New Approach for Multiphase-Flow Rate and Pressure Transient Analysis in Hydraulically Fractured Porous Media: Deterministic Models for Reservoir Total Mobility and Compressibility
Authors: Al-Rbeawi Salam , Owayed Jalal 
Published: November 2018

Abstract
This paper introduces new approach for analyzing multiphase-flow rate and pressure transient behaviors in conventional and unconventional reservoirs. This approach focuses on introducing two deterministic models for two pressure-time variant parameters. The first is the total reservoir mobility (Mt) representing the variance with time and pressure in reservoir three-phase mobility ratio using relative permeability and viscosity of each individual phase. While the second is the total reservoir fluid compressibility (Ct*) representing the variance in reservoir fluid properties and formation compressibility with time and pressure. The main objective is eliminating the uncertainty of assuming single phase flow in porous media and approaching substantially to realistic patterns of pressure, rate, cumulative rate, and productivity index with production time. This objective is reached by assembling the mobility and compressibility models proposed in this study to the analytical models of transient wellbore pressure drop (constant Sand face flow rate) and decline rate profile (constant bottom hole flowing pressure).
In this study, two phases were conducted. In the first, a randomly chosen PVT data were used to develop the deterministic models of total reservoir mobility and compressibility by developing several curve-fitting models for several physical and petrophysical properties. These curve-fitting models were employed together to generate the pressure-dependent reservoir fluid total compressibility (Ct*) and time-dependent reservoir total mobility (Mt). Accordingly, equivalent pressure function was derived using total reservoir mobility deterministic model while equivalent time function was derived using the deterministic model of reservoir total mobility-compressibility ratio. In the second, a hybrid multilinear flow regimes model is used for describing rate and pressure response of hydraulically fractured reservoirs by applying equivalent pressure and time functions. The hybrid model is used to generate pressure behavior, rate transient and cumulative rate profile, and productivity index for reservoirs where multiphase-flow conditions are dominant in porous media. The results of this model are interpreted and several flow regimes are characterized. Analytical models for these flow regimes are developed for the two conditions of constant rate and constant wellbore pressure.
The outcomes of this study can be summarized as: 1) Developing two deterministic models for reservoir total mobility and compressibility using PVT data and curve-fitting process. 2) Generating equivalent pressure and time functions based on reservoir total compressibility and mobility deterministic models respectively. 3) Generating hybrid analytical models for pressure, rate, cumulative rate, and productivity index for hydraulically fractured reservoirs considering multiphase flow. 4) Generating analytical models for flow regimes considering constant Sandface flow rate and constant wellbore pressure. The study has pointed out: 1) Pressure and pressure derivative behavior, flow rate and cumulative flow rate profile, and productivity index of multiphase-flow conditions are different than those of single phase flow. 2) Reservoir total mobility may have significant impact on pressure behavior and rate transient response while the changes in reservoir total compressibility may not have reasonable impact. 3) The developed flow regimes are not affected by multiphase flow i.e. bi-linear flow, formation linear flow as well as boundary dominated or pseudo-steady state flow regimes are all observed for single and multiphase flow. 4) Even though pressure behavior is impacted by multiphase flow, starting time of pseudo-steady state flow indicates no changes compared to single phase flow. 5) Stabilized productivity index of multiphase-flow is less than the index of single phase flow.