Percolation theory of two-phase relative permeability

Conference · Wed Sep 01 04:00:00 EDT 1982 · Soc. Pet. Eng. AIME, Pap.; (United States)

OSTI ID:5455297

Heiba, A A; Davis, H T; Sahimi, M; Scriven, L E

Fluid distributions and flow through the pore space of reservoir rock depend not only on pore sizes and shapes but also on local pore connectivity, i.e. topology. This topology can be described in terms of the network concept of coordination, which is central in most of the development to date of the percolation theory of transport in chaotic media, a theory advanced by Larson et al. for multiphase flow in porous media. The transport-path accessibility function from percolation theory summarizes the topological aspects of porespace important to describing the capillarity-controlled spatial distributions of two fluids; the transport-path conductivity function summarizes the topological aspects of porespace important to describing the creeping flow of two fluids, each continuously connected in a distinct set of channels. From these functions, and statistical distributions of pore configurations, the authors derive general formulas for the drainage and imbibition relative permeabilities of two phases, one of which is completely wetting. Inputs required for calculations are a network analog of pore connectivity, or the coordination number of its Cayley or Bethe tree approximation (for which the accessibility and conductivity functions can be evaluated in closed form); and distributions of flowcontrolling and inventory-controlling pore dimensions. Results for Bethe tree approximations to pore topology, and for several simple statistical distributions of pore dimensions, agree well with all the features of oil and water relative permeabilities reported for Berea sandstones. The theory is so founded that it can be extended in consistent ways to two-phase relative permeability when neither phase is completely wetting, and to the phase relative permeabilities.

• Research Organization: University of Minnesota
• OSTI ID: 5455297
• Report Number(s): CONF-820927-
• Conference Information: Journal Name: Soc. Pet. Eng. AIME, Pap.; (United States) Journal Volume: SPE11015
• Country of Publication: United States
• Language: English

Related Subjects

02 PETROLEUM
020200* -- Petroleum-- Reserves
Geology
& Exploration
42 ENGINEERING
420400 -- Engineering-- Heat Transfer & Fluid Flow
CALCULATION METHODS
CRYSTAL STRUCTURE
DISTRIBUTION
DRAINAGE
FLUID FLOW
FLUID MECHANICS
FLUIDS
HYDRAULIC CONDUCTIVITY
MATHEMATICS
MECHANICS
MICROSTRUCTURE
OIL WELLS
PERMEABILITY
POROSITY
RESERVOIR FLUIDS
RESERVOIR ROCK
ROCK-FLUID INTERACTIONS
ROCKS
SANDSTONES
SEDIMENTARY ROCKS
SPATIAL DISTRIBUTION
TOPOLOGY
TWO-PHASE FLOW
WELLS
WETTABILITY