Summary
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.
Introduction
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.
© 2009. Society of Petroleum Engineers
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History
- Original manuscript received:
1 August 2007
- Meeting paper published:
4 December 2007
- Revised manuscript received:
23 October 2008
- Manuscript approved:
24 October 2008
- Published online:
15 April 2009
- Version of record:
15 April 2009
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