#### Identifier

etd-11052014-045926

#### Degree

Doctor of Philosophy (PhD)

#### Department

Petroleum Engineering

#### Document Type

Dissertation

#### Abstract

Accurate estimation of production from frac-pack completed gas wells requires reliable estimation of flow properties from reservoir rocks and proppants. This study is composed of three parts: core-scale, pore-scale and reservoir-scale analyses of this problem. In the core-scale analysis, simultaneous estimation of permeability, non-Darcy, and Klinkenberg coefficients of reservoir rock is conducted from steady-state and pulse-decay experiments. Confidence intervals of the estimated parameters are determined from the Bootstrap method. The duration of pulse-decay experiments has a large impact on confidence intervals; therefore, correlations are developed to estimate the experimental duration for both 1-tank and 2-tank set-ups from the core properties and design parameters. In the pore-scale analysis, the Lattice Boltzmann method (LBM) and network modeling are used to calculate proppant flow properties. For reliable simulation, resolution- and relaxation-time effects on LBM simulation are investigated; resolution and network-structure effects for network modeling are investigated. It is found that the minimum particle diameter should be represented with 30 voxels for reliable estimations. Statistically significant permeability and non-Darcy coefficient correlations are developed by using other calculated petrophysical properties and network model parameters. A new approach, path analysis, is applied to petrophysical properties to show the relationship between them. Compaction and sand-migration effects on porosity, permeability and the non-Darcy coefficient are investigated. Trends in permeability and the non-Darcy coefficient as a function of porosity and sand concentration are found. Pore-scale simulations indicate that non-Darcy coefficients obtained from correlations always underestimate the inertial effects. A reservoir simulator is developed using the finite difference method by integrating the continuity and sand-migration equations, and by using the compaction and sand-migration correlations developed from pore-scale simulations. A parametric study is conducted for the rate constants for sand migration equations, critical velocity, flow rate, and initial movable sand concentration, to investigate their effects on sand production, reservoir flow properties, and pressure profile near the wellbore. While pore-throat plugging has a large impact on the pressure profile and reservoir flow properties, it causes an insignificant decrease in sand production. In addition, a sensitivity analysis is conducted for fracture dimensions and fracture conductivity to investigate their effects on sand production. Sand production does not decrease linearly with sensitivity parameters; therefore, designing fractures with moderate half-length, width, and conductivity is recommended.

#### Date

2014

#### Document Availability at the Time of Submission

Secure the entire work for patent and/or proprietary purposes for a period of one year. Student has submitted appropriate documentation which states: During this period the copyright owner also agrees not to exercise her/his ownership rights, including public use in works, without prior authorization from LSU. At the end of the one year period, either we or LSU may request an automatic extension for one additional year. At the end of the one year secure period (or its extension, if such is requested), the work will be released for access worldwide.

#### Recommended Citation

Anbar, Sultan, "Multiscale Estimation of Inertial Effects for Frac-Pack Completed Gas Reservoirs" (2014). *LSU Doctoral Dissertations*. 1715.

https://digitalcommons.lsu.edu/gradschool_dissertations/1715

#### Committee Chair

Thompson, Karsten E