A Critical Review for Proper Use of Water/Oil/Gas Transfer Functions in Dual-Porosity Naturally Fractured Reservoirs: Part II
- Mohammed Al-kobaisi (Colorado School of Mines) | Hossein Kazemi (Colorado School of Mines) | Benjamin Ramirez (Marathon Oil Co.) | Erdal Ozkan (Colorado School of Mines) | Safian Atan (Marathon Oil Co.)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- April 2009
- Document Type
- Journal Paper
- 211 - 217
- 2009. Society of Petroleum Engineers
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- 1,422 since 2007
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This paper continues the work presented in Ramirez et al. (2009). In Part I, we discussed the viability of the use of simple transfer functions to accurately account for fluid exchange as the result of capillary, gravity, and diffusion mass transfer for immiscible flow between fracture and matrix in dual-porosity numerical models. Here, we show additional information on several relevant topics, which include (1) flow of a low-concentration water-soluble surfactant in the fracture and the extent to which the surfactant is transported into the matrix; (2) an adjustment to the transfer function to account for the early slow mass transfer into the matrix before the invading fluid establishes full connectivity with the matrix; and (3) an analytical approximation to the differential equation of mass transfer from the fracture to the matrix and a method of solution to predict oil-drainage performance.
Numerical experiments were performed involving single-porosity, fine-grid simulation of immiscible oil recovery from a typical matrix block by water, gas, or surfactant-augmented water in an adjacent fracture. Results emphasize the viability of the transfer-function formulations and their accuracy in quantifying the interaction of capillary and gravity forces to produce oil depending on the wettability of the matrix. For miscible flow, the fracture/matrix mass transfer is less complicated because the interfacial tension (IFT) between solvent and oil is zero; nevertheless, the gravity contrast between solvent in the fracture and oil in the matrix creates convective mass transfer and drainage of the oil.
Characterization and quantification of fractures in naturally fractured reservoirs is a very difficult task; nonetheless, when natural fractures contribute significantly to fluid movement and hydrocarbon drainage in the reservoir, a dual-porosity approach is adopted to quantify reservoir performance. The dual-porosity concept can be perceived and quantified in several ways, as shown in Fig. 1.
The dual-porosity concept was conceived on the premise that a very highly conductive fracture medium was formed as an interconnected network of secondary porosity within a pre-existing porous rock of primary porosity. A third medium of lower-conductivity fractures (i.e., microfractures) can be added to the flow system in some important applications. Regardless of the formulation, the flow in the high-conductivity fracture network takes place at high velocities from one grid cell to another irrespective of the flowing phase. In two- or three-phase flow, there is usually a local exchange of fluids between the fractures and the adjacent matrix at comparatively low velocities. Contrast in fluid velocities in the two flow systems is a very important issue in naturally fractured reservoirs because, in multiphase flow, typically water or gas can move rapidly in the fractures and surround the matrix blocks partially or totally. Once a matrix block is surrounded partially or totally by a particular fluid, then transfer of fluid phases and components takes place between the fracture and matrix. Deciphering the recovery mechanisms and describing the pertinent equations of mass transfer constitute the heart of this paper--both Part I (Ramirez et al. 2009) and Part II. Similar issues extend to any variants of the dual-porosity concept, such as the triple-porosity, irrespective of the idealization concept.
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