A Novel Semi-Analytical Model for Multi-branched Fractures in Naturally Fractured-Vuggy Reservoirs

Abstract

In the past few decades, scholars have made great breakthroughs in the study of well test analysis of carbonate rock. The previous studies are based on horizontal wells, straight wells, fractured wells, and inclined wells. With the development of fracturing technology, acid fracturing technology is considered to be the most effective measure to develop carbonate reservoirs. As the carbonate rock is easily dissolved in carbonic acid, multi-branched fractures will be produced near a vertical well. This article presented a semi-analytical model for multi-branched fractures in naturally fractured-vuggy reservoirs for the first time, which laid a theoretical foundation for solving well test analysis for finite conductivity multi-branched fractures. The model can quantify the wellbore flow pressure and applied to obtain more parameters reflecting comprehensive flow characteristics through using history matching procedure. The results were compared with numerical simulation and the existing analytical solutions of a single fracture model. Then in this paper, flow characteristics are recognized and there are five flow regimes found in the type curves, e.g. bi-linear flow region, linear flow region, inter-porosity flow region between vugs and fractures, inter-porosity region between matrix and fractures, and radial flow region. Finally, the influence factors analysis shows fracture number will mainly affect flow behavior of bi-linear flow and linear flow. The angle analysis showed that as the fractures were closer, their interaction became stronger. The conductivity would seriously affect the flow behavior in the early time. Linear flow cannot be observed when the conductivity is less than 1 and bi-linear flow cannot be observed when the conductivity is more than 20. And the effect of fracture length on flow behavior occurs in the early time. Bi-linear flow and linear flow characteristics cannot be observed when the fracture length is reduced.

A new analytical model for flow in acidized fractured-vuggy porous media

“…Recently, the fluid flow and transport behavior in fractured-vuggy porous media have been analyzed with theoretical methods 3,9,29–34 . Wu et al .…”

“…In 2018, Wang et al . 34 also investigated flow characteristics in fractured-vuggy carbonate reservoirs using semi-analytical model considering wormholes as multi-branched fractures. Other scholars proposed composite model to study the pressure transient characteristics in fractured-vuggy reservoirs within which the pore networks in acidized region are equivalent to homogeneous medium of Euclidean geometry 35,36 .…”

Velocity dependent up-winding scheme for node control volume finite element method for fluid flow in porous media

“…The pressure equation is elliptic and the transport equations of fluids are hyperbolic. These governing equations have been implemented in various studies to predict fluid flow in naturally fractured reservoirs 7 and even in pore-scale modelling of heterogeneous porous media 8 . Moreover, the hydrology community relies on similar numerical models to simulate groundwater movement, contaminants transport in aquifers chemical reactions between minerals 9,10 .…”