FWL moves upward into increasingly oil-wet rock, increasing volumes of oil are imbibed downward (see Figs. 6c and 6d). S wi increases with depth below the FWL until it reaches (1 S or ). Waterflood S or is lower in regions where wettability has been altered (Fig. 7); these are the regions toward the top of the transition zone where S wi following drainage was lower. Therefore, S wi following movement of the FWL is lower in the more oil-wet rocks toward the top of the transition zone, increasing with depth toward the paleo-owc, reflecting the increasingly water-wet conditions. Causin and Bona 44 have suggested that the wettability of a reservoir can be estimated by in-situ measurements of the FWL, SOR (the maximum depth at which oil is still mobile), and SWI (the minimum depth at which water is still mobile) using wireline tools. They argued that in water-wet reservoirs, the sequence SWI- SOR-FWL is observed with increasing depth (the conventional case), while in oil-wet reservoirs the sequence is SWI-FWL-SOR. Our results indicate that the former sequence is observed in all reservoirs where S wi is governed by the balance of gravity and drainage capillary forces irrespective of wettability (Fig. 6a). In this case, SWI corresponds to the top of the transition zone and SOR corresponds to the OWC. However, if S wi is governed by the balance of gravity and waterflood capillary forces following movement of the FWL, then we do observe their predicted sequence of SWI-SOR-FWL for the water-wet case and SWI-FWL-SOR for the oil-wet case (Fig. 6b through 6d). Only if the FWL has moved June 2005 SPE Journal 189

7 Fig. 7 Waterflood residual oil saturation (S or ) (for example, following movement of the FWL) vs. initial water saturation (S wi ) following primary drainage (initial reservoir filling). As the initial water saturation following drainage decreases, the rock becomes increasingly oil-wet and the waterflood residual oil saturation decreases. upward can oil be imbibed downward to increase SOR relative to the FWL; only in this case can the wettability of the reservoir be determined from their suggested in-situ measurements. Oil cannot imbibe downward into water-wet rock below the original (drainage-controlled) OWC. In each of Causin and Bona s oil-wet field examples, the logged OWC is much lower than SOR, consistent with upward movement of the FWL. 44 Parker and Rudd 5 reported anomalous dry oil production from a transition zone in a carbonate reservoir offshore of the United Arab Emirates. Dry oil production was anomalous because the logged water saturation over the test interval was greater than connate. Other examples of anomalous dry oil production have been reported. 45 Our results can explain dry oil production in terms of wettability alteration. If the transition zone is drainage controlled, then the water cut at a given S wi is the same irrespective of wettability alteration, because it is governed by the drainage relative permeability curves. If the FWL moves but the reservoir remains water-wet, then the water cut is similar to the drainage curve (Fig. 8). In neither case is anomalous dry oil production observed. However, if the FWL moves following wettability alteration, then a significantly lower water-cut is observed compared to the waterwet case for S wi up to approximately At this saturation, the water cut increases rapidly from a few percent to approximately 55%. At higher water saturations, the water cut is similar irrespective of wettability alteration. Essentially dry oil production (water cut less than 0.5%) is observed for S wi < 0.55 in the oil-wet case, compared to S wi < 0.34 in the water-wet case. These water cuts are predicted at a specific depth; a well completed over a larger interval would record a composite water cut. Even then, dry oil production is predicted in the oil-wet case. For example, a well completed from the top of the transition zone to a depth corresponding to a saturation of 0.65 in the oil-wet case would record a water cut of 0.2%, while in the water-wet case it would record a water cut of 4%, which is over an order of magnitude higher. Dry oil production is explained by the shape of the water relative permeability curves (Fig. 5). The water relative permeability originating at low drainage S wi remains low until a threshold saturation is reached, at which the larger oil-wet pores form a connected network. The water relative permeability then increases rapidly. Following movement of the FWL, a low water cut will be Fig. 8 Initial water cut vs. initial water saturation for water-wet and oil-wet conditions (plotted as lines), corresponding to the case shown in Fig. 6d, where the initial water saturation is dictated by the balance of gravity and waterflood capillary forces following upward migration of the FWL by approximately 84 m from its original position after reservoir filling. Also shown for comparison is the initial watercut vs. initial water saturation corresponding to the case shown in Fig. 6a, where the initial configuration is dictated by the balance of gravity and drainage capillary forces following reservoir filling (plotted as points). observed in regions where the new S wi is less than the threshold saturation. The threshold will depend upon the size and spatial distributions of the pores and throats. For our Berea model, the threshold saturation appears to be approximately 0.65, but it will probably be different in the carbonate reservoir discussed by Parker and Rudd. 5 Nevertheless, generic aspects of the behavior predicted by the network model are likely to be observed in all reservoirs wherein movement of the FWL follows wettability alteration. Impact of Wettability Variation on Waterflooding We next investigated whether wettability variation has a significant impact on waterflooding, even if the transition zone is governed by drainage capillary forces. We began with a simple 2D model that is geologically homogeneous; permeability and porosity are constant, and relative permeability and capillary pressure vary only with S wi and wettability. We then considered whether the impact of wettability variation is significant in the presence of realistic geological heterogeneity. We used a conventional simulator (Eclipse 100) to predict production in each case, in conjunction with the relative permeability and capillary pressure curves obtained from the network model. In the homogeneous model, the dimensions, fluid mobilities, and balance of forces are described by four dimensionless parameters. 46,47 Their values, which are typical of reservoir-scale displacements, are listed in Table 1. The fluid viscosities are the same as those used in the previous section. The model is a simple rectangular box with an aspect ratio of 7.5:100, which dips at an angle of d 5. The initial distribution of water in the model is dictated by the drainage capillary pressure curve shown in Figs. 4 and 5. The height of the transition zone above the OWC is chosen such that the water saturation falls to connate (S wc ) at the top of the model; the thickness of the transition zone is thus comparable with the thickness of the reservoir. Simulations are performed on a grid of cells; water is injected over the right face of the model, and fluid produced over the left face. We simulated waterflooding for four different cases: (1) assuming that pores and throats invaded by oil remain water-wet and 190 June 2005 SPE Journal

8 neglecting hysteresis, using only the bounding waterflood relative permeability curves shown in Fig. 4 (water-wet; no hysteresis); (2) assuming that pores and throats invaded by oil become oil-wet and neglecting hysteresis, using only the bounding waterflood relative permeability curves shown in Fig. 5 (oil-wet; no hysteresis); (3) assuming that pores and throats invaded by oil become oil-wet and attempting to include hysteresis by applying the Killough model 38 implemented in Eclipse 100, 48 with the bounding drainage and waterflood curves shown in Fig. 5; and (4) assuming that pores and throats invaded by oil become oil-wet and properly including hysteresis by using the suite of relative permeability curves from the network model described in the previous section, each of which corresponds to a different S wi within the simulation model (scanning curves derived from network model). A subset of this suite of curves is shown in Fig. 5. In all simulations we also include waterflood capillary pressure, either predicted by the network model (for instance, Figs. 4 and 5) or by the Killough model. We find that recovery is significantly higher if hysteresis is properly included using scanning curves generated by the network model (Fig. 9). Recovery after 1 PV injected is similar for the other cases regardless of whether the reservoir remains water-wet or becomes oil-wet and hysteresis is neglected, or the reservoir becomes oil-wet and hysteresis is included using the Killough model. Production using the Killough model is almost indistinguishable from that obtained using only the oil-wet curves. It would seem that the oil-wet character of the bounding waterflood curves has dominated (Fig. 5). Note that in all cases, oil recovery measured in rock PV appears low because of the high average initial water saturation (approximately 0.37) within the transition zone. The impact of the changing water relative permeabilities with height can be seen in the unusual water saturation distribution (Fig. 10). These results suggest that relative permeability (and capillary pressure) variations associated with wettability alteration may have a significant impact on recovery from a transition zone. However, it has often been argued that relative permeability effects are secondary compared to permeability heterogeneity. We therefore repeated the above comparison using a realistic 3D reservoir model based upon the Maureen field, which is located in Block 16/29a of the U.K. sector of the North Sea. The Maureen reservoir consists of Paleocene sandstones, which are interpreted to have been deposited as a broad submarine clastic fan across an extensive basin plain. 40,49 The oil is trapped in a four-way dip closure over a salt dome. The Maureen lithofacies is dominated by very clean, sand-rich, stacked massive sand sequences that characteristically show significant lateral facies variations and that are separated by shales of varying lateral extent. The sandstones range from 140 to 400 feet in thickness and have good reservoir properties, with porosities ranging from 0.18 to 0.25 and permeabilities ranging from 30 to 3000 md. The field originally contained undersaturated oil with no gas cap and was produced by waterflooding, initially with 12 production and 7 water-injection wells. The reservoir model used in this study was constructed using stochastic techniques conditioned to nine of the operator s exploration and development wells. 49 The model was designed to capture the architecture of the shales that separate the sandstones and the lateral and vertical variations in sandstone porosity and permeability. It was constructed on a grid containing cells, Fig. 9 (a) Pore volumes (PV) of oil produced and (b) watercut as a function of PV of water injected, for each of the simulations run in the homogeneous model. Oil recovery appears low in terms of rock PV because of the high average initial water saturation within the transition zone. June 2005 SPE Journal 191

9 Fig. 10 Water saturation distribution after 0.2 PV of water injected in the homogenous model: (a) water-wet; no hysteresis; (b) oil-wet, no hysteresis; (c) Killough model; (d) scanning curves derived from network model. Dark colors denote high water saturations; vertical exaggeration 2. Water injection is at the right boundary, production at the left boundary. which was sufficiently refined to capture the significant permeability heterogeneities, yet was not too large to be used directly for flow simulation (Fig. 11). Consequently, the model was not upscaled. Shales were modeled as barriers to flow. The model was not history matched to Maureen production data because it was not intended to be a close representation of the Maureen field; it was intended simply to capture realistic permeability heterogeneity and be based upon real field data. As in the homogeneous model, the initial distribution of water (S wi ) within the model was dictated by the drainage capillary pressure curve obtained from the network model (Figs. 4 and 5). We were not concerned that the network model is a representation of Berea sandstone rather than Maureen sandstone, because we were interested only in investigating the impact on waterflooding of wettability variations in the presence of realistic geological heterogeneity. The height of the transition zone above the OWC was chosen such that the water saturation falls to connate (S wc )atthe top of the model; the thickness of the transition zone is thus comparable to the thickness of the reservoir. The oil viscosity is 0.8 cp and the water viscosity is 0.4 cp, as in the previous section. The capillary pressure was scaled to different values of sandstone porosity and permeability using a J-Function approach, so the variation in S wi around the field reflects both the transition zone and the variation in sandstone reservoir quality. Our waterflood simulations employed eight production wells located on the crest of the field, supported by four water-injection wells on the flanks of the field. We simulated waterflooding for the same four cases as in the homogeneous model. As in the homogeneous model, we find that recovery is significantly higher if hysteresis is included using scanning curves generated by the network model (Fig. 12). Neglecting hysteresis and assuming that the reservoir is uniformly oil-wet yields the lowest recovery. Including hysteresis using the Killough model yields higher recovery than the purely oil-wet case, but the oil-wet character of the bounding waterflood curves has again dominated (Fig. 5). Neglecting hysteresis and assuming that the reservoir remains water-wet yields higher recovery than the oil-wet and Killough cases, but recovery is still lower than if hysteresis is included using the network model. Even in the presence of realistic geological heterogeneity, incorporating hysteresis in the oil-wet case by using the network model to generate scanning curves predicts significantly higher recovery, because the scanning curves display both water-wet and Fig. 11 Reservoir model of the Maureen field in the UKCS, used in the heterogeneous simulations, showing the distribution of sandstone (light colors) and shale (dark color). The areal model dimensions are approximately m. The OWC is a flat surface located at 8,700 ft TVDSS. Production wells (P1 through P8) were located on the crest of the field, injection wells (I1 through I6) on the flanks. 192 June 2005 SPE Journal

10 Fig. 12 (a) PV of oil produced and (b) watercut as a function of PV of water injected for each of the simulations run in the heterogeneous (Maureen field) model. oil-wet characteristics, depending upon the initial water saturation and therefore their location within the model. Residual oil saturations are generally much lower than for the water-wet case, yet water relative permeabilities are generally much lower than for the oil-wet case (Fig. 5). This delays water breakthrough and yields a higher oil recovery. Conclusions We have used a pore-scale network model in conjunction with conventional reservoir-scale simulation to predict the impact of wettability variation within a transition zone on production. We have confidence in the network model because we can successfully predict experimental relative permeability and waterflood recovery data for water-wet and mixed-wet Berea sandstone. We find that: 1. If the initial water saturation within the transition zone is controlled by the primary drainage process by which the reservoir first fills with oil, then initial production will be the same regardless of wettability, because initial production is dictated by the drainage relative permeability curves that are not affected by wettability alteration following drainage. 2. If the initial water saturation has been modified by movement of the FWL following reservoir filling and wettability alteration, then both the initial water saturation and the initial production are different depending upon the wettability. If the reservoir has remained uniformly water-wet, there will be no mobile oil below the FWL, and the paleo-oil saturation will be approximately constant ( waterflood residual oil) until close to the paleo- OWC. If wettability varies with height through the transition zone, there may be a significant interval of mobile oil below the FWL from which dry oil is produced. The paleo-oil saturation will initially increase with depth below the FWL, but then will decrease until close to the paleo-owc. 3. The wettability of a reservoir cannot be estimated from the in-situ measurements suggested by Causin and Bona 44 if the initial water saturation is controlled by primary drainage. Their method may work if the initial water saturation has been modified by movement of the FWL following reservoir filling and wettability alteration. This is consistent with their oil-wet field examples, in which the logged OWC is much lower than the FWL. 4. If the initial water saturation has been modified by movement of the FWL following reservoir filling and wettability alteration, then anomalous dry oil production from the transition zone may be observed. This is because the water relative permeability remains very low at water saturations below a critical threshold, above which the larger oil-wet pores form a connected network. This threshold will depend upon the size and spatial distributions of the pores and throats within a given rock, so it will be different in different reservoirs. 5. The long-term waterflood production behavior of a reservoir is likely to be significantly affected by wettability alteration within the transition zone, even if the initial water saturation is controlled by primary drainage. Using the network model to generate scanning relative permeability curves yields a significantly higher recovery than assuming the transition zone is uniformly water- or oil-wet. This is because the scanning curves display both water-wet and oil-wet characteristics, depending upon the initial water saturation. Residual oil saturations are generally much lower than for the water-wet case, yet water relative permeabilities are generally much lower than for the oil-wet case. Wettability variation has a significant impact on production even in the presence of realistic geological heterogeneity. We suggest that network models based on the structure of real rocks and incorporating the pertinent pore-scale displacement processes may be used as a tool to predict wettability variations and their impact on fluid flow at the reservoir scale. Nomenclature g gravitational acceleration, Lt 2,ms 2 h height of model volume, L, m k permeability L 2,m 2 k e ro oil endpoint relative permeability k e rw water endpoint relative permeability L length of model volume, L, m M e endpoint mobility ratio N h height number (aspect ratio) N Pc capillary number N vg viscous-to-gravity ratio OWC oil/water contact, L, m S or residual oil saturation S w water saturation S wc connate water saturation S wi initial water saturation u T total flow velocity, Lt 1,ms 1 water-oil density contrast, ml 3, kgm 3 a advancing contact angle, degrees d dip of model, degrees r receding contact angle, degrees o oil viscosity, ml 1 t 1,Pas w water viscosity, ml 1 t 1,Pas interfacial tension, mlt 2, mnm 1 porosity June 2005 SPE Journal 193

11 Acknowledgments The members of the Imperial College consortium on Pore-Scale Modeling (BHP, Enterprise Oil, Gaz de France, JNOC, PDVSA- Intevep, Schlumberger, Shell, Statoil, the U.K. Dept. of Trade and Industry, and the EPSRC) are thanked for their financial support. We also thank Pål-Eric Øren (Statoil) for sharing his Berea network data with us, and John Matthews for interesting discussions on dry oil production in transition zones. References 1. Muskat, M.: Physical Principles Of Oil Production, McGraw Hill, New York City (1949), reprinted by IHRDC (1981). 2. Archer, J.S. and Wall, C.W.: Petroleum Engineering: Principles and Practice, Graham and Trotman, London (1986). 3. Reed, R.N. and Wheatley, M.J.: Oil and Water Production in a Reservoir With a Significant Transition Zone, JPT (September 1984) Masalmeh, S.K.: High Oil Recoveries From Transition Zones, paper SPE presented at the 2000 SPE Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, October. 5. Parker, A.R. and Rudd, J.M.: Understanding and Modeling Water Free Production in Transition Zones: A Case Study, paper SPE presented at the 2000 SPE Asia Pacific Conference on Integrated Modeling for Asset Management, Yokohama, Japan, April. 6. Jerauld, G.R.: Prudhoe Bay Gas/Oil Relative Permeability, SPERE (February 1997) Jerauld, G.R.: General Three-Phase Relative Permeability Model for Prudhoe Bay, SPERE (November 1997) Jerauld, G.R.: Wettability and Relative Permeability of Prudhoe Bay: A Case Study in Mixed-Wet Reservoirs, SPERE (February 1997) Hamon, G.: Field-Wide Variations of Wettability, paper SPE presented at the 2000 SPE Annual Technical Conference and Exhibition, Dallas, Texas, 1 4 October. 10. Buckley, J.S., Takamura, K., and Morrow, N.R.: Influence of Electrical Surface Charges on the Wetting Properties of Crude Oils, SPEFE (August 1989) Buckley, J.S.: Asphaltene Precipitation and Crude Oil Wetting, SPE Advanced Technology Series (April 1995) Buckley, J.S. and Liu, Y.: Some Mechanisms of Crude Oil/Brine/ Solid Interactions, J. Petroleum Sci. and Eng. (1998) 20, Dubey, S.T. and Waxman, M.H.: Asphaltene Adsorption and Desorption From Mineral Surfaces, SPERE (August 1991) 389; Trans., AIME, Dubey, S.T. and Doe, P.H.: Base Number and Wetting Properties of Crude Oils, SPERE (August 1993) 195; Trans., AIME, Wolcott, J.M., Groves, F.R. Jr., and Lee, H.-G.: Investigation of Crude-Oil/Mineral Interactions: Influence of Oil Chemistry on Wettability Alteration, paper SPE presented at the 1993 SPE International Symposium on Oilfield Chemistry, New Orleans, 2 5 March. 16. Salathiel, R.A.: Oil Recovery by Surface Film Drainage in Mixed Wettability Rocks, JPT (October 1973) 1216; Trans., AIME, Morrow, N.R., Lim, H.T., and Ward, J.S.: Effect of Crude-Oil- Induced Wettability Changes on Oil Recovery, SPEFE (February 1986) 89; Trans., AIME, Morrow, N.R.: Wettability and Its Effect on Oil Recovery, JPT (December 1990) 1476; Trans., AIME, Jadhunandan, P.P. and Morrow, N.: Effect of Wettability on Waterflood Recovery for Crude-Oil/Brine/Rock Systems, SPERE (February 1995) 40; Trans., AIME, Jackson, M.D., Valvatne, P.H., and Blunt, M.J.: Prediction of wettability variation and its impact on flow using pore- to reservoir-scale simulations, J. Petroleum. Sci. and Eng. (2003) 39, Blunt, M.J.: Physically-based network modelling of multiphase flow in intermediate-wet porous media, J. Petroleum Sci. and Eng. (1998) 20, Bakke, S. and Øren, P.E.: 3D Pore-Scale Modeling of Sandstones and Flow Simulations in the Pore Networks, SPEJ (June 1997) Øren, P.E., Bakke, S., and Arntzen, O.J.: Extending Predictive Capabilities to Network Models, SPEJ (December 1998) Oak, M.J.: Three-Phase Relative Permeability of Water-Wet Berea, paper SPE presented at the 1990 SPE/DOE Enhanced Oil Recovery Symposium, Tulsa, April. 25. Valvatne, P.H. and Blunt, M.J.: Predictive pore-scale modeling of two-phase flow in mixed-wet media, Water Resources Research (2004) 40: doi /2003wr Blunt, M.J.: Effects of Heterogeneity and Wetting on Relative Permeability Using Pore Level Modeling, SPEJ (March 1997) Blunt, M.J.: Pore Level Modeling of the Effects of Wettability, SPEJ (December 1997) Dixit, A.B., McDougall, S.R., and Sorbie, K.S.: A Pore-Level Investigation of Relative Permeability Hysteresis in Water-Wet Systems, SPEJ (June 1998) Zhou, D., Blunt, M., and Orr, F.M. Jr.: Hydrocarbon Drainage Along Corners of Noncircular Capillaries, Journal of Colloid and Interface Science (1997) 187, Firincioglu, T., Blunt, M.J., and Zhou, D.: Three-Phase Flow and Wettability Effects in Triangular Capillaries, Colloids and Surfaces A (1999) 155, Patzek, T.W.: Verification of a Complete Pore Network Simulator of Drainage and Imbibition, SPEJ (June 2001) Hilfer, R. and Øren, P.E.: Dimensional Analysis of Pore Scale and Field Scale Immiscible Displacement, Transport in Porous Media (1996) 22, Lenormand, R. and Zarcone, C.: Role of Roughness and Edges During Imbibition in Square Capillaries, paper SPE presented at the 1984 SPE Annual Technical Conference and Exhibition, Houston, September. 34. Lenormand, R., Touboul, E., and Zarcone, C.: Numerical models and experiments on immiscible displacements in porous media, J. Fluid Mechanics (1988) 189, Hirasaki, G.J.: Wettability: Fundamentals and Surface Forces, SPEFE (June 1991) 217; Trans., AIME, Zhou, X., Morrow, N.R., and Ma, S.: Interrelationship of Wettability, Initial Water Saturation, Aging Time and Oil Recovery by Spontaneous Imbibition and Waterflooding, SPEJ (June 2000) Buckley, J.S., Bousseau, C., and Liu, Y.: Wetting Alteration by Brine and Crude Oil: From Contact Angles to Cores, SPEJ (September 1996) Killough, J.E.: Reservoir Simulation With History-Dependent Saturation Functions, SPEJ (February 1976) 37; Trans., AIME, Carlson, F.M.: Simulation of Relative Permeability Hysteresis to the Nonwetting Phase, paper SPE presented at the 1981 SPE Annual Technical Conference and Exhibition, San Antonio, 4 7 October. 40. Cutts, P.L.: The Maureen Field, Block 16/29a, U.K. North Sea, U.K. Oil and Gas Fields, 25 Years Commemorative Volume, Geol. Soc. Lon. Special Memoir (1991) 14, Ingsoy, P.B. et al.: Introducing Imbibition Capillary Pressure in the Assessment of the Smoerbukk and Smoerbukk South Fields Offshore Norway, paper SPE presented at the 1998 SPE International Petroleum Conference and Exhibition of Mexico, Villahermosa, Mexico, 3 5 March. 42. Woodhouse, R.: Accurate reservoir saturations from oil-mud cores: Questions and answers from Prudhoe Bay and beyond, The Log Analyst (May June 1998) De ath, N.G. and Schuyleman, S.F.: The geology of the Magnus oilfield, Petroleum Geology of the Continental Shelf of North-West Europe, Illing and Hobson (eds.), Inst. of Petroleum, London (1981). 44. Causin, E. and Bona, N.: In-Situ Wettability Determination: Field Data Analysis, paper SPE presented at the 1994 SPE European Petroleum Conference, London, October. 45. Matthews, J.D.: Geological and Physical Assessment of the Oil Reservoir Transition Zone, PhD dissertation, Imperial College, London (2004). 46. Shook, M., Li, D., and Lake, L.W.: Scaling Immiscible Flow Through Porous Media by Inspectional Analysis, In Situ (1992) 16, Jackson, M.D. and Muggeridge, A.H.: Effect of Discontinuous Shales on Reservoir Performance During Horizontal Waterflooding, SPEJ (December 2000) Eclipse 100 Reference Manual, Schlumberger Geoquest (2004). 49. Gringarten, A.C. et al.: A Petroleum Engineering Educational Model Based on the Maureen Field UKCS, paper SPE paper presented at the 2000 SPE Annual Technical Conference and Exhibition, Dallas, 1 4 October. 194 June 2005 SPE Journal