Modeling Well Performance for Fractured Horizontal Gas Wells

Abstract

In tight gas reservoirs, horizontal wells have been used to increase reservoir contact and hydraulic fracturing has been applied to further extend the contact of the reservoir. Point source solution has been used to describe the flow behavior. The method was advanced to the volumetric sources, and pressure change inside the source was considered. We have developed a method that can predict horizontal well performance, and the model can also be applied for fractured horizontal wells. The method solves the problem by superposing a series of slab sources under transient or pseudo-steady state flow conditions. The principle of the method comprises calculation of the semi-analytical response of a rectilinear reservoir with closed outer boundaries. The slab source approach assigns the source a geometry dimension, similar to the volumetric source method, but has the solution similar to the point source method by neglecting the effect of the flow inside the source. When solving the source problem the pressure/flow effect inside source is considered sequentially by superposition principle over multiple sources. The pressure response is integrated over time to provide continuous pressure behavior. Flow effect inside of fractures can be studied by dividing the fracture into several segments, and each can be treated as a slab source. The method is validated by comparison with the results of analytical solutions of horizontal wells with uniform flux and infinite conductivity, and fractured wells with uniform flux, finite or infinite conductivity. The method provides an effective tool for horizontal well design and well stimulation design for gas reservoirs. In this paper, we present the details of model development. The examples will be used to illustrate how the model can help to optimize wellbore and fracture design. The method in this paper is more accurate compared with conventional point-source solution, and can handle the transaction from transient flow to pseudo-steady state flow smoothly. The results of the study show that in low permeability formation, hydraulic fracturing has more impact on horizontal well performance.

Volumetric Source Model to Predict Productivity of Fractured Horizontal Well in Naturally Fractured Reservoirs

“…(11)(12)(13) show the effect of hydraulic fracture's factors on the ratio of flow rate. Increasing the number or conductivity of hydraulic fracture, the curve becomes smoother and the time node of the highest point shows up earlier.…”

“…While main analytical [1][2][3][4] and semi-analytical models [5][6][7][8] are ignoring the direct flow to horizontal well, which fitted to hydraulic fractured casedhole horizontal wells. But, for hydraulic fractured open-hole horizontal wells, ignoring the flow to horizontal well will cause tremendous error, especially at early time [9][10][11][12][13].…”

“…Since Gringarten and Ramey [14] introduced to solve transient flow problems for the first time, various source functions [5][6][7][8][9][10][11][12][13] are developed to simulate pressure behavior and productivity of fractured horizontal wells. But most works have been focusing on point source functions which neglected the flow in source and its volume.…”

A new analytical multi-linear solution for gas flow toward fractured horizontal wells with different fracture intensity

“…Al-Kobaisi et al (2006) presented a hybrid numerical-analytical transient pressure model of horizontal wells with vertical fractures. Zhu et al (2007) and Lin and Zhu (2010) developed volumetric source methods to model fractured horizontal wells in box-shaped reservoirs and describe pressure behaviors. Rbeawi and Tiab (2013) introduced analytical models to study pressure behaviors and flow regimes of horizontal well with multiple longitudinal or transverse, vertical or incline, symmetrical or asymmetrical fractures.…”