Systems and methods for detecting a proppant in a wellbore

A method includes acquiring a first set of data before a proppant is pumped into a wellbore. The method also includes acquiring a second set of data after the proppant is pumped into the wellbore. The method also includes determining a weighted average median of the first set of data and of the second set of data. The method also includes determining a location of the proppant in a subterranean formation based at least partially upon the weighted average medians.

BACKGROUND

A proppant includes a plurality of particles dispersed in a fluid. The proppant is injected into a wellbore in a subterranean formation during or after a hydraulic fracturing operation. The particles in the proppant are designed to hold open fractures formed by the hydraulic fracturing operation.

Recently, some users have employed electrically-conductive proppants to help determine the location of the proppant (and thus the fractures) in the subterranean formation. Once the electrically-conductive proppant is injected, the user applies an electromagnetic (EM) field to the subterranean formation. One or more sensors then measure the response of the EM field, which may be analyzed to determine the location of the proppant (and the fractures). However, in a typical oilfield environment, there are other sources of electromagnetic fields, which may also be detected by the sensors. These other sources may represent noise, which may make determining the location of the proppant (and thus the fractures) more difficult. Therefore, what is needed is an improved system and method for determining the location of a proppant in a subterranean formation.

BRIEF SUMMARY

A method includes acquiring a first set of data before a proppant is pumped into a wellbore. The method also includes acquiring a second set of data after the proppant is pumped into the wellbore. The method also includes determining a weighted average median of the first set of data and of the second set of data. The method also includes determining a location of the proppant in a subterranean formation based at least partially upon the weighted average medians.

A method for determining a location of a proppant in a subterranean formation is also disclosed. The method includes acquiring a set of data from a sensor. The set of data includes a first portion corresponding to a first electromagnetic field introduced into the subterranean formation by an electric current source and a second portion corresponding to a second electromagnetic field introduced into the subterranean formation by equipment. The second portion is noise. The method also includes determining median values of one or more data points in the set of data using JackKnife statistics. The method also includes determining a likelihood that a selected data point of the one or more data points is a true median value of the set of data. The method also includes determining a weighted average of the median values based at least partially upon the likelihood, wherein the likelihood is used as a weighting factor. The method also includes determining a stacked value based at least partially upon the weighted average. The method also includes determining a location of a proppant in the subterranean formation based at least partially upon the stacked value using geophysical inversion.

A system for determining a location of a proppant in a subterranean formation is also disclosed. The system includes an electric current source configured to introduce an electric current into a subterranean formation at an injection point that is positioned in a wellbore. The electric current produces a first electromagnetic field. The system also includes a sensor configured to measure the first electromagnetic field and to produce a set of data therefrom. The system also includes a computing system configured to determine a weighted average median of the set of data and determine a location of the proppant in the subterranean formation based at least partially upon the weighted average median.

DETAILED DESCRIPTION

FIG. 1illustrates a schematic view of a wellsite100, according to an embodiment. The wellsite100includes a wellbore102, which extends from the Earth's surface104to a subsurface geologic formation106that may contain oil, natural gas, and/or other geothermal resources. While the wellbore102is shown as being vertical in nature, it is to be understood that the wellbore102and/or the formation106may be vertical, horizontal, dipping, diagonal, slanting, or any combination thereof. The wellbore102may extend generally vertical to reach the subsurface formation106and then turn to extend horizontally or laterally through the formation106. A well casing108may be positioned in the wellbore102. Typically, the well casing108is formed of metal (e.g., steel). A cement stabilizer110may be formed to stabilize the well casing108in the wellbore102. The cement stabilizer110stabilizes the casing108as fracture fluid and/or a proppant is pumped into the formation106, possibly under high pressure. The cement stabilizer110can also stabilize the well casing108as natural gas, oil, or thermal fluids are extracted from the formation106by way of the wellbore102.

Through utilization of a fracturing fluid under high pressure, a fracture117including first portions118and second portions120may be induced in the formation106. In this embodiment, the fracture117is shown simplified as first and second portions118;120, however, it should be understood that the fracture117may contain several or multiple fractures, extending horizontally, vertically, and at various angles, and separate or branching from other induced fractures and combinations thereof. The fracture117may extend laterally and vertically some distance in one or more directions from wellbore102. A proppant119is pumped into the wellbore102and fills or partially fills the first portions118of the fracture117, thereby causing the first portions118to remain open (and thus causing the formation106to be more permeable for fluid flow). The proppant119filling the first portions118may be referred to as a “proppant pack.” The second portions120of the fracture117are not filled by the proppant119and are typically filled with water, sand, gas, and/or other rock particles from the surrounding formation106.

An electric current source112, which may reside on the Earth's surface104, is coupled to the casing108at a current injection (or current application) point116(e.g., positioned near the bottom of wellbore102and in contact with casing108proximate to the formation106and the first portion118). In another embodiment, the electric current source112may reside on or below the surface104. In another embodiment, the current injection point116may be located within the formation106, but not in contact with first portion118, or it may be located entirely outside the formation106. Electric current is carried from the electric current source112to the injection point116via an insulated wire114within the wellbore102. Alternately, the insulated wire114may be located on the exterior of the casing108(i.e., between the casing108and cement110). In still another embodiment, the electric current source112may be located within wellbore102proximate to the current injection point116. The electric current source112may be configured to generate current waveforms of various types (e.g., pulses, continuous wave, or repeating or periodic waveforms). Accordingly, the well casing108can be electrically energized and act as a spatially-extended source of electric current.

Some of the electric current generated by the electric current source112can travel from the well casing108through the proppant119of the induced fracture117of the formation106. A first electromagnetic field122generated by the electric current can be altered by the presence of the proppant119.

The proppant119can be selected to have electromagnetically suitable properties for generating, propagating, scattering, and/or altering electromagnetic fields that can be detected at the Earth's surface104. For example, the proppant119may be selected to have a particular electrical permittivity, magnetic permeability, current conductivity, and/or other electromagnetic or mechanical properties that are different from the corresponding properties of the formation106. In this way, the first portions118of the fracture117that are filled with the proppant119may have different electromagnetic properties from the second portions120of the fracture117not filled with the proppant119, as well as the rock of the surrounding formation106. The proppant119can, for example, be formed from an electrically-conductive material to enhance the electric conductivity of the first portion118.

In one or more embodiments, at least a portion of the proppant119is electrically conductive, or conductive proppant. The conductive proppant can contain a coating of an electrically conductive material, such as a conductive polymer and/or metallic coating. Suitable conductive proppants and methods for their manufacture are disclosed in U.S. Pat. Nos. 8,931,553, 9,250,351, 9,434,875, 9,551,210, 9,927,549, and 10,106,732, the entire disclosures of which are incorporated herein by reference.

In one embodiment, all of the proppant119that is injected into the wellbore102and the fracture117can be formed from the conductive proppant material. However, this is merely illustrative. In various embodiments, the proppant119can include portions having different electromagnetic properties in different portions of the wellbore102and/or the fracture117. For example, in some circumstances, it may be desirable to have conductive proppant in one portion of a fracture117(e.g., a portion of the fracture that is furthest from the wellbore102or a portion of the fracture117that is nearest to the wellbore102) and non-conductive proppant in another portion of the fracture117or in the wellbore102. In yet another example, in may be desirable to have proppant material with continuously or discretely varying electromagnetic properties as a function of the position of the proppant material in the fracture117.

Providing proppant119having differing electromagnetic properties (e.g., non-conductive and conductive proppant) into the fracture117may include mixing conductive materials of differing concentrations into the proppant119as it is injected into the wellbore102in continuously or discretely varying time intervals or may include a first injecting conductive proppant into the wellbore102followed by injecting a non-conductive proppant. In an embodiment, the proppant119may include both conductive and non-conductive proppant materials. For example, the first five, ten, or twenty percent of the proppant material that is provided into the wellbore102may be conductive proppant, and the remaining ninety-five, ninety, or eighty percent of the proppant material that is provided into the wellbore102may be non-conductive proppant so that only the fracture117(or only a leading portion of the fracture117) may be filled with the conductive portion of the proppant material. It should be appreciated that these examples are merely illustrative and that in general any electromagnetically suitable proppant material can be provided.

The electrically conductive material(s), or conductive material(s), can be or include any suitable magnetic or electrically conductive material(s). For example, the conductive materials can be or include pyrolytic carbon, carbon black, graphite, graphene, derivatives of graphene, petroleum coke, coke breeze, carbon fiber, fullerenes, or carbon nanotubes or any mixture or combination thereof. In one or more embodiments, the conductive materials can be or include any metal selected from Groups 3-13 of the Periodic Table, any alloys thereof and/or any oxides thereof. For example, the conductive materials can be or include aluminum, tin, iron, cobalt, copper, nickel, zinc, or oxides thereof, or any combination, mixture or alloy thereof. The conductive materials can also be or include ferromagnetic material.

The conductive materials can be in the form of particles having any suitable size and shape. In one or more embodiments, the conductive materials can be substantially spherical in shape, can have a fibrous material, can be polygonal shaped (such as cubic), can have an irregular shape, or any combination thereof. In one or more embodiments, the conductive materials can be substantially round and spherical. In one or more embodiments, the conductive materials can be in the form of particles, each having a size of about 0.001, about 0.01, about 0.1, about 0.5, about 1, about 5, about 10, or about 25 to about 50, about 75, about 100, about 150, about 200, about 250, about 500, about 750, or about 1,000 microns as measured in the particles largest dimension. For example, the conductive materials can be in the form of particles, each having a size of about 0.001 micron to about 0.1 micron, about 0.1 micron to about 5 microns, about 5 microns to about 25 microns, or from about 30 microns to about 100 microns. At least a portion of the particles can be in the form of discrete particles or in the form of an agglomeration of particles.

The non-conductive proppant can be a conventional proppant such as a ceramic proppant, sand, plastic beads and glass beads. Such conventional proppants can be manufactured according to any suitable process including, but not limited to continuous spray atomization, spray fluidization, spray drying, or compression. Suitable conventional proppants and methods for their manufacture are disclosed in U.S. Pat. Nos. 4,068,718, 4,427,068, 4,440,866, 5,188,175, and 7,036,591, the entire disclosures of which are incorporated herein by reference. In one or more exemplary embodiments, the proppant can be manufactured using a drip casting method. Suitable drip casting methods and proppants made therefrom are disclosed in U.S. Pat. Nos. 8,865,631, 8,883,693, 9,175,210, and 9,670,400, the entire disclosures of which are incorporated herein by reference. According to certain embodiments described herein, the proppants are made in a continuous process, while in other embodiments, the proppants are made in a batch process.

The electric current source112situated on the Earth's surface104generates electric current that flows down the insulated wire114to the current injection point116proximate to the formation106and the first portions118contained therein. As the injection point116is in direct physical contact with the well casing108and/or the first portions118of the fracture117, the electric current can flow from the injection point116to the conductive well casing108and the first portions118. Electric current flow within well casing108is generally vertically upwards and downwards from the injection point116, whereas it is laterally outwards into the formation106within the first portions118. The first electromagnetic field (e.g., waves)122generated by the electrical current in both the well casing108and the proppant119propagates to various locations in a three-dimensional volume of the Earth.

Electric currents associated with the first electromagnetic field122flow generally toward a current grounding point124situated on the Earth's surface104. In another embodiment, the grounding point124may be located on or slightly beneath the Earth's surface104near to or far from the wellbore102. In another embodiment, the grounding point124can be located beneath the surface104in another wellbore that is relatively near to or far from the wellbore102. The other wellbore may or may not be used in the fracturing process. The grounding point124is connected to the electric current source112via an insulated wire126. In this manner, the insulated wire114, current injection point116, well casing108, first portions118, first electromagnetic field122propagating within the Earth, grounding device124, and/or insulating wire126constitute a “closed loop” that carries electric current from and ultimately back to the electric current source112.

One or more sensors, such as sensors128, are positioned on the surface104of the Earth. In another embodiment, the sensors128may be positioned on, above, or below the surface104. The sensors128are used to detect the first electromagnetic field122(e.g., that propagates from the energized well casing108and the first portions118to the sensors128). The sensors128include a transducer for sensing the first electromagnetic field122.

The sensors128may be located at corresponding locations such as sensor locations L1and L2. The sensors128may be deployed in a one-, two-, or three-dimensional distribution at or near the surface104. For example, the sensors128may be positioned on the surface104, beneath the surface104, and/or suspended or mounted above the surface104. Additionally, the sensors128may be deployed in various other subsurface wellbores located adjacent to, near to, or at some distance away from, the formation106. In one or more embodiments, at least a portion of the sensors128may be located in the wellbore102, such as on or in the casing108. The sensors128may include various types of antennas and/or physical transducers appropriate for detecting electric fields and/or magnetic fields, and converting these physical signals to voltage that are subsequently forwarded to a data recording system130. In particular, sensors commonly used for geophysical exploration or characterization purposes (e.g., porous pots, metal electrodes, electric/magnetic pickup coils, antennas) may be used.

The sensors128are connected to the data recording system130. The data recording system130has the capability to receive, amplify, filter, digitize, process, and otherwise handle the voltage signals generated by sensors128in response to the incident first electromagnetic field122. Additionally, the data recording system130may store these digitized and processed signals on an appropriate recording medium contained therein. Alternately, the data recording system130may transmit the received signals to a computing system1100where additional processing operations may be conducted and the data is/are stored therein. The computing system1100may be located proximate to the data recording system130, or it may be situated in a remote location. Transmission of data between the recording system130and the computing system1100may be via an electrical wire, or via radio-transmission techniques.

The computing system1100may be used to generate and/or store a geophysical/geological model representing the three-dimensional volume of the Earth supporting the propagating first electromagnetic field122(which includes the particular formation106containing the fracture117). It may also generate and/or store data corresponding to the known location of the current injection point116, as well as the known amplitude and waveform of the electric current generated by the electric current source112. It may also generate and/or store the known three-dimensional configuration of the wellbore102with associated casing108and cement110, and the known locations of the sensors128.

The sensors128may be used to gather electromagnetic field data before, during, and/or after the hydraulic fracturing and proppant injection operations. Equipment such as drilling and extraction equipment134for creating, reinforcing, pumping, extracting, or other drilling and/or extraction operations may be present in the vicinity of the wellbore102. In at least one embodiment, the equipment134may also introduce a second electromagnetic field (e.g., waves)136into the formation106, which may be detected by the sensors128. As discussed in more detail below, the second electromagnetic field136may be considered to be noise, which may make determining the location of the proppant119and the fractures117more difficult.

The measurements/recordings, taken before and/or after fracturing and proppant insertion, can subsequently be used to determine the location of the first (e.g., proppant-filled) portion118of the fracture117within the formation106. As used herein, the term “location” can refer to the position, geometry, and/or orientation of the fracture portion118relative to the surface104, the wellbore102, and/or the current injection point116. The term “geometry” can refer to the size, shape, length, height, width, orientation, etc. portions of the first (e.g., proppant-filled) portions118of the fracture117. The term “orientation” can refer to the orientation of at least a portion of the first (e.g., proppant-filled) portions118relative to the surface104or the wellbore102in the subsurface. Additional details regarding the wellsite100may be found in U.S. Pat. No. 9,250,351, the content of which is hereby incorporated by reference.

FIG. 2illustrates a flowchart of a method200for determining a location of the proppant119(and thus the fractures117) in the formation106, according to an embodiment. The method200may include acquiring (e.g., measuring and/or receiving) a first set of data before the proppant119is pumped/injected into the wellbore102, as at202. Acquiring the first set of data may include introducing an electrical current into the formation106using the electric current source112. The electrical current may generate the first electromagnetic field122that is measured by the sensor(s)128.

In at least one embodiment, in addition to measuring the first electromagnetic field122generated by the electrical current source112, the sensor(s)128may also measure the second electromagnetic field136generated by the equipment134(e.g., drilling and extraction equipment). This second electromagnetic field136may be considered to be noise. The measurements of the (e.g., first and/or second) electromagnetic fields122,136may be or include voltage vs. time measurements.

FIG. 3illustrates a graph300showing voltage vs. time measurements of the first electromagnetic field122captured by the sensor(s)128, according to an embodiment. The graph300represents a hypothetical scenario and therefore does not include the measurements of the second electromagnetic field136(i.e., the noise). In other words, the graph300is noise-free. As may be seen, the graph300is an oscillating square pulse sequence of voltage in the time domain. Because there is no noise present, the amplitude of the voltage is substantially equal in each cycle302,304.

FIG. 4illustrates a graph400showing voltage vs. time measurements of the first and second electromagnetic fields122,136captured by the sensor(s)128, according to an embodiment. Here, the graph400does include the measurement of the second electromagnetic field136(i.e., the noise). Similar to the graph300, the graph400is an oscillating square pulse sequence of voltage in the time domain. However, due to the noise, the amplitude of the voltage varies in the different cycles402,404.

The measurements (e.g., of the first and second electromagnetic fields122,136) may be transmitted from the sensor(s)128to the data recording system130and/or the computing system1100, which may process the measurements to produce the first set of data.

The method200may also include introducing (e.g., pumping, injecting, etc.) the proppant119into the wellbore102, as at204. The proppant119may flow into the first portion118of the fractures117. The proppant119may include any of the properties discussed above. For example, the proppant119may be electrically-conductive such that the first electromagnetic field122is altered by the presence of the proppant119.

The method200may also include acquiring (e.g., measuring and/or receiving) a second set of data after the proppant119is pumped/injected into the wellbore102, as at206. Acquiring the second set of data may be accomplished in a similar manner to acquiring the first set of data. The second set of data may also include the first and second electromagnetic fields122,136. However, now the first electromagnetic field122of the second set of data may include information related to the proppant119(e.g., due to the first electromagnetic field122being altered by the presence of the proppant119in the fractures117).

The measurements captured by the sensor(s)128may look similar to the measurements in the graph400inFIG. 4; however, as will be appreciated, they may have different amplitudes due to the first electromagnetic field122being altered by the presence of the proppant119in the fractures117. The measurements (e.g., of the first and second electromagnetic fields122,136) may be transmitted from the sensor(s)128to the data recording system130and/or the computing system1100, which may process the measurements to produce the second set of data.

The method200may also include converting the first set of data and/or the second set of data from a time domain to a frequency domain, as at208.FIG. 4shows the first set of data in the time domain. As mentioned above, the second set of data may have a similar appearance but (e.g., slightly) different amplitudes.

FIG. 5shows the first set of data (fromFIG. 4) after being converted into the frequency domain. More particularly,FIG. 5illustrates a graph500showing voltage vs. frequency measurements of the first set of data, according to an embodiment. A corresponding graph showing voltage vs. frequency measurements of the second set of data is not shown; however, as will be appreciated, the second set of data may have a similar appearance toFIG. 5but (e.g., slightly) different amplitudes when converted into the frequency domain. The conversion into the frequency domain may be performed by the sensor(s)128, the data recording system130, and/or the computing system1100. As may be seen, the graph500includes a plurality of voltage values. The largest voltage value502corresponds to the fundamental frequency of the first set of data (or the second set of data). The other, smaller voltage values504,506correspond to harmonics thereof. Each of the voltage values502,504,506may correspond to a single cycle (e.g., cycle402) inFIG. 4.

FIG. 6illustrates a graph600showing a spectral variation of the fundamental frequency voltage value502(fromFIG. 5) corresponding to a single cycle (e.g., cycle402fromFIG. 4), according to an embodiment. As discussed above with respect toFIG. 4, there is a variation in the peak value of the voltage measured in different time cycles402,404. The spectral voltage value obtained by transforming an individual time cycle into the frequency domain (referred to as a “bin” inFIG. 6) may produce a corresponding variation from bin to bin (the bins are identified by reference number602). These bins602can belong to the fundamental frequency or any of the odd harmonic frequencies obtained from the time series. The dotted line604corresponds to an average (i.e., mean, stacked) amplitude value for a given frequency in the spectra. As used herein, “spectra” refers to the distribution of amplitudes and/or other attribute values in frequency domain for a given time series.

The method200may also include determining whether the first set of data and/or the second set of data is/are unimodal, as at210. The determination may be made by the data recording system130and/or the computing system1100. As used herein, “unimodal data” refers to data having a distribution of values clustered around a single peak, or mode, and all other values occurring less frequently than this modal value. In at least one embodiment, unimodal data may have a Gaussian noise variation. More particularly, in a normal Gaussian distribution, the average and median values are the same as the modal value. As used herein, “average” and “mean” have the same meaning and are used interchangeably.

FIG. 7illustrates a graph (e.g., a histogram)700showing a unimodal average (i.e., mean, stacked) signal amplitude, according to an embodiment. If the variation in amplitude (e.g. of the first set of data and/or the second set of data) inFIG. 6is unimodal, then the histogram700inFIG. 7may be used to show the spectra. In addition, if the variation in amplitude (e.g. of the first set of data and/or the second set of data) inFIG. 6is unimodal, the method200may proceed to step214below. However, if the variation in amplitude (e.g. of the first set of data and/or the second set of data) inFIG. 6is not unimodal, the method200may include removing one or more outliers, as at212.

FIG. 8illustrates a graph (e.g., a histogram)800showing a non-unimodal average (i.e., mean, stacked) signal amplitude, according to an embodiment. The graph800may be similar to the graph700; however, the graph800may include one or more strong outliers802,804that distort the stacked output. As used herein, an “outlier” refers data points whose values exceed the median or modal values by an order of magnitude or more. The outliers802,804may be caused by the noise (e.g., from the equipment134). The outliers802,804may be removed from the stacked output to allow for a more accurate signal estimate.

Once the first set of data and/or the second set of data is/are determined to be unimodal, the method200may include determining a Weighted Average Median (WAM) of the first set of data and/or the second set of data, as at214. Utilization of JackKnife statistics to determine the Weighted Average Median (JKWAM) allows for a more robust method of stacking, which helps reduce the influence of human bias that may be introduced after the selective removal of potential outliers802,804. JackKnife statistics is a mathematical resampling technique that is useful for variance and bias estimation. For example, JackKnife statistics may be used to select statistical attributes such as mean, median, and/or mode of a sample data set. It utilizes the principle of replacing individual data points in the sample by the mean, median, mode, or any other statistical attribute of the remaining data points.

Determining the weighted average median (e.g., using JackKnife statistics) of the first set of data and/or the second set of data may include determining (e.g., JackKnife) median values of one or more data points (e.g., one or more of points602inFIG. 6) in the first set of data and/or the second set of data.

Determining the weighted average median (e.g., using JackKnife statistics) of the first set of data and/or the second set of data may also include determining a likelihood that a selected data point (e.g., a selected one of the points602inFIG. 6) is the true median value of the first set of data and/or the second set of data. As used herein, a “true median value” differs from a “median value” in the preceding paragraph in that the true median value is the median of the entire population, as opposed to the median of the sample data set. The likelihood may be determined, for example, using a folded cumulative distribution formula for a Gaussian distribution.

FIG. 9illustrates an example of a normal Gaussian probability density function900, andFIG. 10illustrates an example of a folded cumulative probability distribution function1000, according to an embodiment. The folded cumulative distribution formula is determined as a combination of the standard normal cumulative distribution function F(x) and its complement Q(x), also known as the cumulative probability of non-exceedance. F(x) is given by the equation

F⁡(x)=Φ⁡(x-μσ)=12⁡[1+erf⁢x-μσ⁢2]Equation⁢⁢(1)
where F represents density, μ represents the mean (i.e., average), σ represents the deviation, x represents a given sample data point, and Φ is the representative function of z-score of x. The z-score of a sample data point represents how many standard deviations away from the mean the data point is. For example, a z-value of 1 will mean that ‘x’ is 1 standard deviation away from the mean of the sample data set. Q(x) is the complementary equation of F(x) and is given as:
Q(x)=1−Φ(x)   Equation (2)

Determining the weighted average median (e.g., using JackKnife statistics) of the first set of data and/or the second set of data may also include determining a weighted average of the (e.g., JackKnife) median values based at least partially upon the determined likelihoods, where the determined likelihoods may be used as weighting factors. A final stacked value of the population may then be determined based at least partially upon the weighted average. The utilization of a weighted average of median values and/or a final stacked value is a unique approach to determining the stacked signal value of a geophysical signal.

The method200may also include determining a noise parameter of the weighted average median (e.g., of the final stacked value), as at216. The noise parameter may be or include a standard error of the weighted average of the median values. The noise parameter may be determined by determining the standard deviation of the population or the average of the JackKnife standard deviations of all the points in the population. The standard deviation divided by the square root of the number of samples in the population provides the Standard Error of the Mean (SEM).

The method200may also include determining a location of the proppant119in the formation106based at least partially upon the weighted average median and/or the noise parameter, as at218. More particularly, this may include determining the location of the proppant119in the first portions118of the fractures117in the formation106based at least partially upon the weighted average median (e.g., the final stacked value) and/or the noise parameter. In one example, one or more portions of the method200may be used as an input to an algorithm which then determines the location and the geometry of the fracture117using the methods of geophysical inversion. In this example, the application of the method200prior to the geophysical inversion leads to higher confidence results regarding the location and geometry of the (e.g., first portions118of the) fracture117.

The method200may also include performing a physical action at the wellsite100, as at220. The physical action may be performed in response to the location and/or geometry of the (e.g., first portions118of the) fracture117. The physical action may be or include determining a placement of a future wellbore, drilling a future wellbore, determining a spacing of a fracture treatment in the wellbore102or the future wellbore, performing the fracture treatment in the wellbore102or the future wellbore, or a combination thereof.

FIG. 11illustrates an example of such the computing system1100, in accordance with some embodiments. The computing system1100may include a computer or computer system1101A, which may be an individual computer system1101A or an arrangement of distributed computer systems. The computer system1101A includes one or more analysis modules1102that are configured to perform various tasks according to some embodiments, such as one or more methods disclosed herein. To perform these various tasks, the analysis module602executes independently, or in coordination with, one or more processors1104, which is (or are) connected to one or more storage media1106. The processor(s)1104is (or are) also connected to a network interface1107to allow the computer system1101A to communicate over a data network1109with one or more additional computer systems and/or computing systems, such as1101B,1101C, and/or1101D (note that computer systems1101B,1101C and/or1101D may or may not share the same architecture as computer system1101A, and may be located in different physical locations, e.g., computer systems1101A and1101B may be located in a processing facility, while in communication with one or more computer systems such as1101C and/or1101D that are located in one or more data centers, and/or located in varying countries on different continents).

A processor may include a microprocessor, microcontroller, processor module or subsystem, programmable integrated circuit, programmable gate array, or another control or computing device.

The storage media1106may be implemented as one or more computer-readable or machine-readable storage media. Note that while in the example embodiment ofFIG. 11storage media1106is depicted as within computer system1101A, in some embodiments, storage media1106may be distributed within and/or across multiple internal and/or external enclosures of computing system1101A and/or additional computing systems. Storage media1106may include one or more different forms of memory including semiconductor memory devices such as dynamic or static random access memories (DRAMs or SRAMs), erasable and programmable read-only memories (EPROMs), electrically erasable and programmable read-only memories (EEPROMs) and flash memories, magnetic disks such as fixed, floppy and removable disks, other magnetic media including tape, optical media such as compact disks (CDs) or digital video disks (DVDs), BLURAY® disks, or other types of optical storage, or other types of storage devices. Note that the instructions discussed above may be provided on one computer-readable or machine-readable storage medium, or may be provided on multiple computer-readable or machine-readable storage media distributed in a large system having possibly plural nodes. Such computer-readable or machine-readable storage medium or media is (are) considered to be part of an article (or article of manufacture). An article or article of manufacture may refer to any manufactured single component or multiple components. The storage medium or media may be located either in the machine running the machine-readable instructions, or located at a remote site from which machine-readable instructions may be downloaded over a network for execution.

In some embodiments, computing system1100contains one or more proppant detection module(s)1108. In the example of computing system1100, computer system1101A includes the proppant detection module1108. In some embodiments, a single proppant detection module may be used to perform some aspects of one or more embodiments of the methods disclosed herein. In other embodiments, a plurality of proppant detection modules may be used to perform some aspects of methods herein.

It should be appreciated that computing system1100is merely one example of a computing system, and that computing system1100may have more or fewer components than shown, may combine additional components not depicted in the example embodiment ofFIG. 11, and/or computing system1100may have a different configuration or arrangement of the components depicted inFIG. 11. The various components shown inFIG. 11may be implemented in hardware, software, or a combination of both hardware and software, including one or more signal processing and/or application specific integrated circuits.

Computational interpretations, models, and/or other interpretation aids may be refined in an iterative fashion; this concept is applicable to the methods discussed herein. This may include use of feedback loops executed on an algorithmic basis, such as at a computing device (e.g., computing system1100,FIG. 11), and/or through manual control by a user who may make determinations regarding whether a given step, action, template, model, or set of curves has become sufficiently accurate for the evaluation of the subsurface three-dimensional geologic formation under consideration.

It is understood that modifications to the invention may be made as might occur to one skilled in the field of the invention within the scope of the appended claims. All embodiments contemplated hereunder which achieve the objects of the invention have not been shown in complete detail. Other embodiments may be developed without departing from the spirit of the invention or from the scope of the appended claims. Although the present invention has been described with respect to specific details, it is not intended that such details should be regarded as limitations on the scope of the invention, except to the extent that they are included in the accompanying claims.