Inversion method to estimate fracture propagation velocity and fracture volume with cross-well distributed fiber-optic strain data before fracture hit
Systems and methods are provided to obtain fracture parameters of a hydraulic fracturing operation using strain data obtained before a fracture hit. A system may include a strain sensor and processing circuitry. The strain sensor may be disposed downhole in a monitoring well and may obtain strain data while a fracture caused by a hydraulic fracturing operation propagates from a treatment well toward the monitoring well before a fracture hit occurs in the monitoring well. The processing circuitry may perform an inversion based on the strain data to estimate fracture parameters associated with the propagation of the fracture before the fracture hit.
1 . A system comprising:
a fiber-optic strain sensor configured to be disposed downhole in a monitoring well to obtain strain data while a fracture, caused by a hydraulic fracturing operation in an adjacent treatment well, propagates from the treatment well toward the monitoring well, the strain data obtained even before a fracture hit occurs in the monitoring well, wherein obtaining the strain data comprises:
measuring strain rate data; and
integrating the strain rate data over a time period to obtain the strain data; and
processing circuitry configured to:
perform an inversion based on the strain data to estimate fracture parameters associated with the propagation of the fracture even before the fracture hit occurs in the monitoring well, wherein the performing the inversion to estimate the fracture parameters comprises:
calculating a modeled strain using a 3D displacement discontinuity method (3D DDM), wherein the modeled strain is a function of a height of the fracture, a width of the fracture, and a length of the fracture;
performing a gradient-based inversion by iteratively reducing a residual between the modeled strain and the strain data; and
estimating, based on the gradient-based inversion, the fracture parameters before the fracture hit occurs in the monitoring well.
2 . The system of claim 1 , wherein the strain sensor comprises a low-frequency distributed acoustic sensing (LF-DAS) fiber-optic sensor.
3 . The system of claim 1 , wherein the fracture parameters comprise a fracture half-length.
4 . The system of claim 1 , wherein the fracture parameters comprise a fracture propagation velocity.
5 . The system of claim 1 , wherein the fracture parameters comprise a fracture cross-section area.
6 . The system of claim 1 , wherein the fracture parameters comprise a fracture volume.
7 . The system of claim 1 , wherein the fracture parameters comprise a fracturing fluid efficiency.
8 . The system of claim 1 , wherein the processing circuitry is configured to estimate the fracture parameters by:
determining a fracture half-length and fracture width distribution from the inversion; and
determining, based on the fracture half-length and the fracture width distribution, a fracture propagation velocity, a fracture cross-section area, a fracture volume, a fracturing fluid efficiency, or any combination thereof.
9 . The system of claim 1 , wherein the monitoring well is disposed a well spacing from the treatment well, and wherein the processing circuitry is configured to validate the fracture parameters by verifying that a fracture half-length of the fracture is within a threshold distance of the well spacing at a time the fracture hit occurs.
10 . The system of claim 1 , where the fracture hit comprises a fracture extending from the treatment well into the monitoring well.
11 . A method comprising:
positioning a fiber-optic strain sensor in a monitoring well;
performing a hydraulic fracturing operation in a treatment well positioned adjacent the monitoring well;
obtaining strain data from the fiber-optic strain sensor positioned in the monitoring well, wherein obtaining the strain data comprises:
measuring strain rate data; and
integrating the strain rate data over a time period to obtain the strain data;
performing an inversion on a portion of the strain data from the fiber-optic strain sensor obtained during the hydraulic fracturing operation between a fracture perforation of the treatment well and even before a fracture hit of the monitoring well, wherein the performing the inversion comprises:
calculating a modeled strain using a 3D displacement discontinuity method (3D DDM), wherein the modeled strain is a function of a height of the fracture, a width of the fracture, and a length of the fracture; and
performing a gradient-based inversion by iteratively reducing a residual between the modeled strain and the strain data; and
estimating, based on the gradient-based inversion, a fracture parameter of the performed hydraulic fracturing operation before the fracture hit occurs in the monitoring well.
12 . The system of claim 1 , wherein the modeled strain is denoted (E), wherein the strain data is denoted (d), and wherein the gradient-based inversion comprises determining an optimization of w 0 and L to minimize a residual between (ε) and (d) based on a residual function ε=GSw 0 −d, where G is a Green-function matrix that depends on L, S is a shape operator, W 0 is a width of a perforation point of the fracture, and L is a length of the fracture.
13 . The system of claim 12 , wherein the optimization of w, and L are determined within a bounded region min{f(L,w 0 ): L min ≤L≤L max , w 0,min ≤w 0 ≤w 0,max }, where f=GSw 0 −d.
14 . The method of claim 11 , where the fracture hit comprises a fracture extending from the treatment well into the monitoring well.
15 . The method of claim 11 , wherein the fracture parameter comprises a fracture half-length, a fracture propagation velocity, a fracture cross-section area, a fracture volume, a fracturing fluid efficiency, or any combination thereof.
16 . The method of claim 11 , comprising adjusting the hydraulic fracturing operation based on the fracture parameter.
17 . The method of claim 16 , wherein adjusting the hydraulic fracturing operation comprises adjusting a pumping pressure, adjusting a pumping rate, pausing pumping, stopping pumping, or any combination thereof.