Using Step-Rate Test to Prove Gradient of Propagation Equations

Abstract

Abstract Performing rock-mechanics studies using core samples can be expensive. Researchers trying to obtain these samples for laboratory analysis often find the samples are broken or cracked. This leads to various attempts to obtain samples from a rock. In addition to the rock analysis, other challenges include stress relaxation relative to the subsurface and fluid exchange during the experiment. Based on this, other methods for obtaining values involving rock mechanics, such as the current charts from hydraulic fracturing, are now a focus and a part of "optimizations" or innovations in the calculation processes. The studies presented in this paper include derivation of rock-mechanics equations and the values from empirical results correlated with field application by step-rate tests. The proposed equations show different results from those presented in other studies. However, the values are different as a function of the specific conditions of each formation, such as depth, overburden stresses, compaction, and pore pressure. To avoid this scenario, it is important to know the minimum pressure that causes fractures. The estimation can be based on density, overburden, Poisson's ratio, and minimum horizontal stress. However, it is now possible to monitor fracturing-stimulation operations in real time, which allows understanding of formation-pressure response. This includes fracture-extension behavior and avoiding screenout risks related to unexpected high pressure applied on the formation while drilling and maintaining well and equipment integrities. There are few scenarios where the formulated equations can be proven. One is presented in this paper using a step-rate test. The paper uses modified Eaton's equations that are representatives of interest. The modified equations are used to estimate parameters of the minimum horizontal stress, fracture-extension gradient, overburden, and Poisson's ratio. To validate the present method, the estimation results are compared to available step-rate test results from the Sergipe basin.