Single-Phase Flow Through Natural Fractures

Abstract

Abstract It is well known that for a single-phase fluid flowing between smooth parallel plates, the pressure drop is proportional to the cube of the aperture separating the plates. Some investigators have looked at the effect of surface roughness on flow using fabricated surfaces, induced fractures, or saved surfaces and have found deviation from that law at small apertures. This paper presents new laboratory data for single-phase flow through open rough natural fractures. Two types of petroleum reservoir rocks (sandstones and cherts) were used, each having a different surface roughness. Flow through both open and closed fractures is evaluated with apertures ranging between 0.002 to 0.0253 in. A technique for measuring apertures in-situ has been developed which avoids backcalculating apertures from flow data, as other investigators have had to do. Fluids with viscosities of about 1 and 18 cp were used. At large apertures (0.0253 in), compared to the surface roughness, the cubic law is followed; at smaller apertures for rough fractures, deviation is seen. Transition from laminar to turbulent flow is smooth but is dependent on surface roughness for smaller fracture apertures. Critical Reynolds Number, the Reynolds Number where laminar flow ends, is seen to decrease with decreasing fracture aperture for rough fractures. Data are correlated using plots of friction factor versus Reynolds Number. Introduction Many reservoirs are fractured to some degree. These natural fractures may have substantial or little contribution to the overall flow characteristics of a reservoir. depending on the difference between the matrix and fracture permeabilities and the number of fractures. In reservoirs having good matrix porosity and permeability, production contributed by fractures may be so insignificant that fractures in the matrix are undetected. In other fractured reservoirs which have low matrix permeability, fracture permeabilities may contribute most of the fluid flow and control fluid production. A reservoir fracture system is a complex matrix of interconnecting and non-connecting fractures. A complete understanding of single and multi-phase flow is currently precluded by the lack of experimentally derived equations for flow in fractured channels or across a fracture/matrix interface. Before these multiple fracture cases can be considered, flow through a single fracture must first be understood. Flow in a fracture is normally characterized by using the classical cubic law equation (Witherspoon et al) for steady-state isothermal, laminar flow between two parallel plates: ..................(1) where Q = flow rate (bbl/day) W = width of fracture face (ft) = pressure differential (psi) b = fracture aperture (in) L = length of fracture (ft) = fluid viscosity (cp) As noted, this equation assumes that the walls of a fracture are smooth parallel plates; the walls of natural rock fractures are not. Work in the 1940's by Lomize showed that flow between artificially fabricated fracture faces does not always follow the cubic law. His rough fractured faces were fabricated by gluing quartz sand onto smooth plates. P. 687