Meta-analysis of propped fracture conductivity data—fixed effects regression modeling

Abstract

Previous empirical models of propped fracture conductivity are based either on data sourced from single investigations or on data not in the public domain. In this work, statistically rigorous models of propped fracture conductivity are developed using a database of fracture conductivity experiments reported in technical literature over the last 40 years.The database contains about 2700 data points. Propped fracture conductivity is the dependent variable and proppant type, mesh size, proppant concentration, formation hardness, closure stress, formation temperature, and polymer concentration are the independent variables. The full, original database was pared down to various subsets, each having complete information in relation to some subset of the independent variables. The number of independent variables included in each of the resulting databases varied from three to six. Seventy percent of the data was used to develop the models while thirty percent of the data was used to validate them.Fixed effect models were selected using all subsets regression analysis in three, four, and five experimental factors for each of two types of proppant. The five factor model appeared to be the most useful model for both proppant types from a predictive point of view. Five-factor model predictions also compared favorably with an existing propped fracture conductivity model and different case histories published in literature.This project provides engineers with access to a propped fracture conductivity database based on experiments reported over the past 40 years in technical literature. The models developed based on this database can be used to generate predictions of propped fracture conductivity for a variety of proppant characteristics and formation conditions. Also, the models presented here are based on data from experimental investigations in different laboratories, potentially reducing biases that may be present in single laboratory investigations.