Mathematical model study on the damage of the liquid phase to productivity in the gas reservoir with a bottom water zone

Abstract

The production process in the gas reservoir with an aquifer is complex. With gas production, aquifer water could possibly flow into the production well and accumulate within the well bore, which leads to a lower production rate and may even block the producer. However, few studies in the literature investigate the damage caused by the liquid phase in this kind of reservoir or predict gas productivity using the relationship between reservoir pressure and water gas ratio (WGR). For this reason, it is important to know the effects of the formation of liquid phase behavior on production when an aquifer is present under a gas reservoir.

From the results of published literature reviews, we found that studies focused on the production of a gas reservoir with bottom water. Nevertheless, for gas well damage from the liquid phase behavior, we found that there was no statistical data or mathematical model of the relationship between reservoir pressure and the gas oil ratio (GOR), which affects production.

In this research, based on the theory of fluid flow in porous media, a new mathematical model of water and gas production and a new equation on gas well productivity is developed. To verify the model and equation, gas production data collected from the field are applied. By analyzing the typical gas reservoir with bottom water and the collected data, influences from the liquid phase behavior are shown. In this way, mathematical relationships between reservoir pressure and the WGR and between the GOR and production decline were obtained. The new gas productivity model is derived from the gas and water pseudo pressure functions, which can be applied to analyze well damage caused by the liquid phase.

In order to verify the mathematical model, production data were collected from a typical gas reservoir with an aquifer located in the Changxing gas reservoir. The results indicate that a semi-logarithmic linear relationship is obtained between the WGR and productivity decrease. When the WGR increases from 0.5 to 15 m³/10⁴ m³, damage caused by liquid phase decreases to 59%.

The tendency of gas productivity in the Changxing gas reservoir was obtained so that it decreases as reservoir pressure decreases and increases as the WGR decreases. The gradient of the gas productivity deduction increases as the WGR increases. By the end of the data analysis, two linear equations indicating the relationship between gas productivity and reservoir pressure and the relationship between gas productivity and the water gas ratio are obtained: QAOF=−A1lnWGR−B1 and QAOF=A2lnP−B2, respectively.

The new model and these two equations can be applied to predict gas productivity in the gas reservoir with an aquifer and determine the damage level to the gas well. They also can be used to guide development plans in the gas reservoir with an aquifer.

Keywords

Mathematical model / Liquid phase / Well productivity / Gas reservoir with an aquifer

Acknowledgements

The authors acknowledge the technical and financial support of the National Natural Science Foundation of China study titled “Study on thewater invasion mechanism of fracture gas condensate reservoirs with bottom water” (Grant No. 51374269) and the Chongqing Science and Technology Research project titled “The effect of fracturing fluid on the productivity of ultra-low water cut shale gas wells” (Grant No. KJ1601333).

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