There are many potential factors that can cause errors when using the DTS system. The errors which arise from the instrumentation, the fiber, the nature of the installation, and other sources show up as depth discrepancies and temperature errors [
3]. In order to specify the exact location of thermal events and to analyze the events more quantitatively, we applied depth correction and temperature calibration before interpreting thermal events for the well completion processes.
3.1. Depth Correction
Depth mismatch is an unavoidable issue in the field. Unlike temperature correction, depth discrepancies cannot be pre-calibrated before installation. Even though the cables were carefully handled during the installation, many factors such as cable coiling up around the tubing, stretching of fiber optic cable itself, the usage of a decentralizer, and inner fiber optic twisting may inevitably introduce depth discrepancies. Although it may depend on the application, Smolen and van der Spek [
3] stated that generally a depth mismatch of ± 0.3 m is realistic for most applications. With the depth issue comes the issue of determining the end of the fiber depth. The length measured by DTS should be mapped for depth correction to a real physical profile length of interest. In dual-ended or partially returned configurations in borehole applications, the end of the fiber can be easily identified with the peak temperature due to ambient geothermal gradient and it can be confirmed in the raw data by a sudden intensity drop around the splicing point.
In our case, the peak temperature was observed mostly around 1197.114 m in fiber length. On the other hand, the maximum intensity drop occurred between 1196.606 m and 1196.860 m with the difference of 21.17 A.U. (relative decrease of 10.4%) and the second maximum drop occurred between 119.860 m to 1197.114 m with the difference of 18.62 A.U. (relative decrease of 9.3%). Although there is a difference of 0.5 m between the peak temperature point and the maximum intensity drop point, we used the peak temperature point as the fiber-end to determine total fiber length because such a difference is negligible considering our spatial sampling interval of 0.25 m and the width of the probe pulse. With respect to this fiber end, the fiber cable length () that corresponds to total casing length of 1082.56 m is 1095.599 m. Therefore, in our case, a depth mismatch () of 13.039 m was identified, which is 1.2% longer than the total casing length.
A simple way to match depth discrepancies is to redistribute the amount of depth mismatch to the total length. Thus, we redistributed total depth error throughout the total length under the assumption that the rate of depth mismatch is constant throughout the total length.
For the confirmation of depth correction accuracy, we compared the temperature profiles before and after correction for gas lift process in May and November, 2017 as shown in
Figure 4. Since the casing material is changed from steel to FRP casing at 791.90 m as shown in
Figure 2, any temperature anomaly associated with the heat conductivity difference of two casing material should be identified around this depth. The effect of casing transition is clearly identifiable with the temperature increase pattern from data in both May and November, regardless of depth correction.
After correcting the depth, the depth of thermal changes due to casing transition moved up 9.494 m from 801.430 m to 791.936 m. The depth after correction, 791.936 m matches well with the true depth of the casing transition point (791.90 m) within one sampling-point difference, which is 0.25 m in terms of the DTS system’s sampling interval. In both May and November, the difference to the true depth was 0.036 m.
Considering the true depth of casing transition point is known and the position of the thermal anomaly due to casing transition can be clearly identifiable, we may redistribute total depth error to each section above and below the transition point section by section under the assumption that the rate of depth mismatch is constant but different in each section. However, the recalculated sampling interval turns out to be the same to the third decimal place regardless of the section division. Thus, no major improvement in depth calibration using sections was seen.
The new sampling interval was applied to the cement injection data for the verification of the depth correction effect again as shown in
Figure 5. Although there is no known absolute position of the top of the gravel pack and the bottom of cementing, the top of the gravel pack should be near 911 m and bottom of cement injection near 910 m according to the completion schematic shown in
Figure 2.
Once the cement slurry meets the gravel pack, it will permeate slowly into the gravel pack. This process can be delineated by a temperature transition between the low temperature of the cooler cement slurry and the high temperature caused by the warmer gravel pack as shown in
Figure 5, and this thermal transition remains until the temperature goes back to the normal geothermal gradient.
Considering this, we can interpret the start and the end of the thermal transition zone to the top of gravel pack and the bottom of cement slurry, respectively. The top numbers and the bottom numbers in the figure indicate the depth of the bottom of cement and the depth of the top of gravel pack, respectively. After correcting the depth, the top of gravel pack moved up 10.934 m from 922.937 m to 912.003 m that is 2.003 m difference with expected depth of 910 m. The bottom of cement moved up 10.949 m from 924.208 m to 913.259 m that is 2.259 m with expected depth of 911 m.
3.2. Temperature Correction
Many DTS acquisition systems have an internal calibration system, however higher accuracy is needed for geoscience operating environments where the fiber optic cable may be under conditions of rapid change and large temperature fluctuations. Under static conditions, the accuracy of calibrated temperatures is generally within ± 0.3 °C, however under rapid operating conditions, the accuracy range becomes widened to ± 2 °C [
6]. The temperature measurement accuracy also declines as the length of the fiber is increased due to the power loss of the laser pulse [
3]. In our experiment, pre-calibration could not be done before installation, therefore we suggest a post-calibration method that is within the acceptable range of error, ± 0.3 °C.
Three calibration methods were investigated in the JG-M borehole in April 2018 and the experimental setting is displayed in
Figure 6. In a dual-ended configuration, only one absolute temperature point is needed because knowing the temperature at a point results in having two points in this configuration. The “water tub” is the conventional method of correction by submerging about one or more pulse width lengths of fiber cable into water to find the stable absolute temperature. However, submerging enough length of fiber longer than a pulse width length into water may not be possible once the cable is installed. Therefore, two pointwise temperature correction methods are investigated. The ‘heat coil’ heats a portion of fiber cable near the well with a heat coil. The “in-well” is another pointwise method of correction by using the position of a heat coil to apply a slope correction and using the absolute temperature value inside the well to apply the offset correction. For all cases, the slope correction was applied to temperature profile with no events in the well, and background temperature data was collected for 15 min before the calibration method experiments.
3.2.1. Long Point Calibration Method with Mater Tub
In the water tub experiment, 22 m of fiber optic cable, which is longer than a pulse width length of a laser, was submerged in water.
Figure 7 shows the process of the temperature being stabilized in the calibration bath. The temperature fluctuation became smaller as time went by, and about 1 h later, finally stabilized to that of water inside the calibration bath.
The position of the cable submerged in water could be clearly seen both on the left and right side of the DTS data, due to the dual-ended installation of the fiber. The stable range on the left side of the data ranges from 48.896 m to 64.148 m, and the stable range on the right side of the data, though it is not displayed in the figure, ranges from 2329.826 m to 2345.078 m. Since the submerged part of the fiber optic cable must have the same temperature, the inner 60 points were averaged to eliminate fluctuation of the temperature value on each side. The midpoint on the left side was at 56.522 m, and midpoint on the right side was at 2337.706 m. To make sure the right midpoint matched the left midpoint, same number of 4887 points to max peak were used.
In order to find a better slope correction factor, the temperature change of water within an hour was considered. Even though the specific heat of water is lower than air, the minimum difference of average temperature between the left side and the right side was considered for better estimation of the reference temperature. The ten-minute range which gave the minimum difference between the left and the right side is from 17:53 to 18:02. From the best ten-minute range, the minimum, maximum, and average slope value was used to find the slope equation. The maximum slope gave the minimum difference between the left and the right value. The minimum slope gave the maximum difference between the left and the right value. The slope curve of minimum, maximum and average slope is shown in
Figure 8a. In the figure, “all” represents using all the data points without considering the temperature change of water, “DTS” represents the best ten-minute data in terms of minimum difference between the left and the right endpoints. The “Diver” represents the most stable temperature measured with the diver in the water tub for ten minutes.
The “DTS” method gave the best result when 60 points were averaged to eliminate fluctuations of the reference temperature as shown in
Figure 9a. This was confirmed again by comparing all three methods as displayed in
Figure 8. The averaging of 60 points was the most effective in all three cases as it had smaller slope and difference range.
For all three cases, the slope equation was applied to the background data from April 12 before any experiment because it is best to apply to the data without any events. The temperature accuracy improved after temperature correction, as the difference to true temperature decreased from 2.6 °C before correction to 0.02 °C, as illustrated in
Figure 9b.
3.2.2. Pointwise Calibration Method with Heat Coil
The heat-coil was used to locate the position on the DTS data for slope correction. A heat coil of 0.5 m in length was wrapped around the fiber optic cable near the well and insulated with a sponge tube of 1.5 m and wrapped in tape to prevent the temperature from fluctuating due to the wind as shown in
Figure 6. The distance from the middle of heat coil to the well was 70 cm. In the heat coil experiment, obtaining a stabilized absolute temperature was difficult because the heat coil was shorter than the pulse width of interrogation system and air temperature varied too quickly. Therefore, the ambient temperature value at the heat coil position was used for slope correction. On April 12, the fiber optic cable was heated with heat coil to about 50 °C for about 10 minutes and the cooling observed for 27 min.
The slope curves are displayed in
Figure 10a, which shows very different slope difference from the long point water tub method. In this case, only slope correction was applied because the absolute temperature was not determined.
Even with only slope correction, we could evaluate if the calibration is done correctly by comparing the two endpoints because two endpoints on the left and the right should have the same temperature value after correction. However, we can identify in
Figure 10b, that temperature at the right endpoint, even with an increase of 1.1 °C after correction, still has a 1.5 °C difference with that of the left endpoint.
3.2.3. In-Well Pointwise Calibration Method
To compensate the difficulty of obtaining a stable absolute temperature with the heat coil method, three divers were lowered into the well at 10 m, 20 m, 30 m below groundwater which has lower specific heat constant than the air. The diver position on the DTS could be located by counting from the known heat-coil position. The position could also be confirmed by temperature change when the fiber optic meets groundwater, which was only 1 m to in-well water from the heat-coil position.
The slopes found with the pointwise in-well method are presented in
Figure 11. Compared to the long point water tub method, the variation ranges are wider than the long point method but the average slopes are similar to that of the long point method. The slope and its range did not vary greatly with the depth of diver. The temperature after correction with pointwise in-well diver at 10 m is presented in
Figure 12. The temperature accuracy improved as the difference to true temperature is only 0.06 °C compared to the difference of 2.8 °C before correction.
3.2.4. Discussion
The slope and temperature difference curves of three calibration methods are summarized in
Figure 13. The long point calibration method with water tub gave the best result. Although the pointwise calibration method using the diver showed a larger range than the long point method, it gave an average slope and the average temperature difference comparable with that of the long point method. Comparing the variation range of the heat coil method and the in-well method, we can conclude that it is crucial to obtain accurate and stable absolute temperatures.
The stability analysis was carried by dividing the total round-trip length of the fiber into 10 sections in terms of the same number of sample points per section. The downward trip sections, from wellhead to well bottom, are marked as L5–L1 and the upward trip sections are marked as R1–R5. The number of samples per each section is 897 points for the long point method, 855 points for the pointwise method with in-well diver, and 862 points the pointwise method with heat coil.
The stability curve of all three calibration methods is as shown in
Figure 14, which displays the stabilities at 13 points including two top points (Endpt), a bottom point (Maxpeak), and ten midpoints of each section. The slope stability curve of long point calibration method has a range of +0.06 °C and −0.03 °C. The slope stability curve of pointwise calibration method with in-well of 10 m has a range of +0.35 °C and −0.25 °C. The slope stability curve of pointwise calibration method with heat coil has a range of +0.7 °C and −0.6 °C. The temperature difference increases as the length of fiber increase in all three calibration methods as expected due to the power loss that increases as the traveling distance become longer.
The appropriate temperature error range is within 0.3 °C, and both water tub and in-well data fall within the range. However, the error range with water tub slope correction is within 0.3 °C with stability of 0.05 °C and the temperature error range with diver slope correction is within 0.1 °C with a stability of 0.3 °C. Therefore, even though the long point calibration works best, the pointwise calibration method can be a useful alternative where long point calibration cannot be done.