Well injectivity profiling using distributed temperature sensing transient data

Abstract

A system for determining an injectivity profile of an injection well penetrating a subsurface formation includes at least one distributed temperature sensing (DTS) cable deployed along at least a portion of the injection well to provide temperature measurements along the well depth over time, memory storing instructions, and at least one processor configured to execute the instructions to generate a temperature transient in the injection well, receive temperature measurements from the DTS cable, automatically simulate transient thermal and fluid flow behavior of the wellbore and subsurface formation using a model, automatically solve a supplementary inverse problem based on comparing simulated transient thermal behavior and received temperature measurements, estimate an inlet injection temperature at or above the top of a perforated interval, automatically solve a main inverse problem to fine tune model parameters, and estimate an injectivity profile along the perforated interval.

Description

PATENT SLB Docket No. IS23.1678-WO-PCTWELL INJECTIVITY PROFILING USING DISTRIBUTED TEMPERATURE SENSING TRANSIENT DATACROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of U.S. Provisional Application No.63 / 778,828, filed March 27, 2025, which is incorporated by reference herein in its entirety.INTRODUCTION

[0002] This section is intended to introduce the reader to various aspects of art that may be related to various aspects of the present disclosure, which are described and / or claimed below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present disclosure. Accordingly, it should be understood that these statements are to be read in this light, and not as admissions of prior art.Field of the Disclosure:

[0003] The present disclosure relates to well monitoring and characterization using distributed fiber optic sensing and, more particularly, to systems and methods for determining injectivity profiles in injection wells.Description of Related Art:

[0004] Injection well injectivity or intake profiling is a widely used technique for characterizing the efficiency of injections. For injection wells, flow profiling allows characterization of reservoir pressure sustaining efficiency, carbon dioxide sequestration efficiency, enhanced oil recovery (EOR) efficiency, well treatment (e.g., matrix acidizing efficiency), and other operational parameters.

[0005] In cases where use of well logging with mechanical flow metering devices (e.g., spinners) is not applicable technically or economically, distributed temperature measurements with fiber optics may be used for this purpose, either with permanent Distributed Temperature Sensing (DTS) cable deployment or with temporary well intervention, such as with a DTS cable inside coiled tubing.P+S Ref. No.: SLBR / 0384PC Page 1 of 48PATENT SLB Docket No. IS23.1678-WO-PCT

[0006] Depending on the well trajectory and pumping duration, different techniques may be used for temperature data interpretation with respect to injectivity profiling. One approach is analysis of temperature warmback profiles during well shut-in. Analysis of warmback profiles provides qualitative estimation of the injectivity without use of sophisticated models, by evaluating the speed of temperature warmback in different well sections via respective change of DTS profiles in the time domain. Quantitative interpretation may also be performed with different techniques, using models of different levels of sophistication, from simple analytical techniques to numerical simulators.

[0007] Several challenges exist in applying warmback techniques, including crossflows between different reservoir layers, lack of temperature signal during initial shut-in time after long-term injection, and vertical heat conduction. The latter two challenges are more pronounced in vertical wells, while crossflows can impact the quality of temperature data interpretation in both vertical and horizontal injectors.

[0008] An alternative approach (referred to as “hot slug”) sometimes used in horizontal injectors is based on the restart of injection after shut-in and on the difference of shut-in temperature restoration dynamics in different well sections. The temperature warmback proceeds faster in vertical non-injected well sections and slower in injected horizontal well sections, creating warmer temperature columns above the heel of the injected well section. This warmer fluid is shifted down into the injected well interval after restart of pumping. While this technique addresses some challenges of warmback data interpretation, it has its own shortcomings, including dependence of the temperature front shape and speed of movement on the heat transfer between the wellbore flow and formation, and relatively low spatial resolution of the determined injectivity profile.

[0009] An intermediate time-range approach to horizontal well injectivity profiling is based on the impact of convective-conductive heat transfer between the wellbore flow and formation on the temperature profile along the wellbore during pumping. This leads to the presence of transitional dynamics in DTS data between relatively fast temperature dynamics in the injected interval and long-term injection when temperature signatures of the injectivity profile disappear. Depending on the duration of the injection and the length of the injected depth range, these intermediate temperature transients may last from weeks to months. However, use of this technique may be cumbersome, as it can require sophisticated models and calibration workflows.P+S Ref. No.: SLBR / 0384PC Page 2 of 48PATENT SLB Docket No. IS23.1678-WO-PCT

[0010] An alternative way of creating temperature disturbance in the injected interval of vertical or horizontal wells sensitive to the injectivity is based on utilizing changes in the injection flow rate. Any flow rate change leads to change in the convective heat transfer conditions in the upper completion and thus changes the temperature profiles along this part of the wellbore. This in turn creates inlet injection temperature changes at the heel of the injected interval. Unlike restart after shut-in, this does not create a distinct temperature front event but leads to a series of temperature transient profiles along the injected depth range. This type of DTS data is sensitive to the injectivity but comes with its own shortcomings, including the use of sophisticated models for DTS data interpretation and having accurate data on the inlet injection temperature dynamics on top of the injected or perforated interval that is not available directly from DTS data in cases of cable permanent deployment behind the casing or on the liner.

[0011] A temperature gradient exists across the wellbore and near wellbore zones, particularly in the non-perforated interval and in the presence of a stagnant-fluid annulus above the packer. Thus, the mass-average wellbore flow temperature used in simulations can be different from the DTS temperature behind the casing at the same depth. Moreover, the dynamics of the two temperatures may be similar qualitatively but different quantitatively. Therefore, use of the DTS temperature itself, without correction, may lead to mismatch with the real wellbore flow temperature and thus affect the accuracy of quantitative injectivity profiling.

[0012] Accordingly, there is a general desire for improved workflows and systems for injectivity profiling in vertical and horizontal wells that address the challenges of using transient DTS data after shut-in and change of flow rate.SUMMARY

[0013] This summary is provided to introduce a selection of concepts in a simplified form that are further described below in the detailed description. This summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter.

[0014] According to an aspect of the present disclosure, a system for determining an injectivity profile of an injection well penetrating a subsurface formation is provided. The system includes at least one distributed temperature sensing (DTS) cable deployed alongP+S Ref. No.: SLBR / 0384PC Page 3 of 48PATENT SLB Docket No. IS23.1678-WO-PCTat least a portion of the injection well and configured to provide temperature measurements along a depth of the injection well overtime. The system includes memory storing instructions. The system includes at least one processor configured to execute the instructions to generate a temperature transient in the injection well. The at least one processor is configured to receive temperature measurements from the DTS cable. The at least one processor is configured to automatically simulate, using a model, transient thermal and fluid flow behavior of the wellbore and the subsurface formation. The at least one processor is configured to automatically solve a supplementary inverse problem based on a comparison of the simulated transient thermal behavior and the received temperature measurements from the DTS cable. The at least one processor is configured to estimate an inlet injection temperature at a top, or above the top, of a perforated interval of the injection well based on the solving the inverse problem and the received temperature measurements from the DTS cable. The at least one processor is configured to automatically solve a main inverse problem to fine tune one or more parameters of the model by iteratively over multiple time instances determining residuals between the received temperature measurements and the simulated thermal and fluid flow behavior, and adjusting one or more parameters of the model to minimize the residuals. The at least one processor is configured to estimate, using the fine-tuned model and the determined inlet injection temperature, an injectivity profile of the injection well along the perforated interval.

[0015] According to another aspect of the present disclosure, a method for determining an injectivity profile of an injection well penetrating a subsurface formation is provided. The method includes generating a temperature transient in the injection well. The method includes receiving DTS measurements along a depth of the injection well over time. The method includes automatically simulating, using a model, transient thermal and fluid flow behavior of the wellbore and the subsurface formation. The method includes automatically solving a supplementary inverse problem based on a comparison of the simulated transient thermal behavior and the received DTS measurements. The method includes estimating an inlet injection temperature at a top, or above the top, of a perforated interval of the injection well based on the solving the inverse problem. The method includes automatically solving a main inverse problem to fine tune one or more parameters of the model by iteratively over multiple time instances determining residuals between the received temperature measurements and the simulated thermal and fluid flowP+S Ref. No.: SLBR / 0384PC Page 4 of 48PATENT SLB Docket No. IS23.1678-WO-PCTbehavior, and adjusting one or more parameters of the model to minimize the residuals. The method includes estimating, using the fine-tuned model and the determined inlet injection temperature, an injectivity profile of the injection well along the perforated interval.

[0016] According to another aspect of the present disclosure, a non-transitory computer-readable medium storing instructions that, when executed by at least one processor, cause the at least one processor to perform operations for determining an injectivity profile of an injection well penetrating a subsurface formation is provided. The operations include generating a temperature transient in the injection well. The operations include receiving temperature measurements from at least one distributed temperature sensing (DTS) cable deployed along at least a portion of the injection well, the temperature measurements being along a depth of the injection well over time. The operations include automatically simulating, using a model, transient thermal and fluid flow behavior of the wellbore and the subsurface formation. The operations include automatically solving a supplementary inverse problem based on a comparison of the simulated transient thermal behavior and the received temperature measurements from the DTS cable. The operations include estimating an inlet injection temperature at a top, or above the top, of a perforated interval of the injection well based on the solving the inverse problem and the temperature measurements from the DTS cable. The operations include automatically solving a main inverse problem to fine tune one or more parameters of the model by iteratively over multiple time instances determining residuals between the received temperature measurements and the simulated thermal and fluid flow behavior, and adjusting one or more parameters of the model to minimize the residuals. The operations include estimating, using the fine-tuned model and the determined inlet injection temperature, an injectivity profile of the injection well along the perforated interval.

[0017] Other aspects provide: an apparatus operable, configured, or otherwise adapted to perform any one or more of the aforementioned methods and / or those described elsewhere herein; a computer program product embodied on a computer-readable storage medium comprising code for performing the aforementioned methods as well as those described elsewhere herein; and / or an apparatus comprising means for performing the aforementioned methods as well as those described elsewhere herein.P+S Ref. No.: SLBR / 0384PC Page 5 of 48PATENT SLB Docket No. IS23.1678-WO-PCT

[0018] The foregoing general description of the illustrative embodiments and the following detailed description thereof are merely exemplary aspects of the teachings of this disclosure and are not restrictive.BRIEF DESCRIPTION OF DRAWINGS

[0019] The appended figures illustrate only exemplary embodiments and are therefore not to be considered limiting of the scope of the disclosure, as the disclosure may admit to other equally effective aspects. It is emphasized that, in accordance with the standard practice in the industry, various features are not drawn to scale. In fact, the dimensions of the various features may be arbitrarily increased or reduced for clarity of discussion.

[0020] Figure 1 is an example wellbore with a distributed temperature sensing (DTS) system.

[0021] Figure 2 depicts a flow diagram illustrating example operations for injection profiling using DTS transients.

[0022] Figure 3 depicts a graph of field distributed temperature sensing profiles at different flow rates and shut-in conditions.

[0023] Figure 4 depicts a temperature profile graph showing field distributed temperature sensing data within a perforated interval.

[0024] Figure 5 depicts a graph of simulated distributed temperature sensing profiles at different flow rates in metric units.

[0025] Figure 6 depicts a graph illustrating an injection well flow rate scenario with multiple flow rates and shut-in periods.

[0026] Figure 7 depicts an injectivity profile graph showing intake percentage as a function of depth for the flow rates and shut-ins shown in Figure 6.

[0027] Figure 8 depicts a graph showing simulated DTS profiles of injection temperature behind casing over a full depth range for flow rates and shut-ins of Figure 6.P+S Ref. No.: SLBR / 0384PC Page 6 of 48PATENT SLB Docket No. IS23.1678-WO-PCT

[0028] Figure 9 depicts a graph of simulated distributed temperature sensing profiles within a perforation interval at different flow rates of Figure 6.

[0029] Figure 10 depicts a distributed acoustic sensing data visualization from a vertical injection well.

[0030] Figure 11 depicts simulated distributed temperature sensing profiles after a change of flow rate from lower to higher values.

[0031] Figure 12 depicts simulated distributed temperature sensing profiles after a restart after shut-in.

[0032] Figure 13 depicts a simulated distributed temperature sensing profiles after a change of flow rate from higher to lower values.

[0033] Figure 14 depicts a graph showing the difference between DTS temperature behind casing and DTS temperature in-casing.

[0034] Figure 15 depicts a solution of the supplementary inverse problem using a numerical forward model.

[0035] Figure 16 depicts a physics-informed neural network architecture for inlet injection temperature determination, according to aspects of the present disclosure.

[0036] Figure 17 depicts an example automated injection profiling system.

[0037] To facilitate understanding, identical reference numerals have been used, where possible, to designate identical elements that are common to the figures. It is contemplated that elements and features of one aspect may be beneficially incorporated in other aspects without further recitation.DETAILED DESCRIPTION

[0038] The following description sets forth example aspects of the present disclosure. It should be recognized, however, that such description is not intended as a limitation on the scope of the present disclosure. Rather, the description also encompasses combinations and modifications to those example aspects described herein.P+S Ref. No.: SLBR / 0384PC Page 7 of 48PATENT SLB Docket No. IS23.1678-WO-PCT

[0039] Aspects of the present disclosure provide apparatuses, methods, processing systems, and computer-readable mediums for determining injectivity profiles in injection wells using transient distributed temperature sensing data during transitional pumping regimes.

[0040] The present disclosure addresses problems with current approaches by providing a workflow that generates temperature transients in the injection well through controlled flow rate changes or shut-in and restart operations, and then interprets the resulting transient DTS data using model-based approaches. The system deploys a DTS cable along the injection well and receives temperature measurements during transitional pumping stages. The temperature transients may be generated at preconfigured periodicities or in response to alarms generated by comparing distributed acoustic sensing profiles with previous profiles. Additional measurements from bottom hole assemblies and wellhead sensors may be incorporated into the main inverse problem solution.

[0041] A supplementary inverse problem is solved to accurately estimate the inlet injection temperature at or above the top of the perforated interval by comparing simulated transient thermal behavior with received DTS measurements. This inlet injection temperature determination uses a wellbore calibration section above the perforation top where a residual is calculated as a sum of differences between formation temperature interpolated to the effective radial position of the DTS cable and the actual DTS temperature measurements. The system may employ different computational approaches for the supplementary inverse problem, including a full transient multiphase thermal-hydrodynamic forward numerical model, a simplified numerical model for a small wellbore section above the perforated interval, or a physics-informed neural network trained on simulations.

[0042] A main inverse problem is then solved to fine tune model parameters by iteratively determining residuals between received temperature measurements and simulated thermal and fluid flow behavior.

[0043] The disclosed techniques provide several technical advantages. The workflow enables injectivity profiling in wells (horizontal or vertical wells) that would otherwise not be possible with DTS data alone due to lack of temperature variations inside the perforated depth range after long-term injection. By accurately determining the inletP+S Ref. No.: SLBR / 0384PC Page 8 of 48PATENT SLB Docket No. IS23.1678-WO-PCTinjection temperature through the supplementary inverse problem, the system overcomes the significant temperature gradient that exists across the wellbore and near wellbore zones, enabling quantitative rather than merely qualitative injectivity profiling. The use of a simplified numerical model or physics-informed neural network for the supplementary inverse problem provides computational efficiency suitable for real-time interpretation while maintaining accuracy. The physics-informed neural network approach, once trained on multiple forward simulations covering the expected range of input parameters, enables very fast inference for real-time applications. The integration of DAS data for triggering temperature transient generation provides adaptive monitoring that responds to detected changes in well injectivity. The ability to use multiple types of flow rate changes, including transitions from lower to higher flow rates, restart after shut-in, and transitions from higher to lower flow rates, provides operational flexibility while maintaining the temperature signal necessary for accurate profiling.Example Wellbore with Distributed Temperature Sensing System

[0044] Oil and gas production operations utilize various well configurations to extract hydrocarbons from subsurface reservoirs and to inject fluids for reservoir management purposes. Injection wells may be used for water injection to maintain reservoir pressure, carbon dioxide sequestration for environmental purposes, and enhanced oil recovery operations. Production wells may be used to extract oil, gas, and other hydrocarbons from reservoirs. Monitoring flow profiles in these wellbores provides information for optimizing injection efficiency, tracking reservoir pressure sustaining efficiency, evaluating carbon dioxide sequestration performance, assessing enhanced oil recovery effectiveness, and characterizing production efficiency including geological and lithological structure inflow profiles, gas breakthrough inflow profiles, and water breakthrough inflow profiles.

[0045] Figure 1 depicts an example well system 100 with a distributed temperature sensing (DTS) system for real-time monitoring of fluid flow rate in a wellbore penetrating a subsurface formation is illustrated. The wellbore may be a production well or an injection well.

[0046] DTS is a fiber optic sensing technology that enables continuous temperature measurement along the entire length of an optical fiber. The technology operates byP+S Ref. No.: SLBR / 0384PC Page 9 of 48PATENT SLB Docket No. IS23.1678-WO-PCTtransmitting laser pulses through the fiber and analyzing the backscattered light. When light travels through an optical fiber, a small portion is scattered back toward the source due to interactions with the fiber material. The backscattered light contains components at different wavelengths, including Rayleigh scattering at the same wavelength as the incident light and Raman scattering at shifted wavelengths. Raman scattering produces two components: Stokes scattering at longer wavelengths and anti-Stokes scattering at shorter wavelengths. The intensity ratio between the anti-Stokes and Stokes components is temperature-dependent, enabling temperature determination at each point along the fiber. By measuring the time delay between pulse transmission and backscatter detection, the position along the fiber where the scattering occurred can be determined, providing spatially resolved temperature measurements. DTS systems may achieve spatial resolutions on the order of one meter and temperature resolutions on the order of 0.1 degrees Celsius, with measurement ranges extending tens of kilometers along a single fiber. The fiber optic cable serves as both the sensing element and the signal transmission medium, enabling distributed measurements without requiring discrete sensors at each measurement location.

[0047] The well system 100 includes a DTS system deployed along at least a portion of the wellbore and configured to provide real-time temperature measurements along a depth of the wellbore over time during operation of the wellbore. The portion of the wellbore may include at least a portion of an intake zone of an injection well or at least a portion of a production zone of a production well.

[0048] The DTS system of the well system 100 includes a fiber optic interrogation system 104 positioned at a surface of the wellbore. The fiber optic interrogation system 104 includes an interrogator that produces light beams, a reference fiber optic cable, and may include an array of discrete temperature gauges. The discrete temperature gauges may be used to acquire reference absolute temperature data for anchoring measured relative temperature changes in depth and time to absolute values. The DTS measurements are based on Raman scattering for detecting relative changes of temperature rather than absolute temperature values. The reference temperature gauge anchors the measured relative temperature changes to absolute values, enabling accurate temperature profiling along the wellbore depth.P+S Ref. No.: SLBR / 0384PC Page 10 of 48PATENT SLB Docket No. IS23.1678-WO-PCT

[0049] Fiber optic cable 114 extends from the fiber optic interrogation system 104 downward into the wellbore. The fiber optic cable 114 may be deployed behind a casing 120, inside a production tubing 118 within the wellbore, on the tubing 118, or on a sand screen. When deployed on a sand screen, the fiber optic cable 114 may be positioned on a shroud or other type of cable protector. Deployment behind the casing 120 enables permanent monitoring for both production and injection wells and provides sensitivity to flow rate profiles due to proximity to a sand face and inflow from the reservoir. Deployment on the tubing 118 passing across a perforated interval is a feasible approach for production wells, though in this configuration the temperature signal measured by the DTS system represents not only the signal from a study zone but also a mixture of signals from zones below the point of measurement.

[0050] The well system 100 includes a bottom hole assembly (BHA) 116 positioned at a lower portion of the wellbore. The bottom hole assembly 116 comprises one or more sensors configured to measure at least one of bottom hole temperature or bottom hole pressure. Packers 122 are installed within the wellbore to isolate different zones of the formation, enabling zone-specific monitoring and interpretation of flow profiles.

[0051] At the surface, the well system 100 includes a well head 110 with at least one additional sensor configured to measure at least one of well head pressure or well head temperature. The well head 110 may include flow metering equipment. For production wells, the well head 110 may include multi -phase flow rate metering systems capable of measuring oil, gas, and water flow rates. For injection wells, the well head 110 may include single-phase metering equipment for measuring injection fluid flow rates.

[0052] As further shown in Figure 1, the fiber optic interrogation system 104 may be connected to cloud computational resources 102 via a first network interface 106. The well head 110 may be connected to the cloud computational resources 102 through a second network interface 108. The well head 110 may also be connected to a central processing unit (CPU) / storage media 112 via a third network interface 108. The CPU / storage media 112 includes CPUs, data storage units, main memory units, and network connections. The CPU / storage media 112 may provide memory storing instructions and at least one processor configured to execute the instructions for data processing and interpretation.P+S Ref. No.: SLBR / 0384PC Page 11 of 48PATENT SLB Docket No. IS23.1678-WO-PCT

[0053] The well system 100 enables real-time streaming of DTS data from the fiber optic cable 114 along with pressure and temperature data from the bottom hole assembly 116 and flow rate data from the well head 110. Data collected via the network interfaces 106 and 108 may be transferred to the CPU / storage media 112 and the cloud computational resources 102 for processing, interpretation, and storage. The well system 100 may process data from multiple wells connected to one on-site computational resource through several instances of software executing on the central processing unit storage media 112.

[0054] The well system 100 may utilize Distributed Acoustic Sensing (DAS) data that can be integrated with DTS data and other data in the interpretation workflow. DAS is a fiber optic sensing technology that detects acoustic vibrations and strain along the length of an optical fiber. DAS systems operate by transmitting coherent laser pulses through the fiber and analyzing the Rayleigh backscattered light. Unlike DTS which relies on Raman scattering, DAS utilizes the phase and amplitude variations in Rayleigh backscatter caused by acoustic disturbances impinging on the fiber. When acoustic waves or vibrations interact with the fiber, they cause minute changes in the fiber's refractive index and physical dimensions, which modulate the backscattered light. By analyzing these modulations, DAS systems can detect and characterize acoustic signals along the entire fiber length. DAS systems achieve high temporal sampling rates, enabling detection of acoustic frequencies ranging from sub-hertz to several kilohertz. In wellbore applications, DAS can detect flow-induced noise, fluid movement, sand production, and other acoustic signatures associated with production and injection operations. The integration of DAS data with DTS data provides complementary information, as DAS responds to dynamic flow events while DTS provides thermal signatures of fluid movement and heat transfer processes.

[0055] Data processing routines include denoising, filtering outliers, and averaging as preliminary data processing performed with on-site computational resources of the CPU / storage media 112. The preliminary data processing prepares the acquired data for subsequent model-based interpretation and inversion procedures.

[0056] Conventional approaches to wellbore flow profiling face significant limitations when applied to real-time monitoring scenarios. Manual interpretation by domain experts, while capable of producing accurate results, creates bottlenecks inP+S Ref. No.: SLBR / 0384PC Page 12 of 48PATENT SLB Docket No. IS23.1678-WO-PCTdelivering interpretation results and cannot scale to continuous monitoring of multiple wells over extended time periods. Existing automated interpretation methods often rely on simplified steady-state assumptions that fail to capture the dynamic nature of reservoirwellbore interactions during actual operations. The transient behavior of the temperature signal measured by DTS, along with the complexity of its origins caused by multiphase and multi-physics processes, requires sophisticated enough simulation tools for reliable and robust quantitative interpretation. Furthermore, the inherent ambiguity of inverse problems used to derive flow profiles from temperature data presents challenges for automated systems, as multiple parameter sets may potentially match observed data, necessitating techniques to address solution non-uniqueness while managing computational resources efficiently.Example Injection Profiling using DTS Transient Data

[0057] Aspects of the present disclosure provides for injectivity profiling based on using DTS data during transitional stages. Aspects of the present disclosure may provide for injectivity profiling in vertical wells that is otherwise not possible with DTS data only, due to lack of temperature variations inside the perforated depth range after long-term injection or inaccuracy without using the proposed technique for quantitative estimation of the injected fluid temperature.

[0058] Figure 2 shows a method 200 for determining an injectivity profile of an injection well penetrating a subsurface formation.Acquired Data:

[0059] Method 200 begin with deploying at least one distributed temperature sensing (DTS) cable along at least a portion of the injection well. In one aspect, the DTS cable is a DTS fiber optic cable deployed behind a casing or on a liner in the injection well.

[0060] In some aspects, method 200 further includes receiving bottom hole measurements from a bottom hole assembly including one or more sensors configured to measure at least one of: bottom hole temperature or bottom hole pressure.

[0061] In some aspects, method 200 further includes receiving well head measurements from at least one additional sensor at a surface of the wellbore configuredP+S Ref. No.: SLBR / 0384PC Page 13 of 48PATENT SLB Docket No. IS23.1678-WO-PCTto measure at least one of: well head pressure, well head temperature, or well head flow rate.Generation of Temperature Transient:

[0062] Method 200 includes, at step 205, generating a temperature transient in the injection well.

[0063] The method includes, at step 210, receiving DTS measurements along a depth of the injection well over time.

[0064] In some aspects, method 200 includes controlling injection of fluid into the injection well at a first flow rate during a first duration, and receiving the DTS, during the first duration, first temperature measurements from the DTS cable at a first sampling rate.

[0065] In some aspects, the first sampling rate is between 5 minutes and 240 minutes.

[0066] In some aspects, generating the transient temperature in the injection well at the step 205 includes controlling injection of fluid into the injection well at a second flow rate during a second duration, and receiving the temperature measurements from the DTS cable associated with the temperature transient at step 210 includes receiving, during the second duration, second temperature measurements from the DTS cable at a second sampling rate.

[0067] In some aspects, the second sampling rate is a higher sampling rate than the first sampling rate. In some aspects, the second sampling rate is ten minutes or less.

[0068] In one aspect, the second flow rate is higher than the first flow rate, the second duration is at least six hours, and method 200 further comprises injecting fluid into the injection well at the first flow rate during a third duration.

[0069] In some aspects, the first flow rate comprises a shut-in of the injection well, and the second flow rate comprises a restart of injection after the shut-in.

[0070] In some aspects, the second flow rate is lower than the first flow rate, the second duration is at least six hours, and method 200 further includes injecting fluid into the injection well at the first flow rate during a third duration.P+S Ref. No.: SLBR / 0384PC Page 14 of 48PATENT SLB Docket No. IS23.1678-WO-PCT

[0071] In one aspect, method 200 further includes transmitting optical pulses into a distributed acoustic sensing (DAS) fiber optic cable deployed along at least a portion of the injection well, receiving backscattered optical signals, generating an acoustic profile based on the backscattered optical signals, automatically comparing the acoustic profile with one or more previous acoustic profiles, and generating an alarm when a difference between the acoustic profile and the one or more previous acoustic profiles exceeds one or more predefined thresholds.

[0072] In some aspects, generating the temperature transient in the injection well at the step 205 is performed at least one of: at a preconfigured periodicity or in response to an alarm generated based on the DAS system.

[0073] Figure 3 depicts a graph 300 showing field DTS profiles of injection temperature behind casing at two different flow rates and shut-in conditions. The graph 300 includes four curves: a geothermal curve representing the static temperature profile after long shut-in; a first flow rate curve representing a lower injection flow rate; a second flow rate curve representing a higher injection flow rate; and a shut-in curve shown as a dashed line.

[0074] As shown, the geothermal curve in the graph 300 increases gradually from approximately 55 degrees Fahrenheit at the surface to approximately 195 degrees Fahrenheit at 9000 feet depth. The geothermal curve represents the static temperature profile that the formation approaches during extended shut-in periods when no injection is occurring. The shut-in curve closely follows the geothermal curve, indicating temperature restoration toward geothermal conditions during shut-in periods.

[0075] As shown, the first flow rate curve and the second flow rate curve both start at approximately 80 degrees Fahrenheit near the surface and increase with depth. The shape of the profiles at shallow depths is dependent on the wellhead inlet injection temperature. The shape of the profiles at deeper depths is dependent on the injection flow rate and heat transfer to the surrounding formation via the fluid-filled annulus. The first flow rate curve shows higher temperatures at deeper depths compared to the second flow rate curve due to greater heat transfer from the formation at lower flow rates. At lower flow rates, the injected fluid has more time to exchange heat with the surroundingP+S Ref. No.: SLBR / 0384PC Page 15 of 48PATENT SLB Docket No. IS23.1678-WO-PCTformation as the fluid travels down the wellbore, causing the temperature to approach the geothermal profile more closely than at higher flow rates.

[0076] The temperature profiles in the graph 300 demonstrate that at depths below approximately 6000 feet, the temperature difference between the two flow rate curves increases due to differences in injection rates and, consequently, in the intensity of heat conduction with the surrounding formation. At the perforated interval top depth of approximately 8400 feet, the temperature difference between two DTS profiles during pumping at different flow rates may be about 12 to 15 degrees Fahrenheit. The temperature difference between pumping and shut-in profiles at the perforated interval top depth may be 20 to 30 degrees Fahrenheit.

[0077] These temperature contrasts provide the temperature signal for generating temperature transients. The temperature differences between different flow rate conditions and between pumping and shut-in conditions represent the temperature dynamic disturbance that can be introduced into the injected interval via either change of the flow rate or making shut-in and restarting pumping.

[0078] Figure 4 depicts a temperature profile graph 400 showing field DTS data example of injection temperature trends inside of the perforated interval. Two temperature trend lines are shown in the temperature profile graph 400, identified in the legend as 8407 and 8481, representing temperature measurements at two different depths within the perforated interval measured in feet.

[0079] The temperature trends in the temperature profile graph 400 demonstrate the dynamic temperature response during various flow rate changes and shut-in periods. The temperature measurements at the two depths 8407 and 8481 within the perforated interval provide spatially resolved temperature information that captures the thermal response of the wellbore during transitional pumping regimes. The sharp temperature changes visible in the temperature profile graph 400 around 230 hours and 320 hours correspond to flow rate transitions or shut-in events that generate the temperature transients.

[0080] Figure 5 depicts a graph 500 showing simulated DTS profiles of injection temperature behind casing at two different flow rates and shut-in conditions in metric units. The graph 500 plots temperature (in degrees Celsius) as a function of depth (in meters) for a geothermal curve representing the static temperature profile after long shut-P+S Ref. No.: SLBR / 0384PC Page 16 of 48PATENT SLB Docket No. IS23.1678-WO-PCTin; a lower flow rate curve; a higher flow rate curve; and a shut-in curve shown as a dashed line. The simulated DTS profiles in the graph 500 are simulated using the full numerical model approach. As shown in Figure 5, the simulated DTS profiles using the full numerical model are close to the measured profiles shown in the Figures 3-4.

[0081] Figure 6 depicts a graph 600 showing flow rate in barrels per day as a function of time in hours for multiple flow rates and shut-ins. The graph 600 demonstrates the various transitional pumping regimes that may be used to generate temperature transients for injectivity profiling as described with respect to the step 205 of the method 200 shown in Figure 2.

[0082] A first type of transition comprises a transition from a lower flow rate to a higher flow rate. As shown in Figure 6, such transitions occur at approximately 230 hours when the flow rate increases from approximately 600 barrels per day to approximately 1100 barrels per day, and at approximately 320 hours when the flow rate increases from zero to approximately 1500 barrels per day following the second shut-in period.

[0083] A second type of transition comprises a shut-in of the injection well followed by a restart of injection after the shut-in. As shown in Figure 6, the first shut-in period occurs from approximately 100 hours to approximately 140 hours, and the second shut-in period occurs from approximately 260 hours to approximately 320 hours. The restart of injection after shut-in creates temperature transients due to the difference in shut-in temperature restoration dynamics in different well sections.

[0084] A third type of transition comprises a transition from a higher flow rate to a lower flow rate. As shown in Figure 6, such a transition occurs at approximately 350 hours when the flow rate decreases from approximately 1500 barrels per day to approximately 800 barrels per day.

[0085] Figure 7 depicts an injectivity profile graph 700 showing an intake percentage as a function of depth across a perforated interval for the flow rates and shut-ins shown in Figure 6. Each data point in the graph 700 represents the relative fluid intake at a corresponding depth location. According to certain aspects, the injectivity profile shown in Figure 7 may be obtained using DTS data and, optionally, bottom hole pressure, bottom hole temperature, and / or surface flow metering data.P+S Ref. No.: SLBR / 0384PC Page 17 of 48PATENT SLB Docket No. IS23.1678-WO-PCT

[0086] As shown in Figure 7, the data points near the deeper portion of the interval between approximately 2585 and 2595 meters show relatively low intake values approaching zero percent. The shallower portions and the deepest section near 2600 meters exhibit moderate intake values between 2 and 12 percent. The heterogeneous distribution of intake values across the perforated interval reflects the multi-layer reservoir model with contrast productivity index (PI) values.

[0087] Figure 8 depicts a graph 800 showing simulated DTS profiles of injection temperature behind casing over a full depth range for flow rates and shut-ins of Figure 6.The graph 800 includes multiple curves corresponding to different operational conditions including a geothermal profile, injection at approximately 600 barrels per day, injection at approximately 800 barrels per day, shut-in conditions, injection at approximately 1100 barrels per day, and injection at approximately 1500 barrels per day.

[0088] The geothermal curve represents the undisturbed formation temperature that the wellbore approaches during extended shut-in periods. The shut-in profile closely follows the geothermal curve, indicating temperature restoration toward geothermal conditions when injection is not occurring. The injection temperature profiles at the various flow rates diverge from the geothermal profile throughout the wellbore depth. Lower flow rates result in temperature profiles that more closely approach the geothermal temperature at deeper depths due to increased heat transfer from the formation to the wellbore flow.

[0089] Figure 9 depicts a graph 900 showing simulated DTS profiles of injection temperature behind casing within the perforation interval at different flow rates and shut-in condition of Figure 6. The graph 900 includes multiple temperature profile curves corresponding to different injection conditions: a geothermal profile, profiles at approximately 600 barrels per day, approximately 1100 barrels per day, approximately 1500 barrels per day, and approximately 800 barrels per day flow rates, and a shut-in profile.

[0090] The graph 900 demonstrates that at the end of each flow period, the temperature signal in the perforation interval applicable for injectivity profiling is minimal. Comparing the temperature profiles at different flow rates within the perforated interval, temperature variations appear at almost impermeable or non-perforated depthP+S Ref. No.: SLBR / 0384PC Page 18 of 48PATENT SLB Docket No. IS23.1678-WO-PCTranges, but the temperature signal within the actively injecting zones diminishes during constant flow rate pumping. The minimal temperature signal during steady-state injection conditions prevents characterization of the injectivity profile from DTS data alone without introducing temperature disturbances.

[0091] The graph 900 demonstrates that at the end of each flow period, the temperature signal in the perforation interval applicable for injectivity profiling is almost missing during steady-state injection conditions. The temperature profiles at different flow rates in the graph 900 provide the basis for generating temperature transients that enable injectivity profiling across the heterogeneous reservoir layers penetrated by the injection well.

[0092] The approach and schedule for generating temperature transients for injectivity profiling may be based on any of the listed types of flow rate change, or a combination of them — increasing flow rate, decreasing flow rate, and / or shut-in.

[0093] Figure 10 depicts a data visualization 1000 showing DAS data from a vertical injection well. The data visualization 1000 shows the DAS data as a function of depth and time. The data visualization 1000 uses a color scale where variations in color intensity represent acoustic signal characteristics at different depths and times during injection operations.

[0094] The data visualization 1000 demonstrates how acoustic signatures vary across different depth zones and overtime during injection operations. The non-perforated depth ranges marked by darkened rectangular areas exhibit reduced acoustic activity compared to the perforated zones where fluid injection into the formation generates acoustic signals. The temporal variations visible across the horizontal axis of the DAS data visualization 1000 capture changes in acoustic characteristics that may correspond to flow rate changes, shut-in events, or changes in injectivity conditions within the wellbore.

[0095] The integration of DAS data with DTS data provides complementary information for injectivity profiling. While DTS responds to thermal signatures of fluid movement and heat transfer processes, DAS responds to dynamic flow events and acoustic disturbances associated with injection operations. DAS data may indicate qualitatively some changes in injectivity that demand new temperature transients to be generated to update the injectivity profile from DTS data. The DAS data shown in theP+S Ref. No.: SLBR / 0384PC Page 19 of 48PATENT SLB Docket No. IS23.1678-WO-PCTDAS data visualization 1000 provides qualitative indication of changes in injectivity that may trigger generation of temperature transients for updating the injectivity profile from DTS data. The at least one processor may be configured to execute the instructions further to automatically compare the acoustic profile with one or more previous acoustic profiles. The comparison may identify changes in acoustic signatures that indicate variations in injectivity conditions, flow distribution, or other wellbore characteristics. The at least one processor may be configured to execute the instructions further to generate an alarm when a difference between the acoustic profile and the one or more previous acoustic profiles exceeds one or more predefined thresholds. The predefined thresholds may be configured based on expected acoustic variations during normal injection operations, with deviations beyond the thresholds triggering the alarm.Supplemental Inverse Problem:

[0096] Continuing with reference again to the Figure 2, method 200 then proceeds to step 215 with automatically simulating, using a model, transient thermal and fluid flow behavior of the wellbore and the subsurface formation.

[0097] Method 200 then proceeds to step 220 with automatically solving a supplementary inverse problem based on a comparison of the simulated transient thermal behavior and the received DTS measurements.

[0098] In some aspects, automatically solving the supplementary inverse problem at step 220 includes, for a wellbore calibration section above the perforation top, determining a residual A as a sum of differences between (i) formation temperature and a time instance n interpolated to an effective radial position of the DTS cable and (ii) a DTS temperature measurement for the time instance n for a plurality of spatial points along the wellbore, and determining the inlet injection temperature that minimizes the residual.

[0099] Method 200 then proceeds to step 225 with estimating an inlet injection temperature at a top, or above the top, of a perforated interval of the injection well based on the solving the inverse problem.

[0100] Figures 11-13 illustrates DTS temperatures during transitions from shut-in to injection. The simulated DTS profiles in graphs 1100-1300 include multiple curvesP+S Ref. No.: SLBR / 0384PC Page 20 of 48PATENT SLB Docket No. IS23.1678-WO-PCTrepresenting temperature measurements at different time instances. The perforated interval extends from 2557 meters to 2599 meters.

[0101] Figure 11 depicts a graph 1100 illustrating simulated DTS profiles showing injection temperature behind casing as a function of depth. In some aspects, the graph 1100 may illustrates the simulated DTS profiles one hour after a change of flow rate from lower to higher values at 230 hours. The curve 1105 represents a DTS profile taken earliest after the change of flow rate and the curve 1110 represents a DTS profile taken latest after the change of flow rate from the among the curves shown in Figure 11.

[0102] Figure 12 depicts a graph 1200 illustrating simulated DTS profiles showing injection temperature behind casing as a function of depth. In some aspects, the graph 1200 may illustrates the simulated DTS profiles one hour after injection restarting after shut-in at 320 hours. The curve 1205 represents a DTS profile taken earliest after the restarting injection and the curve 1210 represents a DTS profile taken latest after restarting injection from the among the curves shown in Figure 12.

[0103] Figure 13 depicts a graph 1300 illustrating simulated DTS profiles showing injection temperature behind casing as a function of depth. In some aspects, the graph 1300 may illustrates the simulated DTS profiles one hour after a change of flow rate from higher to lower values at 350 hours. The curve 1305 represents a DTS profile taken earliest after the change of flow rate and the curve 1310 represents a DTS profile taken latest after the change of flow rate from the among the curves shown in Figure 13.

[0104] The temperature profiles in the graphs 1100, 1200, and 1300 demonstrate that generating a temperature transient in the injection well creates a disturbance at the inlet or top of the perforated interval via either shut-in with following restart or changing flow rate. The temperature transients introduce measurable temperature dynamics into the perforated interval that may be captured by the DTS system and interpreted using modelbased approaches to determine the injectivity profile.

[0105] Figure 14 depicts a graph 1400 showing the difference between simulated DTS temperature behind casing and simulated DTS temperature in-casing. In-casing flow temperature may be used for simulation and qualitative data matching. As shown, the difference between the DTS temperature behind casing and in-casing may be high.P+S Ref. No.: SLBR / 0384PC Page 21 of 48PATENT SLB Docket No. IS23.1678-WO-PCT

[0106] According to certain aspects, the simulated temperature difference dynamics may be compared with the measured temperature difference dynamics to validate the model parameters and ensure accurate representation of the heat transfer processes occurring in the wellbore and near wellbore zone.

[0107] Interpretation of the DTS data may be performed by the simulation software, the model, offline, or in real-time for automatic flow profiling. The simulated and measured DTS data may be analyzed for detailed temperature dynamics during transitional pumping regimes, allowing characterization and real-time flow monitoring for operational decision support.

[0108] Thus, solving the inverse problem of determining in-casing temperature from the measured DTS data is desirable.

[0109] Solving the inverse problem may provide the estimated inlet injection. Aspects of the disclosure provide three approaches for solving the supplement inverse problem (1) using a numerical forward model, (2) using a simplified numerical forward model, and (3) using a physics-informed neural network (PINN) model.Numerical Forward Model:

[0110] In some aspects, the supplemental inverse problem is solved using a full numerical forward model. In some aspects, the supplemental inverse problem is solved using the forward model used for solving the full inverse problem.[oni] In some aspects, the model is a transient multiphase thermal-hydrodynamic forward numerical model of the wellbore and the subsurface formation configured to use the inlet injection temperature as a boundary condition for wellbore temperature simulation, and simulate multiphase fluid flow, transient heat transfer, and coupled wellbore-formation behavior including pressure distribution, temperature distribution, and flow rate distribution.

[0112] However, the inlet injection temperature may not be known (e.g., unless DTS is located immediately inside wellbore flow). Thus, the inlet injection temperature may be determined based on DTS data by solving an inversion.P+S Ref. No.: SLBR / 0384PC Page 22 of 48PATENT SLB Docket No. IS23.1678-WO-PCT

[0113] In some aspects, solving the inversion includes choosing a wellbore section where calibration of injection may be conducted.

[0114] In some aspects, solving the main inverse problem includes minimizing the residual between measured and simulated DTS values. The residual may be a function of the inlet injection temperature. The minimum of the residual may be found using a gradient-based method. The gradient-based method iteratively adjusts the inlet injection temperature value and evaluates the resulting residual until the minimum residual is achieved. The inlet injection temperature that minimizes the residual represents the solution of the supplementary inverse problem for the current time step, providing the boundary condition for wellbore temperature simulation in subsequent forward model calculations. The solution of the supplementary inverse problem for time instance n may be determined as:= arg inin R (7^)

[0115] Thus, the numerical forward model may be used as a direct solver for the inverse problem. Figure 15 depicts a solution of the supplementary inverse problem using a numerical forward model. Figure 15 depicts curves showing measured DTS data behind case, simulated DTS temperature data, and the simulated in-casing injection inlet injection temperature obtained via the inverse problem solution. The simulated in-casing temperature curve may represent the estimated inlet injection temperature estimated at a top, or above the top, of a perforated interval of the injection well based on solving the supplementary inverse problem. The simulated in-casing inlet injection temperature curve may provide an accurate boundary condition for the main inverse problem solution.Simpli fied Numerical Model:

[0116] In some aspects, a simplified numerical model is used to solve the supplementary inverse problem.

[0117] In some aspects, the simplified numerical model is configured to, for a portion (e.g., 10 meters or less) of the wellbore calibration section from the perforation top upward, solve a transient heat transfer equation and a radial conduction equation for an adjacent formation section to determine the inlet injection temperature. The transient heat transfer equation describes the temperature evolution of the injected fluid flowing throughP+S Ref. No.: SLBR / 0384PC Page 23 of 48PATENT SLB Docket No. IS23.1678-WO-PCTthe wellbore calibration section, accounting for convective heat transfer between the wellbore flow and the surrounding formation. The radial conduction equation describes the heat conduction within the adjacent formation section surrounding the wellbore calibration section, enabling calculation of the formation temperature at the effective radial position of the DTS cable.

[0118] The temperature offset between the simulated in-casing injection inlet injection temperature curve and the DTS curves may correspond to the temperature gradient across the wellbore and near wellbore zone, where the DTS cable measures temperature at a radial position behind the casing while the in-casing temperature represents the mass-average wellbore flow temperature of the injected fluid.

[0119] The simplified numerical model approach for solving the supplementary inverse problem may provide an alternative to using the full numerical model as a forward engine. The simplified numerical model may solve the inverse problem with reduced computational resources compared to the full numerical forward model while maintaining accuracy for inlet injection temperature determination.

[0120] The simplified numerical model may use no more than 10 meters in the wellbore for the calibration section, reducing the amount of computation while still providing sufficient spatial resolution for accurate temperature simulation within the calibration section.

[0121] The simplified numerical model may assume the injected fluid is incompressible and neglects impact of gravity and friction losses for the temperature equation. Because the calibration section does not include the reservoir layers where fluid injection into the formation occurs, only a heat conduction equation may be solved in the formation rather than the full coupled flow and heat transfer equations used in the complete numerical forward model. The simplified problem statement enables solving only the temperature equation in the wellbore without the additional computational burden of pressure and flow calculations.

[0122] The transient heat transfer equation for the wellbore flow in the simplified model may be expressed as:dTwdTwC^~dz~+~ ? lr=rw)=0P+S Ref. No.: SLBR / 0384PC Page 24 of 48PATENT SLB Docket No. IS23.1678-WO-PCTwhere Pf is the fluid density, c is the fluid heat capacity, Twis the wellbore fluid temperature, rwis the wellbore radius, t is time, z is the coordinate along the wellbore, h is a convective heat transfer coefficient used in the heat transfer equation for coupling wellbore flow temperature with formation temperature at the wellbore wall, and G is a mass flow rate parameter. G may be expressed as G = nr^p^v, where v is the fluid velocity.

[0123] The boundary condition for the wellbore flow specifies the inlet injection temperature at the top of the calibration section asTw(z = z0) = Tinj.

[0124] The radial heat conduction problem for the adjacent formation section may be expressed as:dT > 1 d / dT\PmCm~dt ~ 7dr \rAm'dr)where T is the formation temperature over radius, and r is the radial coordinate. The formation thermal conductivity Am, rock density pm, and heat capacity cmare used as parameters in the radial heat conduction problem. The boundary condition at the wellbore wall couples the formation heat conduction with the wellbore flow through the convective heat transfer coefficient:dT^m~dr 'r=rw — —T lr=rw)

[0125] A far-field boundary condition specifies that the formation temperature approaches the undisturbed geothermal temperature at large radial distances:T1I ir=oo = T1co •

[0126] Use of the simplified numerical model may accelerate simulations by at least an order of magnitude compared to using the full numerical model because the simplified model solves equations for only a small fraction of the wellbore above the perforated interval rather than the full wellbore section and all respective formation radial layers including the reservoir layers. The reduced computational domain and simplified physics enable faster forward model evaluations during the iterative inverse problem solution while maintaining sufficient accuracy for inlet injection temperature determination.P+S Ref. No.: SLBR / 0384PC Page 25 of 48PATENT SLB Docket No. IS23.1678-WO-PCTPhysics-Informed Neural Network (PINN) Model based on Simplified Model:

[0127] In some aspects, the model is a physics-informed neural network (PINN) trained on simulations generated by solving a transient heat transfer equation and a radial conduction equation for an adjacent formation section to determine the inlet injection temperature.

[0128] In some aspects, the PINN is trained using a loss function comprising: (i) a first component corresponding to a wellbore heat transfer equation; (ii) a second component corresponding to a radial formation heat conduction equation; (iii) a third component corresponding to a boundary condition at a wellbore wall; (iv) a fourth component corresponding to a far-field formation boundary condition; and (v) a fifth component corresponding to a residual between the simulated thermal behavior and the received temperature measurements from the DTS cable.

[0129] Figure 16 depicts the neural network architecture 1600 of an example PINN for determining the inlet injection temperature. The neural network architecture 1600 may incorporate a governing system of differential equations and is trained to reproduce evolution operators of the original system for solving the supplementary inverse problem.

[0130] The PINN 1605 may receive multiple inputs including, for example, a radial spatial grid parameter ( / ) that defines the discretization of the radial coordinate used for solving the radial heat conduction problem in the formation surrounding the wellbore; a vertical spatial grid parameter (z) that defines the discretization of the coordinate along the wellbore within the calibration section where the inlet injection temperature is determined; a temperature distribution inside the wellbore from a previous time instance (u”-1) that provides the initial condition for advancing the temperature solution forward in time within the wellbore calibration section; a temperature distribution in the formation from a previous time step (T^1) that provides the initial condition for advancing the radial heat conduction solution forward in time within the adjacent formation section surrounding the wellbore; DTS data for a new time instance (TTSf) that comprises the temperature measurements received from the DTS cable at the current time instance for which the inlet injection temperature is being determined; and fluid and formation properties used in the wellbore heat transfer equation including density (p) and heat capacity (c).P+S Ref. No.: SLBR / 0384PC Page 26 of 48PATENT SLB Docket No. IS23.1678-WO-PCT

[0131] The PINN 1605 may process the inputs and output a simulated temperature distribution inside the wellbore calibration section at the new time instance (u”) that represents the simulated wellbore fluid temperature along the calibration section after advancing the solution forward by one time instance; a simulated temperature distribution in the adjacent formation part at the new time instance (T- ) that represents the simulated formation temperature over the radial coordinate after advancing the radial heat conduction solution forward by one time instance; and a simulated inlet injection temperature at the new time instance (T^j) that represents the solution of the supplementary inverse problem for the current time instance. The inlet injection temperature output provides the boundary condition for wellbore temperature simulation in the main inverse problem solution.

[0132] The neural network architecture 1600 may be trained on multiple forward simulations covering the expected range of input parameters. The forward simulations solve the transient heat transfer equation for the wellbore flow and the radial conduction equation for the adjacent formation section to generate training data for the PINN.

[0133] The PINN may be trained using a loss function comprising multiple components. The loss function L for the PINN includes weighting coefficients y for each component to balance the contributions of different terms. The total loss function may be expressed as:L = y1L1+ y2L2+ y3L3+ y4L4+ y5L5The weighting coefficients Yi, Y2, Y3, Y4, and Ys may be adjusted to balance the relative contributions of the differential equation terms, boundary condition terms, and data matching term during training of the neural network architecture 1600. The weighting coefficients enable tuning of the PINN training process to achieve accurate reproduction of the physical behavior while matching the observed DTS measurements.

[0134] The first component L corresponds to a wellbore heat transfer equation. The first component Ljmay be expressed as:y( du du fGv2\2[Prcr-gi-crGgz-+ h^-T- —P+S Ref. No.: SLBR / 0384PC Page 27 of 48PATENT SLB Docket No. IS23.1678-WO-PCTwhere u represents the wellbore fluid temperature, and the summation is performed over the vertical spatial grid points Zj along the wellbore calibration section. The first component L4penalizes deviations from the wellbore heat transfer equation at each spatial grid point.

[0135] The second component L2corresponds to a radial formation heat conduction equation. The second component L2may be expressed as:dt rdr\mdr)“I'' Jwhere the summation is performed over both the vertical spatial grid points Zj and the radial spatial grid points rj. The second component L2penalizes deviations from the radial heat conduction equation at each point in the two-dimensional spatial domain.

[0136] The third component L3corresponds to a boundary condition at a wellbore wall. The third component L3may be expressed as: / dT \2\m~dr 'r=rw —~lr=r^ )ZiThe third component L3penalizes deviations from the heat flux continuity condition at the wellbore wall, where the conductive heat flux in the formation equals the convective heat transfer between the wellbore flow and the formation.

[0137] The fourth component L4corresponds to a far-field formation boundary condition. The fourth component L4may be expressed as:The fourth component L4penalizes deviations from the far-field boundary condition where the formation temperature approaches the undisturbed geothermal temperature at large radial distances from the wellbore.

[0138] The fifth component L5corresponds to a residual between the simulated thermal behavior and the received temperature measurements from the DTS cable. The fifth component L5may be expressed as:P+S Ref. No.: SLBR / 0384PC Page 28 of 48PATENT SLB Docket No. IS23.1678-WO-PCT(^(r^zD - T^CzD)2where Tn(rDTS,Zi) is the formation temperature at time instance n interpolated to the effective radial position of the DTS cable, and T^TS(Zi) is the DTS temperature measurement for time instance nat spatial point Zj. The fifth component L5penalizes deviations between the simulated formation temperature at the DTS cable position and the actual DTS measurements received from the DTS cable.

[0139] Once trained on multiple forward simulations with the full expected range of all input parameters, the neural network architecture 1600 may be used to calculate the inlet injection temperature for any spatial grids and any model properties. The trained PINN enables fast inference for real-time application of injectivity profiling because the neural network evaluation is computationally efficient compared to iterative numerical solution of the differential equations. The fast inference capability of the trained PINN makes the PINN approach suitable for real-time interpretation where computational speed is a consideration.Main Inverse Problem:

[0140] Method 200 then proceeds to step 230 with automatically solving a main inverse problem to fine tune one or more parameters of the model iteratively over multiple time instances.

[0141] In some aspects, automatically solving the main inverse problem to fine tune the one or more parameters of the model at step 230 includes, iteratively over the multiple time instances, determining residuals between the received bottom hole measurements and the simulated thermal and fluid flow behavior at step 235.

[0142] The residual calculation may incorporate multiple data sources. The residuals between the received temperature measurements from the DTS cable and the simulated thermal behavior provide the primary constraint for the inverse problem. In some aspects, residuals between received bottom hole measurements from the bottom hole assembly 116 and the simulated thermal and fluid flow behavior are also determined. The bottom hole measurements may include bottom hole temperature and bottom hole pressure data that provide additional constraints on the model parameters. In some aspects, residuals between received well head measurements from sensors at the well head 110 and theP+S Ref. No.: SLBR / 0384PC Page 29 of 48PATENT SLB Docket No. IS23.1678-WO-PCTsimulated thermal and fluid flow behavior are determined. The well head measurements may include well head pressure, well head temperature, and well head flow rate data.

[0143] In some aspects, solving the inverse problem includes determining a residual R as a sum of differences between (i) formation temperature at a time instance n interpolated to an effective radial position of the DTS cable and (ii) a DTS temperature measurement for the time instance n for a plurality of spatial points along the wellbore. The residual R quantifies the mismatch between the simulated formation temperature at the DTS cable position and the actual DTS temperature measurements received from the DTS cable. The formation temperature at the time instance n is interpolated to the effective radial position of the DTS cable to account for the radial temperature distribution within the formation surrounding the wellbore.

[0144] In some aspects, solving the inversion includes taking the injection temperature and temperature inside the wellbore and formation layers from a previous time instance n-1 as known. For a new time instance n, a residual between the simulated and measured DTS temperatures may be determined as:R=ft*zj) ~ TVTSJ, where Tn(rDTS,Zi) is the formation temperature at time moment n interpolated to the effective radial position of the DTS cable, whereis the DTS temperature for time moment / / , and where z. is the spatial points along the wellbore.

[0145] Automatically solving the main inverse problem at step 230 includes, at step 240, adjusting one or more parameters of the model to minimize the residuals. The parameter adjustment at the step 240 of the method 200 minimizes the residuals by modifying one or more parameters of the model. The parameters subject to adjustment may include formation permeability values for different reservoir layers, skin factors characterizing near-wellbore damage or stimulation, and thermal properties of the formation. Gradient-based optimization methods or ensemble-based methods may be employed to efficiently search the parameter space and identify parameter values that minimize the total residual across all time instances and measurement types.P+S Ref. No.: SLBR / 0384PC Page 30 of 48PATENT SLB Docket No. IS23.1678-WO-PCT

[0146] The main inverse problem utilizes the inlet injection temperature determined through the supplementary inverse problem as a boundary condition for the forward model simulations. The forward model simulates the transient thermal and fluid flow behavior within the perforated interval, where the injectivity characteristics of the formation determine the temperature distribution along the wellbore. The simulated temperature profiles are compared with the received DTS measurements at each time instance to calculate residuals that quantify the mismatch between model predictions and observations.

[0147] The iterative nature of the main inverse problem solution enables progressive refinement of the model parameters as additional time instances are processed. Each iteration updates the parameter estimates based on the cumulative information from all processed time instances, improving the accuracy and reducing the uncertainty of the estimated parameters. The convergence of the iterative process may be monitored through the magnitude of parameter changes between iterations or through the reduction in total residual values.Injectivity Profile Determination:

[0148] Method 200 then proceeds to step 245 with estimating, using the fine-tuned model and the determined inlet injection temperature, an injectivity profile of the injection well along the perforated interval. For example, the injectivity profile graph 700 shown in Figure 7 may be estimated using the fine-tuned model and the determined inlet injection temperature, an injectivity profile of the injection well along the perforated interval. The injectivity profile shown in the injectivity profile graph 700 provides quantitative characterization of fluid distribution across the multiple reservoir layers penetrated by the injection well. The contrast in intake percentages between different depth locations enables identification of high-injectivity zones and low-injectivity zones within the perforated interval, supporting optimization of injection operations and reservoir management decisions.Control Based on Injectivity Profile:

[0149] In some aspects, method 200 further includes, at step 250, controlling a well activity based on the determined injectivity profile. The control actions may addressP+S Ref. No.: SLBR / 0384PC Page 31 of 48PATENT SLB Docket No. IS23.1678-WO-PCTidentified issues with fluid distribution, optimize injection efficiency, or respond to changes in injectivity conditions over time.

[0150] The injectivity profile may reveal zones of low injectivity within the perforated interval that indicate formation damage, scaling, or other factors limiting fluid intake. Identification of low-injectivity zones may trigger well treatment operations such as matrix acidizing to restore formation permeability and improve injection efficiency. The spatial localization of low-injectivity zones provided by the injectivity profile enables targeted treatment of specific depth intervals rather than treating the entire perforated interval.

[0151] The injectivity profile may also reveal zones of unexpectedly high injectivity that may indicate preferential flow paths, fractures, or communication with unintended reservoir intervals. Identification of high-injectivity zones may prompt investigation of potential conformance issues and implementation of remedial measures to ensure proper fluid distribution across the target reservoir layers.

[0152] For injection wells used in reservoir pressure sustaining operations, the injectivity profile enables optimization of injection rates and pressures to achieve desired pressure support across the reservoir. The profile may inform decisions regarding injection well placement, completion design modifications, or the need for additional injection wells to achieve uniform pressure support.

[0153] For injection wells used in CO2 sequestration operations, the injectivity profile provides information for monitoring storage efficiency and ensuring that injected CO2 is distributed across the intended storage intervals. Changes in the injectivity profile over time may indicate geochemical reactions, pressure buildup, or other factors affecting long-term storage performance.

[0154] For injection wells used in enhanced oil recovery operations, the injectivity profile enables optimization of injection patterns to maximize sweep efficiency and oil recovery. The profile may inform decisions regarding injection rates, injection fluid composition, and the timing of injection operations relative to production well operations.

[0155] In one aspect, method 200, or any aspect related to it, may be performed by an apparatus, such as system 1700 of Figure 17, which includes various componentsP+S Ref. No.: SLBR / 0384PC Page 32 of 48PATENT SLB Docket No. IS23.1678-WO-PCToperable, configured, or adapted to perform the method 200. System 1700 is described below in further detail.

[0156] Note that Figure 2 is just one example of a method, and other methods including fewer, additional, or alternative steps are possible consistent with this disclosure.Example Automated Injection Profiling System

[0157] Figure 17 depicts an example system 1700 for automated injection profiling.

[0158] The system 1700 may be implemented as a single device or, in some aspects, components of system 1700 may be implemented across multiple physical devices. In some aspects, the components of system 1700 may be located at a well, remotely from the well, and / or distributed across locations at the well and remote locations.

[0159] The system 1700 includes injection profiling system 1710. The injection profiling system 1710 includes processor(s) 1712, which may be coupled to network interface(s) 1706. The network interface(s) 1706 may be configured to transmit and receive signals for the system 1700 wirelessly, via a wired connection, via mud pulse telemetry, or other suitable techniques. The network interface 1706 may be used for intercommunication between components within the system 1700 and / or for communication with other devices or systems over a network.

[0160] The processor(s) 1712 may be coupled to a computer-readable medium / memory 1740 via a bus or may communicate with the computer-readable medium / memory 1740 via a wired or wireless connection over a network. In certain aspects, the computer-readable medium / memory 1740 is configured to store instructions (e.g., computer-executable code 1742) that when executed by the one or more processors, cause the one or more processors to perform the method 200 described with respect to Figure 2, or any aspect related to it. Note that reference to a processor performing a function of system 1700 may include one or more processors performing that function of system 1700. Computer-readable medium / memory 1740 may further store one or more forward model(s) 1744, such as a full numerical forward model, a simplified numerical forward model, or a PINN.P+S Ref. No.: SLBR / 0384PC Page 33 of 48PATENT SLB Docket No. IS23.1678-WO-PCT

[0161] The processor(s) 1712 includes circuitry configured to implement (e.g., execute) the aspects described herein for real-time flow monitoring. The circuitry may include circuitry for generating a temperature transient 1714, circuitry for receiving DTS measurements 1716, circuitry for receiving surface measurements 1318, circuitry for receiving bottom hole assembly measurements 1720, circuitry for simulating thermal and fluid flow behavior 1722, circuitry for solving a supplementary inverse problem 1724, circuitry for estimating an inlet injection temperatures 1726, circuitry for solving a main inverse problem 1728, circuitry for estimating an injection profile 1730, and circuitry for controlling a well operation 1732. Processing with circuitry 1714-1732 may cause the system 1700 to perform the method 200 described with respect to Figure 2 or any aspect related to it.

[0162] The system 1700 may include one or more input output (I / O) devices 1702. The one or more I / O devices 1702 may include a user interface to accept inputs from a user. In some aspects, the user interface is a graphical user interface (GUI). In some aspects, the GUI accepts touch screen inputs from the user. In some aspects, the I / O devices 1702 include keyboards, displays, mouse devices, pen inputs, microphones, etc., that connect to the system 1700.

[0163] The system 1700 may include a display 1704. The display 1704 may be configured to display output of the automated injection profiling system 1700.

[0164] The system 1700 may include one or more sensors 1708. The one or more sensors 1708 may be configured to collect data for real-time flow monitoring, including real-time DTS temperature data, wellhead data, and bottomhole assembly data.Example Clauses

[0165] Implementation examples are described in the following numbered clauses:

[0166] Clause 1: A method for determining an injectivity profile of an injection well penetrating a subsurface formation, the method comprising: generating a temperature transient in the injection well; receiving distributed temperature sensing (DTS) measurements along a depth of the injection well over time; automatically simulating, using a model, transient thermal and fluid flow behavior of the wellbore and the subsurface formation; automatically solving a supplementary inverse problem based on aP+S Ref. No.: SLBR / 0384PC Page 34 of 48PATENT SLB Docket No. IS23.1678-WO-PCTcomparison of the simulated transient thermal behavior and the received DTS measurements; estimating an inlet injection temperature at a top, or above the top, of a perforated interval of the injection well based on the solving the inverse problem; automatically solving a main inverse problem to fine tune one or more parameters of the model by iteratively over multiple time instances: determining residuals between the received temperature measurements and the simulated thermal and fluid flow behavior; and adjusting one or more parameters of the model to minimize the residuals; and estimating, using the fine-tuned model and the determined inlet injection temperature, an injectivity profile of the injection well along the perforated interval.

[0167] Clause 2: The method of Clause 1, further comprising: receiving bottom hole measurements from a bottom hole assembly comprising one or more sensors configured to measure at least one of: bottom hole temperature or bottom hole pressure, wherein automatically solving the main inverse problem to fine tune the one or more parameters of the model comprises, iteratively over the multiple time instances, determining residuals between the received bottom hole measurements and the simulated thermal and fluid flow behavior.

[0168] Clause 3: The method of any combination of Clauses 1-2, further comprising: receiving well head measurements from at least one additional sensor at a surface of the wellbore configured to measure at least one of: well head pressure, well head temperature, or well head flow rate, wherein automatically solving the main inverse problem to fine tune the one or more parameters of the model comprises, iteratively over the multiple time instances, determining residuals between the received well head measurements and the simulated thermal and fluid flow behavior.

[0169] Clause 4: The method of any combination of Clauses 1-3, wherein the DTS cable comprises a DTS fiber optic cable deployed behind a casing or on a liner in the injection well.

[0170] Clause 5: The method of any combination of Clauses 1-4, further comprising: controlling injection of fluid into the injection well at a first flow rate during a first duration; and receiving, during the first duration, first temperature measurements from the DTS cable at a first sampling rate.P+S Ref. No.: SLBR / 0384PC Page 35 of 48PATENT SLB Docket No. IS23.1678-WO-PCT

[0171] Clause 6: The method of Clause 5, wherein the first sampling rate is between 5 minutes and 240 minutes.

[0172] Clause 7: The method of any combination of Clauses 5-6, further comprising: transmitting optical pulses into a distributed acoustic sensing (DAS) fiber optic cable deployed along at least a portion of the injection well; receiving backscattered optical signals; generating an acoustic profile based on the backscattered optical signals; automatically comparing the acoustic profile with one or more previous acoustic profiles; and generating an alarm when a difference between the acoustic profile and the one or more previous acoustic profiles exceeds one or more predefined thresholds.

[0173] Clause 8: The method of Clause 7, wherein generating the temperature transient in the injection well is performed at least one of: at a preconfigured periodicity or in response to the alarm.

[0174] Clause 9: The method of any combination of Clauses 5-8, wherein: generating the transient temperature comprises controlling injection of fluid into the injection well at a second flow rate during a second duration; and receiving the temperature measurements from the DTS cable associated with the temperature transient comprises receiving, during the second duration, second temperature measurements from the DTS cable at a second sampling rate.

[0175] Clause 10: The method of Clause 9, wherein the second sampling rate is a higher sampling rate than the first sampling rate.

[0176] Clause 11 : The method of Clause 10, wherein the second sampling rate is ten minutes or less.

[0177] Clause 12: The method of any combination of Clauses 9-11, wherein: the second flow rate is higher than the first flow rate; the second duration is at least six hours; and the method further comprises injecting fluid into the injection well at the first flow rate during a third duration.

[0178] Clause 13: The method of any combination of Clauses 9-12, wherein: the first flow rate comprises a shut-in of the injection well; and the second flow rate comprises a restart of injection after the shut-in.P+S Ref. No.: SLBR / 0384PC Page 36 of 48PATENT SLB Docket No. IS23.1678-WO-PCT

[0179] Clause 14: The method of any combination of Clauses 9-13, wherein: the second flow rate is lower than the first flow rate; the second duration is at least six hours; and the method further comprises injecting fluid into the injection well at the first flow rate during a third duration.

[0180] Clause 15: The method of any combination of Clauses 1-14, wherein the model is a transient multiphase thermal-hydrodynamic forward numerical model of the wellbore and the subsurface formation configured to: use the inlet injection temperature as a boundary condition for wellbore temperature simulation; and simulate multiphase fluid flow, transient heat transfer, and coupled wellbore-formation behavior including pressure distribution, temperature distribution, and flow rate distribution.

[0181] Clause 16: The method of Clause 15, wherein automatically solving the supplementary inverse problem comprises, for a wellbore calibration section above the perforation top: determining a residual R as a sum of differences between (i) formation temperature and a time instance n interpolated to an effective radial position of the DTS cable and (ii) a DTS temperature measurement for the time instance n for a plurality of spatial points along the wellbore; and determining the inlet injection temperature that minimizes the residual.

[0182] Clause 17: The method of any combination of Clauses 1-16, wherein the model is configured to for a wellbore calibration section of ten meters or less from the perforation top upward, solve a transient heat transfer equation and a radial conduction equation for an adjacent formation section to determine the inlet injection temperature.

[0183] Clause 18: The method of any combination of Clauses 1-17, wherein the model is a physics-informed neural network (PINN) trained on simulations generated by solving a transient heat transfer equation and a radial conduction equation for an adjacent formation section to determine the inlet injection temperature.

[0184] Clause 19: The method of Clause 18, wherein the PINN is trained using a loss function comprising: (i) a first component corresponding to a wellbore heat transfer equation; (ii) a second component corresponding to a radial formation heat conduction equation; (iii) a third component corresponding to a boundary condition at a wellbore wall; (iv) a fourth component corresponding to a far-field formation boundary condition;P+S Ref. No.: SLBR / 0384PC Page 37 of 48PATENT SLB Docket No. IS23.1678-WO-PCTand (v) a fifth component corresponding to a residual between the simulated thermal behavior and the received temperature measurements from the DTS cable.

[0185] Clause 20: The method of any combination of Clauses 1-19, further comprising controlling a well operation based on the injectivity profile.

[0186] Clause 21: An apparatus, comprising: a memory comprising executable instructions; and one or more processors configured to execute the executable instructions and cause the apparatus to perform a method in accordance with any one of Clauses 1-20.

[0187] Clause 22: An apparatus, comprising means for performing a method in accordance with any one of Clauses 1-20.

[0188] Clause 23: A non-transitory computer-readable medium comprising executable instructions that, when executed by one or more processors of an apparatus, cause the apparatus to perform a method in accordance with any one of Clauses 1-20.

[0189] Clause 24: A computer program product embodied on a computer-readable storage medium comprising code for performing a method in accordance with any one of Clauses 1-20.Additional Considerations

[0190] The preceding description is provided to enable any person skilled in the art to practice the various aspects described herein. The examples discussed herein are not limiting of the scope, applicability, or aspects set forth in the claims. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other aspects. For example, changes may be made in the function and arrangement of elements discussed without departing from the scope of the disclosure. Various examples may omit, substitute, or add various procedures or components as appropriate. For instance, the methods described may be performed in an order different from that described, and various actions may be added, omitted, or combined. Also, features described with respect to some examples may be combined in some other examples. For example, an apparatus may be implemented or a method may be practiced using any number of the aspects set forth herein. In addition, the scope of the disclosure is intended to cover such an apparatus or method that isP+S Ref. No.: SLBR / 0384PC Page 38 of 48PATENT SLB Docket No. IS23.1678-WO-PCTpracticed using other structure, functionality, or structure and functionality in addition to, or other than, the various aspects of the disclosure set forth herein. It should be understood that any aspect of the disclosure disclosed herein may be embodied by one or more elements of a claim.

[0191] The various illustrative logical blocks, modules and circuits described in connection with the present disclosure may be implemented or performed with a general purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic device (PLD), discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general-purpose processor may be a microprocessor, but in the alternative, the processor may be any commercially available processor, controller, microcontroller, or state machine. A processor may also be implemented as a combination of computing devices, e.g., a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, a system on a chip (SoC), or any other such configuration.

[0192] As used herein, a phrase referring to “at least one of’ a list of items refers to any combination of those items, including single members. As an example, “at least one of: a, b, or c” is intended to cover a, b, c, a-b, a-c, b-c, and a-b-c, as well as any combination with multiples of the same element (e.g., a-a, a-a-a, a-a-b, a-a-c, a-b-b, a-c-c, b-b, b-b-b, b-b-c, c-c, and c-c-c or any other ordering of a, b, and c).

[0193] As used herein, “a processor,” “at least one processor,” or “one or more processors” generally refer to a single processor configured to perform one or multiple operations or multiple processors configured to collectively perform one or more operations. In the case of multiple processors, performance of the one or more operations could be divided amongst different processors, though one processor may perform multiple operations, and multiple processors could collectively perform a single operation. Similarly, “a memory,” “at least one memory,” or “one or more memories” generally refer to a single memory configured to store data and / or instructions or multiple memories configured to collectively store data and / or instructions.P+S Ref. No.: SLBR / 0384PC Page 39 of 48PATENT SLB Docket No. IS23.1678-WO-PCT

[0194] As used herein, the term “determining” encompasses a wide variety of actions. For example, “determining” may include calculating, computing, processing, deriving, investigating, looking up (e.g., looking up in a table, a database or another data structure), ascertaining and the like. Also, “determining” may include receiving (e.g., receiving information), accessing (e.g., accessing data in a memory) and the like. Also, “determining” may include resolving, selecting, choosing, establishing and the like.

[0195] It will also be understood that, although the terms first, second, etc., may be used herein to describe various elements, these elements should not be limited by these terms. These terms are used to distinguish one element from another. For example, a first object or step could be termed a second object or step, and, similarly, a second object or step could be termed a first object or step, without departing from the scope of the invention. The first object or step, and the second object or step, are both objects or steps, respectively, but they are not to be considered the same object or step.

[0196] As used herein, the term “if’ may be construed to mean “when” or “upon” or “in response to determining” or “in response to detecting,” depending on the context.

[0197] Those with skill in the art will appreciate that while some terms in this disclosure may refer to absolutes, e.g., all of the components of a wavefield, all source receiver traces, each of a plurality of objects, etc., the methods and techniques disclosed herein may also be performed on fewer than all of a given thing, e.g., performed on one or more components and / or performed on one or more source receiver traces. Accordingly, in instances in the disclosure where an absolute is used, the disclosure may also be interpreted to be referring to a subset.

[0198] The methods disclosed herein comprise one or more actions for achieving the methods. The method actions may be interchanged with one another without departing from the scope of the claims. In other words, unless a specific order of actions is specified, the order and / or use of specific actions may be modified without departing from the scope of the claims. Further, the various operations of methods described above may be performed by any suitable means capable of performing the corresponding functions. The means may include various hardware and / or software component(s) and / or module(s), including, but not limited to a circuit, an ASIC, or processor.P+S Ref. No.: SLBR / 0384PC Page 40 of 48PATENT SLB Docket No. IS23.1678-WO-PCT

[0199] The following claims are not intended to be limited to the aspects shown herein, but are to be accorded the full scope consistent with the language of the claims. Within a claim, reference to an element in the singular is not intended to mean “one and only one” unless specifically so stated, but rather “one or more.” Unless specifically stated otherwise, the term “some” refers to one or more. No claim element is to be construed under the provisions of 35 U.S.C. §112(f) unless the element is expressly recited using the phrase “means for”. All structural and functional equivalents to the elements of the various aspects described throughout this disclosure that are known or later come to be known to those of ordinary skill in the art are expressly incorporated herein by reference and are intended to be encompassed by the claims. Moreover, nothing disclosed herein is intended to be dedicated to the public regardless of whether such disclosure is explicitly recited in the claims.P+S Ref. No.: SLBR / 0384PC Page 41 of 48

Claims

PATENT SLB Docket No. IS23.1678-WO-PCTCLAIMSWhat is claimed is:

1. A system for determining an injectivity profile of an injection well penetrating a subsurface formation, the system comprising:at least one distributed temperature sensing (DTS) cable deployed along at least a portion of the injection well and configured to provide temperature measurements along a depth of the injection well over time;memory storing instructions; andat least one processor configured to execute the instructions to:generate a temperature transient in the injection well;receive temperature measurements from the DTS cable; automatically simulate, using a model, transient thermal and fluid flow behavior of the well and the subsurface formation;automatically solve a supplementary inverse problem based on a comparison of the simulated transient thermal behavior and the received temperature measurements from the DTS cable;estimate an inlet injection temperature at a top, or above the top, of a perforated interval of the injection well based on the solving the inverse problem and the received temperature measurements from the DTS cable;automatically solve a main inverse problem to fine tune one or more parameters of the model by iteratively over multiple time instances:determining residuals between the received temperature measurements and the simulated thermal and fluid flow behavior; and adjusting one or more parameters of the model to minimize the residuals; andestimate, using the fine-tuned model and the determined inlet injection temperature, an injectivity profile of the injection well along the perforated interval.

2. The system of claim 1, further comprising:a bottom hole assembly comprising one or more sensors configured to measure at least one of: bottom hole temperature or bottom hole pressure,P+S Ref. No.: SLBR / 0384PC Page 42 of 48PATENT SLB Docket No. IS23.1678-WO-PCTwherein the at least one processor is configured to execute the instructions further to receive bottom hole measurements from the bottom hole assembly; andwherein to automatically solve the main inverse problem to fine tune the one or more parameters of the model, the at least one processor is configured to execute the instructions further to, iteratively over the multiple time instances, determine residuals between the received bottom hole measurements and the simulated thermal and fluid flow behavior.

3. The system of claim 1, further comprising:at least one additional sensor at a surface of the well configured to measure at least one of well head pressure, well head temperature, or well head flow rate,wherein the at least one processor is configured to execute the instructions further to receive well head measurements from the at least one additional sensor at the surface; andwherein to automatically solve the main inverse problem to fine tune the one or more parameters of the model, the at least one processor is configured to execute the instructions further to, iteratively over the multiple time instances, determine residuals between the received well head measurements and the simulated thermal and fluid flow behavior.

4. The system of claim 1, wherein the at least one processor is configured to:control injection of fluid into the injection well at a first flow rate during a first duration; andreceive, during the first duration, first temperature measurements from the DTS cable at a first sampling rate.

5. The system of claim 4, wherein the first sampling rate is between 5 minutes and 240 minutes.

6. The system of claim 4, further comprising:a distributed acoustic sensing (DAS) fiber optic cable deployed along at least a portion of the injection well; andan optical interrogator configured to:transmit optical pulses into the DAS fiber optic cable; andP+S Ref. No.: SLBR / 0384PC Page 43 of 48PATENT SLB Docket No. IS23.1678-WO-PCTreceive backscattered optical signals,wherein the at least one processor is configured to execute the instructions further to:generate an acoustic profile based on the backscattered optical signals; automatically compare the acoustic profile with one or more previous acoustic profiles; andgenerate an alarm when a difference between the acoustic profile and the one or more previous acoustic profiles exceeds one or more predefined thresholds.

7. The system of claim 6, wherein the at least one processor is configured to generate the temperature transient in the injection well at least one of at a preconfigured periodicity or in response to the alarm.

8. The system of claim 4, wherein:to generate the transient temperature, the at least one processor is configured to control injection of fluid into the injection well at a second flow rate during a second duration; andto receive the temperature measurements from the DTS cable associated with the temperature transient, the at least one processor is configured to receive, during the second duration, second temperature measurements from the DTS cable at a second sampling rate.

9. The system of claim 8, wherein the second sampling rate is a higher sampling rate than the first sampling rate.

10. The system of claim 8, wherein:the second flow rate is higher than the first flow rate;the second duration is at least six hours; andthe at least one processor is further configured to inject fluid into the injection well at the first flow rate during a third duration.

11. The system of claim 8, wherein:the first flow rate comprises a shut-in of the injection well; andthe second flow rate comprises a restart of injection after the shut-in.P+S Ref. No.: SLBR / 0384PC Page 44 of 48PATENT SLB Docket No. IS23.1678-WO-PCT12. The system of claim 8, wherein:the second flow rate is lower than the first flow rate;the second duration is at least six hours; andthe at least one processor is further configured to inject fluid into the injection well at the first flow rate during a third duration.

13. The system of claim 1, wherein the model is a transient multiphase thermalhydrodynamic forward numerical model of the well and the subsurface formation configured to:use the inlet injection temperature as a boundary condition for wellbore temperature simulation; andsimulate multiphase fluid flow, transient heat transfer, and coupled wellboreformation behavior including pressure distribution, temperature distribution, and flow rate distribution.

14. The system of claim 13, wherein to automatically solve the supplementary inverse problem, the at least one processor is configured to for a wellbore calibration section above the perforation top:determine a residual R as a sum of differences between (i) formation temperature and a time instance n interpolated to an effective radial position of the DTS cable and (ii) a DTS temperature measurement for the time instance n for a plurality of spatial points along the wellbore; anddetermine the inlet injection temperature that minimizes the residual.

15. The system of claim 1, wherein the model is configured to for a wellbore calibration section of ten meters or less from the perforation top upward, solve a transient heat transfer equation and a radial conduction equation for an adjacent formation section to determine the inlet injection temperature.

16. The system of claim 1, wherein the model is a physics-informed neural network (PINN) trained on simulations generated by solving a transient heat transfer equation and a radial conduction equation for an adjacent formation section to determine the inlet injection temperature.P+S Ref. No.: SLBR / 0384PC Page 45 of 48PATENT SLB Docket No. IS23.1678-WO-PCT17. The system of claim 16, wherein the PINN is trained using a loss function comprising:(i) a first component corresponding to a wellbore heat transfer equation;(ii) a second component corresponding to a radial formation heat conduction equation;(iii) a third component corresponding to a boundary condition at a wellbore wall; (iv) a fourth component corresponding to a far-field formation boundary condition; and(v) a fifth component corresponding to a residual between the simulated thermal behavior and the received temperature measurements from the DTS cable.

18. The system of claim 1, wherein the at least one processor is further configured to control a well operation based on the injectivity profile.

19. A method for determining an injectivity profile of an injection well penetrating a subsurface formation, the method comprising:generating a temperature transient in the injection well;receiving distributed temperature sensing (DTS) measurements along a depth of the injection well over time;automatically simulating, using a model, transient thermal and fluid flow behavior of the well and the subsurface formation;automatically solving a supplementary inverse problem based on a comparison of the simulated transient thermal behavior and the received DTS measurements;estimating an inlet injection temperature at a top, or above the top, of a perforated interval of the injection well based on the solving the inverse problem;automatically solving a main inverse problem to fine tune one or more parameters of the model by iteratively over multiple time instances:determining residuals between the received temperature measurements and the simulated thermal and fluid flow behavior; andadjusting one or more parameters of the model to minimize the residuals; andestimating, using the fine-tuned model and the determined inlet injection temperature, an injectivity profile of the injection well along the perforated interval.P+S Ref. No.: SLBR / 0384PC Page 46 of 48PATENT SLB Docket No. IS23.1678-WO-PCT20. A non-transitory computer-readable medium storing instructions that, when executed by at least one processor, cause the at least one processor to perform operations for determining an injectivity profile of an injection well penetrating a subsurface formation, the operations comprising:generating a temperature transient in the injection well;receiving temperature measurements from at least one distributed temperature sensing (DTS) cable deployed along at least a portion of the injection well, the temperature measurements being along a depth of the injection well over time;automatically simulating, using a model, transient thermal and fluid flow behavior of the well and the subsurface formation;automatically solving a supplementary inverse problem based on a comparison of the simulated transient thermal behavior and the received temperature measurements from the DTS cable;estimating an inlet injection temperature at a top, or above the top, of a perforated interval of the injection well based on the solving the inverse problem and the temperature measurements from the DTS cable;automatically solving a main inverse problem to fine tune one or more parameters of the model by iteratively over multiple time instances:determining residuals between the received temperature measurements and the simulated thermal and fluid flow behavior; andadjusting one or more parameters of the model to minimize the residuals; andestimating, using the fine-tuned model and the determined inlet injection temperature, an injectivity profile of the injection well along the perforated interval.P+S Ref. No.: SLBR / 0384PC Page 47 of 48

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