Non-Darcy Gas Flow Through Propped Fractures: Effects of Partial Saturation, Gel Damage, and Stress

Abstract

Summary The objective of this work was to identify and quantify important parameters affecting gas production through propped fractures under a non- Darcy gas flow regime. The gas flow capacity of a simulated propped fracture was studied systematically to determine the effects of partial saturation. gel damage, and stress conditions. The flow-capacity response of the 20/40-mesh sand tested throughout this project was affected significantly by variations in the effective gas porosity of the proppant pack. Permeability- and non-Darcy flow characteristics were correlated to effective gas porosity. Partial saturation was found to be a key parameter influencing the permeability and non-Darcy gas flow behavior of a proppant pack. Partially saturated fractures may result from incomplete removal of fracturing fluid, mobility of formation waters. or production of condensates. The partial saturation of the proppant pack, in effect, changes the open porosity available for gas flow, which adversely affects gas permeability and non-Darcy flow parameters. The results from this investigation demonstrate that non-Darcy gas flow behavior through propped fractures in which a saturation phase is present cannot be estimated from results using dry-proppant-pack tests. Introduction The generated equation for linear flow through porous media can be represented by the Forchheimer equation as (1) where -, =pressure gradient, =fluid viscosity, =fluid density, =fluid velocity, =permeability of the porous medium, and =coefficient of inertial resistance or the non-Darcy flow factor. For low fluid velocities, the second term in Eq. 1 becomes negligible, and the equation reduces to Darcy's law. As the velocity of the fluid increases, however, the contribution of the second term to the pressure gradient becomes increasingly significant, especially for low-viscosity fluids. Because gas densities vary with pressure, an integrated form of Eq. 1 that accounts for density variations is generally used to describe the flow of gas through a medium in which the change in gas pressure with flow distance is significant. For example, Dranchuk and Kolada provided a generalized integrated form of Eq. 1 that accounts for Klinkenberg effects at low gas velocities and for variations in gas density with pressure. For characterizing gas flow through proppant packs in the laboratory, however, we can use Eq. 1 while avoiding errors resulting from density and Klinkenberg effects if tests are conducted isothermally and if the mean gas pressure within a proppant pack is maintained at a constant moderate pressure. such as 100 psig [0.69 MPa], throughout each test. A plot of - (L v) vs. pv/ from test data recorded under controlled conditions yields a straight line in which the slope equals the 0 factor and the intercept equals 1/k. Greenberg and Weger found 0 to be independent of pressure for pressures up to 2.000 psi [13.8 MPa] in porous metal. Cooke investigated propped hydraulic fractures and found no appreciable difference in 0 owing to the nature of the test fluid. either brine. gas, or oil. He found that log 0 was inversely proportional to log k for gas flow through stressed sandpacks at irreducible water saturation conditions. Cooke described the fits to his data b), an equation of the form (2) where the constants b and a varied with sand size. Cooke observed that some of his data suggested a slight reduction in inertial resistance with oil or gas flowing at irreducible water saturation compared with brine flow alone, although scatter in the data prevented a clear determination of such an effect. Gewers and Nichols measured, for cores with immobile liquid saturations of up to 30% PV. Their results indicated that gas permeabilities were decreased by immobile partial saturations when compared with dry permeabilities. They found that 3 decreased as saturation increased from 0 to 10% and then increased as saturation increased from 10 to 30 %. They described the decrease in 0 values for low immobile partial saturations as a pore-streamlining effect. Gewers and Nichol found that 0 for carbonate cores containing a partial immobile saturation of up to 30% could be estimated with the correlation of dry-core a vs. k if the effective permeability under saturated conditions was known. For sand proppant packs containing partial saturations, Evans and Evans found that 0 values increased with increasing saturation, whether mobile or immobile, and that the correlations for dry proppants were insufficient for predicting the 0 values of partially saturated proppant packs. Geertsma correlated a wide range of 3, permeability, and porosity data from his work and from the literature. For dry porous media, Geertsma found a general fit to the data by (3) In addition, he hypothesized that, for situations in which an immobile saturation phase is present, (4) where k=gas permeability at 100% gas saturation, SL=saturation-phase fraction, and kr=relative permeability under saturation conditions. Eqs. 3 and 4 are dimensionally correct. Noman et al. used several relationships of 3, k, and 0 to fit data derived from core plugs and reservoir production. They found that the best correlation of their experimental and well test data was obtained by relating beta to () -0.5. The units of ()) -0.5 and 0 are dimensionally equivalent-i. e., cm -which facilitates data comparison. The results from our investigation are correlated with the relation-ships proposed by Cooke, Geertsma, and Noman et al. Experimental Procedures Sandpacks were tested in a 10-in.2 [64.5-CM2] linear-flow conductivity cell at closure stresses from 1.000 to 10,000 psi [6.9 to 69 MPa]. The design of the conductivity cell used in this investigation evolved from the cell Cooke developed that has been widely accepted for proppant conductivity testing. 10–19 Accordingly, the cell has metal walls and makes no provision for leakoff or filtercake effects on test results. Fig. 1 is a schematic of the test system. Throughout the proppant testing program, N, gas was used as the flowing medium to simulate gas production through a propped fracture. The gas pressure was maintained at 100 psig [0.69 MPa] in the center of each test proppant pack to ensure that proper gas density and viscosity values were used in calculations. Gas flow rates through proppant packs were maintained sufficiently high to impose non-Darcy flow conditions. Tests were conducted at room temperature. SPEPE P. 417^