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Summary

A pore-scale network model is presented here for gas-condensate flow. Porous media are modeled by networks of pore bodies interconnected by pore throats. Pore-level laws are identified from previously published micromodel and multiphase pipe flow experiments. The condensate can flow due to three mechanisms: pressure gradient within the sample-spanning condensate phase, movement of condensate slugs, and condensate droplets carried by the gas flow. Inertial effects are important for high rate gas flows. The relative permeabilities and non-Darcy coefficients have been computed for the low capillary number and low condensate saturation-high pressure gradient flow regimes.

Introduction

During production of gas-condensate reservoirs, retrograde condensation can occur in the near-wellbore region if the pressure falls below the dew point. The condensate liquid partially blocks the gas flow channels and reduces gas productivity.¹ Such a reservoir can be divided into three regions based on the type of flow. The first region consists of the inner part of the reservoir (away from the wellbore) with only a single phase present above the dew point. The second region is intermediate between the first and the third regions. It is characterized by pressure slightly below that of the dew point, low condensate saturation, low interfacial tension, and high (but not as high as the wellbore) velocity. The flowing phase is primarily gas in this region. The third region occurs near the wellbore. It has the lowest pressure, higher condensate saturation, low (but not the lowest) interfacial tension, and the highest velocity. Both the gas and the condensate flow in this region. Understanding the relative permeability of these fluids in the second and third regions is critical to the evaluation of possible recovery strategies in gas-condensate reservoirs. Both high capillary number and non-Darcy flow effects are important in modeling the near-wellbore gas-condensate flow. ^2,3

There have been few laboratory studies in the past investigating the gas-condensate relative permeabilities.^4-8 These experiments are difficult to perform and their interpretation can be questionable because flow and phase behavior are intimately coupled in these experiments. Henderson et al.^4,5 have conducted steady-state relative permeability experiments on model gas-condensate fluids to show that relative permeabilities depend on both saturation and capillary number. Hysteresis is unimportant in high capillary number flows. These experiments were conducted at low Reynolds number (<0.01) and thus did not have any non-Darcy effect. The saturation range at which relative permeability was obtained is rather limited. To overcome the difficulty of working with pressure-sensitive condensate fluids, other researchers^6,7 have used model fluids and shown that the condensate permeability can be approximated by the permeability of a wetting fluid by matching the capillary or the bond number. Non-Darcy flow experimental data is available for gas and gas/brine systems,⁹ but not for gas-condensate systems.

Correlations by which to model the capillary number dependence of two-phase flow are available in the literature.¹⁰ Many of them were developed for surfactant flooding or miscible flooding. Pope et al.¹¹ have shown that a two-parameter correlation can be used to match the experimental data of Henderson et al.^4,5

Little work has appeared in the literature on microscopic modeling of gas-condensate reservoirs. Fang et al.¹² used a simple two-dimensional (2D) network composed of vertically interconnected, circular capillary tubes to estimate the critical condensate saturation, S_cc Because of this simplistic geometry, unrealistically high S_cc were calculated and the contact angle hysteresis played an important role in the calculation of S_cc in this model. S_cc was less than 0.1 at low interfacial tension but was over 0.9 at high interfacial tension. Mohammadi et al.¹³ used a Bethe tree to represent the porous media, where only the bonds of the tree contribute to its volume and flow, and the pore bodies act merely as volumeless junctions with infinite conductance. The critical condensate saturation and the relative permeabilities were calculated, but the capillary number effect was not studied. Neither of the two models considered phase trapping within and connectivity through the corners, which are important and ubiquitous in real porous media. Also, the assumption that pore bodies are volumeless is not realistic for naturally occurring porous media. Wang and Mohanty¹⁴ have improved on these models by incorporating three-dimensional (3D) networks of pore bodies and throats with corners to calculate the critical condensate saturation. This pore-level network model is extended in this paper to calculate relative permeabilities and non-Darcy flow parameters.

This study is limited to low condensate saturations (e.g., S_C <0.5) typical of gas-condensate operations. The condensate phase can flow in three ways in general. If there are sample-spanning paths of the condensate phase, it can flow under its own pressure gradient. If the viscous forces can overcome capillary forces, i.e., high capillary number (N _c >10^?5 the (nonsample-spanning) condensate ganglia can move. ¹⁵ At high enough capillary and (gas flow) Reynolds (N_Re ) numbers, tiny condensate drops (smaller than pore throats) can be formed and carried by the gas.¹⁶ The condensate Reynolds number seldom rises above unity. The gas flows under its own pressure gradient because it remains sample spanning at low condensate saturations. At low gas Reynolds numbers (<1), this flow is creeping, i.e., Darcy flow. At N_Re >1, inertial terms are important. At higher N_Re, of the order of 1,000, turbulence sets in but near-well flows seldom approach this condition. Thus the mechanisms in gas-condensate flow depend on three important parameters: S_c, N _c, and N _Re . The physical variables that change the last two dimensionless parameters in most experiments are pressure gradient (? p) and interfacial tension (?). Thus different flow regimes can be identified according to different combinations of S_c, N_c , and N_Re (or ?p and ?). At low values of N_c (or ?p), gas and liquid flow slowly (creeping flow) in their separate sample-spanning paths under their own pressure gradients. At low values of S _c (e.g., <0.2) and high values of ? p , droplets of condensate form and inertial terms can be important to gas flow. At higher values of S _c (e.g., >0.2), low values of interfacial tension and high values of ?p condensate ganglion flow is also important. In this study, we have concentrated on the first two regimes mentioned, i.e., the low N _c regime and the low S_c -high ?p regime.

The geometry of the model porous medium is presented in the next section. The mechanisms of condensation and fluid flow are described in the following section. The effects of geometry and flow parameters in the low N_c regime and the relative permeabilities and non-Darcy coefficients in the low S_c-high ? p regime are described next. Conclusions are summarized in the last section.