Methods and Systems for Determining Subterranean Fracture Closure

Abstract

Methods and systems for determining subterranean fracture closure are disclosed herein. The methods can include electrically energizing a casing of a wellbore that extends from a surface of the earth into a subterranean formation having a fracture that is at least partially filled with an electrically conductive proppant and measuring a first electric field response at the surface or in an adjacent wellbore at a first time interval to provide a first field measurement. The methods can also include measuring a second electric field response at the surface or in the adjacent wellbore at a second time interval to provide a second field measurement and determining an increase in closure pressure on the electrically conductive proppant from a difference between the first and second field measurements.

What is claimed is: 
     
         1 . A method for determining fracture closure, comprising:
 electrically energizing an electrically conductive proppant pack comprising electrically conductive proppant located in a fracture of a subterranean formation;   measuring a first electric field response at a first time interval with one or more sensors to provide a first field measurement;   measuring a second electric field response at a second time interval with one or more sensors to provide a second field measurement; and   determining an increase in closure pressure on the electrically conductive proppant from a difference between the first and second field measurements.   
     
     
         2 . The method of  claim 1 , wherein the sensors are configured to measure three dimensional (x, y, and z) components of electric field responses. 
     
     
         3 . The method of  claim 2 , wherein the sensors are configured to measure three dimensional (x, y, and z) components of electric and magnetic field responses. 
     
     
         4 . The method of  claim 1 , further comprising:
 measuring electric and magnetic field responses at three or more time intervals to provide three or more field measurements; and   determining an increase in closure pressure on the electrically conductive proppant from differences between each of the three or more field measurements.   
     
     
         5 . The method of  claim 1 , further comprising:
 prior to electrically energizing the electrically conductive proppant pack, injecting into the fracture the electrically conductive proppant and wherein the electrically conductive proppant includes electrically conductive sintered, substantially round and spherical particles comprising an electrically conductive material comprising iron, silver, gold, copper, aluminum, calcium, tungsten, zinc, nickel, lithium, platinum, tin, or carbon steel, or any combination or oxide thereof.   
     
     
         6 . The method of  claim 1 , further comprising:
 prior to electrically energizing the electrically conductive proppant pack, injecting into the fracture the electrically conductive proppant and wherein the electrically conductive proppant includes electrically conductive sintered, substantially round and spherical particles comprising an electrically conductive material comprising metal clusters, metal flake, metal shot, metal powder, metalloids, metal nanoparticles, quantum dots, carbon nanotubes, or graphite.   
     
     
         7 . The method of  claim 1 , wherein the increase in closure pressure on the electrically conductive proppant increases the electrical conductivity of the electrically conductive proppant by at least about 50%. 
     
     
         8 . The method of  claim 4 , further comprising determining a closure of the fracture by observing substantially no difference between two successive field measurements. 
     
     
         9 . The method of  claim 1 , wherein, numerical simulations, solving Maxwell's equations of electromagnetism for the electric fields are performed, prior to obtaining the first field measurement, to determine temporal characteristics of an optimum input wave form and a recording sensor array geometry to be used in the field applications, wherein the numerical simulations are based upon an earth model determined from geophysical logs and geological information. 
     
     
         10 . A method for determining fracture closure time, comprising:
 introducing a first electric current to a subterranean formation extending from a wellbore;   obtaining a first measurement by measuring electric field responses from the first electric current at a surface of the earth or in an adjacent wellbore;   injecting a hydraulic fluid into the subterranean formation at a rate and pressure sufficient to open a fracture therein;   injecting into the fracture a fluid containing electrically conductive sintered, substantially round and spherical particles under a first pressure;   introducing a second electric current to the earth at or near the fracture containing the electrically conductive sintered, substantially round and spherical particles;   obtaining a second measurement by measuring electric field responses from the second electric current at a surface of the earth or in an adjacent wellbore;   releasing the first pressure;   introducing a third electric current to the earth at or near the fracture;   obtaining a third measurement by measuring electric field responses from the third electric current at a surface of the earth or in an adjacent wellbore; and   determining a difference between the first and second measurements.   
     
     
         11 . The method of  claim 10 , wherein the fracture is in an open state when the second measurement is obtained. 
     
     
         12 . The method of  claim 10 , further comprising:
 introducing a series of discrete electric current injections (a 1  . . . a N ) to the earth at or near the fracture, wherein N is any integer greater than 3 and a 1  is the first electric current; and   obtaining discrete measurements (b 1  . . . b N ) for each of (a 1  . . . a N ) by measuring electric field responses from each of the (a 1  . . . a N ) electric current injections at a surface of the earth or in an adjacent wellbore, wherein b 1  is the first measurement.   
     
     
         13 . The method of  claim 12 , further comprising iteratively comparing measurements b N  and b N+1  to check for differences between two successive measurements, wherein closure of the fracture is determined by observing no substantial difference between b N  and b N+1 . 
     
     
         14 . The method of  claim 13 , wherein b N+1  is a final measurement when there is no observed substantial difference between b N  and b N+1  and a fracture closure time is determined by calculating time accrued from injecting into the fracture the fluid containing electrically conductive sintered, substantially round and spherical particles under a first pressure to introducing electric current a N+1 . 
     
     
         15 . The method of  claim 10 , wherein the measured three dimensional components of the electric field responses are analyzed with imaging methods selected from the group consisting of an inversion algorithm based on Maxwell's equations of electromagnetism and electromagnetic holography to determine a proppant pack location, wherein, in the inversion algorithm, parameters of an earth model are adjusted to obtain a fit to a plurality of forward model calculations of responses for an assumed earth model, and wherein, in the electromagnetic holography, the electric field responses and a source wave form are projected into an earth volume to form an image of the proppant pack location using constructive and destructive interferences. 
     
     
         16 . The method of  claim 10 , wherein electromagnetic wave forms selected from the group consisting of Gaussian, square and time domain are used as an input signal to generate the three dimensional electric field field responses. 
     
     
         17 . The method of  claim 15 , wherein, numerical simulations, solving Maxwell's equations of electromagnetism for the electric fields are performed, prior to field applications, to determine temporal characteristics of an optimum input wave form and a recording sensor array geometry to be used in the field applications, wherein the numerical simulations are based upon an earth model determined from geophysical logs and geological information. 
     
     
         18 . A method for determining fracture closure time, comprising:
 introducing a first electric current to a subterranean formation extending from a wellbore;   obtaining a first measurement by measuring electric and magnetic field responses from the first electric current;   injecting a hydraulic fluid into the subterranean formation at a rate and pressure sufficient to open a fracture therein;   injecting into the fracture a fluid containing electrically conductive material and proppant under a first pressure to provide an electrically conductive proppant pack;   introducing a second electric current to the earth at or near the electrically conductive proppant pack;   obtaining a second measurement by measuring electric and magnetic field responses from the second electric current;   releasing the first pressure;   introducing a series of discrete electric current injections (a 1  . . . a N ) to the earth at or near the fracture, wherein N is any integer greater than 2 and a 1  is the first electric current; and   obtaining discrete measurements (b 1  . . . b N ) for each of (a 1  . . . a N ) by measuring electric and magnetic field responses from each of the (a 1  . . . a N ) electric current injections; and   determining a difference between the first and second measurements.   
     
     
         19 . The method of  claim 18 , further comprising iteratively comparing measurements b N  and b N+1  to check for differences between two successive measurements, wherein closure of the fracture is determined by observing no substantial difference between b N  and b N+1 . 
     
     
         20 . The method of  claim 19 , wherein b N+1  is a final measurement when there is no observed substantial difference between b N  and b N+1  and a fracture closure time is determined by calculating time accrued from injecting into the fracture the fluid containing electrically conductive material and proppant under the first pressure to introducing electric current a N+1 .