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Summary

An experimental research program to investigate the effects of liquid saturation upon non-Darcy flow coefficients is presented. The presence of a wetting phase fluid plays an important role in high velocity flow of a gas well, producing condensate or water, and in propped fractures containing liquid saturations.

This study initially examines the errors commonly encountered but ignored in evaluating the permeabilities and the coefficient of inertial resistance during the flow of gases through porous media. Experimental techniques, such as constant overburden pressure, changing overburden pressure, forward flow, and backpressure flow, are applied to optimize and obtain accurate evaluations of Klinkenberg parameters and inertial resistance coefficients for a selection of Omani reservoir cores. Gas-slippage factor significantly influences the derived viscous and inertial coefficients from high-velocity gas flow data. An increasing wetting phase saturation increases the non-Darcy coefficient up to thirty-fold.

Analysis of the experimental data revealed that unique relationships exist between the non-Darcy flow coefficients and the equivalent liquid permeability, porosity, and liquid saturation. Heterogeneity of the core as mapped by pore-scale measurements provide an insight into the mechanism for such a large increase in the non-Darcy coefficients.

Introduction

Anomalies have been reported in the literature in laboratory-determined equivalent liquid permeability, k_L, from single-phase gas permeability measurements.¹ It is often found that k_L evaluated for the same dry reservoir core varies from laboratory to laboratory, and that at times the repeatability of evaluated k_L from the same laboratory is difficult.^2,3 As k_L is an important core characterization parameter, this report initially aims to outline the correct experimental and analytical procedure in obtaining the representative k_L values for dry cores.

Klinkenberg-corrected permeabilities are used as industry standards in correlating permeability data of reservoir cores. Any core analysis or Special Core Analysis (SCAL) study is based on k_L measurements to correlate the absolute permeability of the chosen cores. Permeability is regarded as a fundamental reservoir property, and core measurements are used extensively to validate both the well-test data and log-derived data.

The prevalence of non-Darcy flow in gas wells is well known. An important rock parameter that is often used in various pressure calculations and production profiles is the coefficient of inertial resistance, known as β. The use of β as an independent reservoir characterization parameter, which in turn depends on rock parameters, such as porosity, tortuosity, and core heterogeneity, is important for gas wells producing at high rates (non-Darcy flow). The non-Darcy coefficient in such wells is usually determined from analysis of multirate pressure test data. Such data, however, are not always available; hence, calculation of the non-Darcy term requires a knowledge of the coefficient of inertial resistance. The measurement of β in the laboratory is thus examined from steady-state gas-flow data in the transition from laminar to non-Darcy flow. In the gas condensate wells, liquid saturation could build up owing to retrograde condensation, which is caused by a large pressure drop. In the presence of a liquid phase, the non-Darcy effect in the gas phase can increase considerably, thereby causing a loss of productivity. High liquid saturation in the vicinity of a wellbore may also be caused by acidizing or mud filtrate invasion. The increase in the inertial effect in liquid-saturated porous media has been clearly demonstrated by Gewers and Nichol,⁴ who carried out experimental measurements on micro-vugular carbonates with a static liquid phase 0% to 30%. Their work was later extended by Wong⁵ for a mobile phase using same cores and increasing the liquid saturation from 40% to 70%. The inertial resistance coefficient increased eight-fold on increasing the liquid saturation from 40% to 70%. The same behaviour was expected to be observable in sandstones.⁶ However, non-Darcy measurements performed on Berea sandstones⁷ and Ottawa sand propped fractures⁸ (10/20, 20/40) showed the values to increase up to three times that of dry case for immobile liquid saturations up to 20%. Noman and Archer⁹ repeated the measurements on sandstone cores from North Sea gas wells and again found the increases not as rapid as that reported for carbonates.

This study is based on a selection of sandstone reservoir cores from central Oman. It focuses the effect of increasing fluid saturation from 0% to 60% on the non-Darcy coefficient. Data from capillary pressure measurements are used to examine the influence of heterogeneity on the non-Darcy coefficient; Purcell ¹⁰ has shown the relationship between capillary pressure and permeability. This is achieved by relating the magnitude of non-Darcy coefficients with mean porethroat radius. The relationship beween capillary pressure and pore radius, r, where

• Equation 1

is used to indicate the heterogeneity of the samples used. Capillary pressure data are used to obtain the pore size distribution function, D(r ), where D(r) is defined as

• Equation 2

The deviation from the mean pore-throat radius, r, is used in this study to indicate a degree of heterogeneity at the core-scale measurements. While heterogeneity is a complex phenomenon with a number of contributing factors, only pore radius derived from capillary pressure is used. For consistency, mean radii are calculated from similar fluid saturations used in determining the non-Darcy coefficients.