Abstract

A study was carried out to forecast the productivity of a hydraulically fractured well in a retrograde gas-condensate sandstone reservoir using a numerical model. The fracture was explicitly modeled as a set of high-conductivity cells.

At the gas velocities normally encountered in hydraulic fracture proppant packs, non-Darcy pressure drops dominate, and the apparent proppant permeability is one or two orders of magnitude lower than the Darcy permeability measured at single phase low-rate conditions. This is particularly true if a liquid phase is also flowing. The apparent permeability of the proppant is a function of:

  • Gas velocity (hence: rate and flowing pressure)

  • Ratio of free liquid rate to gas rate

  • Stress on the proppant

  • Type of proppant

Thus, apparent proppant permeability will vary with distance from the wellbore, increasing towards the tip of the fracture where liquid ratio and velocity are lower.

This variation of permeability was explicitly modeled in the proppant pack by dividing it into segments and calculating the permeability in each segment. As a result of this modeling, the impact of increased fracture length on productivity was found to be more significant than in simpler modeling where one permeability value is used for the entire proppant pack.

The variation of apparent proppant permeability along the length of the fracture and its impact on well productivity are discussed in this paper. A comparison of predicted well productivity is also made with the use of a constant permeability value for the proppant in numerical and analytic simulators. We will show that using a constant proppant permeability value results in an estimate of optimal fracture length that is too short.

Introduction

A numerical simulator was used to forecast the productivity of a hydraulically fractured well in a retrograde gas-condensate sandstone reservoir. The fracture was explicitly modeled as a set of high-conductivity cells. The impact of condensate dropout was modeled in both the reservoir and the proppant pack. To model the pressure drop in the reservoir rock with a vertical un-fractured well, a set of relative permeability curves and the rock beta factor were adequate. In the rock adjacent to the propped fracture, the gas velocities are low because of the much greater flow area---two orders of magnitude lower than those around a wellbore, and non-Darcy flow is not an issue.

In the proppant pack, however, the high velocity of gas and the presence of liquid means that the apparent permeability of the proppant is a function of gas velocity and ratio of free liquid rate to gas rate. These are in addition to the other factors that determine proppant conductivity in single-phase flow:stress on the proppant and type of proppant.

Thus, apparent proppant permeability will vary with distance from the wellbore, increasing towards the tip of the fracture where both the liquid-to-gas ratio and the velocity decrease.

This variation of permeability was explicitly modeled in the proppant pack by dividing the fracture into segments and calculating the permeability in each segment.

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