CHAPTER 5 PARAMETRIC STUDY OF REPRESSURISATION OF GAS/OIL SYSTEMS

CHAPTER 5 PARAMETRIC STUDY OF REPRESSURISATION OF GAS/OIL SYSTEMS 5.1 Introduction Solution gas-oil ratio (i.e. the ratio of volume of gas dissolved in oil to the volume of oil) in the laboratory setting is generally measured under equilibrium condition and represents the maximum volume of gas that could evolve from an oleic phase at the reference pressure. However, the formation of a new gas phase within a porous medium as a result of lowering the pressure of live oil below bubble point for example, is generally a non-equilibrium phenomenon (Firoozabadi and Kashchiev, 1996) and must be modelled as such. In the context of heavy oil systems, core scale experiments have shown that repressurisation can improve recovery from heavy oil systems after primary depressurisation (Dong et al., 6). The concept behind the work of Dong et al. was a restoration of the solution gas drive mechanism. At pore scale, visual investigation of repressurisation process in glass micromodels conducted by Nejad () also showed an exciting promise. Some of the key pore level observations during repressurisation include: i. A reduction in gas saturation due to compression and re-dissolution of gas into liquid. ii. Break up of large gas clusters into smaller fragments during repressurisation (at both low and high rate). iii. A significant hysteresis in gas saturation and distribution between depressurisation and repressurisation. iv. The dependence of final gas distribution after repressurisation on the primary depressurisation history. v. Apparent retardation in gas growth rate during secondary depressurisation (i.e. post repressurisation). These observations motivated the development of a numerical simulator for modelling such complex non-equilibrium process associated with repressurisation cycles, post 185

depressurisation of gas/oil systems. To improve understanding of such observations as reported in Nejad () and facilitate predictions, this chapter presents the first extensive parametric modelling of repressurisation process involving multiphase flow using both two- and three-dimensional networks. Discussions of results generated using the pore network simulator developed as part of this research would reveal how concepts such as; supersaturation, undersaturation, bubble fragmentation inter alia affect repressurisation of heavy oil systems. For instance, it will be revealed using D simulations that, a high repressurisation rate leaves many more daughter bubbles (as a consequence of fragmentations and undersaturation) within the system prior to secondary depletion in comparison with low rate repressurisation. As a consequence of this, observations from simulations show that for equal primary and secondary depressurisation rates, secondary oil recovery (i.e. recovery during depletion after repressurisation) generally increases with an increase in repressurisation rate. 5. Two-dimensional depressurisation-repressurisation (half cycle) In order to better understand the physics of repressurisation, it was decided to begin by restricting simulations to the case of a single bubble, instantaneously nucleated in the centre of a two-dimensional 8x8 network. This allowed concentration of investigation on gas dissolution in oil by diffusion during re-pressurisation, oil re-imbibition phenomena, gas cluster break-up and non-equilibrium effects resulting from a range of depressurisation and re-pressurisation rates. For the simulations presented in this work, gas is assumed to be strongly non-wetting to oil (i.e. gas-oil contact angle equals zero). All outlets are closed to gas production (mimicking a network in the middle of an infinite reservoir, away from production well effect). Table 5-1 and Table 5- summarise the key fluid and network parameters used as a base case against which later sensitivities could be compared. 186

Table 5-1: Relevant fluid properties Bubble point pressure (Pb) Gas/oil IFT at Pb 75 psia mn/m Gas density at Pb 39 kg/m 3 Oil density at Pb 97 kg/m 3 Gas/oil diffusion coefficient (D g ) at Pb Oil Shrinkage.6 x 1-6 m /day No Table 5-: Network properties and other simulation parameters Dimension Consolidation Gravity: viscous forces 8 x 8 x 1 nodes Unconsolidated model Nil: nil PSD Uniform (,8) µm Pore Length µm Crevice Density Crevice Distribution 1 per 1 pores (5x1 -, 1x1 - ) microns Coordination Number (Dz) Seed 3 Initial water saturation. No. of Bubbles at Pb 1 Depletion Rate Repressurisation Rate Repressurisation start at pressure 1psi/day 1psi/day 31psia 5..1 Base case primary depressurisation simulations This section begins by examining the primary depressurisation of the single bubble at 1psi/day from bubble point pressure, Pb=75psia to the point where no more oil can be displaced. Figure 5.1 shows the pressure history of a number of variables that will be used to interpret all subsequent sensitivities. Figure 5.1(a) shows a plot of supersaturation (defined here as the difference between average dissolved gas concentration in the network 187

at a specific pressure and experimentally measured equilibrium value and reported in units of kg/m 3 or psi in this thesis) against system pressure, which exhibits an initial departure away from equilibrium behaviour diffusion is too slow to compensate for the shift away from equilibrium R s (P) caused by the relatively high depletion rate. As the gas structure grows, however, diffusion distances decrease and it becomes progressively easier for mass transport of gas into the bubble to occur. Consequently, supersaturation begins to decrease. Figure 5.1(b) shows the increase in gas-oil interfacial area responsible for this, facilitating the transfer of an increasing number of moles from the oleic to the gaseous phase (Figure 5.1(c)). The pressure history of gas saturation is shown in Figure 5.1(d) and the corresponding gas and R s contour snapshots are given in Figure 5. and Figure 5.3. The pressure history of different parameter shows a very consistent trend; the system is away from equilibrium during most of the depletion and only approaches equilibrium once large gas saturation has built up within the network. This is clear from the contour plots in Figure 5.3. For future comparisons, it would be useful to know the approximate equilibrium behaviour of the system at different points during primary depletion. As has already been discussed in chapter 3, the non-conservative nature of the process means that laboratory PVT data are not sufficient to allow this to be derived immediately. Consequently, it was decided to carry out a series of numerical experiments involving shut-ins at a number of different pressure values. Figure 5. shows the development of the gas phase during shut-ins at 6psia, psia, and 315psia, both as functions of pressure and time. 188

Supersaturation (kg/m3) a IN(1) 1psi/day 5.5 3.5 3.5 1.5 1.5 1 3 5 6 7 8 Pressure(psia) Area (m) IN(1) 1psi/day 1.E- 1.E- 1.E- 8.E-5 6.E-5.E-5.E-5.E+ 1 3 5 6 7 8 b Mass (kg) c IN(1) 1psi/day 7.E-7 6.E-7 5.E-7.E-7 3.E-7.E-7 1.E-7.E+ 1 3 5 6 7 8 d IN(1) 1psi/day 7.E-1 6.E-1 5.E-1.E-1 3.E-1.E-1 1.E-1.E+ 1 3 5 6 7 8 Figure 5.1. Pressure histories of supersaturation (a), gas-oil diffusion interface area (b), mass in bubbles (c) and network gas saturation (d). Single nucleated bubble at a depletion rate of 1psi/day, (8x8x1, Dz=) Figure 5.. Gas-oil pore occupancies at various pressures during depressurisation (1psi/day). Gas is white, (8x8x1, Dz=) 189

Rs Figure 5.3. R s contours at various pressures during depressurisation (1psi/day). Dissolved gas concentration decreases with intensity of the blue coloration, (8x8x1, Dz=) The corresponding supersaturation plots are given in Figure 5.5. It is interesting to note that, even though the supersaturation is relatively low at 6psia, the system takes approximately 5 days of shut-in to approach equilibrium. This is because the gas phase has had little time to develop spatially, and so the interfacial area available for mass transfer between gas and oil remains small. Conversely, a relatively high supersaturation has built up before shutting in at psia, yet equilibration in this case is approached after only approximately 5 days. The gas phase is well developed prior to shut-in in this case and steep concentration gradients within the system help restore equilibrium more quickly. This effect is even more apparent when the system is shut-in at 315psia in this case, equilibrium is approached after only days. These shut-in simulations allow an equilibrium S g vs. pressure plot to be derived and this is presented in Figure 5.6 this plot shows the maximum gas saturation that could be achieved at any given pressure using the base case parameters. 19

IN(1) 1 psi/day IN(1) 1psi/day 1..9.8.7.6.5..3..1. 1 3 5 6 7 8.1.1.8.6... 1 3 5 6 Days IN(1) 1psi/day IN(1) 1psi/day 1..9.8.7.6.5..3..1. 1 3 5 6 7 8.35.3.5..15.1.5. 1 3 5 6 Days IN(1) 1psi/day IN(1) 1psi/day 1..9.8.7.6.5..3..1. 1 3 5 6 7 8.5..35.3.5..15.1.5. 1 3 5 6 Days Figure 5.. History of gas saturation build-up for shut-in at different pressures, (8x8x1, Dz=) IN(1) 1psi/day IN(1) 1psi/day Supersaturation (kg/m3) 5.5 3.5 3.5 1.5 1.5 1 3 5 6 7 8 Supersaturation (kg/m3) 5.5 3.5 3.5 1.5 1.5 1 3 5 6 7 8 IN(1) 1psi/day Supersaturation (kg/m3) 5.5 3.5 3.5 1.5 1.5 1 3 5 6 7 8 Figure 5.5. Variation of average supersaturation during shut-in, (8x8x1, Dz=) 191

IN(1) Equilibria (eq) 1.9.8.7.6.5..3..1 1 3 5 6 7 8 Figure 5.6. Equilibrium gas saturation estimated from shut-in at several pressures, (8x8x1, Dz=) Gas saturation during depressurisation at 1psi/day is shown in Figure 5.7, which demonstrates that a higher depletion rate leads to suppressed gas growth as a function of pressure. This is due to the fact that the rate of mass transport via diffusion is too low to keep pace with a rapidly decreasing equilibrium pressure. IN(1) 1psi/day 7.E-1 6.E-1 5.E-1.E-1 3.E-1.E-1 1.E-1.E+ 1 3 5 6 7 8 Figure 5.7. Network gas saturation during depressurisation at 1psi/day, (8x8x1, Dz=) 5.. Repressurisation simulations Having thoroughly examined the base case depressurisation scenario, attention now focuses upon repressurisation of the system once a pre-determined pressure has been reached following depressurisation. It was decided to commence repressurisation once the network 19

has been depressurised from bubble point to 31psia, a value chosen as optimal for observing subsequent bubble break-up without encountering end-effects associated with excessive gas build-up at the boundaries of the network that characterises the final stages of depletion. The development of the evolving gas phase during primary depletion and its subsequent break-up during repressurisation is shown in Figure 5.8. A single bubble nucleates at the centre of the network and continues to expand, producing a gas saturation of approximately.5 at 315psia. Contours of dissolved gas concentration exhibit the expected pattern, with gradients in R s driving mass transport via diffusion into the evolving bubble. Repressurisation of the system at 1psi/day, however, is not simply the reverse of primary depletion at 1psi/day. The developed gas phase does not simply retract from the latest pores invaded during depressurisation the process exhibits a large degree of hysteresis. This is evident when comparing gas distributions at equivalent pressures during each part of the cycle. At all pressures, a higher gas saturation resides within the network during repressurisation when compared with that existing during the primary depletion. Most crucial of all, a highly dispersed gas phase persists once the original bubble point pressure of the oil has been reached at the end of repressurisation. This will have important implications for recovery during secondary depletion, as will be shown later. Notice also, that gradients in R s towards bubbles are still apparent in some areas of the system during the early stages of repressurisation (Figure 5.9) time is required for diffusion to reverse these gradients in oil-filled regions far from the gas phase. 193

Figure 5.8. Gas-oil occupancies showing oil re-imbibition and gas break-up during repressurisation. Depletion rate=repressurisation rate= 1 psi/day, (8x8x1, Dz=) 19

Rs Figure 5.9. R s contours at various stages of a depressurisation-repressurisation cycle. (1 psi/day -1 psi/day), (8x8x1, Dz=) 195

So, a degree of hysteresis has been observed during the depressurisation-repressurisation cycle, but what are the causes of this? Consider the plots shown in Figure 5.1, which show the pressure dependence of gas saturation, supersaturation, interfacial area, total number of gas clusters, and the total mass in the gas phase. Hysteresis in gas saturation is essentially a manifestation of hysteresis in more fundamental variables in the system and perhaps the most easily explained is that associated with the number of gas clusters. During depletion, it is clear that only a single gas cluster can exist only one cluster is nucleated and this single cluster simply expands in response to increased mass transfer of gas across the gas-oil interface (recall that gravity and viscous forces are inactive) and reducing external (oil) pressure. Supersaturation increases and then begins to fall for the reasons outlined earlier. Now, the process of depressurisation is a seeded invasion percolation process, with gas filling the lowest capillary entry pressure pores connected to the evolving gas cluster (i.e. accessibility plays a role during depletion). During repressurisation, however, oil initially reimbibes into gas-filled pores characterised by the highest capillary entry pressures and accessibility is less of an issue. [In fact, if reimbibition were allowed exclusively via snapoff, then no accessibility effect would be evident. For the system here, however, piston type imbibition is considered first for dangling gas pores (i.e. gas pores directly to oil-filled neighbours), in the sense that perimeter gas-filled pores are more likely to re-imbibe than those deep within the gas structure. Consequently, accessibility during reimbibition plays a minor role in this case]. So, the reimbibition process is not simply the reverse of the growth process, just as two-phase imbibition is not the reverse of two-phase drainage. Reimbibition acts to fragment the gas structure, leading to an increase in the number of gas clusters as pressure increases (Figure 5.1a). These evolving cluster fragments are now the new gas source during repressurisation and the diffusive drive towards equilibrium is now governed by the efficacy of these fragments in supplying gas to the enveloping oil phase. The fragmentation process means that, at any given pressure, the interfacial area between oil and gas is greater during repressurisation than during depletion (Figure 5.1b) and it may be expected that this would help restore equilibrium relatively quickly. Now, during 196

the early stages of repressurisation, gas actually continues to diffuse into the gas phase (due to the fact that the oil continues to be locally supersaturated) and this does apparently help to bring the system closer to equilibrium (Figure 5.1c). As repressurisation continues, the average supersaturation continues to decrease however, zero supersaturation is not approached asymptotically. In fact, this suggests that it is not sensible to make an equivalence between zero average supersaturation and system equilibrium. For the base case presented here, the system never achieves a steady-state condition, as evidenced by the way in which supersaturation switches from being positive to negative within the space of a single pressure step. Continued repressurisation beyond 55psia is characterised by negative supersaturation (i.e. undersaturation), as the shrinking gas bubbles become unable to act as effective sources for diffusion to compete with the 1psi/day repressurisation rate. The assertion that supersaturation does not tend to zero asymptotically, and that zero supersaturation does not imply equilibrium here, requires further investigation. Hence, a number of shut-ins were undertaken at various points during repressurisation (to check that equilibrium would be restored). The results in Figure 5.11 show that equilibrium is indeed approached during shut-in, regardless of whether the oil is supersaturated or undersaturated beforehand. 197

Supersaturation (kg/m3) No. Clusters IN(1) (1,1) 6 5 3 1 1 3 5 6 7 8 IN(1) (1,1) 5 3 1 - -1 1 3 5 6 7 8 Mass in Gas (kg) Area (m) IN(1) (1,1) 7.E-5 6.E-5 5.E-5.E-5 3.E-5.E-5 1.E-5.E+ 1 3 5 6 7 8 IN(1) (1,1).E-7 3.5E-7 3.E-7.5E-7.E-7 1.5E-7 1.E-7 5.E-8.E+ 1 3 5 6 7 8.5.5..35.3.5..15.1.5. IN(1) (1,1) Figure 5.1. Pressure histories of the number of gas clusters, interfacial area, supersaturation, mass of free gas in bubbles and network gas saturation for the base case depletion-repressurisation cycle, (8x8x1, Dz=) 1 3 5 6 7 8 IN(1) (1,1).3.5..15.1.5. 1 3 5 6 7 8 a IN(1) (1,1).3 Supersaturation (kg/m3) IN(1) (1,1) 5.5 3.5 3.5 1.5 1.5 1 3 5 6 7 8 b 5 IN(1) (1,1).5..15.1.5. 1 3 5 6 7 8 c Supersaturation (kg/m3) 3 1 1 3 5 6 7 8-1 d Figure 5.11. Network gas saturation and average supersaturation for two shut-in schemes during repressurisation starting with supersaturated (a & b) and undersaturated (c & d) oil respectively, (8x8x1, Dz=) 198

As an aside, it is worth noting that the way in which supersaturation varies during continuous repressurisation depends upon a number of parameters, including: the rate of mass transfer via diffusion from the bubbles into the oil, the repressurisation rate, and the rate at which the primary depletion was carried out. It is this last parameter that dictates how far the system is away from equilibrium prior to repressurisation and there appears to be little way of predicting subsequent behaviour without recourse to simulation. This is a vitally important point the behaviour of the system during repressurisation depends crucially upon the pressure history of the system during the earlier depletion. 5..3 Sensitivity to rate combinations Before we proceed, a formulation was developed for calculating equilibrium gas saturation from network simulation results regardless of the depressurisation rate. To derive this, it is recognised that gas mass may either exist exclusively as dissolved component (prior to nucleation) or as both free and dissolved gas (post nucleation). Of course for a given network/fluid system, free gas mass is larger as we approach equilibrium (e.g very low rate depressurisation) while gas mass is more in dissolved form away from equilibrium (e.g. very high rate depressurisation). Going forward, equation 5-1 can easily be solved at specified pressure for equilibrium gas saturation as all other parameters are known. eq eq eq avg avg avg [ S. + R ( 1 S )] = [ S. ρ + R ( 1 S )] g ρ (5-1) g s g g g s g Average gas saturation S avg avg g and average dissolved gas concentration R s represent the network gas saturation and dissolved gas concentration respectively at the reference pressure. ρ g = gas density (kg/m 3 ). Note that, prior to bubble nucleation, S eq g = S avg g = and R s eq = R s avg. Consequently, equilibrium gas saturation curves presented for discussion henceforth have been calculated using the above formulation. Three rates were selected for the study of interest in this section: 1, 1, and 5psi/day and 6 combinations were examined in detail. The results are summarised in Figure 5.1 to Figure 5.15 and show a wide range of hysteresis behaviour depending upon the depletion and repressurisation rates used. Note that depletion only continued down to 5psia in these simulations. Further investigations 199

presented in later section would reveal the impact of point in pressure where repressurisation is started. Figure 5.1 represents a case similar to the base case ((depletion rate=1psi/day, repressurisation rate=1psi/day) (1,1)). Depletion at 1psi/day results in the lowest supersaturation observed, as expected, and a subsequent repressurisation at 1psi/day exhibits the least hysteresis in the corresponding variables. Conversely, depletion at 5psi/day exhibits largest supersaturation effects (not shown). Perhaps the most interesting effect, however, is that involving depletion and repressurisation at different rates. Firstly, high rate depletion followed by low rate repressurisation is presented in Figure 5.1 while Figure 5.15 shows simulation results for low rate depletion followed by high rate repressurisation. Observe that, in the former (i.e. high rate depletion/ low rate repressurisation), a prolonged period of gas growth is observed during the repressurisation phase the supersaturation is so high, that concentration gradients are still sufficiently steep to drive dissolved gas into bubbles via diffusion. Conversely, for simulation with low rate depletion/ high rate repressurisation, the system is close to equilibrium at onset of repressurisation resulting in near instantaneous reversal of concentration gradient. The snapshots of Figure 5.16 very clearly highlight the implication of rate variability on instantaneous phase occupancies. Figure 5.1. Network data from depressurisation at 1psi/day followed by a repressurisation at 1psi/day. The line represents an approximation to PVT equilibrium conditions, (8x8x1, Dz=)

Figure 5.13. Network data from depressurisation at 1psi/day followed by a re-pressurisation at 1psi/day (Note that Ssat=supersaturation and Conc=R s ). The line represents an approximation to PVT equilibrium conditions, (8x8x1, Dz=) Figure 5.1. Network data from depressurisation at 1psi/day followed by a repressurisation at 1psi/day (Note that Ssat=supersaturation and Conc=R s ). The line represents an approximation to PVT equilibrium conditions, (8x8x1, Dz=) 1

It is clear that the amount of gas remaining at the end of the repressurisation process is a function of the relative rates of primary depletion and repressurisation. The final gas saturations after repressurisation back to bubble point pressure are presented in Table 5-3, where it is evident that this remaining saturation is maximised under condition of slow depletion followed by high-rate repressurisation. The low rate depletion allows a large gas saturation to form within the network, whilst rapid repressurisation precludes the bubbles from acting as efficient gas sources. Figure 5.15. Network data from depressurisation at 1psi/day followed by a re-pressurisation at 1psi/day. The line represents an approximation to PVT equilibrium conditions, (8x8x1, Dz=)

Figure 5.16. Gas saturation profile for (DP,)=(1,1)psi/day simulation scheme. The model is still showing increased gas growth even after the start of repressurisation, (8x8x1, Dz=) 3

Table 5-3: Gas saturation at bubble point after re-pressurisation DP/ (Pb)..378.1.7..96 5.3 1.58 5.5 5.. Effects of commencing repressurisation at different pressures It has already been reported how supersaturation increases up to a maximum during depressurisation before decreasing down to zero. But what would be the effect on gas saturation of starting repressurisation at different pressures during depletion, corresponding to varying levels of supersaturation? Figure 5.17. DP- (1, 1) psi/day scheme showing points at which repressurisation was started, (8x8x1, Dz=) Points a, b and c on Figure 5.17 coincide with depleting the system [i.e., Pb P(t)] by psi, 7 psi and 67 psi respectively, before the start of re-pressurisation. A superimposed plot of supersaturation levels, starting re-pressurisation at points a, b, c and base is presented in Figure 5.18. Clearly, supersaturation (+ve) or undersaturation (-ve) are measures of deviation from equilibrium. For ease of discussion therefore, the absolute

values of undersaturation after repressurisation back to initial bubble point pressure are plotted in Figure 5.19. Ssat(psi) 3 5 c a b 15 base 1 5-5 5 1 15 5 3-1 -15 - -5 Pb- Figure 5.18. Simulated supersaturation history for varying re-pressurisation starting pressure, (8x8x1, Dz=) 5 Absolute Ssat at Pb 15 1 5 a b c base 5 1 15 5 3 Pb- Figure 5.19. Absolute supersaturation, re-pressurisation starts at different points, (8x8x1, Dz=) Points a, b, c and base in Figure 5.19 represent the final degree of undersaturation once the system has returned to bubble point pressure. This initially increases and begins to asymptote after point c. The maximum increase in undersaturation however occurred when moving from a to b. Figure 5.19 shows that although point b represents the maximum supersaturation during depressurisation, starting a re-pressurisation at that point does not lead to the most undersaturated system at the end of the simulation. The issue of when to begin repressurising the system will be revisited later in section 5.3. in the context of secondary depletion, where it will be shown that this choice greatly affects subsequent recovery. 5

5..5 Stepwise depressurisation (intermittent shut-ins) This section begins by returning to primary depletion and examines the impact of carrying out such a process in a stepwise manner. All previous investigations of depressurisation reported so far rate effects, nucleation, and gas evolution have focused on a continuous, constant depletion rate. However, field (and indeed some laboratory) applications seldom operate under such invariant conditions. Production can be interrupted for a number of different operational, environmental, or economic reasons, both in the laboratory and in the field. Studies have therefore been extended to investigate the possible changes that could occur at the pore scale caused by disruption to the depletion process and how these may impact the results of a depressurisation experiment. A progressive nucleation model was adopted and simulations were carried out on a D 8 x 8, network model (Dz=), at a depletion rate of 1psi/d. Relevant oil properties used are those presented in Table 5-1. The model was shut-in for a period of 5 days after 3 days of depressurisation at 1psi/day and results were then compared with those from a continuous constant rate of depressurisation. Figure 5.(a) shows that gas saturation increases in the network during the shut-in. The final recovery, however, is the same as that resulting from continuous depletion. Figure 5.(b) clearly shows that all possible sites (controlled by the local supersaturation) had been nucleated before shut-in and so the evolving gas would be topologically similar in both shut-in and continuous cases at high gas saturations. Further simulations were carried out to examine the effect of shutting in when only a fraction of the total number of bubbles (6%) had nucleated. In this case, the shut-in lasted for 83 days to allow reasonable time for mass transfer from oil into the gas bubbles. Figure 5.1 shows that average supersaturation in the network decreases to a very small value as the system approaches equilibrium at the shut-in pressure. Although the average supersaturation in the network increases again on resumption of depressurisation, the local supersaturation in the oil pores remained below the critical value required for further nucleation. A step change in gas saturation is observed during the shut-in (Figure 5.), once again due to the system returning to equilibrium. However, the difference in final gas saturation between the continuous depressurisation and stepwise depressurisation in this case was still only.6%. 6

In summary, simulation results seem to indicate that shut-in may result in an apparent increase in recovery during an interrupted core depressurisation experiment due to the supersaturated system gradually returning towards equilibrium over a period of constant pressure. However, the shut-in does not appear to significantly affect the ultimate recovery if the depletion is resumed down to very low pressures. The results show how a high bubble density and a well dispersed gaseous phase are important factors in bringing a gasoil system close to equilibrium diffusion paths are shortened and this allows mass transfer to operate efficiently. This effect will be important when explaining the secondary depletion simulations presented in the section 5.3..7 continuous.6 step.5..3..1. 1 3 5 6 Pb- Nbubbles 18 16 1 1 1 8 6 continuous step 5 1 15 5 Pb- (a) (b) Figure 5.. (a) build up in network for continuous and step depletion (a), cumulative number of bubbles nucleated in the network from continuous and step model (b) (Note that Nbubbles history is similar in both cases since all bubbles nucleated before shut-in), 1psi/day, (8x8x1, Dz=) Figure 5.1. Average supersaturation plots for 83 days shut-in after nucleation of 6% of possible bubbles at 1psi/day, (8x8x1, Dz=) 7

.7.6.5..3..1. 1 3 5 6 Pb-p(psi) Nbubbles 1 1 8 6 5 1 15 Pb- (a) Figure 5.. build up in network for step depletion following a shut-in of 83 days (a), Cumulative number of bubbles nucleated in the network before shut-in model (b), 1psi/day, (8x8x1, Dz=) (b) 5.3 Two-dimensional repressurisation and secondary depletion (full-cycle) To extend understanding of gas evolution and oil recovery during secondary depletion (post-repressurisation), this section presents simulations results and discussions following an extensive parametric study involving full pressure cycles. Firstly, simulations were designed to eliminate any complications due to nucleation effects. Therefore, all the simulations were initially conducted using instantaneous nucleation model which allows a predefined number of bubbles to nucleate at fixed locations. Simulations adopting progressive nucleation model have also been conducted and are discussed in later sections. 5.3.1 Base case secondary depressurisation Once again a base case simulation was carried out and, in keeping with earlier simulations; it was decided to use a secondary depletion rate of 1psi per day. Snapshots at a number of different pressures are shown in Figure 5.3 and Figure 5. and a full set of variables for the three part cycle from 75psia down to 31psia and back to 75psia are plotted in Figure 5.5. 8

Figure 5.3. Gas-oil occupancies showing growth, break-up and collapse of gas for the full pressure cycle. Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=) 9

Figure 5.. R s contours for the full pressure cycle for a single nucleated bubble; Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=) 1

IN(1) (1,1,1).35.3 I.5..15.1.5. a 6 8 Supersaturation (kg/m3) b IN(1) (1,1,1) 5 3 1 I -1 6 8 - Area (m) c 8.E-5 7.E-5 6.E-5 5.E-5.E-5 3.E-5.E-5 1.E-5.E+ IN(1) (1,1,1) I 6 8 No. Gas Clusters d IN(1) (1,1,1) 6 5 3 1 I 6 8 IN(1) (1,1,1) Mass in Gas (kg).5e-7.e-7 3.5E-7 3.E-7.5E-7.E-7 1.5E-7 1.E-7 5.E-8.E+ e I 1 3 5 6 7 8 Figure 5.5. Pressure histories of gas saturation (a), supersaturation (b), gas-oil diffusion interface area (c), number of gas clusters (d) and mass of free gas in bubbles (e); Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=) The hysteresis behaviour between primary depletion and repressurisation has already been discussed in sections 5. and this clearly impacts upon the secondary depletion behaviour that follows. At the beginning of secondary depletion, there is evidently a high bubble density compared with the single bubble nucleated at the start of primary depletion. As pressure declines once more, these bubbles begin to coalesce as evidenced by the snapshot Figure 5.3 and Figure 5.5(d), which shows the pressure dependence of the total number of gas clusters. Moreover, gradients in dissolved gas concentration are still sloping away from some gas structures during the early stages of secondary depletion (Figure 5.) and a little time is required for diffusion to reverse this trend. 11

The snap-off seen during repressurisation, which served to increase interfacial area, is partially reversed once pressure decreases again (nearby disconnected clusters are reconnected) and this, coupled with the lag in concentration gradients, leads to hysteresis in interfacial area between repressurisation and secondary depletion. Consequently, mass transport of gas into the bubbles also exhibits hysteresis and this explains the observation that gas saturation during secondary depletion is lower than that observed at an equivalent pressure during repressurisation (Figure 5.5a). However, the most important aspect of the simulation cycle is the fact that recovery during secondary depletion is higher that that achieved during primary depletion over the full pressure range of the cycle. Figure 5.6 shows that the difference in recovery (fraction of original oil in-place or OOIP) over the range 75psia to 31psia varies from around % to 1%, depending upon the pressure. IN(1) (1,1,1) (I)-().1.1.8.6... 6 8 Figure 5.6. Incremental oil recovery (fraction of OOIP) after performing a repressurisation/secondary-depletion cycle; Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=) Although increased recovery is evident in the foregoing secondary depletion simulation, it should be remembered that the final recovery from the network achieved when depleting to lower pressures until no more oil can be physically removed from the system (psia for the case considered here) is almost the same as that obtained from primary depletion (Figure 5.7). Hence, the merits of secondary depletion depend upon the abandonment pressure of the system in question. 1

a IN(1) (1,1,1).7.6.5..3 I..1. 6 8 IN(1) (1,1,1).1.1.8.6... 6 8 b (I)-() Figure 5.7. network gas saturation profiles ( and I) (a); incremental oil recovery over the full pressure range (i.e. down to low pressures) (b); Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=) 5.3. Sensitivity to repressurisation pressure To start with, sensitivity study considered as part of the examination of secondary depletion processes initially focuses upon the pressure at which repressurisation is initiated how does this parameter impact upon the degree of improved recovery during secondary depletion? To this end, two full cycles of primary-depletion/repressurisation/secondarydepletion were simulated with repressurisation starting at 6psia and psia results were then compared against the base case (Figure 5.5). The resulting pressure dependencies of the relevant variables are shown over the pressure range 75psia to 31psia in Figure 5.8 and Figure 5.9. The first thing of note in Figure 5.8 is that the gas phase is only ever a single cluster, which grows during primary depletion, shrinks during repressurisation, and grows again during secondary depletion. Nevertheless, a small degree of hysteresis is still evident in interfacial area, demonstrating that oil reimbibition is not simply the reverse of gas growth topologically even over this relatively short pressure range (i.e. 75psia-6psia-75psia). This hysteresis in the area available for mass transport subsequently affects local supersaturation and the total mass of gas in bubbles throughout the second depletion. Hence, although the gas remains as a single bubble throughout the cycle, the small topological changes caused by oil reimbibition are still sufficient to increase recovery during secondary depletion. This is clear from Figure 5.3, which shows the difference in recovery between primary and secondary depletion over the full pressure range (75psia to psia) even this small amount of repressurisation can result in an increase of over 5% 13

in recovery for this parameter set. Note that, incremental recovery plot for the full pressure range (Figure 5.3) was derived from the difference between pressure cycles with secondary depletion and single pressure primary depletion down to psia. A similar, and even more encouraging, situation occurs when repressurisation begins at psia. Figure 5.9 shows that a larger degree of hysteresis occurs in all variables in this case. In addition, bubble fragmentation during repressurisation is delayed relative to that seen when the system was repressurised at 31psia (Figure 5.5), and the total number of daughter bubbles at the end of repressurisation is around half that found in the base case. The daughter bubbles being smaller than those in the base case prior to secondary depletion results in relatively lower total interfacial area. This remains the case throughout most of the secondary depletion, as daughter bubbles coalesce and the total number of bubbles in the system falls rapidly. At around 3psia, during secondary depletion, the gas exists only as a single structure (in comparison to the base case, where approximately 15 smaller clusters exist at this pressure). It is only during the latter stages of the cycle that the total mass of gas in bubbles begins to exceed that found in the base case (due to reduced competition for solute amongst fewer daughter bubbles and the topology of trapped oil). Increased recovery during secondary depletion over the full pressure range is again observed (up to 1% in this case, see Figure 5.31) and even exceeds that found in the base case. It is interesting to note that the degree of additional recovery seems to depend nonlinearly upon the pressure at which repressurisation is begun. 1

Area (m) a c IN(1) (1,1,1).35.3 I.5..15.1.5. 6 8 IN(1) (1,1,1) 7.E-5 I 6.E-5 5.E-5.E-5 3.E-5.E-5 1.E-5.E+ 6 8 Supersaturation (kg/m3) No. Gas Clusters b d.5 3.5 3.5 1.5 1.5 -.5 1.8.6.. IN(1) (1,1,1) I 6 8 IN(1) (1,1,1) 6 8 IN(1) (1,1,1) Mass in Gas (kg) e.e-7 3.5E-7 3.E-7.5E-7.E-7 1.5E-7 1.E-7 5.E-8.E+ I 6 8 Figure 5.8. Pressure histories of gas saturation, supersaturation, gas-oil diffusion interface area, number of gas clusters and mass of free gas in bubbles. Repressurisation started at 6psia. Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=) 15

a IN(1) (1,1,1).35.3.5 I..15.1.5. 6 8 Supersaturation (kg/m3) b IN(1) (1,1,1) 5 3 I 1-1 6 8 - Area (m) c 9.E-5 8.E-5 7.E-5 6.E-5 5.E-5.E-5 3.E-5.E-5 1.E-5.E+ IN(1) (1,1,1) I 6 8 No. Gas Clusters d IN(1) (1,1,1) 5 15 I 1 5 6 8 IN(1) (1,1,1) Mass in Gas 5.E-7.E-7 I 3.E-7.E-7 1.E-7.E+ 6 8 e Figure 5.9. Pressure histories of gas saturation, supersaturation, gas-oil diffusion interface area, number of gas clusters and mass of free gas in bubbles. Repressurisation started at psia. Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=) IN(1) (1,1,1) (I)-().6.5..3..1. 6 8 Figure 5.3. Incremental oil recovery (fraction of OOIP) after performing a repressurisation/secondary-depletion cycle. Repressurisation started at 6psia. Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=) 16

IN(1) (1,1,1) (I)-().1.1.1.8.6... 6 8 Figure 5.31. Incremental oil recovery (fraction of OOIP) after performing a repressurisation/secondary-depletion cycle. Repressurisation started at psia. Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=) 5.3.3 Variation of repressurisation rates The next set of sensitivities relate to the effect of repressurisation rate upon oil production. A set of 3 repressurisation rates was examined in detail: 1psi/day, 1 psi/day (base case), and 1 psi/day. Figure 5.3 shows data from the 1psi/day simulation. In comparison to Figure 5.5 (the base case), it is found that repressurising at a higher rate leaves more daughter bubbles in the network prior to secondary depletion (55 compared with 38) and a higher residual gas saturation. Supersaturation declines approximately linearly at this higher repressurisation rate and the system remains slightly more undersaturated when it returns to bubble point in comparison with the base case. The fact that more bubbles remain at the end of repressurisation at 1psi/day also means that additional interfacial area is available for mass transport. When secondary depletion begins, gas initially continues to leave the gas bubbles (Figure 5.3), interfacial area decreases, and gas saturation also decreases (due to the fact that concentration gradients still slope away from bubbles due to the history of the high rate repressurisation). However, continued depletion causes bubbles to coalesce, concentration gradients to re-adjust and slope towards gas structures, and gas saturation to increase once again. The degree of improvement in oil recovery as a function of pressure is summarised in Figure 5.33. Incremental oil recovery (fraction of OOIP) after repressurisation/secondary-depletion cycle; Rates (,, I) = (1, 1, 1) psi/day and is comparable to the base case result. So, despite the fact that more daughter bubbles 17

remained at the end of the high rate repressurisation, these bubbles rapidly join together and the system behaves in a similar way to the base case during secondary depletion. Two shutin simulations have been undertaken during high rate repressurisation one at psia and a second at 7psia. Plots of gas saturation and supersaturation for the two cases are shown in Figure 5.3. It is interesting to see equilibrium restored in different ways shut-in at psia leads to an increase in gas saturation and a decrease in supersaturation over time, whilst shut-in at 7psia exhibits the opposite trends. Although perhaps not of immediate importance, these additional sensitivities give added confidence in the modelling approach and demonstrate that the system behaves in a physically sensible way during unorthodox pressure histories. IN(1) (1,1,1).35.3.5 I..15.1.5. 6 8 Supersaturation (kg/m3) IN(1) (1,1,1) 5 3 1 I -1 6 8 - -3 Area (m) 8.E-5 7.E-5 6.E-5 5.E-5.E-5 3.E-5.E-5 1.E-5.E+ IN(1) (1,1,1) I 6 8 No. Gas Clusters IN(1) (1,1,1) 6 5 3 I 1 6 8 IN(1) (1,1,1) Mass in Gas.5E-7.E-7 3.5E-7 3.E-7.5E-7.E-7 1.5E-7 1.E-7 5.E-8.E+ I 6 8 Figure 5.3. Pressure histories of gas saturation, supersaturation, gas-oil diffusion interface area, number of gas clusters and mass of free gas in bubbles; Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=) 18

IN(1) (1,1,1) (I)-().1.1.8.6... 6 8 Figure 5.33. Incremental oil recovery (fraction of OOIP) after repressurisation/secondarydepletion cycle; Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=).3 IN(1) (1,1,1) shut@psi.3 IN(1) (1,1,1) shut@7psi.5..5..15.1.5.15.1.5 Supersaturation (kg/m3). 1 3 5 6 7 8 a IN(1) (1,1,1) 5 3 1 6 8 c shut@psi Supersaturation (kg/m3). 1 3 5 6 7 8 b - IN(1) (1,1,1) 5 3 1-1 6 8 d shut@7psi Figure 5.3. Average supersaturation and gas saturation data during shut-in at different pressures (psia and 7 psia) during the 1 psi/day repressurisation leg of the cycle, (8x8x1, Dz=) The low repressurisation rate simulation is summarised in Figure 5.35 and snapshots are shown in Figure 5.36 and Figure 5.37. In this case, the gas cluster in the network at the end of primary depletion breaks up dramatically during repressurisation and a large number of daughter bubbles are produced. The low repressurisation rate, however, means that diffusion has sufficient time to eventually remove most of these bubbles, which go back into solution. At the end of repressurisation, only three bubbles remain. Supersaturation is seen to decline asymptotically towards zero and then the oil becomes gradually more undersaturated. Eventually almost all gas goes back into solution (i.e. gas saturation at 19

the end of repressurisation). Although small concentration gradients persist at the end of repressurisation, secondary depletion is almost a repeat of the primary depletion, as low rate repressurisation brings the system close to equilibrium before the third stage of the cycle. It is unfortunate that the choice of network used in this particular simulation leaves bubbles close to the edges of the system and that no central bubble remains. This boundary effect results in poorer recovery during secondary depletion in this case. It should be expected, however, that the central bubble would re-nucleate at the start of secondary depletion and that recovery would actually be close to that obtained after primary depletion. Indeed, this was later confirmed by re-nucleating the central bubble as demonstrated by the results presented in Figure 5.38, which exhibit very little hysteresis in interfacial area, mass of free gas, and gas saturation between primary and secondary depletion. Consequently, for this parameter set, little additional recovery should be expected when a low repressurisation rate is used.

IN(1) (1,1,1)..35.3.5..15.1.5 I. 1 3 5 6 7 8 Supersaturation (kg/m3) IN(1) (1,1,1) 5 3 1 I -1 1 3 5 6 7 8 - Area (m) 9.E-5 8.E-5 7.E-5 6.E-5 5.E-5.E-5 3.E-5.E-5 1.E-5.E+ IN(1) (1,1,1) I 1 3 5 6 7 8 No. Gas Clusters IN(1) (1,1,1) 7 6 5 3 1 I 1 3 5 6 7 8 IN(1) (1,1,1) Mass of Gas (kg) 5.E-7.5E-7.E-7 3.5E-7 3.E-7.5E-7.E-7 1.5E-7 1.E-7 5.E-8.E+ I 1 3 5 6 7 8 Figure 5.35. Pressure histories of gas saturation, supersaturation, gas-oil diffusion interface area, number of gas clusters and mass of free gas in bubbles; Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=) 1

Figure 5.36. Gas-oil occupancies showing growth, break-up and collapse of gas for the full pressure cycle. Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=)

Figure 5.37. R s contours for the full pressure cycle for a single nucleated bubble; Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=) 3

IN(1) (1,1,1)..35.3.5..15 I.1.5. 1 3 5 6 7 8 Supersaturation (kg/m3) IN(1) (1,1,1) 5 3 1 I -1 1 3 5 6 7 8 - Area (m) 9.E-5 8.E-5 7.E-5 6.E-5 5.E-5.E-5 3.E-5.E-5 1.E-5.E+ IN(1) (1,1,1) 1 3 5 6 7 8 No. Gas Clusters IN(1) (1,1,1) 7 6 5 3 I 1 1 3 5 6 7 8 IN(1) (1,1,1) Mass of Gas (kg) 5.E-7.5E-7.E-7 3.5E-7 3.E-7.5E-7.E-7 1.5E-7 1.E-7 5.E-8.E+ 1 3 5 6 7 8 Figure 5.38. Pressure histories of gas saturation, supersaturation, gas-oil diffusion interface area, number of gas clusters and mass of free gas in bubbles. Central bubble is re-nucleated at the start of secondary depletion; Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=) 5.3. Impact of pore connectivity In order to address the issue of pore connectivity, it was first decided to run primary depressurisation benchmark simulations at a reduced coordination number (Dz=.66) at rates of 1 psi/day and 1 psi/day. Plots of gas saturation are shown in Figure 5.39. It is clear that reduced connectivity suppresses gas evolution during depletion (diffusion path lengths are longer), as does increased depletion rate. Hence, these two parameters act synergistically and are crucial in determining oil recovery. So, how does connectivity affect repressurisation and secondary depletion?

The pressure dependency of the system variables for depletion and repressurisation rates of 1psi/day is shown in Figure 5. and snapshots of the cycle are shown in Figure 5.1 and Figure 5.. Compared with Figure 5.5, it is clear that supersaturation at the end of primary depletion is far higher than that seen in the base case simulation. Furthermore, bubble fragmentation is delayed during repressurisation in the less connected system and the number of bubbles remaining when the pressure returns to bubble point is lower (13 compared with 38 for the base case). However, these bubbles are well dispersed in the network they may appear close to one another spatially but the poor connectivity of the network means that these bubbles are actually far apart in terms of diffusion path lengths and this will be an important factor when interpreting oil recovery later. Interfacial area is an order of magnitude lower than that seen in the base case and this clearly suppresses the amount of gas leaving bubbles during repressurisation. In fact, gas continues to enter bubbles for approximately 1psi (or 1 days) of pressure increase, compared with only 3psi (or 3days) in the base case. IN(1) 1psi/day Z= Dz=.66.5.5..35.3.5..15.1.5. 1 3 5 6 7 8 IN(1) 1psi/day Z= Dz=.66.5.5..35.3.5..15.1.5. 1 3 5 6 7 8 Figure 5.39. Gas saturation plots at 1psi/day and 1psi/day in a poorly connected network, (8x8x1, Dz=.66) 5

Dz=.66 Dz=.66 I I Dz=.66 Dz=.66 I Dz=.66 I Figure 5.. Pressure histories of gas saturation, supersaturation, gas-oil diffusion interface area, number of gas clusters and mass of free gas in bubbles. A poorly connected (Dz=.66) network was used in this case; Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=.66) Although oil production is lower overall in the less connected system (as expected), the increase in production through performing a repressurisation-secondary depletion cycle is considerable larger (Figure 5.3). In the less connected system recovery can be improved by over 5% at lower abandonment pressures and by approximately 1% at an abandonment pressure of 31psia. Final recovery is also higher if the full cycle is carried out instead of a primary depletion alone. 6

Figure 5.1. Gas-oil occupancies showing growth, break-up and collapse of gas for the full pressure cycle. Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=.66) 7

Figure 5.. R s contours for the full pressure cycle for a single nucleated bubble; Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=.66) 8

IN(1) (1,1,1) Z= Dz=.66.6 I.5..3..1. 6 8 a (I)-() IN(1) (1,1,1) Z= Dz=.66.3.5..15.1.5. 6 8 b Figure 5.3. Network gas saturation plots ( vs I), (a); Incremental oil recovery (fraction of OOIP) after performing a repressurisation/secondary-depletion cycle, (b). Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=.66) Recovery improvement for the less connected system using a repressurisation rate of 1psi/day is summarised in Figure 5.. Suppression of gas evolution during primary depletion is so dramatic, that a repressurisation-secondary depletion cycle can improve recovery even more by over 5%. Once again, secondary depletion also increases the final recovery (the point at which no more oil can be physically displaced). IN(1) (1,1,1) Dz=.66 IN(1) (1,1,1) Z= Dz=.66.6 I.5..3..1. 6 8 a (I)-().6.5..3..1. 6 8 b Figure 5.. Network gas saturation plots ( vs I), (a); Incremental oil recovery (fraction of OOIP) after performing a repressurisation/secondary-depletion cycle, (b). Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=.66) 5.3.5 Sensitivity to network topological structure (seed number) It is important to make sure that the foregoing results are not simply artefacts of the random number seed chosen for the particular simulation. To this end, two additional simulations were undertaken using different seeds. Plots of gas saturation and supersaturation are 9

shown in Figure 5.5, where it is clear that, although some statistical variation exists, the broad trends are similar in all three cases. There consequently appears to be little concern regarding the impact of random number seed upon general conclusions derived earlier and one can be confident that results are not pathological. IN(1) (1,1,1) IN(1) (1,1,1).7.6.5..3..1. 6 8 Series1 Series Series3 Supersaturation (kg/m3) 5 3 1-1 6 8 - -3 Figure 5.5. Gas saturation and supersaturation data comparing simulation cases with different random seeds, (8x8x1, Dz=) 5.3.6 Sensitivity to pore size distribution The radius distribution used so far a uniform function varying between and 8 microns has a relatively small variance and it was thought necessary to examine a broader pore size distribution. To this end, a uniform distribution with lower and upper bounds of 1 micron and 1 microns, respectively, was used. Results are shown in Figure 5.6 and snapshots of gas saturation and dissolved gas concentration are shown in Figure 5.7 and Figure 5.8. It appears that increasing the variance of the pore size distribution plays a similar role to that of reduced connectivity. The fragmentation of gas is again delayed and the total number of daughter bubbles remaining at the end of repressurisation is lower than the base case. Interfacial area at the end of primary depletion is similar to that observed in a less connected network Figure 5., although the behaviour of this variable during repressurisation differs somewhat here, the area increases after approximately 5 days of repressurisation in contrast to the Dz=.66 system. Supersaturation and mass transfer into bubbles are also similar in the two cases: i.e. supersaturation is higher than that found in the base case and the total mass of gas in bubbles is approximately 5 times less. 3

The snapshots demonstrate how an increased variance and smaller average pore size (55.5µm as opposed to 6µm) serve to decrease the overall gas concentration in the network at a given pressure compared with the base case this is primarily due to a reduction in the average cross sectional area of pores available for diffusive transport. The impact of carrying out a cycle of repressurisation and secondary depletion upon oil recovery is shown in Figure 5.9. In line with the result obtained by reducing pore connectivity, secondary depletion yields up to 5% more oil at 18psia even at 31psia, the improvement in oil recovery is approximately 1% over that obtained by primary depletion alone..18.16.1.1.1.8.6... IN(1) (1,1,1) U(1,1) I 1 3 5 6 7 8 Supersaturation (kg/m3) IN(1) (1,1,1) U(1,1) 7 6 5 I 3 1-1 1 3 5 6 7 8 - Area (m) IN(1) (1,1,1) U(1,1) 1.E-5 1.E-5 I 8.E-6 6.E-6.E-6.E-6.E+ 1 3 5 6 7 8 No. Gas Clusters IN(1) (1,1,1) U(1,1) 16 1 1 1 8 I 6 1 3 5 6 7 8 IN(1) (1,1,1) U(1,1) Mas of Gas.E-7 1.8E-7 1.6E-7 1.E-7 1.E-7 1.E-7 8.E-8 6.E-8.E-8.E-8.E+ I 1 3 5 6 7 8 Figure 5.6. Pressure histories of gas saturation, supersaturation, gas-oil diffusion interface area, number of gas clusters and mass of free gas in bubbles. Uniform (1,1) µm pore size distribution. Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=) 31

Figure 5.7. Gas-oil occupancies showing growth, break-up and collapse of gas for the full pressure cycle. Rates (,, I) = (1, 1, 1) psi/day. Uniform PSD (1,1) µm, (8x8x1, Dz=) 3

Figure 5.8. R s contours for the full pressure cycle for a single nucleated bubble; Rates (,, I) = (1, 1, 1) psi/day. Uniform PSD (1,1) µm, (8x8x1, Dz=) 33

IN(1) U(1,1) (I)-().3.5..15.1.5. 1 3 5 6 7 8 Figure 5.9. Incremental oil recovery (fraction of OOIP) after performing a repressurisation/secondary-depletion cycle. Rates (,, I) = (1, 1, 1) psi/day. Uniform PSD (1,1) µm, (8x8x1, Dz=) 5.3.7 Influence of gas-oil diffusion coefficient Increasing the gas-oil diffusion coefficient is expected to bring the system closer to equilibrium during both depressurisation and repressurisation. Consequently, an increase in this parameter should reduce observed differences in recovery between primary and secondary depletion. [Of course, a high diffusion coefficient leads to better recovery at any given pressure but here the focus is upon incremental recovery]. This was checked by increasing and decreasing D gas-oil by a factor of ten either side of the base value. Plots of gas saturation versus pressure are presented in Figure 5.5 for D gas-oil =.6 x 1-5,.6 x 1-6 and.6 x 1-7. IN(1) Diffusion Coeffs.7.6.5..3.6e-6.6e-5..6e-7.1. 1 3 5 6 7 8 Figure 5.5. gas saturation plots for three different gas-oil diffusion coefficients, (8x8x1, Dz=) The broad trend appears to be confirmed, with very little difference observed between primary and secondary depletion when D gas-oil =.6 x 1-5. For D gas-oil =.6 x 1-7, recovery at 31psia is improved by approximately 5%, whilst a 7% improvement is found for D gas- 3

oil=.6 x 1-6. Consequently, there exists the possibility that the efficacy of secondary depletion could be optimal at some intermediate D gas-oil. These results clearly highlight the need to measure diffusion coefficients as accurately as possible before attempting to predict subsequent recovery. 5.3.8 Low rate cycle Just as a high diffusion coefficient could be expected to reduce hysteresis during a depletion/repressurisation/secondary depletion cycle, undertaking the entire cycle at a low rate could be expected to do likewise. In order to confirm this, a complete three-stage cycle was carried out at a rate of 1psi/day and the results for the full pressure range down to residual oil saturation (S or ) are shown in Figure 5.51. The hysteresis in all variables is found to be much reduced in comparison with previous simulations. Supersaturation remains relatively low during the cycle (approaching zero at the end of depletions but diverging from zero during repressurisation as bubbles move away from enveloping oil), interfacial area is far higher than previous cases, and the number of daughter bubbles formed during repressurisation is almost twice that seen previously. Interestingly, interfacial area during secondary depletion is generally lower than that seen in primary depletion, leading to slightly higher supersaturation and lower gas saturation over most of the pressure range. Incremental recovery for the low rate cycle is actually negative, with secondary depletion giving up to % less recovery than that obtained from primary depletion alone (Figure 5.5). However, it should be noted that all secondary depletion simulations run thus far have only used daughter bubbles left at the end of repressurisation as their starting condition. Hence, the single bubble nucleated at the start of primary depletion has not been re-nucleated if it happened to have gone back into solution during repressurisation. It is unfortunate that the choice of network used in this particular simulation once again leaves bubbles close to the edges of the system (C.f. Section 5.3.3 and Figure 5.53) and that no central bubble remains after repressurisation back to bubble point. It is probably this boundary effect that results in poorer recovery during secondary depletion in this case. As discussed earlier in Section 5.3.3, it should be 35

expected, however, that the central bubble would re-nucleate at the start of secondary depletion and that the secondary depletion would exhibit behaviour very similar to that seen during primary depletion. IN(1) (1,1,1) IN(1) (1,1,1).7.6.5..3..1 I Supersaturation (kg/m3) 1.5 1.5 -.5 I 1 3 5 6 7 8. 1 3 5 6 7 8-1 IN(1) (1,1,1) IN(1) (1,1,1) 1.E- 1.E- I 1 1 Area (m) 1.E- 8.E-5 6.E-5.E-5.E-5.E+ 1 3 5 6 7 8 No. Gas Clustars 8 6 I 1 3 5 6 7 8 IN(1) (1,1,1) 8.E-7 7.E-7 6.E-7 Mass in Gas (kg) 5.E-7.E-7 3.E-7.E-7 1.E-7 I.E+ 1 3 5 6 7 8 Figure 5.51. Pressure histories of gas saturation, supersaturation, gas-oil diffusion interface area, number of gas clusters and mass of free gas in bubbles; Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=) 36

IN(1) (1,1,1) (I)-().5. -.5 1 3 5 6 7 8 -.1 -.15 -. -.5 -.3 -.35 -. -.5 Figure 5.5. Incremental oil recovery (fraction of OOIP) after performing a repressurisation/secondary-depletion cycle. Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=) Figure 5.53. Gas-oil occupancies during the early stages of secondary depletion showing the structural location of daughter bubbles away from the original nucleation site, (8x8x1, Dz=) 5.3.9 Secondary depressurisation versus shut-in Results from the base case depressurisation simulation presented earlier in Section 5..1 demonstrated how shutting in a primary depletion process could yield additional oil recovery as the oil and gas equilibrate via diffusional mass transport. It is therefore reasonable to ask whether or not it is worth performing a repressurisation/secondarydepletion cycle instead of simply shutting in the system and leaving it to equilibrate. Of course, in practice, it may seldom be possible to avoid some degree of repressurisation during shut-in and so results presented in this section can be viewed as being rather artificial and pessimistic. However, they do serve a useful purpose in gauging the relative importance of repressurisation during a shut-in period. Beginning with the well-connected (Dz=) case (the base case), gas saturation history from a primary depletion simulation shut in at 315psia is compared with that from a full 37

depletion/repressurisation/depletion cycle in Figure 5.5(a-b). It is clear that, for this particular set of parameters, shutting in the system actually produces more oil than completing a full pressure cycle. Moreover, the temporal evolution of gas build up for the two cases (as shown in Figure 5.5(c-d)) demonstrates that the shut-in protocol increases recovery more quickly than if the pressure cycle were used (S g =3% after approximately 8 days for shut in: S g =33% after 13 days for the full three-stage pressure cycle). a.5..35.3.5..15.1.5. IN(1) 1psi/day 1 3 5 6 7 8 b.5..35.3.5..15.1.5. IN(1) (1,1,1) I 6 8 c.5..35.3.5..15.1.5. IN(1) 1psi/day 6 8 1 1 1 Days d.5..35.3.5..15.1.5. IN(1) (1,1,1) 6 8 1 1 1 Days I Figure 5.5. Pressure history of following shut-in at 31psia (a); full repressurisation cycle (b); temporal evolution of following shut-in at 31psia (c); full repressurisation cycle (d); depletion at 1psi/day, (8x8x1, Dz=) How does a less well connected system compare? Figure 5.55(a-b) shows plots of free gas saturation from a poorly connected network (Dz=.66) as a function of pressure for the two protocols. Once again, shutting in and leaving the system to approach equilibrium gives better recovery (~% as opposed to ~%) but how long do the two protocols take to generate these values? Figure 5.55(c-d) shows that equilibration during shut-in takes approximately days to reach equilibrium (far longer than the Dz= case due to the presence of longer diffusion pathways), whereas the three-stage pressure cycle again takes 13 days to carry out. Note, however, that shutting in the system can generate % recovery after only ~75 days (~5 days of depletion followed by a ~3 day shut-in), and so, 38

even in this less connected system, shutting in without repressurising would appear to give optimal recovery compared to pressure cycle. a IN(1) (1,1,1) Z=.5..35.3.5..15.1.5. 1 3 5 6 7 8 b.5..35.3.5..15.1.5. IN(1) (1,1,1) Z= I 1 3 5 6 7 8 c.5..35.3.5..15.1.5. IN(1) Z= Shut In 5 5 75 1 15 15 175 5 5 Days d.5..35.3.5..15.1.5. IN (1) (1,1,1) I 5 5 75 1 15 15 175 5 5 Days Figure 5.55. Pressure history of following shut-in at 31psia (a); full repressurisation cycle (b); temporal evolution of following shut-in at 31psia (c); full repressurisation cycle (d); depletion at 1psi/day, (8x8x1, Dz=.66) Although the foregoing results point to the fact that shutting in may be preferable to carrying out a repressurisation/secondary depletion cycle, it is not clear whether this would be possible operationally. Any shut-in would generally be accompanied by some degree of simultaneous repressurisation and this has implications for recovery. As an example of simulating novel protocols, this section concludes by examining whether shutting in a network midway through primary depletion could increase recovery at abandonment. A simulation was run that incorporated base case parameters (oil, network, rates, etc.) but which incorporated a shut in period at psia during primary depletion. The evolution of the various variables is shown in Figure 5.56. As expected, the shut-in period allows the system time to approach equilibrium supersaturation approaches zero and the interfacial area increases monotonically and recovery is enhanced over the remaining pressure range (psia to 315psia) by between 11% and % (Figure 5.57). This far exceeds the 39

improvement seen in the base case pressure cycle, which could only manage a maximum increase of around 1%. The temporal evolution of gas saturation is given in Figure 5.58, which shows that, although the network was shut-in for days, a shut-in period of approximately 15 days would have been sufficient to give the same degree of additional recovery (a perfect example of the way in which the simulator can be used to optimise depletion strategies). IN(1) 1psi/day Shut In at psia.7.6.5..3..1. 1 3 5 6 7 8 Supersaturation (kg/m3) IN(1) 1psi/day Shut In at psia 5.5 3.5 3.5 1.5 1.5 1 3 5 6 7 8 Area (m) IN(1) 1psi/day Shut In at psia 1.E- 1.E- 1.E- 8.E-5 6.E-5.E-5.E-5.E+ 1 3 5 6 7 8 No. Gas Clusters IN(1) 1psi/day Shut In at psia 1.9.8.7.6.5..3..1 1 3 5 6 7 8 IN(1) 1psi/day Shut In at psia Mass of Gas (kg) 8.E-7 7.E-7 6.E-7 5.E-7.E-7 3.E-7.E-7 1.E-7.E+ 1 3 5 6 7 8 Figure 5.56. Pressure histories of gas saturation, supersaturation, gas-oil diffusion interface area, number of gas clusters and mass of free gas in bubbles. Primary depletion at 1psi/day, shut in at psia, followed by continued depletion, (8x8x1, Dz=)

IN(1) 1psi/day Shut In at psia.5 (ShutIn)-()..15.1.5. 1 3 5 6 7 8 Figure 5.57. Incremental oil recovery (fraction of OOIP) over primary depletion alone. Primary depletion at 1psi/day, shut in at psia, followed by continued depletion, (8x8x1, Dz=) IN(1) 1psi/day Shut In at psia.7.6.5..3..1. 1 3 Figure 5.58. Temporal evolution of gas saturation for shut-in at psia (for days) followed by continued depletion at 1psi/day, (8x8x1, Dz=) Days 5.3.1 Effect of increased bubble density The final sensitivity using the instantaneous nucleation algorithm centred upon the effect of increased bubble density at the start of primary depletion. Results from this section form a useful starting point for the analysis of pressure cycles incorporating progressive nucleation to be presented later. In order to assess the impact of increased bubble density, the base case simulation was repeated using four bubbles nucleated symmetrically in the network. Results are shown in Figure 5.59 and the corresponding snapshots are shown in Figure 5.6 and Figure 5.61. Increasing the bubble density to four results in no additional recovery compared with that obtained via primary depletion, although the increased bubble density does give better 1

overall recovery than the single bubble case (as expected), when primary and secondary recoveries of both cases are analysed separately. Supersaturation remains low compared to the single bubble case and the total number of daughter bubbles is far higher during repressurisation of the four bubble system. Interfacial area is consequently higher than the single bubble case during primary depletion and repressurisation, although this difference is greatly reduced during secondary depletion, as both simulations begin this phase of the cycle with similar bubble densities (approximately 3 bubbles). Snapshots of the four bubble simulation show that the main difference between primary and secondary depletion for the four bubble system is mainly due to a missing gas finger (circled in Figure 5.6), caused by the dissolution of one of the original bubble nuclei. As discussed in Section 5.3.3, the original nuclei should ideally be re-nucleated for accurate comparisons to be made between primary and secondary depletion, but it can be inferred that doing this would lead to the same conclusion namely, that increasing the bubble density to four results in little or no incremental recovery after a repressurisation/secondary-depletion cycle. The small sensitivity study presented here has only examined the impact of increased bubble density upon incremental recovery for one combination of rates (1,1,1) psi/day. In Section 5.3.1, the sensitivity will be extended considerably to look at a number of different rate combinations in the context of progressive nucleation.

IN() (1,1,1) IN() (1,1,1).5.5..35.3.5..15.1.5. I 1 3 5 6 7 8 Supersaturation (kg/m3) 3.5 1.5 1.5 I -.5 1 3 5 6 7 8-1 -1.5 IN() (1,1,1) IN() (1,1,1) Area (m) 1.E- 1.E- 8.E-5 I 6.E-5.E-5.E-5.E+ 1 3 5 6 7 8 No. Gas Clusters 1 9 8 7 6 5 3 1 I 1 3 5 6 7 8 IN() (1,1,1) Mass of Gas (kg) 7.E-7 6.E-7 5.E-7 I.E-7 3.E-7.E-7 1.E-7.E+ 1 3 5 6 7 8 Figure 5.59. Pressure histories of gas saturation, supersaturation, gas-oil diffusion interface area, number of gas clusters and mass of free gas in bubbles. Rates (,, I) = (1, 1, 1) psi/day. bubbles instantaneously nucleated symmetrically in network, (8x8x1, Dz=) 3

Figure 5.6. Gas-oil occupancies showing growth and collapse of gas for the full pressure cycle. Rates (,, I) = (1, 1, 1) psi/day. bubbles nucleated, (8x8x1, Dz=)

Figure 5.61. R s contours for the full pressure cycle for a single nucleated bubble; Rates (,, I) = (1, 1, 1) psi/day. bubbles nucleated symmetrically, (8x8x1, Dz=) 5

5.3.11 Progressive nucleation (Large nucleation density) Repressurisation involving the instantaneous nucleation (IN) has been presented in foregoing sections of this chapter. This section therefore focuses on investigating the effects of repressurisation rate and other inherent properties of the porous medium on improving recovery from network adopting oil properties presented in ( Table 5-1) and progressive nucleation model after Yortsos and Parlar (1989) and Li and Yortsos (1991). Gas-oil diffusivity for heavy oils is generally smaller compared to light oils and, during the early stage of depressurisation, the low gas-oil diffusivity may increase the local nonequilibrium state of the oil pores far from the bubble leading to further increase in average supersaturation. Hence a progressive nucleation model may represent more accurately the nucleation process in the heavy oil porous network. In the following sections, a Raleigh distribution function was used to randomly distribute nucleation sites (cavities) in oil pores. The cavity density was chosen to be 1/ (1 cavity per pores). The network was firstly depressurised by psi at a rate of 1psi/day. Repressurisation to the initial bubble point pressure at 1psi/day was followed by a second depressurisation at 1psi/day, thereby completing a pressure cycle. During the early stages of primary depressurisation, the average gas concentration remains fairly constant and above that predicted by equilibrium PVT (Figure 5.6). Figure 5.63 shows the cavity distribution histogram for the network. The first bubble was nucleated after 11psi of depletion (Figure 5.6a), providing a sink for mass transfer from the supersaturated oil. Due to the high nucleation density, many nucleation sites were activated resulting in a steep decline in the average concentration in oil. A total of 17 bubbles were nucleated during the primary depressurisation. 6

Figure 5.6. Average and equilibrium PVT concentrations in oil as functions of pressure, 1-1-1 psi/day, (8x8x1, Dz=). [Note that concentration = Rs] 9 8 7 6 5 f(r) 3 1.E+.E-8.E-8 6.E-8 8.E-8 1.E-7 1.E-7 r(micron) Figure 5.63. Cavity distribution following a Rayleigh function The early stages of repressurisation are characterised by average supersaturation quickly declining to near zero (Figure 5.6b) and this is followed by a long intermediate phase, where the average remains close to the equilibrium line. During the latter stages of repressurisation, the average supersaturation once again moves away from the equilibrium line. The steep decline in average supersaturation seen during the early stages can be attributed to the combined effects of large concentration gradients and the large surface area of the gas-oil interface (Figure 5.6c). The intermediate phase represents the period when the gas-oil interface area remains relatively large while the mass flux rate gradually decreases due to smaller concentration gradients. Figure 5.6(d) also shows that although the total number of gas clusters increases during the intermediate phase, the effective gasoil diffusion area continued to decline at higher rate and may explain the fairly gentle 7

decline in supersaturation during this phase. The average concentration in oil at the end of repressurisation was lower than that predicted by PVT at the initial bubble point pressure. As mentioned earlier, the network composition is not simply reversed during repressurisation indeed previous authors have reported the irreversible nature of bubble dissolution (Dunn and Mehrotra, 1995). Figure 5.65 shows that distinct individual concentration contours exist during the early stages of primary depressurisation and that these contours eventually meet at lower pressures. During repressurisation, higher dissolved gas concentrations emerge around the gas clusters (dark blue colour) due to mass flux from gas clusters into the surrounding oil. Concentration contours at different pressures during, and I can be compared and demonstrate that gas evolution (nucleation and growth by drainage) and re-dissolution (collapse and shrinkage by imbibition) in a porous medium are not simply the reverse of one another. Note also, that the topological structure of the gas cluster is different when and I are compared at equivalent pressures (Figure 5.66). Non-zero gas saturation at the end of repressurisation, (Figure 5.67), is indicative of the undersaturated state of the network and the early stages of secondary depressurisation are characterised by a very steep build up in gas saturation, resulting in higher recovery when compared with primary depressurisation at the same pressure. However, the converse is true after 6psi of depletion recovery actually appears to be worse during secondary depletion (even though an additional 8 bubbles were nucleated, see Figure 5.6). Considering the small size of the network, it is likely that for a nucleation density of 1 cavity per oil pores, any additional increase in effective bubble density resulting from gas break-up during repressurisation would give little additional recovery after secondary depletion. However, this base case progressive nucleation simulation utilises only one combination of depletion and repressurisation rates. To fully investigate the impact of repressurisation upon incremental recovery, a full suite of simulations is required using a range of different rate combinations. This is explored in the following section. 8

PN_1-1-1 PN_1-1-1 3 Nucleated bubbles 5 15 1 5 Supersaturation(psi) 15 1 5 I 1 3 5-5 7 6 5 3 38 8 58 68 7 6 5 3-1 Pb- (a) (b) PN_1-1-1 PN_1-1-1 G-O Diff Xsectional area 1.E- 1.E- 8.E-5 6.E-5.E-5.E-5.E+ I 6 8 MinGOXarea No. of gas clusters 1 1 1 8 6 I 3 5 6 7 8 (c) (d) Figure 5.6. Pressure history of cumulative nucleated bubbles during pressure cycling (a); Average supersaturation (b); Gas-oil diffusion area (c); Total number of gas clusters in the network (d), (8x8x1, Dz=) 9

P =75 psi P =75 psi P =9 psi P=53 psi P =9 psi P =3 psi P =psi P = 3psi P =36 psi P =36 psi P =36 psi P =31 psi P =31 psi Rs Figure 5.65. Dissolved gas concentration contours in the network at various pressures during the cycle for progressive nucleation. Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=) 5

P = 75psi P = 75psi P = 9psi P = 53psi P = 9psi P=3psi P=psi P=3psi P=36psi P=36psi P=36psi P=31psi P=31psi Figure 5.66. Gas-oil occupancies in the network at various pressures during the cycle for progressive nucleation. Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=) 51

PN_1-1-1.6.5..3..1 I. 6 8 Figure 5.67. Gas saturation build-up in the network. Progressive nucleation; Rates (,, I) = (1, 1, 1) psi/day, (8x8x1, Dz=) 5.3.1 Rate combinations adopting progressive nucleation A suite of twenty seven (7) simulation combining three different rates was designed to investigate the effect of rate combination upon secondary recovery. Table 5- summarises 7 rate combinations used. Simulation cycles with a primary depressurisation rate of 1psi/day seem to give the most promising secondary recovery, while cycles using a 1psi/day primary depressurisation rate resulted in the worst secondary recovery. Figure 5.68 (a) shows the gas saturation behaviour for cycle label 9 in Table 5-. Additional recovery of 8% (at 31psi) was calculated as a result of carrying out a repressurisation/secondary depletion cycle for this case. Figure 5.68(b) shows that gas break-up also occurred in the model during repressurisation. In contrast to the simulation at --I of 1-1-1psi/day (see Figure 5.6(b)); the system remained highly supersaturated here, at the end of primary depressurisation (Figure 5.68(c) and Figure 5.68Figure 5.3(d)). It is the large amount of dissolved gas still in solution that contributes to increased expansion and growth of gas clusters during I for cycle 9, resulting in higher secondary recovery. Repressurisation may therefore be more effective when started at a high supersaturation and performed at a high rate. Comparing cycles 7, 8 & 9, a trend emerges that suggests better recovery for cases where a high 5

repressurisation rate is followed by a low secondary depressurisation rate. This may be network and fluid specific, however, and requires additional study. Table 5-: Rate combinations for the full repressurisation cycle case# (31psi) (75psi) I (31psi) (I-) 31psi - (%) Rate (psi/day) 1 1 1 1 +13.5 1 1 1 +13.3 3 1 1 1-1. 1 1 1 +19.1 5 1 1 1 +18.8 6 1 1 1-5.6 7 1 1 1 +1.8 8 1 1 1 +.8 9 1 1 1 +8. 1 1 1 1-1.6 11 1 1 1-7.5 1 1 1 1 -.6 13 1 1 1 +1. 1 1 1 1-3. 15 1 1 1-1.8 16 1 1 1 -.3 17 1 1 1 -.9 18 1 1 1-8.3 19 1 1 1-1.7 1 1 1-6.6 1 1 1 1 -. 1 1 1 -.1 3 1 1 1-3.7 1 1 1-16.1 5 1 1 1 +. 6 1 1 1 -. 7 1 1 1-7.5 53

Gas saturation and concentration profiles for the full suite of 7 simulation runs are presented in Figure 5.69 to Figure 5.7 a rich pattern of hysteresis behaviour is observed. For the sake of brevity, a case-by case analysis of each plot is not presented here, although each is clearly interpretable by considering the methods used in earlier sections. PN_1-1-1.35.3.5..15.1.5. 1 3 5 6 7 8 (a) I No. of gas clusters 1 8 6 PN_1-1-1 I 6 8 (b) 1 1 Cav Ceq PN_1-1-1 Concentration(kg/m3) 1 8 6 I 3 5 6 7 8 (c) (d) Figure 5.68. Pressure history of gas saturation (a); Number of gas clusters in the network (b); Average concentration and PVT equilibrium concentration in the oil (c); Dissolved gas concentration after psi depletion (d); (1-1-1 psi/day), (8x8x1, Dz=) 5