ESTIMATING THE REMAINING LIFETIME OF CO2 REMOVAL MEMBRANES USING PERMEANCE DATA

Description

1 / 18 ESTIMATING THE REMAINING LIFETIME OF CO2 REMOVAL MEMBRANES USING PERMEANCE DATA FIELD OF THE INVENTION

[01] The present invention falls within the field of petroleum and gas engineering. More specifically, the present invention relates to a method for estimating the remaining service life (RSL) of a gas treatment membrane, particularly for CO2 removal, based on the membrane's reference permeance. FUNDAMENTALS OF THE INVENTION

[02] The method of separating CO2 from natural gas using polymeric membranes is widely employed in production units in the pre-salt fields. The high gas flow associated with CO2 concentrations that can reach up to 60% makes this application economically advantageous. However, inefficient monitoring or lack of standardization of this equipment often results in accelerated membrane degradation, reducing its expected lifespan. To provide efficient predictive monitoring of membrane systems, it is essential to robustly and consistently estimate indicators such as the remaining useful life (RUL) of this equipment. The lack of predictability resulting from the absence of such indicators leads to high costs due to reactive maintenance, low separation efficiency, and production losses.Currently, there are no methods available on the market or in academia capable of predictively monitoring the CO2 removal system, providing the user with an indication of how long the membranes can still operate until they reach a certain minimum quality criterion.

[03] Due to the absence of methods for predictive monitoring of CO2 removal membranes, the monitoring of these devices is generally based only on measurable data, such as the CO2 content in the treated gas. However, it is important to highlight that these measurements are influenced by other process variables, which can obscure information about the actual condition of the membranes. Furthermore, these uncertainties prevent a reliable estimate of the remaining useful life (RUL) of these devices. As a result, it is rare for any indicator of this type to be calculated for this system. STATE OF THE ART Petition 870250015444, dated 25 / 02 / 2025, page 39 / 67 2 / 18

[04] Document US11992803B2, entitled “Method of determining remaining useful lifetime of membrane for separation process” reveals that membranes used in membrane separation technologies change over time due to changes in the membrane’s physical characteristics. Predicting the remaining useful lifetime of a membrane is performed by fitting a membrane evolution model to the real-time performance characteristics recorded for the membrane and comparing the membrane’s subsequent performance characteristics to the evolution model. Updating an evolution model during membrane operation improves estimates of the membrane’s remaining useful lifetime and allows for accurate estimates of the membrane’s estimated end-of-life.A method is proposed for estimating the remaining service life (RSL) of a gas separation membrane unit to achieve membrane replacement in a prognostic or predictive manner, rather than a responsive manner based on performance criteria exceeding a predetermined replacement criterion. The disclosed method is applicable to service life estimates for many different types of membranes, not just membranes used in gas separation. A feature of a membrane separation system amenable to using the method disclosed here is that real-time performance data of membrane operation can be recorded during membrane operation for the feed flow, permeate flow, and non-permeate flow associated with a membrane separation system. The determination of the remaining service life is performed using a physical model, trained on data acquired through in situ non-destructive monitoring of membrane operations. SUMMARY OF THE INVENTION

[05] The proposed invention presents a methodology for estimating the remaining useful life (RUL) in CO2 removal systems using polymeric membranes, based on indicators consistent with the physics of the membrane system. The invention comprises a combination of: (i) measured data from the membrane system, obtained through the PI historian, which collects, processes, and stores process plant data in real time; (ii) design data for the development of the temperature reference curve; and (iii) membrane performance indicators (KPIs - Key Performance Indicators) generated by a specially developed library and optionally integrated into a platform. Petition 870250015444, dated 25 / 02 / 2025, page 40 / 67 3 / 18 web specially developed. The proposed procedure is divided into two stages: one offline and one online. In the offline stage, the design data is used to obtain a reference value for the membrane KPI. This reference value allows comparison of the operational KPI values ​​with those expected in the design phase. In the online stage, a comparison is made between the design reference value and the KPI calculated under the current operating conditions of the membranes. For this comparison to be accurate, it is necessary to eliminate the effects of process conditions on the KPI. The invention proposes methods for normalizing the KPI in terms of temperature and flow, as well as suggesting a coherent way to obtain an average KPI for the membrane system. Correcting the KPI estimated by the library for the same base temperature is crucial, as the KPI varies with temperature, being affected by operational adjustments in the gas treatment plant.Without this correction, unadjusted KPIs could lead to erroneous conclusions about their behavior over time, attributing changes to temperature variations in the gas treatment process, rather than to the natural degradation of the polymeric membranes. Flow normalization aims to make the KPI independent of variations in gas flow rate and changes in the number of aligned membranes (variations in permeation area). With these adjustments, monitoring the average KPI of the membrane system over time allows extrapolation of the dynamic degradation behavior of the membranes, enabling the prediction of the remaining service life. To ensure the robustness of the methodology, the invention uses a robust linear regression on the KPI data. BRIEF DESCRIPTION OF THE DRAWINGS

[06] The present invention will now be described with reference to typical embodiments thereof and also with reference to the accompanying drawings, in which: Figure 1 is a flowchart representing the method according to the present invention; Figure 2 is a flowchart representing the monitoring steps for inferring permeance according to the present invention; Figure 3 is a flowchart representing the dew point calculation algorithm according to the present invention; Petition 870250015444, dated 25 / 02 / 2025, page 41 / 67 4 / 18 Figure 4 is a schematic representation of the gas flows related to a CO2 removal membrane according to the present invention; Figure 5 is a representative graph of the permeance trends calculated against temperature for different CO2 contents in the waste gas according to the present invention; Figure 6 is a schematic representation of the proposed methodology for simulating the effect of membrane capacity loss according to the present invention; Figure 7 is a representative graph of the operational permeance correction for reference temperature according to the present invention; Figure 8 is a comparative graph of different linear regression techniques; Figure 9 is a representative graph of estimated CO2 permeances according to the present invention; Figure 10 is a representative graph of CO2 permeances corrected for alignment with 3% CO2 according to the present invention; Figure 11 is a representative graph of CO2 permeances corrected for alignment with 6% CO2 according to the present invention; Figure 12 is a representative graph of CO2 permeances corrected for alignment with 10% CO2 according to the present invention; Figure 13 is a representative graph of the VUR estimate according to the present invention; Figure 14 is a screenshot of the methodology according to the present invention implemented in real time on the SmartMonitor platform. DETAILED DESCRIPTION OF THE INVENTION

[07] Specific embodiments of this disclosure are described below. In an effort to provide a concise description of these embodiments, all features of an actual implementation may not be described in the descriptive report. It should be appreciated that in the development of any actual implementation, as in any engineering or design project, numerous specific implementation decisions must be made to achieve the specific objectives of the developers, such as compliance with system and business-related constraints, which may vary from one implementation to another. Furthermore Petition 870250015444, dated 25 / 02 / 2025, page 42 / 67 5 / 18 of this, it should be appreciated that such a development effort may be complex and time-consuming, but it would nevertheless be a routine design and manufacturing undertaking for those of ordinary ability, having the benefit of this disclosure.

[08] Figure 1 schematically presents the methodology developed for estimating the VUR of CO2 removal membranes, from data acquisition, recorded in the PI system (PI System™), to model adjustment for prediction. The concept proposed by the flowchart in Figure 1 foresees the existence of a reference KPI and a current KPI, calculated under operating conditions. In Figure 1, the dashed line shows the calculation flow performed offline, while the solid line represents the calculations performed in real time, using the information calculated by the offline stage.

[09] Over time, the difference between the reference KPI and the current KPI reflects the degradation and aging of the membranes. This disclosure adopts permeance as the standard KPI and its reference as being derived from the design data sheets. All permeances shown are presented in MNm3 / (dia.m2.bar).

[010] The methodology will be explained below based on practical cases observed in a real oil extraction and production plant, which served as validation for the proposed methodology. REFERENCE PERMEANCE VALUE CURVE

[011] The calculation of reference permeance values ​​was based on the design cases presented in the polymer membrane manufacturer's datasheet. For the plant in question, the documentation presents eight independent cases, where conditions such as CO2 content in the feed, flow rates, and temperatures varied. All scenarios produced, in the second stage of membrane separation, waste streams with a CO2 content of 3%, varying the number of trains aligned for treatment. The original design dataset, referred to here as "PRJ," was presented to a library specifically developed for this methodology in order to calculate the permeances of each of the eight cases. Throughout this text, a library is defined as a set of instructions organized in a structured and generic way, or, in other words, as ready-made code packages that can be exported for use in Petition 870250015444, dated 25 / 02 / 2025, page 43 / 67 6 / 18 different projects. The results obtained allowed us to evaluate the effect of feed temperature on permeances. Calculation of the permeances of each membrane

[012] Real-time monitoring of a membrane separation unit on an offshore industrial platform was based on two inferred pieces of information: selectivity and dew point temperature of the waste stream, i.e., the gas stream treated by the membrane. The first piece of information is linked to the estimated parameters: the permeances. Once the permeance estimation procedure is completed, the selectivity calculation is performed and monitored. Selectivity is calculated as the ratio between two permeances of key components, which in this case are CO2 and CH4 (methane). Thus, selectivity provides overall information about the process: whether the membrane is operating within the appropriate conditions or whether it is facing a problem that is affecting the gas separation performance.

[013] The second piece of information is associated with the energy balance and thermodynamic equations. The dew point temperature is calculated sequentially after the waste flow data are optimized in the parameter estimation stage. This information is fundamental for the operation and lifespan of the membranes, as condensation of water and impurities on the membranes will damage them. Therefore, a threshold safety margin (AT = 10 °C) is monitored between the current temperature of the waste stream and its dew point temperature. Monitoring of the membrane separation unit on an industrial offshore platform is carried out at the waste stream outlet because, at this point, the curves between the current temperature and its dew point converge, forming the most critical point of the process.This effect occurs due to two processes: first, the cooling of the current due to the Joule-Thomson effect; second, the increase in dew point temperature due to the concentration of hydrocarbons (mainly heavy ones) along the membrane. Data reconciliation, parameter estimation, and monitoring.

[014] To provide the necessary monitoring information, the data preprocessing steps, Data Reconciliation (DR), Global Energy Balance (GEB) and Parameter Estimation (PE) Petition 870250015444, dated 25 / 02 / 2025, page 44 / 67 7 / 18 The estimation steps were implemented sequentially and before the monitoring stage, as shown in Figure 2. In the graph of this figure, the sampling frequency is 5 minutes, and the CO2 permeance is given in MSm3 / (day.m2.bar). The measured variables, unmeasured process variables, and KPIs mentioned in Figure 2 are as follows:

[015] - Measured variables: • Flow rates: Total Feed (F); Total Retentate (R); Train Retentates A, B and C (RA, RB and RC) [kNm3 / h]; • Molar composition: Ci (methane), C2 (ethane), C3 (propane), iC4 (i-butane), 1C5 (ipentane), nC4 (n-butane), nC5 (n-pentane), CO2 (carbon dioxide), N2 (nitrogen), H2S (hydrogen sulfide) and Ce+ (pseudocomponent of fractions heavier than pentane) in the 3 streams [%]; • Pressures: Feed (Pf), Retentate (Pr) and Permeate (Pp) [kPa]; and • Temperatures: Feed (Tf) and Retentate (Tr) [°C]. [ 016] - Unmeasured variables: • Flow rate: Total permeate (P) [kNm3 / h]; and • Temperature: Permeate temperature (Tp) [°C].

[017] - KPIs: • Selectivity; • Dew point temperature; and • Hydrocarbon (HC) loss.

[018] To minimize instrumentation errors, identify biases, and estimate unmeasured process variables, the DR step was essential. According to de Menezes et al. (de Menezes, DQF; de Sá, MCC; Fontoura, TB; Anzai, TK; Diehl, FC; Thompson, PH; Pinto, JC Modeling of spiral wound membranes for gas separations—Part II: Data reconciliation for online monitoring. Processes 2020, 8, 1035), the data acquisition and pre-processing steps precede the DR and GEB steps. After pre-processing the raw data, the DR and GEB steps estimate the permeate flow rate and temperature, providing more information for the PE step. Parameter estimation Petition 870250015444, dated 25 / 02 / 2025, page 45 / 67 8 / 18

[019] The first procedure performed before the PE was the selection of the number of parameters of the phenomenological model to be estimated. In fact, the most important parameters of dense membrane models are the permeances of each component (in the case studied, twelve components). Therefore, some hypotheses of possible parameters were raised according to the process configuration. To reduce the number of parameters and avoid overparameterization of the model, it was assumed that the permeances (different for components) are the same for all membrane modules.

[020] The second procedure performed was the reparameterization of the 11 permeance parameters (Si, i = 1 ... nc). This procedure was necessary due to numerical model and convergence problems encountered during PE. Thus, a normalization constant for the permeances was implemented in the model (Smax = 3x10-7 [άίαχ^7χζαΓ], maximum limit found during the numerical model problems).

[021] The last procedure involved generating data to simulate the linear loss of hydrocarbons (HC) over time in a real membrane separation unit on an industrial offshore platform. The datasets represented various degrees of HC loss, ranging from low (18%) to high (23%). The HC simulations were conducted based on the assumption that the permeability of hydrocarbons, represented as SCi, in the hydrocarbon mixture decreases with increasing chain length and molecular weight: SC1 > SC2 > SC3 > ... > SC8. This implies that the permeation behavior of methane (Sci) is intrinsically linked to that of other hydrocarbons, with shorter chain molecules exhibiting higher permeability coefficients. For these simulations, it was assumed that any increase in Sci leads to a proportional linear increase in the permeability of the other hydrocarbons (Sci, i = 2 ...8), while simultaneously satisfying the overall mass balance of the system. This linear relationship ensures that the overall dynamics of the system remain consistent and that the principles of mass conservation are maintained throughout the permeation process.

[022] Next, the PE procedure was applied to estimate the permeances and verify whether the parameter number selection and reparameterization procedures solved the convergence and numerical stability problem. The optimization method Petition 870250015444, dated 25 / 02 / 2025, pp. 46 / 67 9 / 18 The Broyden-Fletcher-Goldfarb-Shanno (BFGS) procedure, as is well known in the technique, was used in the minimization function of the Scipy optimization library.

[023] The determination of the dew point temperature follows the iterative algorithm introduced by O'Connell and Haile (O'Connell, J.; Haile, J. Thermodynamics: Fundamentals for Applications; Cambridge University Press: Cambridge, UK, 2005), as illustrated in Figure 3, which describes an iterative algorithm for calculating the dew point temperature, where: P: System pressure; yi: Molar fraction of component i in the vapor phase; T: System temperature; xi: Molar fraction of component i in the liquid phase; Psat: Saturation pressure of component i at the system temperature; EoS: Equation of state used to calculate the thermodynamic properties of the system; Z: Compressibility factor, calculated by EoS; ZL: Liquid phase compressibility factor; ZV: Vapor phase compressibility factor; φ: Fugacity coefficient of component i; φL: Fugacity coefficient of component i in the liquid phase; φV: Fugacity coefficient of component i in the vapor phase; Ki: Equilibrium constant of component i (Ki = φL / φV); x'i: New molar fraction of component i in the liquid phase, calculated based on the equilibrium constant; S: Sum of mole fractions in the liquid phase (S = Σχϊ); S': Sum of the new molar fractions in the liquid phase (S' = Σχ'ϊ); ε: Tolerance for algorithm convergence; and ξ: Tolerance for convergence of the sum of mole fractions (S').

[024] The 2-D model used allows the calculation of the dew point temperature along the tube and the surface of the membrane layer. This capability facilitates the Petition 870250015444, dated 25 / 02 / 2025, pp. 47 / 67 10 / 18 identification of specific locations where membrane plasticization may possibly occur, according to Fontoura et al (Fontoura, TB; de Sá, MCC; de Menezes, DQF; Oechsler, BF; Melo, A.; de O. Campos, LF; Anzai, TK; Diehl, FC; Thompson, PH; Pinto, JC Modeling of spiral wound membranes for gas separations. Part III: A nonisothermal 2D permeation model. Chem. Eng. Res. Des. 2022, 177, 376-393). Modeling

[025] Figure 4 shows a schematic representation of the elementary volume of the spiral wound membrane layer used for the development of the proposed model, comprising the permeate and retentate (residue) sections. The mass balance and energy balance used were previously described by Dias et al. (Dias, ACS; De Sá, MCC; Fontoura, TB; Menezes, DQ; Anzai, TK; Diehl, FC; Thompson, PH; Pinto, JC Modeling of spiral wound membranes for gas separations. Part I: An iterative 2D permeation model. J. Membr. Sci. 2020, 612, 118278) and Fontoura et al., respectively, according to which the residue flow occurs only along the x-direction, while the permeate flow occurs along the y-direction. Furthermore, the following considerations and assumptions are applied in the membrane model: 1. The permeation mechanism can be described by the solution-diffusion model; 2. Competitive diffusive behavior was not considered; 3. The process operates under steady-state conditions; 4. Very rapid permeation through the membrane barrier and negligible accumulation of gases in the membrane; 5. The membrane has uniform thickness and properties; 6. The pressure drops of the feed gas and permeate flows along the membrane surface are negligible (as observed in real industrial settings); 7. The thermodynamic behavior of the gas can be described by the Virial Equation (Scholz, M.; Harlacher, T.; Melin, T.; Wessling, M. Modeling Gas Permeation by Linking Nonideal Effects. Ind. Eng. Chem. Res. 2013, 52, 1079-1088); 8. Uniform composition and temperature conditions in the feed stream; 9. The permeate flow is subjected to temperature changes due to the Joule-Thomson effect; Petition 870250015444, dated 25 / 02 / 2025, pp. 48 / 67 11 / 18 10. Heat loss to the environment is negligible. MEMBRANE VUR ESTIMATE

[026] Figure 5 shows the permeance behavior estimated by the library applied to the membrane manufacturer's data, which showed a linear increase with the feed temperature in the evaluated range.

[027] As can also be seen from Figure 5, two other gas framing cases were evaluated, with CO2 contents of 6% and 10%, from the perspective that the 3% CO2 framing assumption, imposed by the original design data, might be too restrictive from a practical point of view. To generate new data with different separation efficiencies, the manufacturer's original scenarios were systematically "corrupted": as illustrated in Figure 6, two "by-pass" streams were created to emulate the capacity loss of the membranes. Thus, under the hypothesis that the two stages (pre-membrane and membrane) lose capacity similarly, it is possible to adjust the feed stream ratio (R) in the "by-pass" in order to obtain the desired yCO2 value in the waste stream.This methodology allows for the rapid calculation of different CO2 contents in the treated gas, maintaining consistency with the original scenarios and respecting mass balances. Finally, it should be noted that, although the calculation can be performed for any CO2 content, the choice of values ​​of 6% and 10% was due to restrictions on the exported gas network foreseen for the aforementioned real oil extraction and production plant. Other content values ​​can be freely chosen according to specific applications without departing from the scope of the present invention. Temperature correction

[028] Obtaining a representative curve of permeance behavior at different feed temperatures (Figure 5) is convenient because it allows: i) from the definition of a standard temperature, fixing a single reference value for permeance at that temperature, ii) from the obtained Permeance x Temperature curve, correcting the permeance inferences generated by the library for the defined standard temperature and, finally, iii) after this correction, comparing the permeances estimated by the library over time for different temperature conditions. Figure 7 Petition 870250015444, dated 25 / 02 / 2025, page 49 / 67 Figure 12 / 18 shows how, from the obtained permeance versus temperature curve, the correction is performed on the operational permeance calculated by the library. In general, it is assumed that the KPI responds to temperature in the same way as the results obtained in the datasheets, that is, it presents the same slope as the line estimated by the datasheet. With this, it is possible to bring both permeances (operational and reference) to the same base temperature. The temperature considered was 45°C; however, the present invention is not limited in this way. Specific applications may select any other base temperature.

[029] Correcting the permeance estimated by the library for the same base temperature is important because, as permeance is a function of temperature, it changes according to the operational adjustments made in the gas treatment plant. Thus, if this correction were not performed, the uncorrected permeances could lead to erroneous inferences about their own behavior over time, which could be linked to temperature changes in the gas treatment process and not to the natural degradation of the polymeric membranes. Normalization of permeance by flow

[030] Following the steps of the methodology presented in Figure 1, after correcting the permeance for temperature, this permeance is normalized by the gas flow rate at that stage. The normalized permeance Pfa of a component j at stage i can be calculated from equation 1 below: PT Píí = ——(1)l'jFluxoij' '

[031] The gas flow rate of component j in stage i is calculated by equation 2: Fluxij = ^^(2) where the permeation area of ​​membrane stage i (At) is calculated by equation 3: A = Σ£=1^Ά'ΐ(3) where, in the equations above: P[j is the temperature-corrected permeance T of component j in stage i; P^j is the permeance normalized by the flux of component j in stage i; Flux is the gas flow of component j in stage i; Qt is the volumetric flow rate of gas, under normal conditions, in stage i; Petition 870250015444, dated 25 / 02 / 2025, pp. 50 / 67 13 / 18 yij is the content of component j in the gas at stage i; At is the permeation area of ​​the stage i membranes; FVk,t is the inlet valve status of the k-train of the i-stage membranes; Afc,t is the area corresponding to the elements of train k of stage i of membranes.

[032] In the specific case of monitoring the lifespan of CO2 membranes, the component of interest is CO2 itself. Thus, in the equations above, the parameters used correspond to those of the CO2 component. This normalization aims to make the permeance term independent of variations in gas flow rate and changes in the number of aligned membranes (variations in permeation area). Thus, normalized permeance facilitates and allows for more robust monitoring of membrane performance degradation over time, as it is less sensitive to operational variations in the process. Obtaining an average permeance of the system

[033] As described earlier, a CO2 removal system will be subject to different operating conditions (flow rate, temperature, gas composition, pressure and permeation area). Due to these different operating conditions, the permeance of each separation stage varies unevenly over time.

[034] In this way, given that the permeances of the stages are distinct from each other, having two permeance values, despite providing more information about the state of the plant, makes the interpretation of the useful life of the CO2 removal system more complex, since one membrane stage may be more degraded than another. Thus, for each stage a normalized permeance is estimated, as detailed in the previous steps, and, from these two corrected permeances, it is possible to calculate the average permeance of the entire CO2 removal system. The calculation of this average value is of interest because it summarizes, in a single variable, the degradation of both membrane stages, facilitating the interpretation of the useful life of the entire system.

[035] Thus, it is possible to calculate the average permeance Τ'- of the system for the j-component of the gas from equations 4 and 5 presented below: p Xi=1APijAiPíjjH=1APi,iAi APi,j Çpfeed iyfeed i,j) ÇPperm iyp (4) (5) erm i,j Petition 870250015444, dated 25 / 02 / 2025, pp. 51 / 67 14 / 18 where: π7 is the average permeance of the system for component j; Píj is the permeance normalized by the flux of component j in stage i; Ai is the permeation area of ​​the stage i membranes; Δρί is the partial pressure difference between the feed and permeate of component j in stage i. P / eed is the feed pressure in stage i; yfeedíj is the gas content in the feed of component j in stage i; Pperm í is the permeate pressure at stage i; yperm í,j is the permeate content of component j at stage i.

[036] Again, for the monitoring proposed here, the parameters corresponded to CO2 in the gas. VUR estimate

[037] By carrying out the steps that were previously established in monitoring the permeances of the stages and the entire system over time, it is possible to obtain temporal data of these variables. With these results, it is possible to carry out analyses, evaluations and inferences about how the average permeance behaves over time.

[038] One possible and interesting assessment is to perform a regression based on the permeance estimates obtained using the methodology presented here. With the curve established by the regression, it is possible to extrapolate the dynamic degradation behavior of the membranes, in order to allow a prediction of their service life. One type of regression that proves suitable for use with these permeance data is Robust Regression.

[039] Robustness, from a statistical point of view, refers to how insensitive a given technique is to the presence of “outliers”. The median, for example, is considered a more robust estimator than the mean for the same data set. Similarly, several techniques considered robust are proposed for the linear regression problem. Among them, the repeated median method, proposed by Siegel, is particularly interesting for its robustness, speed, and insensitivity to spurious values ​​up to 50%. Petition 870250015444, dated 25 / 02 / 2025, pp. 52 / 67 15 / 18 of the sample. Figure 8 shows the application of the repeated medians technique, comparing it to the simple least squares technique, for two sets of data.

[040] The presence of “outliers” or even disturbances in the behavior of the data can hinder the simple linear regression method in predicting the trend of data behavior. From Figure 8, it can be seen that the differences between the lines are considerable and, considering the phenomenon that is intended to be verified through regression, the errors estimated by simple linear regression may imply an inefficient process for a longer time. Because of this, throughout the analyses of the VUR estimate, the robust linear regression technique was employed on the average permeance data. RESULTS

[041] In order to validate the proposed methodology, two analyses were conducted on real data from membrane units: an “offline” analysis, whose objective was to observe the degradation of membrane performance in the long term; and another “online” analysis, for real-time monitoring of performance indicators and VUR. Offline results

[042] Historical data dating back to the beginning of the operation of the membranes of an oil production platform were submitted to the proposed methodology. It was expected that, in this way, it would be possible to observe the degradation of the corrected KPI over the years of operation. To enable the analysis of the developed library, the data were obtained at bimonthly intervals. To ensure the representativeness of this information, rigorous analyses of the operating modes and the presence of outliers were conducted for each time window. Figure 9 shows the permeance results obtained by the developed library for each two-month period throughout the operation. The trend curves, even without the applicable corrections, show a downward trend for both the first and second stages. The permeances estimated for the first stage, in turn, tend to be higher than those estimated for the second stage. This is related to the greater degradation of the second stage.Due to the permeation process, in which light hydrocarbons are lost to the permeate stream, the operating gas of the second stage has a higher dew point, making it more susceptible to condensation and, consequently, degradation. Petition 870250015444, dated 25 / 02 / 2025, pp. 53 / 67 16 / 18

[043] Figures 10, 11 and 12 show the same results as Figure 8, but corrected according to the system presented in Figure 1 for each reference case in Figure 5, that is, taking into account the gas specification at 3%, 6% and 10%, respectively. The curve highlighted in green shows the average permeance, obtained according to the calculations presented in the section “Obtaining an average permeance of the system” above.

[044] As can be observed, as the flexibility of the CO2 content in the treated gas increases, there is a divergence between the average permeance curve and the lower limit calculated for a temperature of 45°C as shown in Figure 7. In other words, allowing a higher CO2 content in the exported gas increases the margin between the membrane permeance and the lower limit. Assuming the rigor foreseen by the design condition, it can be observed that the pre-membrane + membrane assembly, represented by the green weighting, reaches its limit in the fourth quarter of 2024. This observation is consistent with the actual operation of the membranes. On the other hand, it is expected that, for a specification of 6% or 10% CO2, it will be possible to extend the service life of these membranes.

[045] Figure 13 shows the results of average permeances over time, linearly extrapolated using the robust regression methodology discussed earlier, where the dark blue points are the estimated permeances for a 3% CO2 setting and the red line is the average of these values ​​calculated by robust linear regression, the green points are the estimated permeances for a 6% CO2 setting and the purple line is the average of these values ​​calculated by robust linear regression, and the orange points are the estimated permeances for a 10% CO2 setting and the light blue line is the average of these values ​​calculated by robust linear regression.

[046] As can be observed, increasing the flexibility of the CO2 content causes the time horizon required for the average permeances to reach the established limit to increase. In this way, it is possible to quantify the expected useful life of the membranes in different scenarios, taking into account the main process factors, such as temperature and flow rate. Online results

[047] The methodology validated by historical results, as seen above, was replicated on the SmartMonitor platform (Anzai, TK, Furtado, PHT, de Brito, GM, Santos, Petition 870250015444, dated 25 / 02 / 2025, pp. 54 / 67 17 / 18 JS, Moreira, PCM, Diehl, FC, Ferreira, LEL, Grava, WM, 2023. Catching Failures in 10 Minutes: An Approach to No Code, Fast Track, AI-Based Real Time Process Monitoring. Offshore Technol. Conf. Bras. OTCB 2023 1-11. https: / / doi.org / 10.4043 / 32898-MS ) for real-time monitoring and proper storage of KPIs. The results generated by SmartMonitor can be recorded in the PI System™ or monitored by SmartMonitor itself, through configurable dashboards. Figure 14 shows the monitoring of permeances for different CO2 emission references, using dashboards created in SmartMonitor itself.

[048] As can be observed, as discussed earlier for the historical analysis, the greater the flexibility of gas framing, the further the average permeances are from the reference curve. By performing real-time analyses, SmartMonitor also allows the calculations predicted by Figure 1 to be performed at a higher frequency than the bimonthly window adopted in the historical evaluation. This allows for more precise monitoring of the process, but makes it difficult to identify long-term dynamics.

[049] The advantages of the present invention will be immediately apparent to those skilled in the art, among which we may highlight:

[050] The invention solves or minimizes the difficulties of the prior art described above by introducing an innovative methodology for estimating the remaining useful life (URL) of CO2 removal membranes in a robust and well-founded manner.

[051] The invention uses indicators consistent with the physics of the membrane system, enabling a more accurate assessment of the actual condition of these devices. To this end, calculated permeance data are corrected for temperature and flow, in order to minimize the impact of operating conditions on monitoring and predictions. These indicators, corrected by the proposed method, can be extrapolated in order to determine the time required for a given limit reference condition to be reached.

[052] The validation phase with historical data demonstrated that the method is able to correctly detect and predict the decline in membrane performance over time. Petition 870250015444, dated 25 / 02 / 2025, pp. 55 / 67 18 / 18 years. With this predictive capability, the method enables real-time monitoring of the membranes, allowing operational maneuvers to be performed to maximize their campaign time.

[053] Furthermore, the greater predictability provided by the accurate VUR estimate allows for more assertive and efficient replacement operations, resulting in greater availability of membranes and reduced costs associated with reactive maintenance.

[054] In this way, the invention directly addresses the limitations of current methods, offering a practical and efficient solution for the predictive monitoring of CO2 removal membranes.

[055] Although aspects of the present disclosure may be subject to various modifications and alternative forms, specific embodiments have been shown by way of example in the drawings and have been described in detail in this document. But it should be understood that the invention is not intended to be limited to the particular forms disclosed. Instead, the invention should cover all modifications, equivalents and alternatives that fall within the scope of the invention, as defined by the following appended claims. Petition 870250015444, dated 25 / 02 / 2025, pp. 56 / 67

Claims

1 / 3 CLAIMS 1. A method for estimating the remaining service life (RSV) of CO2 removal membranes, characterized in that it comprises the steps of: a) Inferring the permeance of a CO2 removal membrane; b) Obtaining a permeance vs. feed temperature curve; c) Defining a reference temperature (Tref); d) Correcting the permeance inference; e) Determining the reference permeance for the defined Tref; f) Normalizing the permeance by the volumetric gas flow rate per stage; g) Repeating the previous steps (b) to (f) at different times of use of the gas membrane; h) Obtaining a normalized permeance vs. time curve based on the normalized permeances obtained in step (g); and i) Estimating the RSL of the membrane based on the curve obtained in step (g) using a robust linear regression.

2. Method, according to claim 1, characterized in that step (f) is performed according to equations 1, 2 and 3: Ar, P*. =—u—(1) l,J Fluxij Fluxes =(2) Ai=ZLiFVwAfc,i(3) where: pL is the temperature-corrected permeance T of component j in stage i; Pb is the flow-normalized permeance of component j in stage i; Fluxij is the gas flow of component j in stage i; Qi is the volumetric gas flow rate, under normal conditions, in stage i; ytj is the content in the gas of component j in stage i; Ai is the permeation area of ​​the membranes of stage i; FVk,i is the status of the inlet valve of the k-train of membrane stage i; and Afc.i is the area corresponding to the elements of the k-train of membrane stage i. Petition 870250015444, dated 25 / 02 / 2025, page 57 / 67 2 / 3 3. Method according to claim 2, characterized in that the CO2 removal membrane comprises a plurality of CO2 removal membranes, and in which step (f) is performed for each membrane, and in which the method further comprises the step of: f2) calculating the average permeance of the plurality of membranes from equations 4 and 5: P = Σ·=ιΔρί,7^ίΡί;7 (4) 1 ZC^PíjAi ' ' Δρί,1 (_pfeed iyfeed i,,') (_pperm iyperm ij') (5) where: p is the average permeance of the system for component j; P-,1 is the flux-normalized permeance of component j in stage i; Ar is the permeation area of ​​the membranes in stage i; Δρί,ί is the partial pressure difference between the feed and permeate of component j at stage i; Pfeed i is the feed pressure at stage i; yfeedi.j is the gas content in the feed of component j at stage i; Pperm i is the permeate pressure at stage i; and yperm i,j is the permeate content of component j at stage i.

4. Method, according to any of the preceding claims, characterized in that step (a) comprises: ai) performing data pre-treatment, wherein the data comprise the following measured variables: Total Feed Flow Rates (F), Total Retentate Flow Rates (R), and Train A, B and C Retentate Flow Rates (RA, RB and RC); Molar compositions of: Ci, C2, C3, iC4, iCs, nC4, nC5, CO2, N2, H2S and Ce+ in said flows (F), (R), and (RA, RB and RC), Feed Pressures (Pf), Retentate Pressures (Pr), and Permeate Pressures (Pp), and Feed Temperatures (Tf), and Retentate Temperatures (Tr); a2) performing Data Reconciliation (DR); Petition 870250015444, dated 25 / 02 / 2025, p.58 / 67 3 / 3 a3) perform Global Energy Balance (GEB); a4) estimate the total permeate flow rate (P) and permeate temperature (Tp) based on the measured variables and steps in (a2) and (a3); a5) perform Parameter Estimation (PE); a6) estimate KPIs (Key Performance Indicators), where the KPIs are Selectivity, Dew Point Temperature and Hydrocarbon Loss (HC); where a normalization constant of the permeances in the model is Smax = 3x10-7 [„. ' ]. Ldiaxm-xüarl Petition 870250015444, dated 25 / 02 / 2025, p. 59 / 67.

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