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We have extended an existing streamline simulator (Batycky et al., SPE Reserv Eng 12(4):246-254, 1997) that considered two phases (aqueous and hydrocarbon) and two components (water and oil) to handle three-phase (aqueous, hydrocarbon, and solid), fourcomponent (water, oil, CO 2 , and salt) transport applied to CO 2 injection. We solved CO 2 transport equations in the hydrocarbon and aqueous phases along streamlines and in the direction of gravity. To capture the physics of CO 2 transport, in the hydrocarbon phase, we used the Todd-Longstaff model (Todd and Longstaff, J Pet Technol 24 (7): [874][875][876][877][878][879][880][881][882] 1972) to represent subgridblock viscous fingering. We implemented a thermodynamic model of mutual dissolution between CO 2 and water with salt precipitation (Spycher et al., Geochim Cosmochim Acta 67 (16): [3015][3016][3017][3018][3019][3020][3021][3022][3023][3024][3025][3026][3027][3028][3029][3030][3031] 2003; Spycher and Pruess, Geochim Cosmochim Acta 69 (13): [3309][3310][3311][3312][3313][3314][3315][3316][3317][3318][3319][3320] 2005). The resultant changes in porosity and permeability due to chemical reaction and salt precipitation were also considered. We accounted for two cycles of relative permeability hysteresis (primary and secondary drainage and imbibition) by applying two different trapping models: Land (SPE J 8:149-156, 1968) and Spiteri et al. (SPE J 13(3):277-288, 2008).Relative permeability changes and variations in the trapped nonwetting phase saturations due to hysteresis were updated on a block-by-block basis. We verified our simulator by comparing one-dimensional simulation results with analytical solutions. We then performed simulations on three-dimensional reservoir models. We first simulated dry CO 2 injection in an aquifer to investigate the effect of salt precipitation. After 2 years of CO 2 injection, the permeability reduced by approximately 20%. We then used the simulator to design CO 2 injection strategies in aquifers to maximize CO 2 storage and in oil reservoirs to optimize both CO 2 storage and oil recovery. Simulations were conducted on a North Sea reservoir description. We propose to inject CO 2 and water simultaneously, followed by chase brine injection, which could render the majority of CO 2 injected immobile while giving a much higher storage efficiency than injecting CO 2 alone.
We have extended an existing streamline simulator (Batycky et al., SPE Reserv Eng 12(4):246-254, 1997) that considered two phases (aqueous and hydrocarbon) and two components (water and oil) to handle three-phase (aqueous, hydrocarbon, and solid), fourcomponent (water, oil, CO 2 , and salt) transport applied to CO 2 injection. We solved CO 2 transport equations in the hydrocarbon and aqueous phases along streamlines and in the direction of gravity. To capture the physics of CO 2 transport, in the hydrocarbon phase, we used the Todd-Longstaff model (Todd and Longstaff, J Pet Technol 24 (7): [874][875][876][877][878][879][880][881][882] 1972) to represent subgridblock viscous fingering. We implemented a thermodynamic model of mutual dissolution between CO 2 and water with salt precipitation (Spycher et al., Geochim Cosmochim Acta 67 (16): [3015][3016][3017][3018][3019][3020][3021][3022][3023][3024][3025][3026][3027][3028][3029][3030][3031] 2003; Spycher and Pruess, Geochim Cosmochim Acta 69 (13): [3309][3310][3311][3312][3313][3314][3315][3316][3317][3318][3319][3320] 2005). The resultant changes in porosity and permeability due to chemical reaction and salt precipitation were also considered. We accounted for two cycles of relative permeability hysteresis (primary and secondary drainage and imbibition) by applying two different trapping models: Land (SPE J 8:149-156, 1968) and Spiteri et al. (SPE J 13(3):277-288, 2008).Relative permeability changes and variations in the trapped nonwetting phase saturations due to hysteresis were updated on a block-by-block basis. We verified our simulator by comparing one-dimensional simulation results with analytical solutions. We then performed simulations on three-dimensional reservoir models. We first simulated dry CO 2 injection in an aquifer to investigate the effect of salt precipitation. After 2 years of CO 2 injection, the permeability reduced by approximately 20%. We then used the simulator to design CO 2 injection strategies in aquifers to maximize CO 2 storage and in oil reservoirs to optimize both CO 2 storage and oil recovery. Simulations were conducted on a North Sea reservoir description. We propose to inject CO 2 and water simultaneously, followed by chase brine injection, which could render the majority of CO 2 injected immobile while giving a much higher storage efficiency than injecting CO 2 alone.
Streamline methods are gaining popularity in the industry by providing fast desktop simulation of large reservoir models or multiple realizations. Traditionally, streamline simulation has been associated with simplified physics, but recent advances have demonstrated its potential also for compressible three-phase or component flows. However, streamline simulation is still most efficient for two-phase incompressible flow, for which one can utilize a particularly efficient front-tracking method to solve 1-D transport equations along streamlines that is unconditionally stable and independent of the strongly irregular time-of-flight grid. In a recent paper (Nilsen and Lie 2008), we presented, for the first time, front-tracking methods for simulating 1-D compressible two-phase flow. We also developed two methods that were particularly efficient for solving compressible flow in which one phase is incompressible, motivated by the simulation of CO 2 injection. Here we apply these methods to streamline simulation of 3-D models, including a real-life model of a North Sea formation, which is under consideration as a potential target for CO 2 deposition. Our numerical results demonstrate that streamlines and front tracking together give very efficient simulation of compressible flow. Similar ideas can also be applied for dual-porosity models, but this is not investigated in great detail herein.
Streamline and streamtube methods have been used in fluid flow computations for many years. Early applications for hydrocarbon reservoir simulation were first reported by Fay and Pratts in the 1950s. Streamline-based flow simulation has made significant advances in the last 15 years. Today's simulators are fully three-dimensional and fully compressible and they account for gravity as well as complex well controls. Most recent advances also allow for compositional and thermal displacements. In this paper, we present a comprehensive review of the evolution and advancement of streamline simulation technology. This paper offers a general overview of most of the material available in the literature on the subject. This work includes the review of more than 200 technical papers and gives a chronological advancement of streamline simulation technology from 1996 to 2011. Firstly, three major areas are identified. These are development of streamline simulators, enhancements to current streamline simulators and applications. In view of the fact that this state of-the-art technology has been employed for a wide range of applications, we defined three major application areas that symbolize the relevance and validity of streamline simulation in addressing reservoir engineering concerns. These are history matching, reservoir management and upscaling, ranking and characterization of fine-grid geological models. Streamline simulation has undergone several phases within its short stretch in the petroleum industry. Initially, the main focus was on the speed advantage and less on fluid flow physics. Next, the focus was shifted to extend its applicability to more complex issues such as compositional and thermal simulations, which require the inclusion of more physics, and potentially reducing the advantage of computational time. Recently, the focus has shifted towards the application of streamline technologies to areas where it can complement finite difference simulation such as revealing important information about drainage areas, flood optimization and improvement of sweep efficiency, quantifying uncertainties, etc.
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