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- Artificial Intelligence (1)
- bourbiaux (1)
- capillary back pressure (1)
- capillary backpressure (2)
- capillary pressure (2)
- cocurrent (1)
- cocurrent spontaneous (1)
- conventional model (2)
- countercurrent (2)
- countercurrent flow (1)
- countercurrent production (1)
- enhanced recovery (3)
- equation (1)
- flow in porous media (3)
- Fluid Dynamics (3)
- generalized model (2)
- imbibition (2)
- interaction (2)
- mobility (2)
- relative permeability (2)
- saturation (2)
- spontaneous imbibition (2)
- Upstream Oil & Gas (3)
- viscosity (2)
- viscous coupling (3)

**File Type**

This paper presents a numerical study of water displacing oil using combined cocurrent/countercurrent spontaneous imbibition (SI) of water displacing oil from a water-wet matrix block exposed to water on one side and oil on the other. Countercurrent flows can induce a stronger viscous coupling than during cocurrent flows, leading to deceleration of the phases. Even as water displaces oil cocurrently, the saturation gradient in the block induces countercurrent capillary diffusion. The extent of countercurrent flow may dominate the domain of the matrix block near the water-exposed surfaces while cocurrent imbibition may dominate the domain near the oil-exposed surfaces, implying that one unique effective relative permeability curve for each phase does not adequately represent the system. Because relative permeabilities are routinely measured cocurrently, it is an open question whether the imbibition rates in the reservoir (depending on a variety of flow regimes and parameters) will in fact be correctly predicted. We present a generalized model of two-phase flow dependent on momentum equations from mixture theory that can account dynamically for viscous coupling between the phases and the porous media because of fluid/rock interaction (friction) and fluid/fluid interaction (drag). These momentum equations effectively replace and generalize Darcy’s law. The model is parameterized using experimental data from the literature.

We consider a water-wet matrix block in one dimension that is exposed to oil on one side and water on the other side. This setup favors cocurrent SI. We also account for the fact that oil produced countercurrently into water must overcome the so-called capillary backpressure, which represents a resistance for oil to be produced as droplets. This parameter can thus influence the extent of countercurrent production and hence viscous coupling. This complex mixture of flow regimes implies that it is not straightforward to model the system by a single set of relative permeabilities, but rather relies on a generalized momentum-equation model that couples the two phases. In particular, directly applying cocurrently measured relative permeability curves gives significantly different predictions than the generalized model. It is seen that at high water/oil-mobility ratios, viscous coupling can lower the imbibition rate and shift the production from less countercurrent to more cocurrent compared with conventional modeling. Although the viscous-coupling effects are triggered by countercurrent flow, reducing or eliminating countercurrent production by means of the capillary backpressure does not eliminate the effects of viscous coupling that take place inside the core, which effectively lower the mobility of the system. It was further seen that viscous coupling can increase the remaining oil saturation in standard cocurrent-imbibition setups.

bourbiaux, capillary backpressure, capillary pressure, cocurrent, conventional model, countercurrent, enhanced recovery, equation, flow in porous media, Fluid Dynamics, generalized model, imbibition, interaction, mobility, relative permeability, saturation, Upstream Oil & Gas, viscosity, viscous coupling

SPE Disciplines:

This paper presents a numerical study of water displacing oil using combined cocurrent/countercurrent spontaneous imbibition (SI) of water displacing oil from a water-wet matrix block exposed to water on one side and oil on the other. Countercurrent flows can induce a stronger viscous coupling than during cocurrent flows, leading to deceleration of the phases. Even as water displaces oil cocurrently, the saturation gradient in the block induces countercurrent capillary diffusion. The extent of countercurrent flow may dominate the domain of the matrix block near the water-exposed surfaces while cocurrent imbibition may dominate the domain near the oil-exposed surfaces, implying that one unique effective relative permeability curve for each phase does not adequately represent the system. Because relative permeabilities are routinely measured cocurrently, it is an open question whether the imbibition rates in the reservoir (depending on a variety of flow regimes and parameters) will in fact be correctly predicted. We present a generalized model of two-phase flow dependent on momentum equations from mixture theory that can account dynamically for viscous coupling between the phases and the porous media because of fluid/rock interaction (friction) and fluid/fluid interaction (drag). These momentum equations effectively replace and generalize Darcy’s law. The model is parameterized using experimental data from the literature.

We consider a water-wet matrix block in one dimension that is exposed to oil on one side and water on the other side. This setup favors cocurrent SI. We also account for the fact that oil produced countercurrently into water must overcome the so-called capillary backpressure, which represents a resistance for oil to be produced as droplets. This parameter can thus influence the extent of countercurrent production and hence viscous coupling. This complex mixture of flow regimes implies that it is not straightforward to model the system by a single set of relative permeabilities, but rather relies on a generalized momentum-equation model that couples the two phases. In particular, directly applying cocurrently measured relative permeability curves gives significantly different predictions than the generalized model. It is seen that at high water/oil-mobility ratios, viscous coupling can lower the imbibition rate and shift the production from less countercurrent to more cocurrent compared with conventional modeling. Although the viscous-coupling effects are triggered by countercurrent flow, reducing or eliminating countercurrent production by means of the capillary backpressure does not eliminate the effects of viscous coupling that take place inside the core, which effectively lower the mobility of the system. It was further seen that viscous coupling can increase the remaining oil saturation in standard cocurrent-imbibition setups.

Andersen, Pål Østebø (Dept. of Energy Resources, University of Stavanger, The National IOR Centre of Norway, University of Stavanger) | Qiao, Yangyang (Dept. of Energy and Petroleum Technology, University of Stavanger) | Standnes, Dag Chun (Dept. of Energy Resources, University of Stavanger) | Evje, Steinar (The National IOR Centre of Norway, University of Stavanger, Dept. of Energy and Petroleum Technology, University of Stavanger)

This paper presents a numerical study of water displacing oil by combined co-current / counter-current spontaneous imbibition (SI) of water displacing oil from a water-wet matrix block exposed to water at one side and oil at the other. Counter-current flows can induce a stronger viscous coupling than during co-current flows leading to deceleration of the phases. Even as water displaces oil co-currently the saturation gradient in the block induces counter-current capillary diffusion. The extent of counter-current flow may dominate the domain of the matrix block near the water-exposed surfaces, while co-current imbibition may dominate the domain near the oil-exposed surfaces implying that one unique effective relative permeability curve for each phase does not adequately represent the system. As relative permeabilities are routinely measured co-currently it is an open question whether the imbibition rates in the reservoir (depending on a variety of flow regimes and parameters) will in fact be correctly predicted. We present a generalized two phase flow model based on momentum equations from mixture theory that can account dynamically for viscous coupling between the phases and the porous media due to fluid-rock interaction (friction) and fluid-fluid interaction (drag). These momentum equations effectively replace and generalize Darcy's law. The model is parameterized using experimental data from the literature.

We consider a water-wet matrix block in 1D that is exposed to oil on one side and water on the other side. This setup favors co-current SI. We also account for the fact that oil produced counter-currently into water must overcome the socalled capillary back pressure, which represents a resistance for oil to be produced as droplets. This parameter can thus influence the extent of counter-current production and hence, viscous coupling. This complex mixture of flow regimes implies that it is not straightforward to model the system by a single set of relative permeabilities, but rather relies on a generalized momentum equation model that couples the two phases. In particular, directly applying co-currently measured relative permeability curves gives significantly different predictions than the generalized model. It is seen that at high water-to-oil mobility ratios, viscous coupling can lower the imbibition rate and shift the production from less counter-current to more co-current as compared to conventional modelling. Although the viscous coupling effects are triggered by counter-current flow, reducing or eliminating counter-current production via the capillary back pressure does not eliminate the effects of viscous coupling that take place inside the core, which effectively lower the mobility of the system. It was further seen that viscous coupling can increase the remaining oil saturation in standard co-current imbibition setups.

Artificial Intelligence, capillary back pressure, capillary pressure, conventional model, countercurrent, countercurrent flow, countercurrent production, enhanced recovery, flow in porous media, Fluid Dynamics, generalized model, imbibition, interaction, mobility, relative permeability, saturation, spontaneous imbibition, Upstream Oil & Gas, viscosity, viscous coupling

SPE Disciplines:

Thank you!