Simulated Mini-Frac Analysis
Authors: Meyer Bruce R. , Hagel M.W. 
Published: March 2010

Abstract
A new mini-frac methodology is presented for the automated simulation of mini-frac analysis. The solution is based on solving the governing momentum, mass conservation and constitutive relationships for Perkins-Kern/Nordgren (PKN), Geertsma-Deklerk (ODK) and penny-shaped type fracture geometries. The analytical technique is unique because the fracture propagation characteristics of length, width, pressure and efficiency are numerically calculated from conservation of momentum and mass principles for power-law type fluids.
Major enhancements to current mini-frac analysis include:momentum and mass conservation,spurt loss,fluid flow-back after pumping,time-dependent fluid loss coefficients,interference closure, anddetermination of formation permeability.
The analysis has the additional advantage of using the measured pressure decline data as a history matching parameter to determine the appropriate fracture model and sensitivity of input data.
A number of mini-frac designs, parametric studies and field case examples are presented to illustrate the applicability of the numerical technique.

Introduction
Mini-frac analysis provides a method of estimating fracture dimensions, efficiency and leak-off coefficients prior to designing a full-scale fracture treatment. Mini-frac analyses as originally formulated by Nolte(1, 2) quantify the fracturing process as estimated from the measured pressure decline data. Most mini-frac analyses are based on Nolte's equations and do not account for the effects of fluid rheology or momentum conservation. The measured pressure data is simply used in place of solving the momentum equation. Neglecting momentum can result in unrealistic estimations of fracture characteristics and fluid leak-off coefficients for the design fracture and geometry models.
Currently, only the width-opening pressure relationship and pressure decline data are used to estimate mini-frac characteristics. Lee(3) has recently improved upon this by including Biot's energy balance equation for GDK-type fractures. To the authors' knowledge, the energy method has not been applied to PKN or penny-shaped type fracture geometries.
The energy balance method does eliminate some of the anomalies in mini-frac analysis. However, this method does not fully account for viscous-driven fractures.
A new mini-frac methodology is reported as formulated from conservation of mass and momentum for power-law type fluids. The methodology utilizes the same fracture propagation equations-of-state as used in the design simulator. The solution technique can be implemented with any hydraulic fracturing simulator and will provide results compatible with the design fracture treatment.
This analysis does not assume the fracture width is proportional to the measured pressure. Instead, the governing mass and momentum equations are coupled with the measured closure time to predict fracture propagation characteristics. From the numerically simulated fracture geometries, pressures, efficiencies and leak-off coefficients, the analyst can determine which fracture model more closely represents the measured pressure response and formation permeability.
The main advantage of this mini-frac technique is that mass and momentum are both satisfied. Additionally, the important effects of flow-back, interference closure, time.::dependent leakoff and fluid rheology are simulated.
The numerical results are used in conjunction with the measured pressure decline data to history match such input characteristics as fracture height, pay zone height, Young's modulus and spurt loss.