Multiphase Linear Flow in Tight Oil Reservoirs

Abstract

Summary The main objective of this work is to gain a general understanding of the performance of tight oil reservoirs during transient linear two-phase flow producing at constant flowing pressure. To achieve this, we provide a theoretical basis to explain the effect of different parameters on the behavior of solution-gas-drive unconventional reservoirs. It is shown that, with the Boltzmann transformation, the highly nonlinear partial-differential equations (PDEs) governing two-phase flow through porous media can be converted to two nonlinear ordinary-differential equations (ODEs). The resulting ODEs simplify the calculation of the reservoir performance and avoid the tedious calculation inherent in solving the original PDEs. Thus, the proposed model facilitates sensitivity studies and rapid evaluation of different hypotheses. Moreover, successful conversion of the highly nonlinear PDEs (in terms of distance and time) to the ODEs (in terms of the Boltzmann variable) implies that the saturation and pressure are unique functions of the Boltzmann variable, and as a result, saturation is a unique function of pressure. This transformation enables us to explain (a) the constant gas/oil ratio (GOR) that has been observed in some hydraulically fractured tight oil reservoirs and (b) the straight-line plot of 1/qo and 1/qg vs. t during constant-pressure two-phase production. An approximate analytical model is also developed. It is shown that the proposed approximate solution can be converted to a form similar to the well-known equations for single-phase flow, which enhances our understanding of two-phase-flow behavior. Extensive sensitivity studies are performed to examine the utility of the proposed model in predicting the performance of tight oil reservoirs. The applicability of the conclusions to the boundary-dominated flow period is investigated. On the basis of numerous simulation studies, it is shown that the impact of various parameters on boundary-dominated flow can be predicted with the transient solution, without the need for running multiple numerical simulations.

Shale gas reservoir modeling and production evaluation considering complex gas transport mechanisms and dispersed distribution of kerogen

“…We use a linear flow model to couple fracture-reservoir gas flow because linear flow is the predominant flow regime in shale reservoirs with hydraulic fractures. Transient linear flow usually occurs in unconventional formations and may last for many years (Arevalo-Villagran et al 2006;Tabatabaie and Pooladi-Darvish 2017). The major reason is that linear flow is associated with hydraulic fractures, and the well-fracture geometry results in linear flow behavior (Arevalo-Villagran et al 2006).…”

“…By matching with a short-time production history, we can also predict the long-term well behavior. A validated linear flow model can be used to conduct extensive sensitivity analyses to examine the reservoir performance (Tabatabaie and Pooladi-Darvish 2017). By further considering the dispersed distribution of kerogen and avoiding the use of the instantaneous kerogen gas source term, the simulation would be closer to real reservoir conditions.…”

A Prediction Method for Flow-Stop Time in Deep-Water Volatile Oilfields: A Case Study of Akpo Oilfield in Niger Delta Basin

“…Nieber et al [29] and Spayd and Shearer [30] modified the Buckley-Leverett equation for two-phase flow in porous media by considering the variation of capillary pressure with saturation and determined the structures of various solutions by numerical simulation of partial differential equations. Tabatabaie and Pooladi [31] solved the fluid flow equation of two-phase linear flow in tight oil reservoirs under constant flow pressure and provided a theoretical basis for the verification of influencing factors in unconventional oil reservoirs. Now, the mathematical models have also been expanded applicable to different types of oil reservoirs, but the theoretical equations still have some obvious shortcomings.…”

Production Decline Analysis and Hydraulic Fracture Network Interpretation Method for Shale Gas with Consideration of Fracturing Fluid Flowback Data

“…Behmanesh et al [7] treat saturation as a function of pressure, linearize the model by defining a two-phase pseudopressure function, and obtain a semianalytical solution for productivity. Due to the difficulty in solving the relationship between saturation and pressure, Zhang and Ayala [8] and Tabatabaie and Pooladi-Darvish [9] used the Boltzmann transformation method to obtain the self-model solution of the oil and gas two-phase seepage model. However, these models are only applicable to the situation before the pressure reaches the boundary.…”