Date of Graduation


Document Type


Degree Type



Statler College of Engineering and Mineral Resources


Petroleum and Natural Gas Engineering

Committee Chair


Committee Member


Committee Member



In hydraulic fracturing, a proppant injection schedule practice typically applies a binary proppant mixture (for example: 100 Mesh sand following by 40/70 Mesh sand in well MIP-3H, Marcellus Shale). The former injection agent is finer in size or less resistant to stress, whereas the latter injection agent is coarser in size or more resistant to stress. This practice creates a special region inside the fracture, in which two injected proppant types co-exist and is defined as the mixture zone. This research concentrates on the variability of the mixture zone under impact of different factors, introduces novel semi-analytical modelling approach to better estimate the hydraulic conductivity inside the mixture zone, and further applies this novel approach to prove its efficacy in conductivity estimation and cumulative production prediction.

Variability of the mixture zone is studied by an OAT (One at A Time) sensitivity analysis to examine the percentage of the mixture zone’s area over the total propped area under variability of different parameters, including reservoir properties, geo-mechanics, and different design parameters in a proppant injection schedule. The novel semi-analytical model is derived by independent modelling for proppant pack’s permeability and width. Permeability model is an improvement from Carman Kozeny equation, in which Internal Specific Area is re-derived to differ a binary mixture from a single proppant type. Fracture width model is derived from Hertzian contact theory under assumptions of parabola distributed stress, elastic behavior and dual-layer schematic. Trust-region method is applied to determine all coefficients in the permeability model, which complies with a non-linear least square problem. Coefficients in the width model are determined by linear approximation from an in-house fracture width database.

Based on satisfied validation results (7.98%-21.82% MRE), trust-region algorithm determines the novel model’s coefficients using lab data of only two Weight Concentration Ratios. The novel model is expanded to predict binary mixture’s conductivity at arbitrary confining stress and Weight Mixing Ratio values, which avoids misleading experimental outcomes. Proppant particle size distribution between two discrete Mesh numbers, deformation complexity between particles (quadratic form) and proppant crush effect are prospective improvements for better modelling validation results. LWAM is proved to overestimate conductivity compared to the novel model. Overestimation degree, which can exceed 70%, is separated into 3 overestimation zones (≤20%, 20-60% and ≥60%) and examined by the comparison matrices. When contrast in density and Mesh size between proppant types in a mixture is clear (for example: mixture 40/70 sand - 20/40 ceramic), overestimation is extreme, and when internal contrast between proppant types in a mixture is reduced (for example: mixture 20/40 sand - 20/40 ceramic), overestimation is dampened.

The case study for Marcellus Shale applies comparison matrices to predict LWAM’s conductivity overestimation and conduct 1-year and 10-year cumulative production analyses. Reduction of confining stress axis in comparison matrices to 5400-6200 psi with a maximum difference of 200 psi between different depths (based on Marcellus Shale minimum horizontal stress data) allows predictive reasoning for conductivity overestimation from weight concentration ratio distribution. Overestimation for cumulative production data is observed to approach 10.73% (3.274 MMSCF in the early production time for a quarter fractured area). This suggests the level of risk caused by application of LWAM in reservoir simulation, depending on the intrinsic contrast between proppant types’ Mesh sizes and densities, in the selected proppant injection mixture.

ETDSignatureForm_PhamVuong.pdf (168 kB)
ETD submission (signed by committee)

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Memorandum (1 year embargo)