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Article

Research on Numerical Simulation and Interpretation Method of Water Injection Well Temperature Field Based on DTS

by
Shengzhe Shi
1,2,
Junfeng Liu
1,2,*,
Ming Li
3,
Chao Sun
3 and
Tong Lei
1,2
1
College of Geophysics and Petroleum Resources, Yangtze University, Wuhan 430100, China
2
Key Laboratory of Exploration Technologies for Oil and Gas Resources (Yangtze University), Ministry of Education, Wuhan 430100, China
3
PetroChina Qinghai Oilfield Branch Testing Company, Mangya 816400, China
*
Author to whom correspondence should be addressed.
Processes 2025, 13(1), 274; https://doi.org/10.3390/pr13010274
Submission received: 25 December 2024 / Revised: 10 January 2025 / Accepted: 15 January 2025 / Published: 19 January 2025
(This article belongs to the Section Energy Systems)
Browse Figures
Figure 1
<p>Schematic diagram of the downhole geometry: (<b>a</b>) schematic diagram of the wellbore; (<b>b</b>) schematic diagram of fiber optic installation location and wellbore cross-section [<a href="#B2-processes-13-00274" class="html-bibr">2</a>].</p> "> Figure 2
<p>Temperature field model.</p> "> Figure 3
<p>Model meshing.</p> "> Figure 4
<p>Wellbore velocity field.</p> "> Figure 5
<p>The temperature field changes when the flow velocity is 0.026 m/s.</p> "> Figure 6
<p>The temperature field changes when the flow velocity is 0.04 m/s.</p> "> Figure 7
<p>The temperature field changes when the flow velocity is 0.07 m/s.</p> "> Figure 8
<p>Temperature at different flow velocities as a function of depth.</p> "> Figure 9
<p>Change in absorbent layer temperature over time.</p> "> Figure 10
<p>Diagram of the temperature field.</p> "> Figure 11
<p>Temperature field maps under different lithologies.</p> "> Figure 12
<p>Histogram of temperature variation difference at different thermal conductivity coefficients.</p> "> Figure 13
<p>Absorbent layer temperature with time for different thermal conductivities.</p> "> Figure 14
<p>Graph of sensitivity analysis results.</p> "> Figure 15
<p>Inversion interpretation flowchart.</p> "> Figure 16
<p>Temperature analysis diagram of the target layer.</p> "> Figure 17
<p>Comparison chart of the results of the inversion interpretation.</p> ">
Versions Notes

Abstract

:
Traditional water injection profile monitoring primarily relies on methods such as isotope tracers and oxygen activation. Conventional resistive temperature instruments, which are drag-measured, are highly sensitive to production interference and can only capture the transient temperature response of the wellbore at a single depth. As a result, the temperature data obtained from well temperature logging has certain limitations. Using DTS (Distributed Temperature Sensing) for pre-and post-well opening and shut-in water injection profile testing, along with quantitative analysis of water absorption, addresses the limitations of traditional well temperature logging, which typically offers only qualitative insights. However, the interpretation of DTS data still requires further refinement to improve its alignment with actual conditions. In this study, COMSOL software 6.1 was used to simulate the temperature distribution within the downhole temperature field, both spatially and temporally. The Sobol method was employed to analyze the influence of fluid flow rate and rock thermal conductivity on the temperature field. The results indicated that the fluid flow rate in the wellbore has a more significant impact and is the primary controlling factor of the downhole temperature field. Based on actual field conditions and the forward simulation results, the differential evolution algorithm was applied to invert and interpret the water injection profile. The inversion results showed minimal error, confirming the feasibility of this approach. It is helpful to interpret the well temperature profile measured by the distributed fiber optic temperature sensor, which is helpful to improve the ability of well temperature logging to identify the output profile, which has important academic value and practical significance for the development of water injection wells.

1. Introduction

Due to its unique advantages, several industries have widely used distributed fiber optic sensing technology (DTS) as an important monitoring tool. The technology is capable of long-distance, high-precision, and real-time monitoring, with remarkable anti-interference ability and stability. Especially in the power industry, fiber optic sensing technology can monitor the temperature, stress, and other key parameters of the power grid in real time to ensure the safe operation of power facilities. In the field of construction and infrastructure, DTS is used to monitor the health of structures such as bridges, dams, tunnels, etc., which helps to detect risks such as cracks and deformations in a timely manner, thus improving the safety of infrastructure. In addition, distributed fiber optic sensing technology has shown strong application potential in areas such as traffic monitoring, environmental protection, industrial manufacturing, and mineral resource exploration. For example, DTS is able to monitor traffic flow on highways, detect water pollution, and enhance production process control.
Distributed fiber optic sensing technology has equally important applications in the oil and gas industry. In the process of oilfield water injection development, well temperature measurement is one of the key methods to analyze the water injection profile [1]. Compared with traditional fixed-point temperature measurement instruments, DTS technology uses a single optical fiber to achieve temperature monitoring and signal transmission, which is capable of continuously collecting temperature data along the wellbore, monitoring production conditions in real time, detecting small temperature changes, providing accurate and continuous temperature data, and realizing real-time multipoint measurements over a wide range and a long distance, so that real-time monitoring of the temperature, pressure changes, and fluid flow of the wells can be performed, thus optimizing the oil recovery and water injection processes, and enhance oil and gas recovery [2,3]. In order to better utilize the well temperature information measured by DTS to interpret the water injection profile, there is an urgent need to understand the factors affecting the temperature characteristics of the injection wells and to have a more in-depth understanding of the distribution of the temperature field in and around the wells. The fluid flow in the wellbore is reflected by comparing the numerical local anomalies of the ground temperature gradient with the wellbore temperature. In the process of water injection, there is a significant heat transfer phenomenon between the wellbore fluid and the surrounding strata, while the fluid flow will transfer the heat to the strata at different depths.
Starting from the Ramey model [4], many scholars at home and abroad have continuously improved and extended the model for predicting the downhole temperature field [5,6,7,8]. The Ramey model divides the wellbore into three different parts and assumes that the heat transfer in the wellbore is in a steady state. Sagar et al. extended the Ramey model to an inclined well and a two-phase flow temperature model [9]. Guo Chunqiu et al. simulated and calculated the downhole temperature field of high-temperature and high-pressure gas-producing wells using the fourth-order Runge–Kutta method [10]. Xiao Zhanshan et al. established a new mathematical model for calculating the temperature field of water injection wells [11]. Yanjie Song et al. used the finite difference method to simulate and calculate the temperature field of polymer injection wells [12]. Hasan et al.’s model split the wellbore into multiple microelements and solved the differential equations controlling each part separately [13]. S. Li used the finite difference method to calculate the downhole temperature field during acid squeeze and water injection [14]. Ren Min calculated the downhole temperature field of oil-water two-phase production wells by the finite difference method [15]. Luo and Li et al. established the DTS data inversion model based on the Markov Chain Monte Carlo (MCMC) algorithm and the SA algorithm, respectively [16]. Ma Hansong et al. considered a variety of trace thermal effects and used orthogonal tests to analyze the influence of multiple factors on the temperature profile and established a temperature profile prediction model [17]. Luo Hongwen et al. used improved dichotomy (ID) as well as the Particle Swarm Optimization (PSO) algorithm to establish a distributed fiber optic temperature monitoring (DTS) data inversion model for shale gas horizontal wells [18]. Waquar Kaleem applied hybrid machine learning techniques to improve the accuracy of multiphase fluid production prediction [19]. Huang Liang et al. combined the PSO algorithm and the LM algorithm for inverse interpretation of DTS data [20]. Anqi Shen et al. explored the influence of temperature-pressure effects on fracture expansion and proposed a method to optimize the fracturing design by combining DTS data [21]. Rui Deng proposed an efficient inversion method by combining deep learning and data assimilation techniques to improve the interpretation efficiency and accuracy of DTS data [22]. Rui Deng proposes to use the K-means++ algorithm to divide the vibration signal frequency bands to represent different downhole events and use the amplitude mean curve envelope area of the reservoir-related frequency bands to calculate the relative production of each production formation [23]. In general, although many advances have been made in current well temperature measurement techniques and downhole temperature field prediction models, they still face problems such as low computational efficiency, insufficient accuracy, and poor fit to complex real-world downhole conditions.
In this paper, the downhole temperature distribution in both time and space domains is simulated using COMSOL software 6.1 for a representative injection well. This approach overcomes the limitations of traditional numerical methods in handling the complex fluid flow and heat transfer processes. Through the application of Sobol sensitivity analysis, the study identifies the primary factors influencing the temperature field, with the injected fluid flow rate found to have a significant impact. To enhance the inversion accuracy of the injection profile, the paper introduces the differential evolution algorithm, which successfully interprets the injection profile through inversion calculations, demonstrating both the efficiency and accuracy of this method. This approach aids in interpreting well temperature profiles measured by distributed fiber optic temperature sensors, improving the ability of well temperature logging to identify injection profiles. Furthermore, it provides timely feedback on subsurface conditions, updates the dynamics of the production layer in real time, and enables adjustments to the operational strategy, ultimately maximizing production efficiency.

2. Numerical Simulation of Injection Wells

2.1. Modeling of Downhole Temperature Field

During the development of water injection in oil fields, tubular columns and packers are typically required. A water distributor is employed to control the injection into each layer by generating a specific throttling pressure difference. The classical heat transfer model associated with the wellbore is shown in Figure 1a. The introduced distributed fiber optic technology provides high-accuracy measurements of the wellbore’s internal temperature, offering critical data support. There are three types of optical fiber installations: retrievable, semi-permanent, and permanent, which correspond to positions 1, 2, and 3, respectively, as illustrated in Figure 1b. Each installation type is suited for measuring temperature distributions at different downhole locations. A detailed study of the variations in the downhole temperature field, along with its modeling and prediction, is essential for the rational and accurate interpretation of DTS measurement data.
In the early stages of water injection, the downhole conditions are complex, often causing abnormal fluctuations in the temperature curve. Therefore, when analyzing the relationship between the temperature field and flow rate, the temperature curves in the steady state—namely the ground temperature curve and the flow temperature curve—are typically selected for processing and analysis. During the injection process, water enters the annular space inside the casing from the distribution pipe column, and the heat it carries remains largely constant. In the steady state, the temperature of the fluid within the distribution pipe column tends to align with the fluid temperature in the annular space inside the casing. To simplify the calculation of the temperature field model, the internal space of the water distribution pipe column and the space between the casing and the distribution pipe column can be treated as a single, unified model.
In modeling the physics of the wellbore and its surrounding environment, it is assumed that neighboring wells have a minimal and negligible impact on the downhole temperature of the injection well. When analyzing the temperature field variation around a specific absorbing formation, it is further assumed that the downhole temperature field exhibits symmetry along the well axis. This allows the three-dimensional temperature field model to be simplified into a two-dimensional one. For the two-dimensional temperature field, it is divided into four distinct regions: the formation, the casing, the injection hole, and the inner space of the casing. During the water injection process, fluid flow occurs in each of these regions. In the inner space of the casing, heat transfer includes both convective heat exchange between fluids at different depths and conductive heat transfer between the fluids and the casing. In the injection hole and formation, heat transfer involves convective heat transfer between the fluids and conductive heat transfer between the fluids and the formation as the fluid carries heat into the surrounding formation. When the injection halts for a period of time, the fluid flow in the wellbore stabilizes and ceases, at which point all modes of heat transfer transition to conduction. Regarding temperature characteristics, the temperature measured by the fiber optic sensor in the wellbore is typically lower than the ground temperature, as the injected fluid temperature is lower than the formation’s ground temperature. At the location of the absorbing layer, the introduction of the low-temperature fluid into the formation results in a sudden temperature drop in the formation, as illustrated in Figure 2.

2.2. Model and Parameter Sensitivity Analysis

To accurately replicate the real downhole temperature field, the simulation incorporates the actual initial conditions of an injection well into the calculation process. Figure 3 illustrates the grid division used in the model, where the wellbore and suction zone are subdivided into finer grids to improve the accuracy of the calculations. Given that the temperature variations downhole are relatively small, and to make the temperature changes more pronounced in the simulation results, this study focuses on the suction layer with the highest water absorption for numerical simulation. The suction layer, located at a depth of 2900 m and with a thickness of 1 m, is modeled with varying suction hole depths on the left and right sides. Table 1 outlines the relevant parameters used in the model setup.
Changes in the downhole temperature field are influenced by several factors, with the injection fluid flow rate and rock thermal conductivity being the primary controlling factors. The injection fluid flow rate directly determines the heat transfer rate in the wellbore. A higher flow rate facilitates faster heat spread, resulting in more noticeable temperature field changes, while a lower flow rate leads to slower temperature changes, potentially forming local temperature gradients. Rock thermal conductivity affects the efficiency of heat propagation within the rock formation. Higher thermal conductivity accelerates heat diffusion, leading to a more uniform temperature field, whereas lower thermal conductivity results in slower and more uneven temperature distribution. Other factors, such as the inner diameter of the casing, the density and specific heat capacity of the injected fluid, the thickness of the absorbing layer, and permeability, also influence the temperature field. A larger inner diameter of the casing reduces fluid flow resistance, promoting a more uniform temperature distribution. The density and specific heat capacity of the injected fluid affect its heat capacity, which in turn influences heat transfer. The thickness and permeability of the absorbing layer determine the diffusion path and speed of heat transfer in the rock layer. Among these factors, the inner diameter of the casing, the density of the injected fluid, its specific heat capacity, the thickness of the absorbing layer, and the injection borehole are fixed for a given well. Based on previous research [24,25], it is evident that the injected fluid flow rate (daily water injection) and rock thermal conductivity exert the most significant influence on the temperature field. These two factors serve as the main controlling variables for many of the other influencing factors. To further explore their impact, a controlled experiment is proposed to compare the effects of injection fluid flow rate and rock thermal conductivity on the temperature field.

2.2.1. Effect of Injected Fluid Flow Rate on Temperature Profiles

A control group and two experimental groups were set up for comparative validation. The initial conditions of the control group were set with reference to the real injection wells, and the daily injection volume was 35 m3, which was converted to the fluid flow rate. The average flow rate of the injected fluid from the first absorbing layer to the wellhead was 0.026 m/s, and the flow rate of the borehole at the time of stabilization was shown in Figure 4. Other conditions of the other two experimental groups remained unchanged, and the flow rates were 0.04 m/s (daily injection volume was 50 m3) and 0.07 m/s (daily injection volume was 90 m3), respectively. water volume is 50 m3, as well as 0.07 m/s (daily water injection volume is 90 m3).
Figure 5, Figure 6 and Figure 7 show the evolution of the temperature field in the wellbore with time for flow rates of 0.026 m/s (35 m3 of daily water injection), 0.04 m/s (50 m3 of daily water injection), and 0.07 m/s (90 m3 of daily water injection), respectively. In the initial shut-in state, the temperature in the wellbore is in equilibrium with the stratigraphic ground temperature gradient. With the injection of low-temperature fluid, heat exchange, and heat conduction occur between the high-temperature fluid and the low-temperature fluid, as well as between the formation and the fluid, resulting in a gradual decrease in the temperatures in the formation and the wellbore. After 2000 s of injection, the downhole temperature field tends to stabilize. Comparing the temperature field changes at different flow rates at the same time, it can be concluded that the faster the flow rate is, the higher the rate of temperature decrease in the wellbore and the greater the decrease in formation temperature. Figure 8 further shows the curves of temperature change with a depth at 0.5 m from the well center axis at different flow rates at 100 s. The results show that the faster the flow rate, the lower the temperature at the corresponding location. This indicates that the effect of the injection flow rate on the downhole temperature field is significant, and the higher flow rate can change the downhole temperature distribution more quickly.
Figure 9 shows the curve of temperature change with time at different flow rates at the suction layer; the faster the fluid flow rate in the wellbore, the shorter the time for the temperature in the wellbore to stabilize. At the same time, there will be a short period of temperature recovery after the temperature decreases because turbulence or reflux will occur at the injection hole when part of the fluid enters the injection hole, and the reflux of the higher-temperature fluid from below will lead to the temperature recovery at the suction layer.

2.2.2. Effect of Rock Thermal Conductivity on Temperature Profiles

Different surrounding rocks will have different effects on the downhole temperature field, and for heat transfer, the thermal conductivity of the rock plays a crucial role. The thermal conductivity of a rock is the amount of heat that passes through it per unit of time, per unit of temperature gradient, and per unit of area. The larger the thermal conductivity of the rock, the faster the heat is transferred inside the rock. In this simulation, three different lithologies are proposed to be used to study the variation in the downhole temperature field, which are shale, sandstone, and graystone. The corresponding thermal conductivities of the three different lithologies are 1.687 W/(m·K), 2.754 W/(m·K), and 3.547 W/(m·K), respectively [26].
Figure 10 shows the cloud diagram of the downhole temperature field changing with time when the flow rate is 0.026 m/s (daily injection volume is 50 m3) and the surrounding rock is sandstone. As the low-temperature fluid continues to be injected, heat exchange and heat transfer occur between the formation and the wellbore, and the low temperature gradually invades the rock around the wellbore. Figure 11 shows the downhole temperature field at 1000 s when the surrounding rocks are shale, sandstone, and gray rock, respectively.
Figure 12 shows the histogram of the difference in temperature change for the three different lithology cases. Changing the thermal conductivity of the strata, with all other things being equal, the difference in temperature between the different depth points ranges within 0.0003 °C, which is a relatively small effect of this influence factor. Figure 13 shows the curves of temperature variation with time for different lithologies at the absorbing layer. Although different lithologies have different thermal conductivity coefficients, the curves basically converge, proving that the thermal conductivity coefficient is not the main controlling factor relative to the fluid flow.

2.3. Sobol Global Sensitivity Analysis

The Sobol method is a global sensitivity analysis tool for quantitatively assessing the contribution of input variables to the model output variance. The method analyzes the significance of variables by calculating the proportion of input variables contributing to the output variance, and at the same time, it can effectively differentiate between the main effect of each input variable and its interaction effect. The Sobol method can simplify the model complexity in the global sensitivity analysis and quantify the uncertainty factors through the interval likelihood theory, so as to construct a robust design method for interval uncertainty based on the sensitivity analysis.
In this paper, a sensitivity analysis of the injected fluid flow rate and rock thermal conductivity was performed using the Sobol method, and the results are shown in Figure 14. The calculations yielded, respectively, a first-order sensitivity index, S, which measures the direct effect of individual variables on the model output, and a total-order sensitivity index, ST, which assesses the combined effect of individual variables and their interactions with other variables on the model output.
From the figure, it can be concluded that for the first-order sensitivity index S, i.e., only considering the influence of a single influence factor on the temperature profile, the flow velocity is much larger than the thermal conductivity. Combined with Figure 8, for the same depth point, different flow rates produce relatively drastic temperature changes; the larger the flow rate, the closer the flow state in the pipe will be to the turbulent state, the more the convective heat transfer capacity of the fluid is enhanced, the more rapidly the heat in the pipe between the fluid and the pipe wall is transferred, and the more pronounced the temperature change is. Comprehensive Figure 12 shows that the effect of changing the thermal conductivity on the temperature profile is not significant, and the curves almost converge, and the change is not obvious. For the total order sensitivity index ST, considering the case that the interaction between flow rate and thermal conductivity jointly affects the temperature profile, the sensitivity of the temperature profile to flow rate is still greater than that of thermal conductivity.
In summary, the sensitivity of the temperature profile to the flow rate is higher than the thermal conductivity in both the first-order response S and the total response ST, indicating that the flow rate has a greater overall influence on the temperature profile and that the flow rate is the main controlling factor of the temperature profile. Therefore, the injected fluid velocity should be emphasized in the subsequent coupled flow solution equations to derive the flow rate of the absorbing layer, so as to make the flow solution more accurate.

3. DTS Data Interpretation Methods

3.1. Volume Flow Rate as a Function of Temperature

For injection wells, H.J. Rameg, Jr. proposed a basic formula for estimating the flow rate from flowing well temperature profile data by solving the heat diffusion equation [25]. The process is as follows:
θ f z , t = θ G S + g G Z − g G A + θ f i − θ G S + g G A e − z A
where Z is the well depth, m; t is the total injection time, d; θ f z , t is the fluid temperature at depth z in the borehole at time t, °C; g G is the average ground temperature gradient, °C; θ G S is the ground surface temperature, °C; θ f i is the initial temperature of the fluid at the ground surface, °C; and A is the relaxation distance, m. The following table shows the initial temperature of the fluid at the surface.
When the downhole fluid flow rate q > 20 m3/d and t (time in the same work regime) is greater than several days, the relaxation distance A can be simplified and expressed as:
A = 0.264 C f f t ρ f q
where q is the volume flow rate of the fluid (all positive), m3/d; ρ f is the density of the fluid, g/cm3; C f is the specific heat capacity of the fluid;
Thus, if ρ f and C f are known, and A and f t can be determined, the volumetric flow rate of the downhole fluid q can be simply estimated from the above equation. f(t) can be estimated from the following equation when t ≥ 100 d:
f t = − l n r c e 2 a t − 0.0290
where r c e is the outer diameter of the casing, m; α is the heat diffusion coefficient of the formation, m2/d;
The relaxation distance A is very complicated if determined from the above equation. It can be solved by using Romero and Juarez to derive a simple method. For the above equation, the derivation of z at any data point depth can be derived:
d θ f d z = − g G − 1 A θ f e − θ G e − g G A e − z A
Also, θ G e − g G Z = θ G is the ground temperature at a depth point. Thereby, the estimated equation for A is:
A = θ G − θ f d θ f / d z
where θ G can be read off from the ground temperature gradient curve and d θ f / d z is taken from the flowing well temperature curve. The right-hand side of Eq. must be taken as an absolute value as a way to ensure that the relaxation distance is positive.
It is obvious that the Romero–Juarez method [27] cannot be used in the case of sudden temperature change and can only be applied to the case where θ f changes exponentially. If the calculated A values are very different between two producing formations, then the averaging method can be used, where multiple data points are selected to calculate the value of A. The average of the A values of the multiple data points is used as the A value of the whole wellbore.
After solving the above equation, it can be concluded that q is calculated as
q = θ G − θ f d θ f / d z / 0.264 C f f t ρ f
where the d θ f / d z value can be replaced by the gradient value of the ground temperature gradient, C f is a definite value, the outer diameter of the casing that affects f t as well as the heat diffusion coefficient can be regarded as a definite value, and ρ f can be calculated.

3.2. DTS Data Inversion Interpretation Model

DTS data inversion interpretation is based on the inversion interpretation model, which will measure temperature profiles repeatedly iterated and finally calculate the flow profile process. In the process of DTS inversion interpretation, it is necessary to compare the calculated predicted temperature profiles with the actual measured temperature profiles so that the error between the two reaches a certain limit, and then the inversion target parameter values reach the optimum, so as to obtain the optimal solution of the flow profiles.

3.2.1. Inversion Error Function

When building the inversion model, the first step is to build an objective function to characterize the error between the calculated predicted temperature profile and the measured temperature profile. The inversion error function is:
E x → = θ μ → − θ G → θ μ → − θ G → T
where E x → is the error function, x → is the inversion target parameter vector, θ μ → is the measured temperature profile, and θ G → is the calculated predicted temperature profile. Based on the inverse interpretation model, the predicted temperature profiles are calculated iteratively so that the inverse error function satisfies
E x → < ε
ε is the inversion interpretation error threshold, which is dimensionless and takes the value of 10−20 in this study.

3.2.2. Injection Profile Inversion Interpretation Process

Differential Evolutionary Algorithms (DEs) have the ability to guide the algorithm to further search by using individual local information and group global information for collaborative search, as well as to operate directly on structural objects without relying on problem information and without qualification of the objective function.
The injection profile inversion interprets the temperature profile using the flow rate or flow volume as the target parameter for the inversion. It consists of the following main steps:
① Based on the measured DTS temperature raw data, the stabilized shut-in and flow temperatures were selected, and the average value was calculated, which was accordingly used as the initial temperature value for the inversion.
② The mutation operation is performed for each initial value of temperature, and the mutation temperature vector is generated as follows:
x i , G + 1 = x r 1 , G + F ∗ x r 2 , G + 1 − x r 3 , G + 1
where x i , G + 1 is the predicted temperature value for layer number i in the G + 1 st generation of the iteration, and F is a variation operator to control the scaling of the bias variable, which is dimensionless and takes the value 0.4.
③ A crossover operation is performed on a dimension of the entire population;
④ The test temperature vector is compared with the target temperature vector x i , G in the current population according to the greedy criterion, and the optimum is selected.
⑤ Checking and processing boundary conditions;
⑥ Calculate the objective function and determine whether the inverse interpretation error threshold ε is satisfied, if not, repeat the cycle once more.
The interpretation flowchart is shown in Figure 15.

4. Example Verification

An example injection well is interpreted using the above method. Well X is a straight well injection well, belonging to the North China Oilfield, and the developed reservoir is a carbonate reservoir, with a measured well section of 2603–2944 m, and an injection well section of 2654–2932.2 m, totaling eight suction layers. The daily injection volume is 35 m3. The related parameters are shown in Table 2.
Well X had been in the open well phase before the fiber was lowered, and the temperature of the well was measured by changing the working regime twice after two hours of measurements after the fiber was lowered, and the table of test time nodes is shown in Table 3.
Different operating regimes correspond to different wellhead injection volumes, which affect the flow state of the downhole fluid and the distribution of the temperature field. When the wellhead injection volume increases, the downhole fluid flow rate increases accordingly, which accelerates the heat transfer and changes the evolution of the downhole temperature field. The rapid flow of downhole fluids causes dramatic fluctuations in heat distribution, and the increase in flow rate promotes the uniformity and extension of the temperature field in the steady state, which affects the heat transfer and the formation of temperature gradients in the wellbore. For the working regimes II and III, the short duration of the working regime results in the measured temperature data not being stable enough to effectively reflect the long-term temperature characteristics in the wellbore. Therefore, data from these phases cannot be used as a basis for analysis. In contrast, working regime I has a long duration and a smoother downhole flow rate, which ensures that the temperature field reaches a steady state within a certain period of time. The stable working regime provides a guarantee for the stability of the temperature field, making the temperature data more representative and reliable. Based on this, this paper selects working regime I with a longer measurement time for flow calculation and analyzes the influence of its downhole temperature field in depth.
Figure 16 shows the temperature waterfall of the destination stratum section and a comparison of the ground and flow temperatures selected for the calculation. There are a total of four working regimes in the figure, and from working regimes one to four, the injection volume gradually decreases, while the injected fluid is heated by the formation in the formation, and the overall temperature tends to increase. On the right, the relatively stable temperature curve at the late stage of the well shut-in phase is selected as the ground temperature curve, and the curve when the temperature stabilizes in working regime I is selected as the flow temperature curve. Injecting low-temperature fluid from the wellhead, the downhole flow temperature is lower than the ground temperature gradient, while the temperature changes at the absorbing layer.
After the inverse interpretation by differential evolution algorithm, the water absorption of each absorbing layer is derived, as shown in Figure 17, and compared and analyzed with the water absorption of each absorbing layer derived by other software. Table 4 shows the error of the inversion interpretation results for this injection well.

5. Conclusions

After analyzing the relationship between downhole temperature changes and flow rate, two key factors affecting the temperature field were selected: total water injection (flow rate) and the thermal conductivity of the surrounding rock. Controlled experiments were conducted using COMSOL software to simulate different conditions, generating temperature field data for various scenarios. The Sobol global sensitivity analysis method was then employed to examine the influence of these factors on the downhole temperature field. Finally, the differential evolution algorithm was applied to invert and interpret the temperature data from the example well. The following conclusions were drawn:
(1)
This study established a transient temperature field model for the suction layer section of the injection well using the numerical simulation software COMSOL. The influence of wellbore flow rate and surrounding rock thermal conductivity on the temperature field distribution was analyzed. Through Sobol global sensitivity analysis, it was found that the first-order response index for flow rate was 0.6627, significantly higher than the 0.1353 for the formation thermal conductivity coefficient. This indicates that the flow rate has a dominant effect on the temperature field, with a much higher sensitivity compared to the thermal conductivity of the surrounding rock.
(2)
Example validation showed that the error in the inverse interpretation of water absorption profiles using the differential evolution algorithm was generally low. The results demonstrate that this inversion method is highly accurate and practical for interpreting data from distributed fiber optic temperature sensors.
(3)
In this study, the numerical simulation model was specifically developed for the injection well in question, reflecting certain unique characteristics of this particular well. However, the inversion model, which is based on the differential evolution algorithm, is universally applicable. It can be effectively used for wells with different geological conditions, making it a versatile tool for temperature field interpretation in various downhole environments. This flexibility enhances the broader applicability and robustness of the proposed method in real-world scenarios.

Author Contributions

Conceptualization, S.S.; methodology, S.S.; software, T.L.; validation, S.S. and T.L.; formal analysis, S.S.; investigation, S.S. and T.L.; resources, J.L.; data curation, S.S.; writing—original draft preparation, S.S.; writing—review and editing, J.L., M.L. and C.S.; visualization, T.L.; supervision, J.L.; project administration, J.L.; funding acquisition, J.L. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

Where data are unavailable due to privacy or ethical restrictions.

Acknowledgments

Thanks to the editorial board for their great support.

Conflicts of Interest

Authors Chao Sun and Ming Li were employed by PetroChina Qinghai Oilfield Branch Testing Company. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

References

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Figure 1. Schematic diagram of the downhole geometry: (a) schematic diagram of the wellbore; (b) schematic diagram of fiber optic installation location and wellbore cross-section [2].
Figure 1. Schematic diagram of the downhole geometry: (a) schematic diagram of the wellbore; (b) schematic diagram of fiber optic installation location and wellbore cross-section [2].
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Figure 2. Temperature field model.
Figure 2. Temperature field model.
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Figure 3. Model meshing.
Figure 3. Model meshing.
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Figure 4. Wellbore velocity field.
Figure 4. Wellbore velocity field.
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Figure 5. The temperature field changes when the flow velocity is 0.026 m/s.
Figure 5. The temperature field changes when the flow velocity is 0.026 m/s.
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Figure 6. The temperature field changes when the flow velocity is 0.04 m/s.
Figure 6. The temperature field changes when the flow velocity is 0.04 m/s.
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Figure 7. The temperature field changes when the flow velocity is 0.07 m/s.
Figure 7. The temperature field changes when the flow velocity is 0.07 m/s.
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Figure 8. Temperature at different flow velocities as a function of depth.
Figure 8. Temperature at different flow velocities as a function of depth.
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Figure 9. Change in absorbent layer temperature over time.
Figure 9. Change in absorbent layer temperature over time.
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Figure 10. Diagram of the temperature field.
Figure 10. Diagram of the temperature field.
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Figure 11. Temperature field maps under different lithologies.
Figure 11. Temperature field maps under different lithologies.
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Figure 12. Histogram of temperature variation difference at different thermal conductivity coefficients.
Figure 12. Histogram of temperature variation difference at different thermal conductivity coefficients.
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Figure 13. Absorbent layer temperature with time for different thermal conductivities.
Figure 13. Absorbent layer temperature with time for different thermal conductivities.
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Figure 14. Graph of sensitivity analysis results.
Figure 14. Graph of sensitivity analysis results.
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Figure 15. Inversion interpretation flowchart.
Figure 15. Inversion interpretation flowchart.
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Figure 16. Temperature analysis diagram of the target layer.
Figure 16. Temperature analysis diagram of the target layer.
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Figure 17. Comparison chart of the results of the inversion interpretation.
Figure 17. Comparison chart of the results of the inversion interpretation.
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Table 1. Parameters related to the model.
Table 1. Parameters related to the model.
Parameter NameNumerical Values and UnitsParameter NameNumerical Values and Units
Injection radius0.01 mCasing O.D.139.7 mm
Density of injected fluid1 g/cm3Casing thickness12.11 mm
Specific heat capacity 4182 J/kg·kCasing thermal conductivity16 W/(m·K)
strata density2.826 g/cm3Casing heat capacity400 J/(kg·°C)
Table 2. Parameters related to water injection wells.
Table 2. Parameters related to water injection wells.
Parameter TypeParameter NameNumerical Values and Units
Reservoir parameterlengths278.2 m
thicknesses34 m
land temperature gradient2.8 °C/100 m
pressures47 MPa
thermal conductivity3.5 W/(m·K)
average density2.86 g/cm3
constant pressure heat capacity300 J/kg·K
Wellbore parametersCasing O.D.139.7 mm
Casing thermal conductivity16 W/(m·K)
Casing constant pressure heat capacity400 J/kg·K
Table 3. Timetable of the work system.
Table 3. Timetable of the work system.
Work SystemStarting TimeExpiration DateDuration
1Initial well opening 35 m3
(System of workings I)		-16:05-
2Injection volume 25 m3
(Work system II)		16:0518:352.5 h
3Injection volume 10 m3
(Work system III)		18:3521:002.5 h
4Well closure phase
(System of work IV)		21:00next day 21:0024 h
Table 4. Error analysis table.
Table 4. Error analysis table.
NumberDeepth (m)Inversion of Water Absorption (m3/d)Measured Water Absorption (m3/d)Absolute Error (m3/d)
12654.0–2658.04.240624.375490.23575
22805.0–2808.45.390755.655610.39310
32814.0–2816.21.736102.038650.34385
42820.0–2823.22.184101.881040.25109
52827.8–2833.01.438512.004310.60002
62895.0–2900.020.1489718.573461.09613
72914.0–2917.22.271192.048950.16821
82929.4–2932.21.003650.922490.05729
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Shi, S.; Liu, J.; Li, M.; Sun, C.; Lei, T. Research on Numerical Simulation and Interpretation Method of Water Injection Well Temperature Field Based on DTS. Processes 2025, 13, 274. https://doi.org/10.3390/pr13010274

AMA Style

Shi S, Liu J, Li M, Sun C, Lei T. Research on Numerical Simulation and Interpretation Method of Water Injection Well Temperature Field Based on DTS. Processes. 2025; 13(1):274. https://doi.org/10.3390/pr13010274

Chicago/Turabian Style

Shi, Shengzhe, Junfeng Liu, Ming Li, Chao Sun, and Tong Lei. 2025. "Research on Numerical Simulation and Interpretation Method of Water Injection Well Temperature Field Based on DTS" Processes 13, no. 1: 274. https://doi.org/10.3390/pr13010274

APA Style

Shi, S., Liu, J., Li, M., Sun, C., & Lei, T. (2025). Research on Numerical Simulation and Interpretation Method of Water Injection Well Temperature Field Based on DTS. Processes, 13(1), 274. https://doi.org/10.3390/pr13010274

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