Development of an Empirical Equation To Predict Hydraulic-Fracture Closure Pressure From the Instantaneous Shut-In Pressure Using Subsurface Solids-Injection Data

Abstract

Summary During hydraulic-fracturing operations, conventional pressure-falloff analyses (G-function, square root of time, and other diagnostic plots) are the main methods for estimating fracture-closure pressure. However, there are situations when it is not practical to determine the fracture-closure pressure using these analyses. These conditions occur when closure time is long, such as in mini-fracture tests in very tight formations, or in slurry-waste-injection applications where the injected waste forms impermeable filter cake on the fracture faces that delays fracture closure because of slower liquid leakoff into the formation. In these situations, applying the conventional analyses could require several days of well shut-in to collect enough pressure-falloff data during which the fracture closure can be detected. The objective of the present study is to attempt to correlate the fracture-closure pressure to the early-time falloff data using the field-measured instantaneous shut-in pressure (ISIP) and the petrophysical/mechanical properties of the injection formation. A study of the injection-pressure history of many injection wells with multiple hydraulic fractures in a variety of rock lithologies shows a relationship between the fracture-closure pressure and the ISIP. An empirical equation is proposed in this study to calculate the fracture-closure pressure as a function of the ISIP and the injection-formation rock properties. Such rock properties include formation permeability, formation porosity, initial pore pressure, overburden stress, formation Poisson's ratio, and Young's modulus. The empirical equation was developed using data obtained from geomechanical models and the core analysis of a wide range of injection horizons with different lithology types of sandstone, carbonate, and tight sandstone. The empirical equation was validated using different case studies by comparing the measured fracture-closure-pressure values with those predicted by using the developed empirical equation. In all cases, the new method predicted the fracture-closure pressure with a relative error of less than 6%. The new empirical equation predicts the fracture-closure pressure using a single point of falloff-pressure data, the ISIP, without the need to conduct a conventional fracture-closure analysis. This allows the operator to avoid having to collect pressure data between shut-in and the time when the actual fracture closure occurs, which can take several days in highly damaged and/or very tight formations. Moreover, in operations with multiple-batch injection events into the same interval/perforations, as is often the case in cuttings/slurry-injection operations, the trends in closure-pressure evolution can be tracked even if the fracture is never allowed to close.

Complex Fracture Closure Pressure Analysis During Shut-in: A Numerical Study

“…Over the last few decades, different fracture closure models have been developed to determine key parameters such as closure pressure, formation permeability, leak-off coefficient, and fluid efficiency. These models include the square root plot, log-log plot, G-function plot, and empirical equation (Nolte, 1986, 1991; Barree et al, 2007; Belyadi et al, 2019; Kholy et al, 2019). The square root plot suggests that closure pressure occurs at the inflection point on the second derivative of pressure (Belyadi et al, 2019).…”

“…However, the pressure data recorded at the time of an injection via a diagnostic fracture injection test (DFIT) can provide a wealth of information on fracture geometry, fluid leak-off characteristics, and fracture closure time (Nolte, 1986(Nolte, , 1991Mayerhofer et al, 1995;Plahn et al, 1997). Among DFITs, fracture pressure decline analysis is a common method of determining the fracture closure pressure and closure time due to the elimination of wellbore friction after shut-in (de Pater et al, 1996;Kholy et al, 2019). Thus, fracture closure analysis has been one of the trending topics in research on hydraulic fracturing over the past decades.…”

“…However, it is not practical to use the aforementioned fall-off analysis methods to determine fracture closure pressure in tight formations because the closure time is very long (Barree et al, 2014). Kholy et al (2019) developed an empirical equation to predict hydro-fracture closure pressure based on the instantaneous shut-in pressure (ISIP) using subsurface solids-injection data. The newly proposed method can be used to obtain the fracture closure pressure with a relative error of less than 3% compared to the closure pressure measured in the oilfield.…”