The temperature-logging tool includes a cage, which is open to the wellbore fluid, at the tool’s bottom end. Inside the cage is a thermistor that senses the surrounding fluid temperature. The preferred sensor is a platinum element because the electrical resistance of the sensor varies linearly with temperature over a wide range and is stable over time. The circuitry of the tool is designed so that the voltage across the sensor is proportional to the sensor’s electrical resistance.
In analog recording, the transmitted spikes per minute are converted to a voltage by a counting circuit. This voltage is recorded on a pen-and-ink strip chart recorded as the temperature (or gradient) trace. This is Trace 1 of Fig. 1. The scale of this trace is in °F. A recording sensitivity of 1°F/in. across the chart is strongly recommended for production wells.
In analog recording, the voltage output of the counting circuit is also input to a differentiating amplifier. The output of the amplifier is recorded as Trace 2 (the differential trace or the derivative of the temperature), and is proportional to the depth-rate-of-change of the temperature curve. Although no absolute scale is associated with the differential trace, it is useful for highlighting important changes of the slope of the temperature curve.
On the log, the temperature trace warms abruptly below Depth B. Because the tool is logging down and the temperature is increasing, the depth-rate-of-change of temperature is positive. Consequently the differential trace shows a strong positive excursion at B, highlighting the change of the slope of the temperature trace at this depth. The differential trace, when properly amplified as on Fig. 1, is easily worth the additional logging charge.
The flowing temperature Trace 1 in Fig. 1 also provides information on the production profile. Production commences at Depth A, where the flowing trace "stands up" to separate to the warm side of static. This location is at the bottom of the bottom set of perforations. The middle set of perforations, on the other hand, contributes nothing to the production. The largest contribution comes from near the bottom of the top set of perforations at Depth B, where a large mixing signature is evident. The volumetric rate of entry here is so large that the mixture temperature is "pulled" almost back to static temperature (i.e., to the entry temperature for the stream). There is one additional smaller entry at Depth C, whose mixing signature is hardly recognizable on the flowing Trace 1 but is clearly evident on the differential Trace 2. The location of this entry suggests that it is composed primarily of oil. The temperature traces therefore show that the top set of perforations is responsible for the majority of both water (the major stream) and oil (the minor stream). The use of these mixing signatures to profile both single-phase and multiphase flow is described in detail in the production logging application tables under production-well profiling. The important point is that the size of a mixing signature relative to static temperature is dependent upon the thermal content (product of density, specific heat, and volumetric rate) both of the entry stream and of the stream in the casing immediately below the entry.
In digital recording, the spikes-per-minute from the logging cable are counted digitally at the surface, and the resulting count rate is converted to a temperature trace by the computer’s program. Again, the temperature trace should be recorded at a sensitivity of 1°F across the chart. Digital recording degrades the sensitivity of the differential trace from that available with analog recording. Thus, the digitally determined differential trace is not as useful for highlighting important changes of the temperature curve’s slope.
Depending on how carefully (or recently) a particular temperature tool was calibrated, there may be several °F difference between the recorded temperature and the true downhole temperature. However, the difference does not degrade the sensitivity of the differential trace. Provided that the temperature curve is recorded at the recommended sensitivity of 1°F/in. across the chart, and that the temperature log is carefully depth-correlated, the resulting temperature curve has more vertical resolution than does a curve from any other production-logging tools.
The temperature tool is most effective when located at the bottom of a tool string. In a production well, the tool should always be logged downward so as to enter undisturbed fluid. The log should be recorded at a constant logging speed not to exceed 30 ft/min. With digital recording, the maximum logging speed should be reduced to 20 ft/min.
Temperature logs and flow tests
Fig. 2 shows temperature logs from an exploration well that was perforated and acidized before the flow test. During the flow test, the surface rates were 2 MMscf/D gas and 500 B/D spent acid and formation water. The formation is gas-saturated limestone.
The temperature profile from the flow test is the solid trace; the line labeled "static" is a temperature log after a 6-day shut-in following the flow test. In the sump below the bottom perforation, there is no flow. The temperature here is approximately 6°F cooler than static. During drilling, mud circulation takes heat from the near-wellbore, leaving the near-wellbore below static temperature. Over time, heat flows from the formation farther away from the wellbore, where the temperature still is static. This heat flow, given enough time, restores the near-wellbore to static. In a no-flow interval, this heat flow is the only process for restoring the near-wellbore to static temperature.
At the time of the flow test, the near-wellbore temperature below the bottom perforation was still below static. The line labeled "cool temp" coincides with the flowing temperature profile below the bottom perforation and is brllel to the static temperature line determined subsequently. The cool temp line shows that, at the time of the flow test, the near-wellbore is below static throughout the perforated interval.
During the flow test, spent acid and formation water enter the wellbore at Depths 1, 2, 3, and 4. Each entry flow begins in the formation at static temperature. At Depth 1, the entry rate is small enough that the flow, after being cooled during passage through the cooler near-wellbore, enters the pipe at a flowing temperature that is considerably below static. Still, the entry causes an abrupt warming at Depth 1. Because the entry at this depth does not mix with a flow from below, the "entry temperature" (i.e., the temperature of the entry as it emerges into the wellbore) is the flowing temperature at the entry Location 1.
At Depth 2, additional liquid enters and mixes in the wellbore with the upward flow from Depth 1; the mixing of the two flows results in the abrupt warming at this depth. The flowing temperature at Location 2 is the final temperature after the mixing. The entry at Depth 2 comes into the wellbore at an entry temperature (before mixing) that exceeds the final temperature after mixing but is no greater than the static. Notice that the final temperature after mixing at Depth 2 is less reduced from static than is the entry temperature at Depth 1. Thus, the entry rate at Depth 2 exceeds that at Depth 1. The entry at 2 is cooled less by passage through the near-wellbore region than is the entry at 1, leaving the entry temperature at 2 higher than that at 1.
At Depth 3, liquid enters and mixes with the flow arriving from below. The mixing of the flows causes the abrupt warming at Depth 3. The flowing temperature at this depth is the final temperature after the mixing. The entry at Depth 3 comes into the wellbore at an entry temperature (before mixing) that exceeds the final temperature after mixing. However, this temperature is less reduced from static than is the final temperature at Depth 2. Thus, the entry rate at Depth 3 exceeds that at Depth 2. The entry at 3 is cooled less by the near-wellbore than the entry at 2, leaving the entry temperature at 3 higher than that at 2.
By similar reasoning, the entry rate at Depth 4 is greater than the entry rate at Depth 3. In a recently drilled well or in an old gas well, provided that the near-wellbore is below static, the deepest entry, if it is a liquid, results in a warming signature. The warming is caused by the liquid’s bringing of its warmer temperature into the wellbore itself. The contrast between the entry temperature and the cooler temperature of the wellbore below the entry is responsible for the warming signature. A common but mistaken view holds that the warming is caused by frictional heating of the liquid as it moves through the near-wellbore region and into the well. The fact that a water rate of only a few B/D is sufficient to produce a warm signature clearly refutes this "frictional" hypothesis. In a gas well, pressure loss in the near-wellbore and completion results in expansion of the gas during its passage into the wellbore. This expansion cools (or warms) the gas to a degree that depends on:
- The flowing bottomhole pressure
- The amount of pressure loss
If the gas is cooled, it absorbs heat as it passes through the near-wellbore region before entry. Over time, the heat spreads up and down the near-wellbore, resulting in a below-static temperature in the near-wellbore region. Any subsequent liquid production produces the same warm signatures as described for a new well. In actual fact, the expanding gas warms at bottomhole pressures in excess of approximately 10,000 psi and cools at pressures lower than 5,000 or 6,000 psi. At intermediate pressures, the amount of cooling or warming is generally not significant.
In reference to the example of Fig. 2, the flowing bottomhole pressure and temperature are 1,325 psia and 200°F, respectively. The well flows at a drawdown in excess of 3,000 psia. At Depths 5 and 6, each temperature mixing signature is caused by expansion of a dry gas as it passes through the near-wellbore and completion. At Depth 5, the colder gas mixes in the wellbore with the warmer liquid arriving from below, giving the cooling signature at this depth. At Depth 6, the colder gas mixes with the warmer flow of gas and liquid arriving from below, giving the cooling signature at this depth. The next calculations focus again on the water entries.
Certain conventions apply to the volumetric rates qi in the relationships to be discussed next. If water is produced, then the rates for all other phases are "water equivalent" rates that represent the multiplication of each actual rate by a ratio. The numerator in this ratio is the product of density and specific heat for the particular phase, whereas the denominator is the same product for water. If only gas and oil are produced, then the gas rate is presumed to be an "equivalent oil" rate obtained with a similar ratio for gas/oil. Once profiling is done by the following expressions, then the equivalent rates are converted to phase rates according to the equivalence ratios. Typically, 3 volumes of oil are the equivalent of 1 volume of water, whereas ~ 10 volumes of gas are the same equivalent.
The entry rates of the four liquid entries can be determined quantitatively from two relationships, a warming relationship where qi (i ≥ 2) refers to a given stream entering the wellbore at temperature Ti to mix with the total stream from below at temperature Ti–1 and produce a mixture with temperature Tmix.
and a warming relationship,
and qi (i ≥ 2) denotes any stream entering the bottom stream – 1. In the ratio for Ri, the temperature Ti refers to the temperature at which stream-i arrives at the wellbore, whereas Tgeo indicates normal geothermal temperature at the depth of the entry, and Tcool is the cooler temperature of the stream coming from below entry-i. Usually, the entry temperature Ti for a given liquid stream will be the same as geothermal temperature Tgeo and only the mixing relationship (Eq. 1) is required to determine the relative size of the rates. The warming relationship (Eq. 2) is required when the wellbore has been cooled below geothermal, and liquid entries arrive at the wellbore at some unknown temperature cooler than geothermal. In this situation, a succession of liquid entries moves the flowing temperature profile successively closer to the geothermal temperature line without bringing the two into coincidence. This is the temperature behavior at Depths 1 through 4 of Fig. 2. The left side of the relationship in Eq. 3 is the ratio qi/q1 (i = 1 to 4 in the present example), which is the ratio of the entry rate qi to the entry rate at Depth 1. The right side of the relationship in Eq. 3 incorporates numerical values that are available from the "cool temp" and "static" lines in the figure. The remaining variable is Ti, which is the temperature of the ith entry as it emerges into the wellbore, before mixing with the flow from below. This is the same as the "entry temperature" used in the text above. T1 is the temperature at the warming signature at Depth 1, because there is no flow below this depth. The value of Ti at higher depths must be determined along with the rate ratios.
On the left side of the mixing equation appears the ratio qi/q1; on the right side all numerical values are available from the temperature profiles of Fig. 2 with the exception of Ti. Thus, there are two unknowns: qi/q1 and Ti. Various trial values of Ti are entered into the warming and mixing relationships to give two values for qi/q1. A solution for Ti is the trial value for which the two values of qi/q1 are substantially in agreement. A trial value for Tini should exceed the final temperature after mixing at Depth i, but should be less than the static temperature at Depth i.
The process of using trial values is shown by Table 1, which relates to finding the value of q2/q1 and T2. As can be seen, the two values of the rate ratio are in close agreement at a trial temperature of 201.54°F.
From the same technique illustrated previously, the ratio of the third entry rate to the first is 4.65, and the ratio of the fourth entry rate to the first is 14.85. These ratios, along with a ratio of 1.00 for Entry 1, sum to 23.0 and provide the fractional value of each entry in the total liquid stream of 500 RB/D. Thus, Entry 1 amounts to 500 × (1/23) = 22 RB/D. Likewise, the entry rate at Depth 2 is 54 RB/D, at Depth 3, 101 RB/D, and at Depth 4, 323 RB/D. In Fig. 2, notice that the entry at Depth 4, with by far the largest rate, moves the temperature after mixing much closer to static than does any other entry, as expected. The density log of Fig. 2 shows that all four streams are composed primarily of water so that no phase conversion is needed.
|flow rate, B/D–scf/D
|inside bend radius (or turning radius), ft
Noteworthy papers in OnePetro
Agnew, B.G. 1966. Evaluation of Fracture Treatments With Temperature Surveys. J Pet Technol 18 (7): 892-898. SPE-1287-PA. http://dx.doi.org/10.2118/1287-PA
Cooke Jr., C.E. 1979. Radial Differential Temperature (RDT) Logging - A New Tool for Detecting and Treating Flow Behind Casing. J Pet Technol 31 (6): 676-682. SPE-7558-PA. http://dx.doi.org/10.2118/7558-PA
Dobkins, T.A. 1981. Improved Methods To Determine Hydraulic Fracture Height. J Pet Technol 33 (4): 719-726. SPE-8403-PA. http://dx.doi.org/10.2118/8403-PA
Jameson, L.R. 1967. Some Applications of Differential Temperature Logging. Presented at the SPE Regional Secondary Recovery Symposium, Pampa, Texas, 26-27 October. SPE-1977-MS. http://dx.doi.org/10.2118/1977-MS
Millikan, C.V. 1941. Temperature Surveys in Oil Wells. Trans. of AIME 142 (1): 15-23. SPE-941015-G. http://dx.doi.org/10.2118/941015-G
Ramey, H.J.J. 1962. Wellbore Heat Transmission. J Pet Technol 14 (4): 427–435. SPE-96-PA. http://dx.doi.org/10.2118/96-PA
Smith, R.C. and Steffensen, R.J. 1975. Interpretation of Temperature Profiles in Water-Injection Wells. J Pet Technol 27 (6): 777-784. SPE-4649-PA. http://dx.doi.org/10.2118/4649-PA
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