On the Use of Low-Frequency Distributed Acoustic Sensing Data for In-Well Monitoring and Well Integrity: Qualitative Interpretation

The purpose of this work is to present theory that can explain observations in LF-DAS data recorded in production and injection wells, and guidelines for qualitative interpretation of these data. Several data examples with our interpretation are presented to show how these data can be used in a qualitative way to obtain insights into processes in a well. Here, we focus on DAS data, but FO data interpretation benefits from combining data from both DAS and distributed temperature sensing. For an overview of the theoretical background and applications of FO data for the oil and gas industry, we refer to Fang et al. (2012), Hartog (2017), and Ashry et al. (2021), and references therein.

In phase-sensitive optical time-domain reflectometry, an interrogating unit emits light into the FO cable and analyzes the backscattering (Rayleigh scattering) from naturally occurring impurities or from engineered high-reflectivity points in the FO cable (Hartog 2017). The output (DAS) data are the changes in optical phase over short intervals along the fiber (gauge length) and are sensitive to changes in both strain and temperature in the fiber core. A change in temperature will lead to axial strain on the fiber and change of the refractive index (Fang et al. 2012). Variations in temperature often occur over longer time periods and can be separated from dynamic strain by applying a simple low-pass filter to the DAS data (Bakku 2015). Hartog (2017) states that ultralow-frequency DAS clearly carries information of interest to the operator, but that the origin is not well understood.

LF-DAS data have been used in characterization and monitoring of hydraulic fracturing (Becker et al. 2017; Jin and Roy 2017; Ichikawa et al. 2019). Geomechanical modeling of DAS response is presented in Sherman et al. (2019). Webster et al. (2013) and Jin and Roy (2017) are examples of early publications mentioning temperature sensitivity for in-well LF-DAS data and focus on monitoring of hydraulic fracture stimulation. Later, several examples showing temperature changes from LF-DAS data were published (Miller et al. 2018; Titov et al. 2019; Karrenbach et al. 2019; Sidenko et al. 2022). Sharma et al. (2021) demonstrates that LF-DAS data can be used for early gas detection. Ekechkwu and Jyotsna (2021) uses a machine learning technique to predict pressure from DAS and distributed temperature sensing data in a well during varying conditions.

In this paper, we use theory based on tubing stress analysis to describe potential sources of LF-DAS response in a well environment. Signals at low frequencies (<0.5 Hz) in DAS data are not just a result of temperature and pressure acting on the FO cable itself, but also a result of how fluids and steel surrounding the FO cable respond to well conditions. By accessing and understanding these data in real time during operations, it will be possible to make better decisions that can improve safety and reduce cost. The value of information in DAS data rapidly decreases with time (Schuberth 2020) and being able to react to processes that potentially pose a health, safety, and environment risk observed in the DAS data in real time is of the utmost importance to ensure safe operations. The use of real-time DAS data has previously been presented in, for example, Raab et al. (2019) and Schuberth et al. (2021). In-well DAS is still an emerging technology, even though it has been around for more than a decade (e.g., Johannessen et al. 2012; Molenaar et al. 2012).

The data volume problem for DAS data is obvious. Data on the order of terabytes are produced per day from each well. For the examples herein, the DAS data from the interrogators are sampled at 10 kHz and cannot be used in a practical matter in their raw format. Data must be refined in a way that keeps the useful information while significantly reducing the data amount. Furthermore, these data need to be readily available to the end user in an interactive way to most efficiently make use of them. All but one of the examples presented here comes from a real-time interactive analysis system (Schuberth et al. 2021), where the user can see data streaming from a well with just a few seconds delay. FO data are covisualized with production-related measurements, typically used by production engineers, and well completion diagrams for reference to the well design. Other features include interactive utilities, changing colormaps, and effective zooming. Such an interactive analysis system is a key enabler for efficient interpretation of FO data.

Textbook signal processing methods can be applied to obtain LF-DAS data. The raw DAS data must be low-pass filtered and resampled according to sampling theory (Nyquist 1928; Shannon 1949).  Appendix A outlines a memory-efficient polyphase resampling approach for data received in fixed-size time packages, which has been used in processing all data shown here.

In the first part of this paper, we present the optical phase and how it changes with variations in strain, temperature, and pressure. Then, we take a closer look at how different well conditions may be linked to changes in optical phase. Several data examples with interpretation are then presented. The purpose is not to show all the potential use cases for LF-DAS but to show examples of observations and our interpretation of these events.

To be able to understand different factors affecting DAS data at low frequencies, we turn to the basics: The DAS method relies on extracting the change in optical phase along the fiber. For practical purposes, we write the change in optical phase as (e.g., Budiansky et al. 1979)

where $Φ$ is the optical phase, $ΔLL=εz$ is the axial strain in the fiber core, and $Δnn$ is the relative change in the refractive index of the fiber. The change in phase is a function of the relative changes in the length of the fiber and the refractive index, which both are sensitive to temperature and strain. The relative change in optical phase due to strain is given as (Bucaro et al. 1977)

where $P12$ and $P11$ are the Pockels’ coefficients of the fiber core and $εr$ is the radial strain in the fiber. From Eq. 1, positive strain means elongation. By assuming $εr=-μgεz$ , where $μg$ is the Poisson’s ratio of the fiber core, a simple relationship between the change in optical phase and axial strain can be obtained

where the photoelastic scaling factor is given as

Eq. 3 is typically used when converting phase data into strain (SEAFOM 2018). The strain in Eq. 2 is the strain in the core of the fiber. Studies on how external pressure affects strain in the fiber core show that the elastic parameters of the cladding and coating significantly influence the pressure sensitivity of the FO cable. Budiansky et al. (1979) found that an FO cable subjected to external pressure will contract, and that the relative change in optical phase due to a pressure change is approximately negative 10⁻¹¹ Pa⁻¹ for pure silica fiber. The sensitivity to pressure increases by an order of magnitude when a plastic clad with six times the radius of the silica glass is introduced. For a thick coating, the sensitivity to pressure is inversely proportional to the bulk modulus of the coating (Lagakos et al. 1982). For harder coating material, such as a metal jacket, the sensitivity may be reduced significantly, and some combinations may result in no sensitivity to pressure (Giallorenzi et al. 1982). A modern FO cable consists of many layers such as a carbon-coated clad fiber surrounded by gel inside a single or several metal tubes. This is to prevent stress on the FO cable that may lead to damage or breaking the fiber (Lumens 2014) and to avoid hydrogen intrusion (Stone 1987). For example, one numerical modeling study (Wu 2011, as cited in Lumens 2014) assuming static strain/stress, illustrates that the radial stress experienced by the core due to pressure on the outside of the cable is reduced by ~19 dB (10^–1) compared with the stress of the outside of the cable. The same modeling shows that the axial strain experienced by the core is less influenced by its surroundings as long as the FO cable is overstuffed in the metal tube. Hence, the optical phase’s sensitivity to pressure is dependent on the design of the FO cable. For the scope of this work, which is qualitative analysis, we use the results from Budiansky et al. (1979) and find an estimate of the relative change in optical phase due to changes in pressure as

The change in optical phase when changing the temperature is given as (Fang et al. 2012)

where $αT=1LdLdT$ is the coefficient of linear expansion, $dndT$ is the thermo-optic coefficient, and $ΔT$ is the change in temperature. Typical values for these coefficients are $αT=0.55×10−6K−1$ and $dndT≈10−5K−1$⁠. The relative change in optical phase due to a change in temperature is then found as

Here, we assume fiber that is clamped to the tubing will experience mechanical strain if the tubing experiences strain due to changes in temperature or pressure. Variations in temperature of the steel give rise to thermal expansion. Variations in pressure inside or outside tubing may also give rise to strain on the tubing. The tubing strain is also dependent on the well design and if a valve is open or closed, for example. We consider the effects of multiple sources of strain including pistoning, ballooning, and friction from fluid flow. The goal of this section is to show that these effects are likely sources of signal in LF-DAS measurements and not to give a complete overview of tubing stress analysis, which can be found in, for example, Bellarby (2009) or Guo et al. (2007). Furthermore, pressure induced temperature changes in gases and liquids are considered.

Tubular ballooning is an effect that occurs when the pressure is changed on the inside or outside of a tubular. The resulting axial strain on the tubing is given as

where $μ$ and $E$ are Poisson’s ratio and Young’s modulus of the tubing steel, respectively; $ΔPo$ and $ΔPi$ are the change in pressure outside and inside the tubing, respectively; and $Ao$ and $Ai$ are the areas that correspond to outer and inner radii of the tubing, respectively. We can find the relative change in optical phase due to ballooning given the assumption that the FO cable experiences the same axial strain as the tubing. By inserting the axial strain due to ballooning from a change in pressure on the inside or outside of the tubing (Eq. 8) into Eq. 3, we get

It is clear that the tubing strain will have opposite polarity for a given change in pressure on the inside and outside of the tubing. This model assumes that the tubing is free to move on one end, for example, with an expansion joint. However, all wells are fixed on both ends in the examples presented later in the Data Examples section.

The axial force resulting from pressure acting on an area is given as:

where $Az$ is the area projected in the axial direction (i.e., the area as seen from the axial direction) and $PA$ is the pressure acting on that area. For example, the resulting axial force acting on a closed safety valve can be given as

where superscripts $a$ and $b$ refer to above and below the valve, and $Av$ is typically either the cross-sectional area of the tubing or annulus. The axial force resulting from pressure at a crossover (i.e., where the tubing diameter is assumed to get smaller with increasing depth) can be given as

where the superscripts i and o refer to inside and outside the tubing, respectively. To evaluate the strain on the tubing due to the piston effect (i.e., a force applied at a single depth in the well), we have to find the internal forces above and below the point of action. For a vertical well, where the strain is limited to the axial direction, we have to solve a statically indeterminate problem (e.g., Khalfallah 2018). For the case of pistoning from pressure acting on a closed valve in a tubing with constant dimension, we get the following strain profile:

where $L=Lb+La$ is the length between the fixed endpoints of the tubing, $Lb$ is the length from the valve position $zv$ to the fixed point at the bottom, $La$ is the length from the valve position to the fixed point on the top, $Fv$ is given in Eq. 11, and $A$ is the cross-sectional area of the tubing. This very simple model only accounts for elasticity and ignores the impact of inertia but is reasonable for qualitative analysis. If we consider a very simple tubing with constant cross-sectional area and a safety valve positioned at a depth corresponding to one-third of the distance between the fixed ends of the tubing, we can find the axial strain in the section above the safety valve as:

For a standard 7-in. tubing, the relative change in optical phase due to pistoning in the tubing from a closed valve can be found (using Eq. 3) as

where $ΔP=Pa-Pb$⁠.

Pistoning from a closed valve is illustrated in Fig. 1. It is clear that the strain above and below the depth of the force will have opposite polarity, which should make it quite visible in data. In practice, we often observe that strain related to pistoning is only visible in a limited interval around the depth corresponding to the source of the pistoning, and this is likely due to friction. Friction along the wall should be taken into account in a deviated well where the tubing is in contact with the casing making up the annulus around the tubing. Axial forces along the well due to pressure variations will occur where there are changes in cross-sectional area of the tubing (e.g., crossovers), where expansion devices are present, and where a pressure difference over a plug or valve (e.g., safety valve testing) exists.

The steel in the well also experiences thermal expansion. The coefficient of thermal expansion of steel is $αS≈10−5K−1$ . If we assume that fiber clamped to the tubing experiences the same axial strain as the tubing, then the relative phase shift due to a temperature change can be found from Eq. 3 as:

where $ξ$ is the photoelastic coefficient given in Eq. 4. This indicates that the relative change in optical phase due to strain transferred by a (thermally expanding) tubing is almost identical to the change in optical phase due to temperature acting on the fiber itself.

The force acting on a production or injection tubing due to flow may also cause strain on the tubing. From Bellarby (2009), the frictional pressure drop can be given as:

where $v$ is the mean flow velocity, $ρf$ is the fluid density, and $d$ is the inner diameter. The friction factor f is dependent on wall roughness for turbulent flow and the Reynolds number. For a pipe with length $L$⁠, fixed at one end, the total displacement due to flow can be found as

A section of tubing of length L that is fixed at both ends is the more interesting case here. The strain as a function of position $z$ in such a pipe can be found as

Here it is assumed that the flow is moving in the positive z-direction. Compared with the case of pistoning, which takes the form of a step function, the strain induced by flow takes the form of a linear ramp. Considering a water injection well with a flow velocity of v = 6.6 m/s in a 3750-m long standard 7-in. tubing (⁠$L$⁠), the Colebrook-White equation gives a friction factor of $f=0.02$⁠, using standard values for wall roughness. The maximum value of the strain will be around 7.5×10⁻⁵ m/m at the two fixed ends. The resulting strain is illustrated in Fig. 2.

By assuming adiabatic gas compression or expansion in an ideal gas, we find the temperature change as a function of the pressure change as:

where $T0$ and $P0$ are the pressure and temperature before applying a pressure change, and $k=Cp/Cv$ is the ratio of specific heats. The approximate solution, given by the first order of a Taylor series expansion, is only valid for the case where the relative pressure change is small. The adiabatic assumption is not correct, since heat transfer to and from gas is quite rapid, which will be clear from the examples. However, the purpose here is to obtain an estimate of the change in optical phase due to pressure changes. Assuming the gas is methane, with $k=1.32,T0=300K,andP0=80bar,$ we find the relative change in optical phase, using Eq. 7, as

Adiabatic expansion of fluids will also result in temperature changes. Following Knoerzer et al. (2010), we find the change in temperature in a liquid due to a pressure change, and its first-order Taylor approximation, as:

where $ρ,αT,$ and $Cp$ are the density, thermal expansion coefficient, and specific heat capacity of the liquid, respectively. These parameters are dependent on the initial pressure and temperature conditions. For water with initial temperature and pressure of 323 K and 75 bar, respectively, we find the relative change in optical phase, using Eq. 7, as

For a light oil at the same conditions, we obtain:

The theory shows that different phenomena will give rise to different responses and often with distinct signatures. So, what should you look for in these data? A rule of thumb is that effects related to movement of fluid with different temperatures (not covered here) are “slow” events, and pressure-related effects are “fast” events. Slow events infer that the events are not seen on several, or all, spatial locations at once. For example, a temperature variation in injection water will give rise to a signal that will propagate with the flowing velocity. Another example is that a moving gas interface can be observed during an unloading process. Typical pressure-propagation speeds range from 300 to 1500 m/s depending on the fluids in the well and may be higher for heavy muds. Pressure changes can be considered instantaneous along the well when looking at hours of LF-DAS in the same view and, therefore, are considered fast. We shall see in the example section that abrupt changes in the LF-DAS data with depth will, for example, show liquid levels or tell if a valve is closed or open.

For clarification, we may see responses related to pressure, temperature, and strain simultaneously in these data. Separation of LF-DAS data into three data sets containing changes in temperature, pressure, and strain is not trivial. Here, we do not attempt to make this separation, but instead show the reader that qualitative interpretation of these data will very often be sufficient to understand what is happening.

Fig. 3 shows a table with color variations that are proportional to the estimates of pressure sensitivity on the optical phase due to some of the effects considered above. It displays the relative signal strength by effect induced by the same given pressure change. Since the LF-DAS data, as presented here, are in rate of change, we should scale these colors with the pressure rate to compare with these data. We see that for pressure changes in Annulus A, where the FO cable is located, LF-DAS is most sensitive to gas expansion and pressure acting directly on the fiber. We should see a combination of these two effects in a gas zone. However, for a pressure manipulation in tubing containing different phases (e.g., gas and liquid), we expect to see the gas zone cool down or heat up, while the temperature in the liquid phase will not change much. We expect to identify the gas/liquid interface quite easily from this kind of pressure manipulation.

Pistoning and fluid-flow induced strain have very characteristic signatures and should also be recognizable. We expect to see a different response above and below the depth of a closed valve when manipulating the pressure above the valve. The pistoning signal should be an order of magnitude smaller than the effect related to gas expansion for the case of gas above the valve.

It is is important to remember that we are looking at rate-of-change data when analyzing LF-DAS data in this paper. For example, this means that the signal from a small change in pressure over short time can be of equal strength as a large change over a longer time period. The reader is encouraged to look at data and compare with the table in Fig. 3 when looking at the examples presented in the next section, Data Examples.

The purpose of this section is to present LF-DAS data examples that illustrate pressure and temperature sensitivity due to different sources mentioned in the theory part. LF-DAS data are presented as the rate of change of the optical phase converted to strain rate using Eq. 3, meaning that we are seeing the changes over time. In the figures with LF-DAS data, we use the following color convention: Red color indicates either that the temperature is increasing or that the fiber is being elongated axially, and blue color indicates that the temperature is decreasing or that the fiber is being shortened. A simple way of memorizing this convention is that steel expands when heated (red) and contracts when cooled (blue). A complicating factor is the pressure response on the fiber itself (positioned inside Annulus A), which is blue when the pressure is increasing and red when the pressure is reduced. When working with these data, it is often necessary to adjust the colormap range to be able to see different aspects of these data. Unfortunately, this is not possible in the context of this paper, so the range of the colormap is chosen to see as much as possible at the expense of saturating the image in some locations. The vertical axis corresponds to depth along the well [measured depth below rotary kelly bushing (RKB)], and the well design is indicated on the left side in all the plots. The horizontal axis is showing time, which increases from left to right. Relevant data from gauges are presented above the DAS data, with labels in the upper left corner. The pressures, temperatures, and injection rates are displayed without numbers as the focus is on qualitative interpretation.

Fig. 4 shows LF-DAS data from a time interval where we can observe changes in pressure in the tubing, Annulus A, and Annulus B. Light oil is produced in this well, and solution gas is expelled when the oil rises to a depth where the pressure is lower than the bubblepoint pressure. The times marked with T₁, T₄, and T₅ indicate changes in the choke setting with corresponding pressure changes. At T₁ and T₄, we observe pressure drops in the tubing as a result of opening the production choke. This causes the gas out of solution to cool down (blue), and shortly after, the entire well heats up (red) due to an increase in flow rate and heat advection from the reservoir. When the well is choked back (T₅), we observe the opposite happening as the gas heats up and the well cools down. We also observe that the bottom depth of the gas response is shifting upward and downward when the wellhead pressure is changing. We interpret this depth to be the bubblepoint pressure depth, indicated with a dashed line in Fig. 4.

At T₂, the pressure in Annulus B is reduced, and we can see a vertical blue stripe all the way down to the depth corresponding to the end of Annulus B (liner hanger depth in Fig. 4), followed by a red tail. Here, Annulus B is water-filled, and we interpret this blue stripe to be a result of a temperature decrease as the pressure is depleted, followed by reheating back to equilibrium temperature. At T₃, the pressure in Annulus A is depleted, and we immediately see a major cooling in the gas phase due to gas expansion. This signal extends from the top of the well to the depth corresponding to the gas lift valve (GLV), where we expect the gas/liquid interface , i.e., the liquid level to be (GLV depth indicated in Fig. 4). This cooling eventually decays (weaker blue), since heat transfer from the warm tubing to the colder gas is very fast. The gas phase heats up very fast (bright red) when the pressure manipulation is finished. An apparent heating can be observed in the water phase in contrast to the response in the gas phase. This signal shape is accurately matching the time derivative of the pressure response measured in Annulus A, where the FO cable is present, and this is a direct response of the pressure acting on the fiber itself.

Data from a different well are observed in Fig. 5, where the FO cable is terminated below the production packer which is sealing Annulus A at the bottom. This is deeper in the well compared with Fig. 4. When the pressure is reduced in Annulus A (T₁), we observe a similar response as in Fig. 4 (T₃), except that the pressure response stops abruptly at the depth of the production packer. Furthermore, we can observe that something cold is moving downward (T₂) in the well and stops at the depth of the GLV or fluid interface (gas/water). This is water leaking from Annulus B to Annulus A, which was intensified when the pressure in Annulus A was reduced. Weak variations between blue and red slanted lines can be seen throughout these data. There is a choking operation (T₃) where we can see the well warming up as more fluids are produced. Furthermore, we can see the response of bleeding off Annulus C (T₄). This response is observable from the top of the well down to the depth that corresponds to the end of Annulus C. In comparison with Annulus B pressure reduction in Fig. 4, which shows a rapid cooling and then reheating, the pressure change in Annulus C appears as a rapid heat up followed by cooling. However, in a zoomed-up view (Fig. 6), it becomes clear that what appears as heating up is due to strain. There is brine in Annulus B and oil-based mud in Annulus C in these wells.

Data in the interval between the vertical dashed lines in Fig. 5 are shown in the left-hand side in Fig. 6. The event that appears as heating up (T_4,1) is seen to be an event that is starting in the middle of the pressure reduction and is followed by the blue signal (T_4,2), which is indicative of cooling down. Furthermore, slanted lines with weak variations between blue and red can also be observed. In the right-hand side of Fig. 6, we can observe data from the interval between the vertical dashed lines in the left-hand side in Fig. 6. Here, it becomes very apparent that the red signal is not continuous along the entire length of Annulus C, which is expected if it was due to a pressure-induced temperature change. We interpret these events as being caused by strain related to bleeding down the pressure, and that the blue is due to a pressure-induced temperature change in the Annulus C fluid. A sudden temperature drop in Annulus C will not immediately be seen on the fiber, which is positioned in Annulus A, since the heat transfer process will take some time. We should also expect to see the temperature heating back again. This is not observed in this case, but we speculate that this would be a slower process and hidden behind other signals in these data.

The next example is from a well with a suspected GLV leak. The production engineers tried to clean potential debris propping the GLV in an open position by running high gas lift rates. The pressure in Annulus A was reduced after running gas lift which resulted in a large differential pressure across the valve. Real-time LF-DAS data were acquired during this operation and are shown in Fig. 7. High-amplitude noise can be seen from the GLV depth during gas lift. Small and rapid pressure variations in Annulus A give rise to temperature variations seen as vertical stripes in the gas phase (T₁). Cooling of the gas phase (blue) and a pressure-on-fiber response in the water zone (red) are observed when gas lift is stopped by a pressure reduction in Annulus A. The Annulus A pressure is then reduced again, but more slowly, resulting in continued cooling of the gas phase and pressure-on-fiber response in the water zone. It becomes apparent after some time that the boundary between the gas and water responses has moved shallower in the well. We then see the gas reheating when the pressure reduction is stopped (T₂). At this point, we observe that the liquid level has moved upward since gas lift ended. After 96 hours, there was a desire to determine how much oil had leaked into Annulus A, and it was decided to manipulate the pressure in Annulus A. The valve between the flaring system and the annulus was subsequently opened, giving rise to a 0.04-bar pressure drop in Annulus A as the volumes combined. This is indicated at T₃, where the liquid level can be clearly identified. The pressure was then reduced by a total of 5 bar in two stages with the initial reduction at T₄. We can now see that there are three depth intervals with different responses corresponding to this pressure change. In the upper part, we observe cooling as the gas expands. At the bottom, we observe a direct pressure response on the fiber in the water zone, and in the middle (i.e., between the two dashed lines), we observe a response that is weaker. Our interpretation of these responses is that there is gas in the upper interval, 28 m of oil in the middle interval, and water in the lower interval. We interpret the weaker response in the middle section to be due to adiabatic expansion of oil, which results in a much smaller temperature drop than in gas. Since we are seeing a combination of the pressure acting directly on the fiber and the oil potentially cooling, the net sum is not blue. This example shows that LF-DAS is a very good tool for estimating liquid levels in Annulus A and gives indications about the fluid content. This can be used in real time to monitor back-production of the oil with low rates before gas lift at high rates can be started to avoid unnecessary wear on the GLV.

A standard procedure during the opening of a new well is to break a glass plug that seals the reservoir from the surface by means of pressure cycling. Live DAS data were not available for the field and well in this example. The DAS data were instead acquired during the operation and processed when received onshore according to the procedure described in  Appendix A. Four unusual pressure cycles were reported during the first hour of pressure cycling. These were disregarded, and cycling was continued until the glass plug was broken. It becomes apparent by inspecting the processed LF-DAS data in Fig. 8 that the main signal, during the four unusual pressure cycles, is originating from the downhole safety valve (DHSV). It is deduced that the valve was closed during these unusual pressure cycles. We observe very strong amplitude events in the box with mark T₁. These events have opposite polarity above and below the depth corresponding to the position of the DHSV and will be discussed in more detail later. In the remaining data, we observe a combination of temperature and pressure changes. The pressure-induced strain effects should in theory be proportional to the rate of change in pressure, and the four black arrows in the period after the DHSV has opened (T₂) indicate locations along the tubing where this can be observed. The uppermost arrow is positioned exactly at the DHSV and displays very good pressure sensitivity and correspondence with the wellhead pressure. The inner diameter in the DHSV is slightly larger than the tubing above and below. The response is interpreted to be pistoning due to the changes in the cross-sectional area. There will be axial forces at depths corresponding to the changes in the cross-sectional area when the pressure is changed in the tubing. These forces will result in compression (blue) when the pressure is reduced and elongation (red) when the pressure is increased because the area inside the DHSV is larger. For the other black arrows and in the rest of the well, there is less sensitivity to the pressure changes, and we see variations in polarity from depth to depth and not a continuous signal as predicted by ballooning.

We see upward moving events in the very top of the well when the pressure is reduced and downward moving events of opposite polarity when the pressure is increased (light arrows). This is related to the movement of fluids in the tubing when changing the pressure (i.e., pushing in or out fluids to manipulate pressure). If nothing is happening in a well, the temperature of the fluids will (eventually) take on the temperature of their surroundings, for example, becoming colder in the sea and warmer in the subsurface. As the fluid column is moving up or down, fluids with a given temperature will move into warmer or colder surroundings, causing the well to cool down or heat up. Afterward, heat conduction will make the fluid temperature change toward its new surroundings.

We observe triangular-shaped features at the very base of the data set and indicate two of them with arrows. These features are a result of pistoning at a crossover from 5.5- to 5-in. tubing below the FO cable. When the pressure is reduced or increased, it results in compression or extension, respectively. Furthermore, we can observe slow changes in the LF-DAS signal which are related to temperature variations and correspond well with the downhole temperature measurements. The pressure variations are on the order of hundreds of bar while the temperature changes are within 2 K for this example. The glass plug breaks at the time corresponding to T₃. The effect of fading (e.g., Hartog 2017) can be observed as high-amplitude spikes occurring sporadically at certain depths.

The lowermost plot in Fig. 9 is a zoom-up of data in the black box in Fig. 8. We observe that the signal seen in the vicinity of the DHSV forms triangular shapes where the polarity above and below is opposite. This is a result of pistoning on the closed DHSV. We observe compression (blue) above the valve and elongation (red) below the valve when the pressure is reduced, and the opposite polarity when the pressure is increased. We also see that triangles are growing as the pressure is changing. The top and bottom of the signal are interpreted to be the depths where the tubing is unable to move because of friction. These fixed points move up and down as the piston force becomes stronger. From the LF-DAS data, it is possible to pick the contact points above and below the depth of the DHSV. These depths, along with the depth of the DHSV, can be used with Eq. 13 to make a simple model for the tubing strain. A linear inversion problem can then be formulated to invert these data for the pressure rate. The uppermost plot in Fig. 9 shows the inverted (i.e., DAS-derived) pressure rate along with the measured pressure rate at the wellhead. The middle plot shows the correspdonding modeled data. This simple model is able to predict these data quite well although not perfectly. We think this example and data provide enough evidence to support the conclusion that DAS data from an FO cable clamped to the tubing are sensitive to tubing strain. This example also shows the benefit of a real-time system, as we would have been able to see that the DHSV was closed and acted immediately, potentially saving 1 hour of operational time and reducing the chance of damaging the DHSV.

LF-DAS data from an operation where the annular safety valve (ASV) was supposed to open are seen in Fig. 10. The opening was triggered at the time where the vertical red bar is seen in the uppermost plot along with the pressure curves. Annulus A was pressurized (T₁), and we could immediately observe heating of the gas phase down to the depth corresponding to the ASV. The Annulus A pressure was still being increased when a clear signal can be seen all the way down to the GLV depth (T₂). This is heating of the gas below the ASV in the annulus due to gas compression. We observe at the same time that something warm is moving downward from the ASV depth as indicated with the arrow (T₃). This is warm gas from above the ASV leaking through it. We can then see a massive cooling in the annulus above the ASV depth which corresponds to reduced pressure above the ASV. However, gas continues to leak until we observe a cooling between the ASV and GLV depths (T₄). Gas is heated above the ASV (T₅) after the pressure reduction in Annulus A has stopped. We see pressure equilibrating across the ASV once it is opened (T₆), with a heating above the ASV as the pressure increases and a cooling below the ASV as the pressure decreases. The choke opening is increased (T₇), and we see the well heating up due to increased production and the depth corresponding to the bubblepoint pressure moving downward in the well.

LF-DAS data from the same offshore water-injection well but for periods during the start and stop of injection are shown in Figs. 11 and 12, respectively. The well was shut in sufficiently long enough before starting injection that temperatures reached equilibrium at all depths except for the reservoir zone. The temperature profile is in general increasing from the top to the toe of the well, whereas the sea and reservoir intervals are relatively cold. The temperature above the reservoir is about 40°C higher than the reservoir. There is also a zone which is slightly warmer and is shown between the dashed lines in Figs. 11 and 12.

We observe noise propagating from the top of the well (T₁) in Fig. 11 after the choke has opened, and this is due to cavitation in the tubing (multidarcy reservoir). Features are seen moving downward in the well as the injection rate increases, and two of them are indicated by curved arrows (T₂). This is due to water with slightly different temperatures moving downward in the tubing. The upper and lower arrows start from the seabed and from the top of the slightly warmer depth interval, respectively. We see that the warmer zone starts to cool down more than the region above as soon as colder water displaces the warmer water. The warmer zone cools down very fast (saturated blue) when water in the tubing from above the seabed reaches this zone (white arrow, T₃). The reservoir section heats up very rapidly as warm water is flowing into the reservoir and cools very fast when colder water from above the warm zone reaches the reservoir (lower arrow, T₃). We start to observe vertical lines that change polarity from red in the top to blue in the bottom when injection is around half of its maximum. Some of these are indicated by short black arrows (T₄), and they correspond to strain of the tubing. The tubing is elongated in the top and compressed in the bottom with little or no strain near the middle. This is interpreted to be flow-induced strain and will be discussed in more detail (Fig. 13).

We observe ongoing injection in the beginning of Fig. 12. The blue and red slanted lines are due to small temperature variations in the injection water flowing down in the well. When the wellhead pressure is changed slightly, we see a small response (indicated by arrow at T₁) that corresponds to pistoning on a crossover into a smaller dimension on the tubing. When the pressure is being reduced, we observe contraction above and extension below the depth of the crossover, and vice versa when the pressure is increased again.

When injection is stopped (T₂), the well immediately starts to warm up in the subsurface and cool down in the sea. The temperature increases faster in the hot zone between the two dashed lines. We also see that vertical lines start to appear but now with opposite polarity compared with the lines in Fig. 11. The vertical lines initially have a limited depth range and originate from two distinct positions in the well corresponding to intervals where the well deviation is increasing. As time increases, the endpoints of the vertical lines are moved further up and down the well. There are no fluids flowing during this time. However, the tubing has stored elastic energy due to displacement of the tubing by flow before stopping injection. We believe the elastic potential will be released over time, and that the tubing will move toward its initial state. We see that these events occur over a period of 25 hours in this figure, but they can extend for several days.

The vertical lines with switching polarities observed in Figs. 11 and 12 were isolated from the background data and integrated over time to produce cumulative strain and displacement profiles which are shown in Fig. 13. The leftmost plot shows the strain estimated by integrating the isolated vertical signal over time for the case where injection is started (Fig. 11). The black curve corresponds to integration over the entire time period shown in Fig. 11. The blue and orange curves correspond to integration from the times indicated by the blue and orange vertical lines in the plot in Fig. 11, respectively. The dashed line shows the theoretical strain profile as estimated by Eq. 19. The second plot from the left shows the corresponding displacements calculated by integration of the strain profiles over depth. The two plots to the right in Fig. 13 are the same as the two leftmost plots but for the case where injection is stopped. There is good correspondence between the estimated and theoretical strain for the case of starting injection. We expect to have differences since friction is not included in the simple model. It is clear from Fig. 13 that the signal is affected in zones where the well deviation is increasing. The estimated strain is not near the theoretical strain for the case after injection is stopped. Potential reasons for this could be that the isolation of these events is not good enough, the time period considered is too short, or that some of these events can be related to thermally induced strain.

It is clear from the examples provided here that LF-DAS data are very rich in information, but that interpretation can be challenging without contextual information. Having access to the well completion and knowledge about the well design, annuli fluids, and the kind of operation to be performed makes it easier to focus on the areas of interest. The measurement gauges downhole and on the wellhead are useful but not critical for qualitative interpretation, as the response to, for example, pressure in the tubing and different annuli have distinct signatures. Understanding the different features that may appear in these data is very important and can often be explained using simple models. Using the very basic concepts in tubing strain analysis (Bellarby 2009), we have shown that strain profiles resulting from pistoning and flow should have a very recognizable and distinct nature and, therefore, can be distinguished from other events. Fluid properties are also important, as variations in the pressure-induced temperature changes will be different for different fluids and easily recognized in these data.

Data representation is also an important aspect in interpretation. All the examples here are shown in a colormap going from blue to red via white. This simplifies interpretation as it can easily be related to warming up, cooling down, or stretch and squeeze. The author’s background is within geophysics, seismic processing, and interpretation, where data are often represented by variable density colormaps. We think that the production engineering and well-integrity communities may similarly benefit and become accustomed to this form of data representation.

We have focused, in this work, on the signal related to pressure changes and flow-induced strain. However, there are many examples where temperature, or its time derivative, is the most important tool. Unloading of Annulus A during start up of a gas lift well is a great example of this, and LF-DAS serves as high-definition temperature-gradient data with higher sensitivity and much greater resolution in time than distributed temperature sensing. However, LF-DAS suffers from higher noise levels in the upper part of the well that are most likely induced by ocean waves.

The presented examples of piston- and fluid-induced strain show that casing-wall friction influences the strain profiles in the wells, and that we can observe stick/slip behavior. There are points and sections along the tubing which remain fixed due to friction. However, the tubing can slip to a new fixed position when the stress increases, and the friction is overcome. This nature is similar to that of earthquakes, where stress accumulates and is periodically released. Without friction, we would expect the flow-induced strain to be (almost) proportional to the time derivative of the fluid flow. While theory predicts that ballooning and thermal expansion should be of equal significance as pistoning, we do not observe these as continuous events in our data, as we do for temperature and pressure variations directly applied to the FO cable. We think the reason for this is that the examples provided here are from wells where the tubing is fixed in both ends and, therefore, are not able to move freely as assumed in Eqs. 8 and 16. However, we speculate that variations in friction along the well can make it possible to get ballooning- or temperature-induced strain in some regions of the well, but our ability to predict or exploit this would be limited. Buckling has not been discussed here, but we are aware that this is something that we might be able to see when the pressure criteria for buckling are reached.

We acknowledge that we cannot explain every detail in these data yet. We can very often infer what is happening in the well even though we do not fully understand the reason why. For example, we are unable at this point to explain how the events which are interpreted as strain resulting from reducing the pressure in Annulus C (Fig. 6) is coupled to the tubing. It could be possible to model this, but again, our ability to exploit this may be limited to the qualitative information gained, that is, there was motion in a region of the well.

For qualitative analysis of LF-DAS data, it is not crucial to know exactly how pressure, temperature, and strain will change the optical phase, as clearly demonstrated here. However, for quantitative analysis, it would be very important to derive transfer functions from pressure, temperature, and strain to optical phase shift. These transfer functions would be dependent on the FO cable design, how the cable is fitted in a well, and most likely the well design/steel properties and fluids too. Separation of effects related to pressure, temperature, and strain can in general not be achieved by using LF-DAS data only. Separation of temperature and pressure can be done for some simple cases, for example, in the case of Annulus A pressure manipulations in a gas lift-assisted well with water below and gas above the GLV. The LF-DAS data from the water zone are mostly sensitive to pressure, while data from the gas zone are sensing pressure and the pressure-induced temperature changes. By subtracting, for example, the average of data from the water zone from the rest of these data, we would be left with the temperature changes in the gas zone.

This paper has not focused on the physical and information technology infrastructure required to aid qualitative analysis in a user-friendly way. The solution used here is described in Schuberth et al. (2021). Continuous development of the functionality in the front-end application has been crucial, and we see that new use cases for FO surveillance are emerging all the time. While this paper focuses on the qualitative analysis, the goal of this work is to perform automated interpretation and quantitative analysis of LF-DAS data. Understanding LF-DAS data and its limitations are crucial in this development.

We have presented relevant theory for understanding LF-DAS signal related to pressure changes and compared the relative contributions from various in-well phenomena. Several examples of LF-DAS data from production and injection wells with FO cables clamped to the tubing have been presented along with our interpretations. LF-DAS data can be very rich in information and knowledge about the different features that may appear, and their distinct signatures are crucial for interpretation. We find that a large degree of pressure dependency observed in LF-DAS data is not due to pressure acting on the fiber itself but rather a range of phenomena that occur in a well due to pressure changes. The relationship between LF-DAS data and pressure and temperature is not straightforward. Here, we have shown that both the pressure inside and outside of the tubing, as well as the fluid phases, well design, and the status of valves can all be important. Access to real-time LF-DAS data gives production engineers and well-integrity personnel unprecedented insights into their wells, and we think it will serve as a standard tool for monitoring production, interventions, and well integrity in the future.

First, thanks to the large group of people working with FO technology in Equinor ASA. This work would not have been possible without feedback and great discussions with my colleagues, as well as the internally developed software for processing and analysis of data. Thanks to the partners in the Johan Sverdrup field, Equinor ASA, ABP Norway AS, Aker BP ASA, Petoro AS, and TotalEnergies E&P Norway AS, for allowing me to use and publish their data. Thanks to the partners in Martin Linge field, Equinor ASA, and Petoro AS for allowing me to use and publish their data. Thanks to Equinor ASA for allowing me to publish this work. Furthermore, thanks to four anonymous reviewers for suggestions that have improved this manuscript.

The effects related to pressure and temperature changes in a well are usually occurring over longer time periods. The raw DAS data must be low-pass filtered and resampled according to signal theory to be able to view these data in a practical and meaningful way. Data used for the analysis in this paper are a result of real-time processing of DAS data. The DAS data are converted to strain (or strain rate) and streamed in packages of $N=$ 8192 samples with sampling frequency of 10,000 Hz, resulting in a period of $Tp=$0.8192 seconds per package. We must apply a low-pass filter to these data to obtain LF strain-rate DAS, $rLFt$ , that is, perform a convolution between the signal, $rt$ , and a low-pass filter, $ft$ ,

where t is the time and $τ$ is an integration variable in the convolution. If the acquired data are strain, that is, not strain rate, we can simply use the derivative of the low-pass filter

where $st$ is the strain data. The limits of the convolution integral can be limited to the length of the filter which is used. In practice, the length of the filter dictates the cutoff frequency. We can now decimate the resulting low-pass filtered data without introducing aliasing based on textbook sampling theory (Nyquist 1928; Shannon 1949). We only calculate the output at the desired output times, similar to polyphase filtering, as our goal is to reduce the amount of data. For our data system, where other features (e.g., frequency-band energy) are calculated from the given size of packages, the desired sampling time is $Tp.$ We rewrite Eq. A-1 slightly as

where T is the length of the filter, and $nTp$ is the output time corresponding to the nth package. For the filter to effectively attenuate frequencies larger than $fNq=1/2Tp$⁠, it must be much longer in time than the length of the packages that are streamed. To achieve zero-phase output, we require data from both earlier and future times, where the latter implies a small time-delay for the processed output. The output at each timestep is now reduced to the dot product between data and the filter. In vector notation, this is given as

where $f$ and $r$ are vectors of length $NM$ containg the filter (in reverse order) and data, respectively, and superscript $T$ denotes the transpose. Assuming M is even, the data vector,

consists of M concatenated packages (with N samples in each). This dot product can be split into smaller dot products, making it very memory efficient. This is achieved by rearranging the filter $f$ of length $NM$⁠, into a matrix $F$ with shape $N×M$ and calculating partial dot products.

where $pnk$ is one of $M$ parts of the full dot product at output time k, from data in the package from time n. The final LF-DAS is found by summing all the parts that are assigned the same output time.

The memory requirements for this process are reduced significantly by using the partial dot products. Instead of holding M packages in memory for the full dot product, we now have to hold a single package and M floats, per channel in depth. The filter we use is a flattop window

where $ak$ is the coefficient given in Tran et al. (2004) under E-ISO filter. We find that choosing $T=10Tp$ yields 89 dB attenuation or more for frequencies larger than $1/2Tp$⁠. This filtering approach is a memory-efficient implementation of polyphase filtering (see Proakis and Manolakis 2007) for data in batches.

After the input data have been low-pass filtered and decimated in real time, the resulting data are sampled according to sampling theory and can be processed to the need of the applications that is to be performed. Due to imperfect phase unwrapping for DAS data, a standard de-piking technique—the moving median filter (Tukey 1977)—is often applied over the depth axis.

Original SPE manuscript received for review 8 September 2022. Revised manuscript received for review 5 November 2022. Paper (SPE 212868) peer approved 10 November 2022.