A Liquid Well Barrier Element for Temporary Plug and Abandonment Operations: A Breakthrough Approach

Abstract

Plug and abandonment (P&A) operations demand valuable time and resources for operational procedures and materials to establish the well barrier element. This study aims to investigate the application of a water-based fluid as a liquid well barrier element for temporary abandonment, based on estimates of its lifespan and the survival probabilities of downhole temperatures acquired through accelerated life tests. To achieve this, the water-based formulation was tested and exposed to 95, 110, 140, and 150 °C temperatures for time intervals ranging from 1 to 10 days. After the temperature exposure, the fluid properties were verified, and failure was detected by accounting for any deterioration in rheological parameters and/or a substantial increase in filtrate volume. A statistical analysis of the failure data was performed in RStudio 4.1.3 software using the Weibull Model, and the fluid average lifespans and survival probabilities were estimated for the P&A temperatures. The results obtained demonstrate that the degradation of the fluid was only observed for 140 and 150 °C temperatures. According to the results, the fluid is a promising alternative for temporary abandonment until 80 °C, with no need for monitoring once its lifetime expectation exceeds three years at this temperature. For downhole temperatures above 80 °C, the fluid is a possible alternative, however, the operation’s maximum time and monitoring requirements should consider reliability metrics for each temperature.

1. Introduction

The energy sector has been facing substantial challenges related to sustainable economic development and global climate change, which require the transition from the use of fossil fuels to renewable energy sources. Therefore, the oil and gas sector is expected to be the most affected in the coming decades, undergoing important structural changes as a result of the end of the activities of many production systems. This scenario requires operators to plan platform decommissioning using the safest and most suitable approaches at the lowest cost possible [1,2,3].

Decommissioning involves many stages, and the most expensive one is the plug and abandonment (P&A) of wells, which corresponds to around 40 to 60% of the total costs [4,5]. This activity avoids environmental and operational catastrophes by preventing well leaks, which result in contamination or extensive damage to the marine ecosystem, soils, groundwater, and methane emissions into the atmosphere [6].

In P&A operations, well barrier elements are settled into the well to prevent the unintentional flow of formation fluids into the external environment and between well intervals, restoring isolation between the different permeable intervals [7,8,9]. For temporary abandonment, mechanical barriers such as packers and DHSVs (downhole safety valves) are typically applied. Another alternative is using cement plugs as well barrier elements [10]. However, the integrity of those elements for this application has often been questioned due to the possibility of mechanical or chemical degradation, which can cause leaks into adjacent regions or the surface [6,11,12].

Several materials have been studied as alternatives or supplements to cement in plugging hydrocarbon reservoirs [11,13,14,15,16]. Some recent research presented the most-used materials for plugging wells as well as the new technologies studied, comprising materials that constitute solid barriers such as blast furnace slag, bentonite, low-melting-point metal alloys, geopolymers, thermites, and sand pastes [10,16,17,18].

Liquid barriers, which consist of fluid columns exerting enough hydrostatic pressure to contain the fluids in the permeable intervals and prevent their flow, are considered alternatives to plugging petroleum wells in the requirements of international guidelines [19]. These types of barriers present environmental and operational advantages since the fluid formulation may be low-toxic and biodegradable, and its settlement inside the well can be rigless through the stationary production unit or platform supply vessel, reducing operating time and costs. On the other hand, the use of liquid barrier fluids in well abandonment operations is innovative and challenging, considering the lack of regulatory standards for its qualification and the need for strategies to demonstrate and guarantee its long-term stability, since its properties can be severely impacted due to the continuous exposure to downhole conditions.

In this sense, this study aims to investigate the application of a water-based fluid as a liquid well barrier element for temporary abandonment based on estimates of its lifespan and the survival probabilities of downhole temperatures acquired through accelerated life tests.

2. Materials and Methods

2.1. Fluid Formulation

This work uses a water-based fluid formulation developed at the Leopoldo Américo Miguez de Mello Research and Development Center—CENPES/PDDP/FCE. The additives of the formulation are typically used in water-based drilling fluids. Their type and quantity were chosen based on initial tests, focusing on properties that would help maintain the hydrostatic pressure of the fluid column over a long term at high temperatures.

The amount of each additive, presented in

Table 1. Water-based fluid formulation.

Product	Function	Amount
Deionized water	-	163.7 mL
Defoamer	-	0.3 g
Sodium bicarbonate	Removal of divalent cations	0.5 g
CMC LV (low viscosity)	Filtrate control/rheological agent	6 g
Sodium bentonite	Rheological agent	15 g
Sodium hydroxide	pH regulation	Qs. pH = 10 *
Magnesium oxide	Buffer	3 g
Sodium chloride brine (36 g/100 mL)	Weighting agent	167.3 mL
CaCO3 2–44	Weighting agent	25 g
Glutaraldehyde	Bactericide	0.3 g

* Quantum satis—sufficient amount to reach pH = 10.

, was used to prepare samples of 350 mL with a density of 9.8 ppg. All additives were supplied by Leopoldo Américo Miguez de Mello Research and Development Center—CENPES/PDDP/FCE (Rio de Janeiro, Brazil).

The fluid was prepared on a high-shear mixer Silverson L5MA. The defoamer, sodium bicarbonate, CMC LV, sodium bentonite, sodium hydroxide, and magnesium oxide were added to the volume of deionized water, keeping a homogenization time of 5 min between the addition of each additive. Then, the fluid remained at rest for 16 h at room temperature to adequately hydrate the products added. The preparation of the fluid was completed after pre-hydration with the addition of brine, CaCO₃ 2–44, and glutaraldehyde.

2.2. Fluid Properties

To investigate the rheological behavior of the fluid, flow curves were obtained using a controlled shear rate method (0.1 to 1000 s⁻¹) at room temperature on a Haake Mars 60 rheometer Thermo Scientific (Karlsruhe, Germany) equipped with parallel plates with a 35 mm sandblaster surface (P35/TI/SB), using a gap of 1 mm between the plates. The rheological parameters of the fluid, including yield stress (τ0), consistency index (K), and behavior index (n), were determined by adjusting the flow curves to the Herschel–Bulkley model in the RheoWin Data Manager software version 4.86.0002.

The chemical stability of the fluid was verified by measuring the pH using a pH meter Plus LineLAB (São Leopoldo, Brazil). The filtration control was evaluated at a high pressure and high temperature (300 psi/150 °F) using an HPHT filter press FANN series 387 (Houston, TX, USA).

2.3. Accelerated Life Tests

Accelerated life tests use high-stress levels associated with an acceleration variable to observe failures and determine potential failure modes for a product in short periods of time [20,21].

In this work, accelerated life tests were carried out with constant stress, using temperature as the acceleration variable to evaluate the life characteristics of the water-based fluid under downhole conditions. The fluid samples were exposed to high temperatures in ovens with air circulation according to the stress levels (temperature) and exposure times presented in the sampling plan in

Table 2. Sampling plan of the accelerated life tests.

Temperature	Inspection Time (Days)	Number of Samples
95 °C	7	7
	8	7
	9	7
	10	6
110 °C	7	7
	8	7
	9	7
	10	7
140 °C	4	6
	5	6
	6	7
	7	7
	8	7
	9	7
	10	7
150 °C	1	7
	2	7
	3	7
	4	7
	5	7
	6	7

. For temperature exposure, the fluid samples were placed in stainless-steel cells with a Teflon liner, pressurized to 100 psi with nitrogen gas.

After the inspection time had been completed, the samples were removed from the oven and tested to obtain the rheological parameters, filtrate volume, and pH following the procedures presented previously.

Fluid failure was recorded for samples that presented reductions in the rheological parameter consistency index (K) and/or increases of at least 40% in the filtrate volume.

2.4. Lifespan Prediction

Based on the failure information extracted from the accelerated tests, the accelerated life model parameters were estimated and these estimators were used to make statistical inferences for the lifespan distribution.

Our study used the Weibull–Arrhenius accelerated life model with constant stress to predict the fluid service life. In addition, an accelerated life test methodology for one-shot experiments was considered, since our methodology included destructive sampling. Similar methodologies have been explored in the literature, such as in the work of Lin and Hu (2020) [22], which shows that optimal accelerated life test designs can be implemented to evaluate the reliability of grease-based magnetorheological fluids, considering one-shot experiments with stepped stress. A Weibull–Arrhenius model was also employed to describe the accelerated degradation performance of rheological characteristics and predict the service life of grease-based magnetorheological fluids [21]. Additionally, studies by Balakrishnan, Ling, and So (2021) [23] provide an important theoretical basis for the development of reliability analysis methodologies in one-shot experiments. Their work on the development and application of probabilistic models, under EM estimation with exponential distribution [24] and Weibull distribution [25], for destructive testing allows for estimating the service-life of materials based on a limited number of samples, which directly aligns with our approach.

All the assumptions considered for our analysis are detailed and presented as follows.

2.4.1. Basic Assumptions

For the analysis of fluid failure data, T (temperature level) was assumed to be a random variable that follows a Weibull distribution, with probability density function (f_W), cumulative distribution function (F_W), and reliability function (R_W) given by

$$f_W\left(t;\eta ,\beta \right)={\displaystyle \frac{\eta }{\eta }}{\left({\displaystyle \frac{t}{\eta }}\right)}^{\eta -1}\exp \left\{-{\left({\displaystyle \frac{t}{\eta }}\right)}^{\eta }\right\},\beta >0,\eta >0, t>0;$$

(1)

$$F_W\left(t;\eta ,\beta \right)=1-\exp \left\{-{\left({\displaystyle \frac{t}{\beta }}\right)}^{\eta }\right\},\beta >0,\eta >0, t>0;$$

(2)

$$R_W\left(t;\eta ,\beta \right)=\exp \left\{-{\left({\displaystyle \frac{t}{\beta }}\right)}^{\eta }\right\},\beta >0,\eta >0, t>0.$$

(3)

where β corresponds to the scale parameter, which determines the smoothness of the distribution curve, while η corresponds to the shape parameter, which affects the geometrical shape of the probability density curve. Since the failure mechanism must remain the same for any accelerated stress, it is assumed that the shape parameter (η) is constant, while the β parameter correlates with the stress level (temperature), following the inverse power law, which derives from Arrhenius’ model. These relationships are specified in Equations (4) and (5).

$$ln\left(\eta \right)=\mathrm{r};$$

(4)

$$ln\left(\beta \right)=s_0+{\displaystyle \frac{1}{Tem{p}_i}}{s}_1, i=1,2,3,\dots ,\mathrm{I}$$

(5)

2.4.2. Estimation Method

The parameters r, s₀, and s₁ were estimated using the maximum likelihood method based on failure data from accelerated fluid life tests. This estimation was performed using a function implemented in the RStudio 4.1.3 software using the EM (Expectation-Maximization) algorithm [26], which consists of a widely used alternative when the model depends on unobserved variables. It is applicable to the data obtained from the accelerated life tests of the water-based fluid since some tests used to verify its properties are destructive, resulting in an incomplete data set. In this case, only the success or failure of the tested samples at a specified time can be observed instead of their actual time to failure. Such data are therefore either left or right censored.

Once the estimated values of these parameters were obtained, represented by $\widehat{s_0}$, $\widehat{s_1}$, and $\widehat{r}$, it was possible to estimate the model parameters ($\widehat{\beta }$ and $\hat{\mathsf{\eta }}$).

To estimate the parameter β, the values assigned to the temperature considered the usual conditions of typical abandonment operations, as well as the temperature levels at which accelerated life tests were carried out, were as follows: 60, 70, 80, 85, 90, 95, 100, 110, 120, 130, 140, and 150 °C.

Once the model parameters were estimated, the function implemented in the R software also estimated the number of failures ($\widehat{n_i}$) expected at each temperature level for a given inspection time, which follows a binomial distribution with parameters K_i and $\widehat{F\left({\tau }_i\right)}$, as shown in Equations (6) and (7):

$${\widehat{n}}_i=K_i\widehat{F}\left(t_i\right) \mathrm{and},$$

(6)

$$\widehat{F}\left(t_i\right)=1-\exp \left\{-{\left({\displaystyle \frac{t_i}{{\widehat{\beta }}_i}}\right)}^{\widehat{\eta }}\right\}.$$

(7)

2.4.3. Model Validation

The goodness-of-fit test was used to validate the model based on an M statistic, which is given by the distance between the observed ($n_i$) and estimated ($\widehat{n_i}$) failure numbers for each condition of temperature and inspection time (Equation (8)):

$$\mathrm{M}=\begin{array}{c}max\\ i\end{array}\left|n_i-K_i\widehat{F}\left(t_i\right)\right|.$$

(8)

When the assumed distribution does not fit the observed data well, a large value for the M statistic should be expected. The descriptive level of the test is given by Equation (9):

$$p\text{-}\mathrm{value}=P\left(\begin{array}{c}max\\ i\end{array}\left|n_i-{\widehat{n}}_i\right|>\mathrm{M}\right)$$

(9)

In this work, a significance level of 5% was considered; therefore, the p-value needed to be greater than 0.05 so that the hypothesis that the lifespan data follow the Weibull model was not rejected, and, therefore, the model was considered adequate.

Once the model was validated, estimates of the average lifespan ($\widehat{{\mu }_w}$) and survival probability ($\widehat{R_w}$), estimated by the reliability function, for a given time t were obtained from the estimated parameters. Also, the estimated lifespan ($t_p$) for a given level of reliability (p, that is, R($t_p$) = p) was obtained. The equations that describe the estimation of these parameters, relating them to the model parameters, are presented in Equations (10)–(12):

$${\widehat{\mu }}_W={\widehat{\beta }}_{0 }\mathsf{\Gamma }\left(1+{\displaystyle \frac{1}{\widehat{\eta }}}\right),$$

(10)

where $\mathsf{\Gamma }\left(\mathrm{r}\right)$ is the gamma function, given by ${{\displaystyle \int }}_0^{\infty }{x}^{r-1}{e}^{-r} dr$

$${\hat{\mathrm{R}}}_W\left(t\right)=1-F_W\left(t;\widehat{\eta },{\widehat{\beta }}_0\right)=\exp \left\{-{\left({\displaystyle \frac{t}{{\widehat{\beta }}_0}}\right)}^{\widehat{\eta }}\right\};$$

(11)

$$\widehat{t_p}={\widehat{\beta }}_0{\left(-\log \left(\mathrm{p}\right)\right)}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\widehat{\eta }$}\right.}}.$$

(12)

To estimate the probability of survival using the reliability function ($\widehat{R_w}$), times from 6 months (183 days) to 3 years (1095 days) were considered, which correspond to the maximum time that the well can remain in a condition of temporary abandonment without monitoring following Brazilian Legislation [9]. Regarding the estimation of the percentile ($t_p$), reliabilities were established from 0.9 to 0.9999999.

3. Results and Discussion

3.1. Rheological Behavior

The graphs in Figure 1 show the flow curves of the water-based fluid, considering the average shear stress values for the samples tested at the same time and temperature conditions.

As observed in the flow curves, the exposure to temperature impacts the rheological behavior of the fluid, resulting in more pronounced reductions in the flow profile for the temperatures of 140 and 150 °C at longer exposure times.

The average values for the rheological parameters and the correlation index (R²), obtained from the adjustment of the flow curves to the Herschel–Bulkley model, are presented in

Table 3. Average rheological parameters and correlation index for the water-based fluid at room temperature and after temperature exposure.

Temperature	Inspection Time (Days)	K (mPa.s)	n	${\mathit{\tau }}_0 \left(\mathbf{Pa}\right)$	R2
Room Temperature		0.44	0.78	32.17	0.9603
95 °C	7	0.90	0.65	6.16	0.9975
	8	0.99	0.63	2.40	0.9996
	9	0.92	0.64	4.79	0.9984
	10	1.85	0.60	13.47	0.9974
110 °C	7	6.05	0.44	20.35	0.9978
	8	4.41	0.49	12.68	0.9991
	9	3.36	0.52	10.65	0.9991
	10	14.90	0.36	34.70	0.9970
140 °C	4	3.58	0.52	15.35	0.9987
	5	3.12	0.52	16.12	0.9977
	6	1.93	0.58	19.34	0.9967
	7	1.55	0.44	6.43	0.9731
	8	2.61	0.42	7.58	0.9879
	9	4.33	0.36	7.47	0.9743
	10	1.47	0.49	8.14	0.9641
150 °C	1	2.83	0.54	4.57	0.9998
	2	2.52	0.51	14.70	0.9978
	3	1.90	0.50	8.73	0.9947
	4	0.81	0.66	12.10	0.9922
	5	2.19	0.36	4.51	0.9650
	6	1.14	0.64	7.30	0.9505

.

The average value of the consistency index at room temperature was 0.44 mPa·s, so failure was recorded for the samples exposed to temperature that showed values lower than that, observed only under the following conditions: 140 °C/7 days (one sample), 140 °C/8 days (one sample), 150 °C/4 days (two samples), and 150 °C/6 days (two samples). As the failure rate was low and only observed at the temperatures of 140 and 150 °C, it can be inferred that the fluid does not present a significant tendency to modify the rheological properties and, consequently, to promotethe sedimentation of solids. This behavior suggests a maintenance of the hydrostatic configuration of the fluid column inside the well during the abandonment operation.

Furthermore, there was a tendency for gradual increases in the average consistency index up to a temperature of 110 °C, with a maximum value of 14.90 mPa·s for the exposure time of 10 days. For 140 and 150 °C, a significant decrease in these values was observed, reaching the minimum average value of 0.81 mPa·s for the condition of 150 °C for 4 days.

This tendency may be related to the behavior assumed by the interactions between bentonite clay particles in the fluid with the increase in temperature. First, at room temperature there was a predominance of dispersed particles. With the increase in temperature to 110 °C, the clay particles tended to flocculate due to face-to-edge interactions, resulting in an increase in viscosity. Finally, the more pronounced increase in temperature, with the exposure of samples to 140 and 150 °C, caused the aggregation of particles due to face-to-face interactions, resulting in the presence of a greater volume of free water in the system and, consequently, reducing viscosity.

Additionally, the reduction in the fluid consistency index with increasing temperature may also be influenced by the degradation of CMC, which guarantees structural rigidity to the system at room temperature [27] once its degradation in the presence of NaCl can be observed at temperatures close to 150 °C [28].

The behavior index (n) presented values below one in all conditions, indicating a maintenance of the pseudoplastic behavior. However, there was a reduction in this with exposure to temperature. At room temperature, the average value of this parameter was 0.78, while a variation from 0.36 (110 °C/10 days) to 0.66 (150 °C/4 days) was observed for samples exposed to temperature. A similar behavior was observed by Ahmad, Kamal, and Al-Harthi (2018) when analyzing the effect of temperature on bentonite clay suspensions added with polymers [29].

Analyzing the yield stress helps predict the appropriate operational procedure and tension needed for circulating the fluid. This is particularly important when the fluid needs replacement during the abandonment period or for re-entry into the well after temporary abandonment. The results for this rheological parameter also indicate a reduction with the exposure to temperature; however, as observed for the consistency index, a high value of yield stress was observed after exposure to 110 °C for 10 days, possibly related to the high degree of the flocculation of clay particles in this condition. On the other hand, the reductions observed for the higher temperatures were attributed to the significant decrease in the reticulated structure due to high temperatures and high salinity, which impact viscosity and yield strength [30].

In addition to the variation in the rheological behavior, the effect of increasing temperature on fluid stability is also evidenced by the change in the physical aspect, as shown in Figure 2, in which a significant supernatant liquid phase is observed for 140 and 150 °C.

The changes in the aspects of the fluid and in the flow profile were compared to the effects of temperature on bentonite clay and CMC, which influence the rheological behavior of the fluid. This was accomplished through saline dispersions/solutions, to which these components were individually added and then exposed to the temperature of 150 °C for 5 days. The results obtained are presented in the flow curves in Figure 3 and images in Figure 4 and Figure 5.

As shown in Figure 3, Figure 4 and Figure 5, the effects of exposure to the temperature of 150 °C after 5 days is much more severe for the CMC solution than for the bentonite clay dispersion. This is noted by a significant reduction in the flow profile, loss of viscous nature, extremely dark color, and characteristic burning smell of the polymeric solution, which highlight the degradation of the polymer. These aspects are similar to those presented by the supernatant aqueous phase of the fluid sample after exposure to higher temperatures. Thus, this comparison suggests that the effect of temperature on the CMC chain was the main agent causing the degradation of the fluid.

The decrease in viscosity of the CMC solutions subjected to temperature was also observed by Zheng, Wu, and Huang (2020), who recorded percentage decreases that ranged from 74 to 94%, depending on the polymer concentration, for temperature increases from 40 to 190 °C [31]. According to the authors, this phenomenon was due to the fact that increasing the temperature tends to increase molecular activity and reduce the interaction of molecules through hydrogen bonds, which lead to a decrease in the system’s viscosity. Furthermore, it should be noted that the long-time exposure in this study intensified the effects related to this variable and may have also enabled degradation of the polymer chain.

3.2. Filtrate Volume

Table 4. Average filtrate volume for the water-based fluid at room temperature and after temperature exposure.

Temperature	Inspection Time (Days)	Filtrate Volume (mL)
Room Temperature		8.3
95 °C	7	8.4
	8	9.2
	9	9.4
	10	8.6
110 °C	7	9.2
	8	8.8
	9	7
	10	8.9
140 °C	4	9.6
	5	10.3
	6	11.54
	7	45.2
	8	30.7
	9	30.9
	10	32.3
150 °C	1	9.2
	2	10.4
	3	10.7
	4	15.4
	5	36.7
	6	93.9

presents the average filtrate volume values for each temperature and time condition.

Based on the results, the fluid presented an average filtrate volume value at room temperature of 8.3 mL. Thus, according to the failure criteria defined for this parameter, which established a maximum increase of 40% of this value, the samples exposed to temperature failed once the filtrate volume exceeded 11.6 mL. For 140 °C, this condition was only observed for the following inspection times: 5 days (one sample), 6 days (three samples), and 7, 8, 9, and 10 days (all samples tested). For 150 °C, failure was observed for the following inspection times: 2 days (one sample), 3 days (one sample), 4 days (five samples), and 6 and 7 days (all samples).

The filtrate volume showed gradual increases with exposure to higher temperatures and longer inspection times, which became more pronounced at temperatures of 140 and 150 °C. As observed for rheological behavior, this increase in filtrate volume may be associated with the progressive thermal degradation of CMC, which acts primarily as a filtration reducer [32]. Additionally, increases in the temperature and changes in the electrochemical balance may interfere in the degree of flocculation and aggregation of bentonite clay particles, causing changes in the permeability of the mudcake [33] and resulting in the presence of free water in the system, favoring the filtration of a greater volume of the liquid phase.

Obtaining greater volumes of filtrate directly impacts the hydrostatic configuration of the well, increasing fluid density due to the loss of water from the fluid column to the formation [34]. Furthermore, a greater volume of the aqueous phase in the formation may be related to the occurrence of damage to the formation, which could impact the reservoir’s production curve. However, significant increases in this parameter were observed only for the temperatures of 140 and 150 °C, which are not usually found. In addition, it is important to note that damage to the formation would only be a concern for wells that are temporarily abandoned with the intention of resuming production activities in the future.

3.3. pH

Table 5. Average pH for the water-based fluid at room temperature and after temperature exposure.

Temperature	Inspection Time (Days)	pH
Room Temperature		10.92
95 °C	7	10.57
	8	10.82
	9	10.35
	10	10.21
110 °C	7	9.62
	8	9.80
	9	9.99
	10	9.60
140 °C	4	10.01
	5	9.88
	6	9.64
	7	8.37
	8	8.61
	9	8.27
	10	8.39
150 °C	1	10.32
	2	9.82
	3	9.57
	4	9.28
	5	8.28
	6	7.80

presents the average pH values of the water-based fluid for each temperature and time condition.

The fluid was basic at room temperature, with an average pH of 10.92. For samples exposed to temperature, a reduction in this parameter was observed as the temperature and exposure time increased, exhibiting minimum values for 150 °C after 6 days, whose average value is 7.80.

The decrease in pH, particularly at 140 °C and 150 °C, offers additional evidence of the thermal degradation of CMC. This degradation involves decarboxylation, which produces carbon dioxide (CO₂). The produced CO₂ then forms carbonic acid (H₂CO₃), leading to an increase in hydrogen ions (H⁺), which results in the acidification of the aqueous medium [35]. This reinforces the correlation between the polymer’s degradation and the previously discussed rheological behavior, filtrate volume, and physical characteristics.

To mitigate adverse effects from contaminating electrolytes, minimize corrosion rates, and curb bacterial action on organic components, it is advisable to maintain a weakly alkaline medium with a pH between eight and eleven for fluids containing clay [36]. However, some samples exhibited a pH below eight after exposure to temperatures of 140 °C for 7 days or more and 150 °C for 5 and 6 days. These conditions align with the failure instances of all samples tested and the highest filtrate volumes, indicating an advanced degradation of the CMC and significant impairment of the formulation.

3.4. Estimation of the Life Characteristics of the Water-Based Fluid

3.4.1. Fluid Failures and Validation of the Statistical Model

Table 6. Number of failures of the water-based fluid after exposure to temperature.

95 °C			110 °C			140 °C			150 °C
τ	K	n	τ	K	n	τ	K	n	τ	K	n
7	7	0	7	7	0	4	6	0	1	7	0
8	7	0	8	7	0	5	6	1	2	7	1
9	7	0	9	7	0	6	7	3	3	7	1
10	6	0	10	7	0	7	7	7	4	7	5
						8	7	7	5	7	7
						9	7	7	6	7	7
						10	7	7

presents the results of the accelerated life tests regarding the occurrence of failure obtained after testing fluids exposed to temperature, where τ represents the inspection time in days, K is the number of samples tested, and n is the number of failures observed.

Based on the data in Table 6, fluid failure occurred only in samples exposed to 140 °C starting on the fifth day of inspection and to 150 °C on the second day of inspection. No failures were observed during inspections at temperatures of 95 °C and 110 °C.

Based on the data set, the following estimates for the model parameters were obtained: s0 = −5.5295, s1 = 1029.2737, and r = 1.9017. The test statistic obtained from these estimates was 0.9038 (with a p-value of 0.6383), indicating that the Weibull model is suitable at the 5% significance level. After the model was validated, the parameter estimates were used to calculate the average lifespan, survival probability, and estimated lifespans for different reliability levels (percentiles).

3.4.2. Average Lifespan

The estimated average lifespans of the fluid for different temperature levels are shown in

Table 7. Average lifespan of the water-based fluid.

Temperature	Average Lifespan (Days)	Average Lifespan (Years)
60 °C	104,397.3	286.0
70 °C	9002.95	24.7
80 °C	1432.70	3.9
85 °C	672.16	1.8
90 °C	343.01	0.9
95 °C	187.89	0.5
100 °C	109.30	0.3
110 °C	42.88	-
120 °C	19.66	-
130 °C	10.16	-
140 °C	5.77	-
150 °C	3.53	-

.

According to the estimated average lifespans, the water-based fluid can be used as a barrier element for the maximum time allowed by Brazilian legislation for temporary abandonment without monitoring, which is 3 years [9], for wells with a downhole temperature of up to 80 °C. For temperatures above 80 °C, where the average lifespan is significantly reduced, the use of the fluid must consider the expected duration of the temporary abandonment and the possibility of periodic monitoring.

The lifespans estimated for the temperatures of 140 °C and 150 °C were compared to failure conditions observed in laboratory tests. At 140 °C, the estimated average lifespan was 5.77 days. In accelerated life tests at this temperature, one failure occurred on the fifth day and three failures on the sixth day. At 150 °C, the estimated average lifespan was 3.54 days. In laboratory tests, a significant number of failures occurred only after the fourth day, with only one failure for the inspections after 2 and 3 days. This comparison shows that the estimated values align with the experimental results and are effective for predicting operational safety related to well maintenance.

3.4.3. Survival Probability

The estimated survival probability, that is, the estimated probability that the water-based fluid survives a given time T (in days) is presented in

Table 8. Estimated survival probabilities of the water-based fluid for a given time interval T (in days).

Temperature	P (T > 183)	P (T > 365)	P (T > 548)	P (T > 730)	P (T > 913)	P (T > 1095)
60 °C	1	1	1	1	1	1
70 °C	1	1	1	1	1	1
80 °C	1	0.9999	0.999	0.9931	0.9697	0.9012
85 °C	0.9999	0.9895	0.8518	0.3347	0.0075	0
90 °C	0.9907	0.3850	0	0	0	0
95 °C	0.5899	0	0	0	0	0
100 °C	0	0	0	0	0	0
110 °C	0	0	0	0	0	0
120 °C	0	0	0	0	0	0
130 °C	0	0	0	0	0	0
140 °C	0	0	0	0	0	0
150 °C	0	0	0	0	0	0

.

Based on the requirements set by Brazilian legislation for well abandonment, it is noted that the probability of the fluid not failing during the maximum allowed time for temporary abandonment without monitoring (3 years—1095 days) is 100% for temperatures of 60 and 70 °C, and greater than 90% for 80 °C.

Downhole temperatures are considered normal up to 80 °C [37]. Thus, these results demonstrate that the application of the water-based fluid as a well barrier element represents a viable and safe alternative in these conditions, making it possible to considerably reduce operational costs since there is no need to monitor these components until the end of the operation.

If the temperature exceeds 80 °C, it is recommended to use the water-based fluid for operations where the well will be temporarily abandoned for a duration less than the maximum allowed time. For temperatures of 85 °C and 90 °C, operational safety is guaranteed with fluid survival probabilities close to 100% for the time intervals of 1 year (365 days) and 6 months (183 days). However, this probability decreases as the specified time increases, with a significant decline observed especially at a temperature of 90 °C, where the fluid survival probability becomes zero after 1.5 years (548 days).

The application of the water-based fluid is limited by the high probability of failure for operations with an expected duration of more than 6 months for wells where the downhole temperature is greater than 95 °C. In these cases, the operation design must consider shorter operating times, based on the estimated values for the other metrics obtained in this study, with well-defined predictions of re-entry into the well, whether for monitoring, permanent abandonment, or resumption of operations.

3.4.4. Estimated Lifespans According to Reliability Level

Table 9. Estimated lifespans (in days) of the water-based fluid for different reliability levels.

	R(t)
Temperature	0.90	0.95	0.99	0.999	0.9999	0.99999	0.999999
60 °C	79,938.67	71,792.56	56,283.96	39,882.29	28,277.35	20,050.44	14,217.13
70 °C	6893.701	6191.202	4853.78	3439.34	2438.564	1729.097	1226.048
80 °C	1097.044	985.2504	772.4169	547.3269	388.0662	275.1637	195.1097
85 °C	514.6853	462.2366	362.3844	256.782	182.0638	129.0948	91.537
90 °C	262.6514	235.8861	184.93	131.0396	92.9098	65.87897	46.71267
95 °C	143.8705	129.2094	101.2976	71.7785	50.89245	36.08599	25.58742
100 °C	83.69593	75.16695	58.92941	41.75679	29.60643	20.99285	14.88536
110 °C	32.83474	29.48813	23.11859	16.3816	11.61489	8.235701	5.839672
120 °C	15.05536	13.52115	10.60032	7.51128	5.325654	3.776228	2.677603
130 °C	7.783012	6.989889	5.479935	3.883027	2.753147	1.952157	1.384212
140 °C	4.421188	3.970649	3.112911	2.205778	1.563942	1.108935	0.78631
150 °C	2.708183	2.432208	1.906803	1.351141	0.957987	0.679274	0.481652

presents the estimated lifespans of the water-based fluid for each specified temperature, given the reliability level (R(t)).

As observed for the average lifespans of the fluid, there is compatibility between the estimated lifespans and the results obtained in the laboratory. Considering a reliability level of 0.95, for example, lifetimes of 3.97 and 2.43 days were obtained for 140 and 150 °C, respectively, and the first failures at these temperature levels were observed on the fifth and second day of inspection. Thus, this comparison indicates that the survival study carried out is an adequate and satisfactory mechanism for anticipating the failure mechanism and qualifying the fluid as a well barrier element in abandonment operations.

The estimates presented in Table 5 reaffirm that the application of the water-based fluid in the temporary abandonment of wells is a highly promising alternative, especially for temperatures of up to 70 °C. For these, it is possible to extend the duration of operation to the maximum time allowed, if necessary, since the lifespans are higher than three years (1095 days).

For temperatures above 80 °C, the feasibility of applying this fluid as a barrier element must be guided by factors such as the degree of risk considered acceptable by the operator when planning the operation, the expected operating time, and the possibility of monitoring during the period of abandonment. In these situations, it is necessary to analyze all the estimated service-life characteristics at the predicted downhole temperature. Additionally, for wells with high downhole temperatures where the use of water-based fluid may raise questions about its service-life characteristics, the reliability of the barrier element acting in conjunction with the fluid should be considered in the operational design. These considerations constitute the main limitations to the use of this fluid as a liquid barrier. As a result, its application must be based on technical knowledge and industry best practices, and may also involve the establishment of guidelines and requirements related to monitoring practices to ensure the early detection of potential failure modes.

4. Conclusions

This study proposes the use of a water-based fluid as a liquid well barrier element for temporary abandonment, based on estimates of its lifespan and the survival probabilities of downhole conditions acquired through accelerated life tests.

Based on the results obtained, it is concluded that, for the inspection times outlined in the sampling plan, the performance of the water-based fluid is compromised only at temperatures of 140 and 150 °C. This is evidenced by physical changes such as a reduction in the flow profile, increase in the filtrate volume, separation of the aqueous phase, and a reduction in pH, and primarily relates to the degradation of CMC.

Additionally, the survival analysis of the water-based fluid, conducted in this work based on accelerated life tests, was considered adequate for the qualification and validation of liquid barriers used in the temporary abandonment of petroleum wells and attested the use of the water-based fluid for this application. Therefore, the reliability metrics estimated for this formulation, based on the application of this methodology, should guide the design of projects for abandonment operations that use this type of barrier based on the expected temperature and time of the operation and should contribute to the selection of monitoring strategies that mitigate risks related to fluid degradation.

5. Patents

The work reported in this manuscript resulted in a patent deposited to the National Institute of Intellectual Property (INPI—Brazil) by the number BR 10 2023 019391-9.