Mathematical Modeling Of Two-Phase Production From Unconventional Wells Using Analogy To Nature

Source abstract

Abstract Determining the changes of production is the key aspect of forecasting the exploitation of unconventional reservoirs. Two-phase flow and flowback after fracturing is observed in that resources. To get to know production profile is needed to find the relationship between produced water and produced gas. This paper presents a new mathematical model for two-phase production forecasting, based on the populations dynamics model. The idea of this work is to use system of two logistic equations with additional term for modeling water and gas production declines. This paper is a continuation of my previous work connected with mathematical modeling of single phase flow in unconventional reservoirs. The production process of unconventional wells divides it into three stages: dewatering, stabilized flow, decline. During the initial phase of exploitation, water production initially exceeds that of methane, but as production continues, the volume of gas increases steadily while the amount of water decreases. Over the stable period the gas rate slowly peaks. After that water production remains low and gas declining tendency begins. The proposed model uses the analogy of processes of competition occurring in nature to two-phase flow phenomena in gas reservoirs. The presented model has a widespread use in modeling the populations dynamics including competition between two species. It is a set of two differential equations, which describe both interspecies and intraspecies interactions. This paper contains two main parts. Part one presents a brief reminder of my preceding work, while part two includes description and explanation of my new model and modeling results. The proposed model was successfully applied to extremely low permeability gas wells. The model can very accurately trend the declines behavior of these wells. The modeling results were verified by the real industrial data.