DAS METHOD OF ESTIMATING FLUID DISTRIBUTION

Abstract

This disclosure describes a method of calculating fluid distribution from a hydraulically fractured well, especially during a plug-and-perf hydraulic fracturing operation. The Distributed Acoustic Sensing (DAS) data is used to quantify the fluid distribution in separate perf clusters during fracturing, and the result can be used for completion design and optimization, hydraulic fracturing, and ultimately for oil and gas production.

Claims

1. A method of optimizing fracturing in a well, the method comprising: a) recording distributed acoustic sensing (DAS) noise intensity signals from a well during a fracturing operation; b) deriving DAS intensity traces from the recorded DAS noise intensity signals, wherein each said DAS intensity trace is a recording of DAS noise intensity over a span of a pre-determined number of fiber depths averaged over a predetermined period of time, and wherein each said trace do not overlap with other said traces on fiber depths; c) locating a baseline channel having no perforations at that fiber depth; d) calculating a volumetric flow rate Q for each said perforation cluster using the following equation: $Q=C_4.Math.{\mathrm{Intensity}}^{\frac{1}{3}}.Math.N^{\frac{2}{3}}.Math.\frac{H^{\frac{4}{3}}}{D^{\frac{1}{3}}}$ wherein D is fluid density, N is the number of perforations in said perforation cluster, H is the diameter of the perforations, Intensity is the DAS intensity from each trace at said perforation cluster minus the DAS intensity from said baseline channel, and C.sub.4 is a constant; and f) using said Q for each said perforation cluster to optimize a fracture plan for subsequent fracture stages in said well and implementing said optimized fracture plan in said well.

2. The method of claim 1, wherein the Intensity is directly proportional to a pump-work factor (W) represented by:
Intensity=C.sub.3.Math.W

3. The method of claim 2, wherein the pump-work factor W is calculated by the following equation:
W=C.sub.1.Math..sub.P.Math.Q wherein C.sub.1 is a constant, .sub.P is the pressure differential between both sides of the perforation.

4. The method of claim 3, wherein the pressure differential .sub.P is calculated by the following equation: ${}_P=C_2.Math.Q^2.Math.\frac{D}{N^2.Math.H^4}$ where C.sub.2 is a constant, D is the fluid density, N is the number of perforations, and H is the diameter of the perforations.

5. The method of claim 1, further comprising step b-1) prior to step c): b-1) identifying cluster locations based on fiber depths of each said perforation cluster inside said well.

6. A system for calculating volumetric flow rate through one or more perforation clusters inside a wellbore, comprising: a) a distributed acoustic sensing (DAS) monitoring device including a optical fiber that runs along the length of the wellbore, wherein the DAS optical fiber is coupled to an interrogating unit for emitting interrogating signals, the DAS monitoring device detects DAS noise intensity signals when strain or temperature deforms the optical fiber; b) a computer coupled to the DAS monitoring device for recording DAS noise intensity signals detected by the DAS monitoring device; c) wherein the computer performs the following steps to obtain volumetric flow rates of the hydraulic fluid through each said perforation cluster: i) deriving DAS intensity traces from the recorded DAS noise intensity signals, wherein each said DAS intensity trace is a recording of DAS noise intensity over a span of a pre-determined number of fiber depths averaged over a predetermined period of time, and wherein each said trace do not overlap with other said traces on fiber depths; ii) locating the fiber depths of each said perforation cluster inside said well; iii) locating a baseline channel having no perforation in that fiber depth for each said trace; iv) calculating a volumetric flow rate Q for each said perforation cluster using the following equation: $Q=C_4.Math.{\mathrm{Intensity}}^{\frac{1}{3}}.Math.N^{\frac{2}{3}}.Math.\frac{H^{\frac{4}{3}}}{D^{\frac{1}{3}}}$ wherein D is fluid density, N is the number of perforations in said perforation cluster, H is the diameter of the perforations, Intensity is the DAS intensity from each trace at the perforation cluster minus the baseline DAS intensity from the same trace, and C.sub.4 is a constant.

7. The system of claim 6, wherein the Intensity is directly proportional to a pump-work factor (W) represented by:
Intensity=C.sub.3.Math.W

8. The system of claim 7, wherein the pump-work factor W is calculated by the following equation:
W=C.sub.1.Math..sub.P.Math.Q wherein C.sub.1 is a constant, .sub.P is the pressure differential between both sides of the perforation.

9. The system of claim 8, wherein the pressure differential .sub.P is calculated by the following equation: ${}_P=C_2.Math.Q^2.Math.\frac{D}{N^2.Math.H^4}$ where C.sub.2 is a constant, D is the fluid density, N is the number of perforations, and H is the diameter of the perforations.

10. A method of plug and perf fracturing a well, the method comprising: a) recording distributed acoustic sensing (DAS) noise intensity signals from a well during a first stage of a plug and perf fracturing operation in said well; b) deriving DAS intensity traces from the recorded DAS noise intensity signals, wherein each said DAS intensity trace is a recording of DAS noise intensity over a span of a pre-determined number of fiber depths averaged over a predetermined period of time, and wherein each said trace do not overlap with other said traces on fiber depths; c) identifying the fiber depths of each said perforation cluster inside said well; d) locating a baseline channel having no perforations at that fiber depth; e) calculating a volumetric flow rate Q for each said perforation cluster using the following equation: $Q=C_4.Math.{\mathrm{Intensity}}^{\frac{1}{3}}.Math.N^{\frac{2}{3}}.Math.\frac{H^{\frac{4}{3}}}{D^{\frac{1}{3}}}$ wherein D is fluid density, N is the number of perforations in said perforation cluster, H is the diameter of the perforations, Intensity is the DAS intensity from each trace at said perforation cluster minus the DAS intensity from said baseline channel, and C.sub.4 is a constant; and f) optimizing a fracture plan for subsequent stages of said plug and perf fracturing operation and implementing said optimized fracturing plan in said well.

11. The method of claim 10, wherein the Intensity is directly proportional to a pump-work factor (W) represented by:
Intensity=C.sub.3.Math.W

12. The method of claim 10, wherein the pump-work factor W is calculated by the following equation:
W=C.sub.1.Math..sub.P.Math.Q wherein C.sub.1 is a constant, .sub.P is the pressure differential between both sides of the perforation.

13. The method of claim 11, wherein the pressure differential .sub.P is calculated by the following equation: ${}_P=C_2.Math.Q^2.Math.\frac{D}{N^2.Math.H^4}$ where C.sub.2 is a constant, D is the fluid density, N is the number of perforations, and H is the diameter of the perforations.

14. A system for calculating volumetric flow rate in a perforation cluster inside a wellbore undergoing hydraulic fracturing process that injects hydraulic fluids into the wellbore, comprising: a) a distributed acoustic sensing (DAS) monitoring device including a optical fiber that runs along the length of the wellbore, wherein the DAS optical fiber is coupled to an interrogating unit for emitting interrogating signals, the DAS monitoring device detects DAS noise intensity signals when mechanical strain causes deformation to the optical fiber; b) a computer coupled to the DAS monitoring device for recording DAS noise intensity signals detected by the DAS monitoring device; c) wherein the computer performs the following steps to obtain volumetric flow rates of the hydraulic fluid through each said perforation cluster: i) deriving DAS intensity traces from the recorded DAS noise intensity signals, wherein each said DAS intensity trace is a recording of DAS noise intensity over a span of a pre-determined number of fiber depths averaged over a predetermined period of time, and wherein each said trace do not overlap with other said traces on fiber depths; ii) locating the fiber depths of each said perforation cluster inside said well; iii) locating a baseline channel having no perforation in that fiber depth for each said trace; iv) calculating a volumetric flow rate Q for each said perforation cluster using the following equation: $Q=C_4.Math.{\mathrm{Intensity}}^{\frac{1}{3}}.Math.N^{\frac{2}{3}}.Math.\frac{H^{\frac{4}{3}}}{D^{\frac{1}{3}}}$ wherein D is fluid density, N is the number of perforations in said perforation cluster, H is the diameter of the perforations, Intensity is the DAS intensity from each trace at the perforation cluster minus the baseline DAS intensity from the same trace, and C.sub.4 is a constant.

15. The system of claim 14, wherein the Intensity is directly proportional to a pump-work factor (W) represented by:
Intensity=C.sub.3.Math.W

16. The system of claim 15, wherein the pump-work factor W is calculated by the following equation:
W=C.sub.1.Math..sub.P.Math.Q wherein C.sub.1 is a constant, .sub.P is the pressure differential between both sides of the perforation.

17. The system of claim 16, wherein the pressure differential .sub.P is calculated by the following equation: ${}_P=C_2.Math.Q^2.Math.\frac{D}{N^2.Math.H^4}$ where C.sub.2 is a constant, D is the fluid density, N is the number of perforations, and H is the diameter of the perforations.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0082] FIG. 1 is the flow diagram of the method of this disclosure.

[0083] FIG. 2 is the fraction amount of volumetric flow rates of 5 perforation clusters in one example of this disclosure.

DESCRIPTION OF EMBODIMENTS OF THE INVENTION

[0084] Turning now to the detailed description of one or more preferred arrangements of the present invention, it should be understood that the inventive features and concepts may be manifested in other arrangements and that the scope of the invention is not limited to the embodiments described or illustrated. The scope of the invention is intended only to be limited by the scope of the claims that follow.

[0085] The DAS technology is briefly explained herein. Through Rayleigh scattering, light transmitted down the cable will continuously backscatter light so that it can be sensed, preferably at the interrogating unit (IU). As light in an optical fiber travels at a speed of approximately 0.2 m/ns, a 10-ns pulse of light occupies about 2 m in the fiber as it propagates. In theory, each 10 nanoseconds of time in the optical echo response can be associated with reflections coming from a 1-m portion of the fiber (two-way time of 10 ns). By generating a repeated pulse every 100 s and continuously processing the returned optical signal, it is possible to interrogate the entire length of up to 10 km of fiber at a 10-kHz sample rate.

[0086] Local changes in the optical signal, such as acoustic pressure or shear waves that impact the fiber to cause deformation, thus backscatter the interrogating light signal, making it possible to use the fiber as a continuous array of sensors with nearly continuous sampling in time and space.

[0087] While DAS has been used in seismic acquisition, no one has yet developed a method of converting DAS data into measuring volumetric flow rate of fracturing fluid into perforations of a treatment well. This disclosure describes a method of calculating or estimating volumetric flow rates of the fracturing fluids/proppant from DAS data that is readily obtained with existing fiber optics, without installation of additional sensors.

[0088] We propose that the DAS noise intensity is directly proportional to pump-work factor (W), which is defined in equation (1) below:

W=C.sub.1.Math..sub.P.Math.Q(1) [0089] where C.sub.1 is a constant, .sub.P is the pressure differential between both sides of the perforation, and Q is the volumetric flow rate of the fluids.

[0090] The pressure differential .sub.P can be obtained by the following equation (2):

[00007]$\begin{array}{cc}{}_P=C_2.Math.Q^2.Math.\frac{D}{N^2.Math.H^4}& \left(2\right)\end{array}$ [0091] where C.sub.2 is a constant, Q is the volumetric flow rate, D is the fluid density, N is the number of perforations, and H is the diameter of the perforations, assuming they are uniform. If not, N and H can be averaged for each relevant perforation cluster.

[0092] To solve the volumetric flow rate Q, we have proposed the proportional relationship between DAS noise intensity and pump-work W as in the following equation (3):

Intensity=C.sub.3.Math.W(3) [0093] where Intensity refers to the DAS noise intensity, i.e. the recorded DAS data for a specific channel minus the baseline noise for the same channel.

[0094] Therefore, the volumetric flow rate Q can be obtained by combining equations (1)-(3):

[00008]$\begin{array}{cc}Q=C_4.Math.{\mathrm{Intensity}}^{\frac{1}{3}}.Math.N^{\frac{2}{3}}.Math.\frac{H^{\frac{4}{3}}}{D^{\frac{1}{3}}}& \left(4\right)\end{array}$ [0095] where C.sub.4=.sup.3{square root over (C.sub.1.Math.C.sub.2.Math.C.sub.3)}

[0096] This data processing methodology can be further refined when seismic data obtained from off-set wells can be used to corroborate the DAS data and justify or calibrate the fluid propagation time, and the results can be used to calibrate fracture and reservoir stimulation model to facilitate optimization of completion and spacing. The results can also refine fracture geometry for new fracking configurations, which is beneficial for predicting well economy for future development.

[0097] We have acquired DAS data as described above from various wells that were undergoing hydraulic fracking, for example in unconventional filed, and exemplary data input is shown below in TABLE 1.

[0098] Scattered light pulses from nearby segments of the fiber are combined in an interferometer. The phase differences between the pulses is then a measure of their relative separations of their origins. A change in separation as small as one one-hundredth of a wavelength can easily and accurately be measured. This typically amounts to a 10.sup.7 percentage change in fiber length (strain). Although DAS was originally designed to record fiber strains due to acoustic waves of frequencies up to 10 kHz, its response also extends to very low frequencies (<0.01 Hz). Preferably, this disclosure utilizes high frequency DAS (1-20 KHz, 5-15 KHz, 8-12 KHz, or about 10 KHz).

Data Acquisition

[0099] DAS signal is recorded in the stimulated well (in-well), and if necessary in the offset wells (cross-well) as well, during the completion and production stages. For example, the distribution delay between the treated wells and the offset wells may be further used to justify or correct the results obtained only from the treated well. However, for the simplicity of the mathematical model, only DAS signals recorded in the stimulated well were processed in this test.

[0100] The distances between the stimulated well and offset monitor wells range from 50 ft to 1200 ft. The fiber-optic cables are installed out of the casing and cemented in place to avoid unwanted DAS noise caused by fiber deformation during fluid injection. Numerous interrogators are available to record optical signals.

[0101] In one embodiment, Pinnacle Gen-1 and Phase-1 interrogators are used for the recording. The raw data are sampled at 10 kHz continuously at more than 6000 locations (referred as channels in this study) with 1 m spatial separation along the fiber. The gauge length is set to 5 m. When recording, the measured optical phase is differentiated in time, so the raw DAS data is linearly associated with strain rate along the fiber.

Data Processing

[0102] FIG. 1 describes the data processing steps employed in our tests. In step 101, the DAS data is measured and recorded as described above. In the case where multi-mode fiber optic sensors are used, additional data collection can also be implemented to corroborate the DAS data.

[0103] In step 103, the recorded data is first divided into traces of DAS noise intensity, in other words the DAS data is first separated by the fiber depths and averaged over time, while the cumulative fiber depths must include all possible depths the fracturing fluids could flow out during the specified pumping period. Examples of processed data are shown below in TABLE 1.

TABLE-US-00002 TABLE 1 EXEMPLARY DAS DATA Input: Intensity values for each cluster and floor Baseline Cluster 5 Cluster 4 Cluster 3 Cluster 2 Cluster 1 Depth (ft) 8236.882309 8259.90756 8296.090097 8332.272634 8371.744493 8404.637709 Channel 2939 2946 2957 2968 2980 2990 # Holes 0 4 4 6 6 8 Jul. 6, 2014 8:41 7.428 10.585 5.156 9.168 7.924 10.041 Jul. 6, 2014 8:41 7.396 10.572 5.152 9.184 8.043 10.042 Jul. 6, 2014 8:41 7.489 10.424 4.997 9.405 7.99 10.233 Jul. 6, 2014 8:41 7.368 10.417 4.952 9.382 7.742 10.241 Jul. 6, 2014 8:41 7.602 10.357 4.926 9.476 7.816 10.252 Jul. 6, 2014 8:41 7.409 10.296 4.703 9.539 7.62 10.159 Jul. 6, 2014 8:41 7.4 9.209 4.685 9.459 7.488 10.121 Jul. 6, 2014 8:41 7.009 7.216 4.544 9.272 7.58 10.892 Jul. 6, 2014 8:41 6.392 6.792 4.588 8.53 7.968 11.306 Jul. 6, 2014 8:41 6.215 7.21 4.381 8.467 7.83 11.21 Adjusted Intensity values CL 1 CL 2 CL 3 CL 4 CL 5 Intensity Intensity Intensity Intensity Intensity Over Floor Over Floor Over Floor Over Floor Over Floor Jul. 6, 2014 8:41 2.613 0.496 1.74 0 3.157 Jul. 6, 2014 8:41 2.646 0.647 1.788 0 3.176 Jul. 6, 2014 8:41 2.744 0.501 1.916 0 2.935 Jul. 6, 2014 8:41 2.873 0.374 2.014 0 3.049 Jul. 6, 2014 8:41 2.65 0.214 1.874 0 2.755 Jul. 6, 2014 8:41 2.75 0.211 2.13 0 2.887 Jul. 6, 2014 8:41 2.721 0.088 2.059 0 1.809 Jul. 6, 2014 8:41 3.883 0.571 2.263 0 0.207 Jul. 6, 2014 8:41 4.914 1.576 2.138 0 0.4 Jul. 6, 2014 8:41 4.995 1.615 2.252 0 0.995

[0104] In step 105, identify the fiber depth of the perforation clusters of interest and confirm with known depths of the perforation clusters in order to avoid any mismatching errors. This would be done by comparing the fiber depths with records of perforations created, or by performing a fluid test run while interrogating the fiber optics for a basic profile of the wellbore.

[0105] In step 107, a baseline channel within a particular trace is located, by selecting the channel where there are no known perforations. The DAS data obtained in this baseline channel will serve as a background noise signal to be subtracted from other DAS data obtained from channels having perforations. For example, in TABLE 2 above, the baseline channel is selected as channel 2939, and its DAS signal is subtracted from the DAS signals of clusters 1-5, as shown in the CL# Intensity over floor columns.

[0106] When the subtraction yields positive values, they are kept as is. When the subtraction yields negative values, the CL# Intensity over floor columns will have a 0 entry because the assumption is that the DAS intensity being directly proportional to the pump-work, which cannot be negative.

[0107] In step 109, the pump-work factor is calculated by applying the DAS intensity values to Equation (4) above. Examples of the resulting pump-work factor is shown in TABLE 2 below:

TABLE-US-00003 TABLE 2 EXAMPLES OF OVERALL INJECTION RATE AND PUMP-WORK FACTOR W Bottom hole Slurry Proppant rate Concentration CL 1 Pump CL 2 Pump CL 3 Pump CL 4 Pump CL 5 Pump Pump Work [bbl/min] [lb/gal] Work Factor Work Factor Work Factor Work Factor Work Factor Factor Sum 1.52400 0.00100 5.509427358 2.613734031 3.971463569 0 3.696563647 15.7911886 1.53400 0.00000 5.53252355 2.855851321 4.007652019 0 3.703964584 16.09999147 1.58600 0.00000 5.6 2.622487392 4.101090331 0 3.607802009 15.93137973 1.58600 0.00000 5.686414759 2.378983159 4.169852142 0 3.653920851 15.88917091 1.58600 0.00000 5.535310015 1.975022699 4.070902451 0 3.532486645 15.11372181 1.73200 0.00000 5.604078661 1.965750155 4.248419251 0 3.588026061 15.40627413 2.99500 0.00000 5.584309822 1.468684092 4.200680162 0 3.070337968 14.32401204 2.99500 0.00000 6.287081953 2.739341664 4.335065711 0 1.490607983 14.85209731 3.20400 0.00000 6.80046133 3.842550389 4.25373144 0 1.856635533 16.75337869 3.31900 0.00000 6.837623058 3.873988637 4.328030331 0 2.515635344 17.55527737

[0108] In step 111, once the pump-work factors for each perforation cluster are calculated, they are then normalized for each trace, and eventually the flow rate contribution from each of the perforation cluster is summed, as shown in TABLE 3 below. Here it is clearly seen that cluster 4 (so far) did not have any fluid flow detectable from DAS, thus did not contribute to the overall flow rate. However, as the fracturing liquid accumulates inside the wellbore, the flow pattern of each perforation cluster may change. In this case, the data indicates that cluster 4 was significantly involved in distributing fracturing fluids into the reservoir (data not shown).

[0109] In step 113, steps 109 and 111 are repeated for each and every trace throughout the stimulation operation, until all DAS traces are processed. The proppant flow rate is similarly calculated by using pump work factor W, but with the proppant concentration added as a weighting factor. However, because proppant was only injected once per stimulation (see TABLE 4), the values do not change over time.

[0110] In this test, 5 perforation clusters are selected, and the exemplary resulting fractional amount of volumetric flow rate of all five clusters is shown in FIG. 2. As shown in FIG. 2, assuming the total volumetric flow rate is 1, the DAS intensity results can be converted to pump-work factor W, which then can be weighted to estimate the fluid distribution to each perforation cluster. As seen in FIG. 2, the fluid distribution of 5 perforation clusters add up to 1, in which cluster 1 has the lowest distribution, whereas cluster 4 has the highest, followed by cluster 3 and 5.

[0111] This information is particularly beneficial because now not only the fluid distribution can be estimated at relatively low cost, the fracking and completion design can also be adjusted accordingly. For example, more fluid may be diverted to cluster 1 for better production thereof, while directing fluid away from cluster 4 because excessive fracking fluid does not contribute to overall production.

[0112] The disclosed method therefore shows that the DAS data can be interpreted according to Equations (1)-(4) to obtain a directly proportional pump-work factor W, which is then used to calculate the volumetric flow rate of that particular perforation cluster. By summing up the flow rates of all clusters, the overall flow rate can be obtained.

[0113] The disclosed method can bring more subtle understanding about fluid/proppant distribution during a fracking operation. For example, if one perforation cluster receives much less fracturing fluids than others, it means the rocks around that depth are less fractured for production. The stimulation can then be optimized to direct more fluids to that cluster. Similarly, if one cluster is found to have excessive fluids/proppants, the resources are wasted and can be redirected to other part of the wellbore.

[0114] When the uneven fluid distribution is caused by fluid pumping mechanism, one can also revise the pumping method so that the fluids and proppants can be distributed more evenly.

[0115] The data processing method can also be used to monitor well performance over a long period of time, such that any significant change in production profile can be addressed with adjusted completion designs.

[0116] To further investigate the validity and applicability of the disclosed method, several corroborating experiments can be performed. For example, measuring and characterizing the DAS response to known variations in fluid flow parameters, such as flow rate, velocity, temperature, fluid phase, number of clusters, perforation diameter, and DAS delay coil length. Also, the fiber optics used in this disclosure are embedded in the external casing to avoid any undesirable deformation, but that would limit the applicability to wells already having fiber optics. We envision that with additional testing and calibration, the same methodology would be applicable to fiber optics deployed inside coiled tubing, thus broadening its use to non-fiber-equipped wells.

TABLE-US-00004 TABLE 3 FLOW RATE CONTRIBUTION PER CLUSTER CL 1 CL 2 CL 3 CL 4 Instantaneous Instantaneous Instantaneous Instantaneous CL 1% CL 2% CL 3% CL 4% CL 5% Rate Rate Rate Rate 0.34889 0.16552 0.25150 0.00000 0.23409 0.53171 0.25225 0.38328 0.00000 0.34364 0.17738 0.24892 0.00000 0.23006 0.52714 0.27210 0.38185 0.00000 0.35151 0.16461 0.25742 0.00000 0.22646 0.55749 0.26107 0.40827 0.00000 0.35788 0.14972 0.26243 0.00000 0.22996 0.56760 0.23746 0.41622 0.00000 0.36624 0.13068 0.26935 0.00000 0.23373 0.58086 0.20725 0.42719 0.00000 0.36375 0.12759 0.27576 0.00000 0.23289 0.63002 0.22099 0.47761 0.00000 0.38986 0.10253 0.29326 0.00000 0.21435 1.16762 0.30709 0.87832 0.00000 0.42331 0.18444 0.29188 0.00000 0.10036 1.26782 0.55240 0.87419 0.00000 0.40592 0.22936 0.25390 0.00000 0.11082 1.30055 0.73487 0.81350 0.00000 0.38949 0.22067 0.24654 0.00000 0.14330 1.29272 0.73242 0.81826 0.00000 CL 1 CL 2 CL3 CL4 CL5 Cumulative CL 5 Cumulative Cumulative Cumulative Cumulative Cumulative Fluid Instantaneous Fluid Fluid Fluid Fluid Fluid Distribution Rate Distribution Distribution Distribution Distribution Distribution Summation 0.35675 0.53171 0.25225 0.38328 0.00000 0.35675 1.52400 0.35291 1.05885 0.52435 0.76513 0.00000 0.70967 3.05800 0.35916 1.61634 0.78543 1.17340 0.00000 1.06883 4.64400 0.36472 2.18394 1.02289 1.58962 0.00000 1.43355 6.23000 0.37069 2.76480 1.23014 2.01681 0.00000 1.80424 7.81600 0.40337 3.39482 1.45114 2.49443 0.00000 2.20761 9.54800 0.64198 4.56244 1.75822 3.37275 0.00000 2.84959 12.54300 0.30059 5.83026 2.31063 4.24693 0.00000 3.15018 15.53800 0.35507 7.13082 3.04549 5.06044 0.00000 3.50525 18.74200 0.47561 8.42354 3.77791 5.87870 0.00000 3.98086 22.06100

TABLE-US-00005 TABLE 4 PROPPANT DISTRIBUTION PER CLUSTER CL 1 CL 2 CL 3 CL 4 CL 5 CL 1 Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Cumulative Proppant Proppant Proppant Proppant Proppant Proppant Distribution Distribution Distribution Distribution Distribution Distribution 0.00053 0.00025 0.00038 0.00000 0.00036 0.00053 0.00000 0.00000 0.00000 0.00000 0.00000 0.00053 0.00000 0.00000 0.00000 0.00000 0.00000 0.00053 0.00000 0.00000 0.00000 0.00000 0.00000 0.00053 0.00000 0.00000 0.00000 0.00000 0.00000 0.00053 0.00000 0.00000 0.00000 0.00000 0.00000 0.00053 0.00000 0.00000 0.00000 0.00000 0.00000 0.00053 0.00000 0.00000 0.00000 0.00000 0.00000 0.00053 0.00000 0.00000 0.00000 0.00000 0.00000 0.00053 0.00000 0.00000 0.00000 0.00000 0.00000 0.00053 CL 2 CL 3 CL 4 CL 5 Cumulative Cumulative Cumulative Cumulative Cumulative Proppant Proppant Proppant Proppant Proppant Distribution Distribution Distribution Distribution Distribution Summation 0.00025 0.00038 0.00000 0.00036 0.00152 0.00025 0.00038 0.00000 0.00036 0.00152 0.00025 0.00038 0.00000 0.00036 0.00152 0.00025 0.00038 0.00000 0.00036 0.00152 0.00025 0.00038 0.00000 0.00036 0.00152 0.00025 0.00038 0.00000 0.00036 0.00152 0.00025 0.00038 0.00000 0.00036 0.00152 0.00025 0.00038 0.00000 0.00036 0.00152 0.00025 0.00038 0.00000 0.00036 0.00152 0.00025 0.00038 0.00000 0.00036 0.00152

[0117] Although the systems and processes described herein have been described in detail, it should be understood that various changes, substitutions, and alterations can be made without departing from the spirit and scope of the invention as defined by the following claims. Those skilled in the art may be able to study the preferred embodiments and identify other ways to practice the invention that are not exactly as described herein. It is the intent of the inventors that variations and equivalents of the invention are within the scope of the claims while the description, abstract and drawings are not to be used to limit the scope of the invention. The invention is specifically intended to be as broad as the claims below and their equivalents.

[0118] The following references are incorporated by reference in their entirety for all purposes. [0119] 1. U.S. Ser. No. 62/305,777 Production Logs from distributed acoustic sensors. [0120] 2. U.S. Ser. No. 62/305,758 Low-Frequency Analysis of DAS Signals [0121] 3. Co-pending application Identifying Frac Spatial Density With Temperature, filed Mar. 8, 2017 [0122] 4. Co-pending application Hydraulic fracture monitoring by low-frequency DAS, filed Mar. 8, 2017 [0123] 5. Co-pending application Temperature measurement by combining DAS/DTS data, filed Mar. 8, 2017 [0124] 6. U.S. Pat. No. 6,778,720, Dual slope fiber optic array interrogator, (2004). [0125] 7. U.S. Pat. No. 8,950,482, Fracture monitoring, (2009). [0126] 8. US20060272809, Wellbores utilizing fiber optic-based sensors and operating devices, (2006). [0127] 9. US20090114386, Systems and methods for distributed interferometric acoustic monitoring, (2009). [0128] 10. US20130298635, Techniques for Distributed Acoustic Sensing, (2013). [0129] 11. US20130298665, System and method for monitoring strain & pressure, (2013). [0130] 12. US20130233537, Fracture Characterisation, (2013). [0131] 13. US20140202240, Flow Velocity and Acoustic Velocity Measurement with Distributed Acoustic Sensing, (2014). [0132] 14. US20140216151, Flow Monitoring, (2014). [0133] 15. US20140260588, Flow Sensing Fiber Optic Cable and System, (2014). [0134] 16. US20140358444, Method of Hydraulic Fracture Identification Using Temperature, (2014). [0135] 17. US20160003032, Matrix Temperature Production Logging Tool, (2016). [0136] 18. WO2016069322, Method of Treatment Design and Optimization of Sequenced Fracturing Technique, (2016). [0137] 19. U.S. Pat. No. 9,416,644, Fracture Characterization, (2011). [0138] 20. Boone, K., (2015), DAS technology expands fiber optic applications for oil, gas industry: Rigzone, May 4 issue. [0139] 21. Webster, P., et al., Developments in Diagnostic Tools for Hydraulic Fracture Geometry Analysis, Unconventional Resources Technology Conference (URTeC), Denver, Colo., 12-14 Aug. 2013. [0140] 22. Optasense, Pipeline Integrity Management: Leak Detection, www.optasense.com (2013).