TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractThe paper describes an integrated pore-to-field scale modeling method of multiphase flow in porous media. Although the method is general, we demonstrate its power and versatility by modeling a WAG process in the Etive formation in a North Sea oil field. The method aims at capturing the relevant flow physics at different scales. Pore scale physics (µm-scale) is accounted for through predictive pore scale modeling of relative permeability and capillary pressure. The computed rock curves (cm-scale) are used to populate detailed geological models with a plausible spatial distribution of constitutive relations. Effective flow properties at the heterogeneous facies scale (m-scale) are determined by a steady state upscaling technique. Finally, the effective flow properties are implemented in a field scale (km-scale) simulation model. The simulation results show that the effective flow properties describe the reservoir WAG performance fairly accurately without any adjustment through history matching.
High-velocity pressure loss in Bentheimer sandstone fractures of varying fracture widths was studied. Direct measurements of the roughness showed that the fractures are self-affine. The new results support a rough fracture high-velocity pressure-loss model. The highvelocity pressure loss was described by a Forchheimer equation with a dominating square term. The square term is a power law in fracture width, and the power is given by a roughness exponent. For low velocities, the pressure loss was not described by the Forchheimer equation. In agreement with theory, a weak-inertia-flow regime exists that separates the Darcy-flow regime from the Forchheimer-flow regime. An expression for the incremental high-velocity skin of a pinched-out hydraulic fracture was derived. Asymptotically for small fracture widths the skin is a power law in fracture width.
In this study we measured high-velocity pressure loss over Bentheimer sandstone fractures with varying fracture widths. Direct measurements of theroughness showed that the fractures were self-affine. The new results support the rough fracture high-velocity pressure loss model. The high-velocity pressure loss was described by a Forchheimer equation with a dominating square term. The square term is a power law in fracture width, and the power is given by a roughness exponent. For low velocities the pressure loss was not described by the Forchheimer equation. In agreement with theory, there exists a weak inertia flow regime, which separates the Darcy flow regime from the Forchheimer flow regime. An expression for the incremental high-velocity skin of a pinched-out hydraulic fracture was derived. The skin is a power law in fracture width.
Saturation histories from simulations on a mesoscopic-scale heterogeneous model at immiscible and miscible conditions are compared with emphasis on gas segregation. Selected models for three-phase flow, and scaling of the end point saturations, relative permeabilities, and capillary pressures have been applied. The flow parameters of the facies were obtained from pore scale network modeling with input from North Sea sandstones. The simulation cases included water, gas, and water-alternating-gas (WAG) injection. Gas injection at irreducible water saturation demonstrates stronger gas segregation as the pressure exceeds the minimum miscibility pressure (MMP). Gas segregation is not so evident at the mesoscopic scale during WAG injection. High water saturation in the set-planes hampers the vertical gas flow. A bank of high oil saturation forms in front of the advancing gas at miscible conditions. Oil segregates to the set-plane below and the water cycle that follows mobilizes the accumulated oil. Introduction WAG and simultaneous water and gas (SWAG) injection have been successfully applied for several North Sea oil fields. 1–4 WAG has, in most cases, been implemented at a later stage of production as an improved recovery process after a long period of water injection. Both immiscible and miscible WAG injections have been applied. Increased recoveries by WAG have been attributed to improved sweep, reduction in residual oil saturation by gas flooding after a water flood, and compositional mass exchange between gas and oil such as swelling and vaporization. In a recent review article of reported worldwide field applications of WAG,5 the increased oil recovery was found to be in the range of 5 to 10% of the original oil in place. Recovery from attic oil or unswept oil of a dipping reservoir may be the most important target for WAG injection. Segregation of gas towards the top of the reservoir is expected to be a fast process in good quality reservoirs with high vertical permeability, high gas mobility, and strong gravity buoyancy for gas. However, low permeable heterogeneities with high capillary entry pressures will hamper immiscible gas to segregate. When approaching miscibility, such as in a multi-contact miscible process, the interfacial tension (IFT) between oil and gas becomes very small. The gas-oil capillary pressure is also reduced, and will vanish if miscible conditions are reached. Experiments have shown that there is an influence on relative permeability and residual saturations at low IFT values. 6 Tracking of the IFT at the gas front by correct fluid modeling is important close to miscibility. Immiscible WAG injection is associated with three-phase flow. WAG flooding under first contact miscible conditions is a two-phase flow situation where water and a single hydrocarbon phase are flowing. The transition from a three-phase gas, oil and water system to a two-phase hydrocarbon and water system must be modeled smoothly and continuously in the vicinity of miscibility. In this work we study gas segregation in a mesoscopic scale heterogeneous simulation model with low permeability layers (cross bedding) at immiscible and miscible conditions. Capillary forces, gravity forces and viscous forces are all expected to be important on this scale. The heterogeneous pattern is based on a North Sea reservoir formation. In ordinary reservoir simulations such heterogeneities are upscaled to a single homogeneous block. Relative permeabilities and capillary pressures of the individual rock types were estimated using a novel approach based on pore scale network modeling. 7,8
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