Development of a monitoring and control method for energy loss in slurry pipelines: a case study

Abstract

The pumping of iron ore slurry through long-distance pipelines requires reliable prediction of energy losses to ensure operational efficiency and maintenance planning. This study develops a predictive model for energy loss by integrating real operational data with statistical validation. Operational data, including slurry properties and flow parameters, were collected over seven months and used to develop a linear regression model, which identified flow rate as the most critical variable, with a Pearson correlation coefficient of 0.735. The model was validated using 12 months of field data from 2022, confirming its ability to detect trends of increasing pressure drop and to anticipate pig-cleaning operations. The application of this monitoring method led to a statistically significant increase in the average flow rate of 11.98 m³/h after pigging campaigns. This operational improvement resulted in an estimated production gain of 13,299 dry metric tons per month. Although the resulting equation is specific to Samarco’s Pipeline 2, the methodology offers a practical and replicable framework for transforming historical data into a proactive tool for maintenance and operational optimization in other slurry pipelines, enhancing efficiency and supporting predictive decision-making.

Keywords:
energy loss; ore slurry pumping; pipeline; pump station.

1. Introduction

The operational efficiency of long-distance slurry pipelines is a critical determinant of the mining industry's competitiveness, directly impacting transportation costs and production throughput. Among key operational parameters, frictional energy loss, or pressure drop, serves as a primary performance indicator, influencing the energy consumption of pumping stations, transport capacity, and overall asset integrity (Joshi et al., 2024; Mishra and Sahoo, 2023). However, accurate monitoring and prediction of this parameter represent a persistent engineering challenge, fundamental to optimizing the entire mineral logistics chain.

Predicting energy loss in mineral slurries is a significant challenge due to the non-Newtonian rheology of high-concentration suspensions and the variability of ore physical properties (Chaves, 2012; Louzada et al., 2022). Classical theoretical hydraulic models, such as the Bernoulli and Darcy-Colebrook equation, often exhibit significant deviations when applied to large-scale, real-world systems with variations in diameter, roughness, and elevation profiles (Abulnaga, 2021; Carvalho, 2023,). This discrepancy between theoretical models and operational reality often forces operators to rely on reactive or schedule-based maintenance strategies, such as fixed-interval pigging, which can lead to unnecessary downtime, or conversely, production losses from unanticipated performance degradation (Nath, 2023).

In this context, the Samarco Mineração S.A. Pipeline 2 system emerges as an emblematic case study. Operating at a 99.7% utilization rate, this approximately 400 km system functions as a critical production bottleneck, where transport optimization has a direct and measurable impact on the company's total output (Carvalho, 2023). Its operational complexity and the availability of extensive historical data make it an ideal subject for the development and validation of a data-driven predictive model for energy loss

Therefore, the objective of this study is to develop a method for monitoring and controlling energy loss in Samarco's Pipeline 2, using real process data. The primary contribution of this research lies in presenting a replicable methodology that transforms historical operational data into a validated predictive tool for optimizing maintenance schedules (pigging campaigns) and directly quantifying the resulting production gains. This approach advances the field from reactive maintenance to a data-driven, predictive framework, aligning with modern practices in predictive maintenance and asset integrity management (Carvalho, 2023).

1.1 The Samarco pipeline 2 system: an operational overview

As established in the introduction, the Samarco Pipeline 2 system was selected as the object of this study due to its critical role as a production bottleneck. This section provides the necessary technical details of its operational configuration to contextualize the subsequent methodological analysis.

Samarco Mineração SA has three slurry pipeline lines for pumping concentrated iron ore slurry. Each one is approximately 400 km long, built on a right-of-way 35 meters wide, covering around 25 cities from its extraction area, located in Mariana (MG), to the pelletizing plant and the port, located in Anchieta (ES) (AUSENCO PSI, 2012). These lines represent 49% of the total length of pipelines in Brazil.

In order to promote adequate displacement of the ore slurry, two pumping stations (EBs) are used for each of the pipelines. These stations are responsible for pushing the slurry through the pipeline, ensuring its safe and efficient arrival at the final destination, the terminal. The first station is in Germano, between the cities of Ouro Preto (MG) and Mariana (MG), where the ore processing plants are installed. The second station is in the city of Matipó (MG), whose function is to provide the necessary force for the slurry to reach the maximum elevation point of the pipeline, which is 1,180 meters.

The company operates two valve stations (EVs) to control static and dynamic pressure along the conveyor line. These stations are in Guaçuí (ES) and Alegre (ES), and are responsible for regulating the pressure along the line, in order to guarantee the constant and safe flow of the ore slurry. (AUSENCO PSI, 2012; Carvalho et al., 2025).

In this research, a case study of Samarco's pipeline 2 will be presented, which began operating in 2008, with a pumping capacity of 8.5 Mtms/year. In Figure 1, the schematic operational flow of pipeline 2 can be seen, comprising two pumping stations EB4 and EB5, and two valve stations EV3 and EV4.

Figure 1
Schematic operational flow of Ore Pipeline 2. Source: Samarco Mineração (2013).

According to Figure 1, the process starts in the storage tanks (1) in EB4, each with a capacity of 3,110 m³ and 148 kW agitators, where the slurry is stored and agitated, preventing solid particles from settling at the bottom of the tank. This system has an uninterrupted power supply: in the event of a power failure at the plant, emergency generators are activated immediately. In cases of maintenance or faults in the agitators, the tank is completely drained.

After the tanks, the slurry passes through one of the charge pumps (2) that are installed upstream of the main pumps, which require a minimum suction pressure above the height of the fluid column available in the tanks. One of the pumps is used in parallel for redundancy and process maneuvers, each of them has a power of approximately 220 kW. Then, the slurry is pumped into the piping, driven by three main Geho pumps (1840 kW)(3), with positive displacement, which are installed in series. Each with a capacity of 338 m³/h and a pressure at the pump station discharge of 155 kgf/cm², (Vidal, 2011; Carvalho et al., 2025).

Then, after 153 km of piping, the slurry arrives in the tanks of the second pumping station, EB5 in Matipó. This station is a mirror of EB4, but has only one storage tank. There is the option of operating with an interconnected pipeline; that is, the pipeline that arrives at EB5 is connected directly to the suction of the main pumps, therefore not using the tank for material storage. However, this practice is normally not used in Pipeline 2 since the system is dependent on the proper functioning of both stations (AUSENCO PSI, 2012; Mattioli, 2016).

Once this is complete, the slurry passes through two valve stations. One controls pipeline shutdowns (4), and the second is for pressure control (5). The process then ends at the Ubu terminal (6).

With this system in operation, pipeline 2 is the bottleneck in Samarco's production process. Its pumping capacity is lower than the ore feed transferred from beneficiation plant 3, requiring maximum utilization capacity, with a 99.7% utilization rate. The pumping system is always continuous, when the pipeline is not pumping slurry, it pumps water to boost the slurry that is in the line. This can occur in cases of maintenance shutdown at the plant or when it operates with a flow lower than the minimum pumping capacity of the pipeline.

In view of the high production demand and utilization rate, it is necessary to know the parameters that directly impact the transport capacity of the system. The study and monitoring of energy loss, according to the flow conditions, pumping speed and slurry concentration, can present different behaviors that interfere with the operating conditions of the pipeline, (Barbosa et al., 2024). Since energy loss occurs partially due to the contact of the ore particles with the pipe wall, the consequence being the dissipation of the pumping energy of the slurry. This loss leads to energy loss, reduced pumping capacity, and consequent production loss (Madagascar, 2014).

2. Materials and methods

The operational data collected every two hours during stable periods between January and July 2022. The dataset included:

• Slurry properties (granulometry, viscosity, concentration, density);

• Instrumentation data from the SCADA system (pressure, flow rate, pump speed);

• Pipeline integrity parameters from design and inspection (length, elevation, roughness, wall thickness).

2.1 Energy loss calculations

Based on these variables, the energy loss was calculated using Bernoulli’s equation, presented in Equation (1), and compared with theoretical estimates from the Darcy-Colebrook equation, shown in Equation (2). The pipeline was divided into 18 segments, including 4 main sections (between pumping/valve stations) and 14 subsections (between pressure monitoring points, PMS), as shown in Figure 2.

Figure 2
Pipeline profile with sections. Source: Ausenco (2014).

Bernoulli's Equation:

(1) $$I_w=\frac{P_1}{\rho }+Z_1-\frac{P_2}{\rho }+Z_2\to I_w=\frac{\mathrm{\Delta }P}{\rho }+\mathrm{\Delta }Z$$

Where: I_w = linear energy loss between points (mca);

Z = geometric dimension (m);

P = absolute pressures (kgf/m²);

ρ = slurry specific mass (kg/m³).

Darcy-Colebrook Equation:

(2) $$J=\frac{f{v}^2}{D\cdot 2g}$$

Where: J = linear energy loss (m/m);

f = Darcy-Weisbach energy loss factor;

v = flow velocity (m/s);

D = tube diameter (m);

g = acceleration due to gravity (m/s²).

The initial analysis was conducted in section 1 (EB4-EB5), chosen due to its reduced operational interferences, proximity to the first pumping station, and absence of intermediate valves.

2.2 Regression model development

A multiple linear regression model was proposed to correlate energy loss with key operational variables. The process followed these steps:

• Variable selection: all candidate variables (flow rate, slurry concentration, viscosity, density, elevation, and pipe roughness) were first tested through correlation analysis (Minitab software). Variables with high collinearity (Variance Inflation Factor - VIF > 10) were excluded.

• Model estimation: the regression model was fitted using the Ordinary Least Squares (OLS) method, with energy loss as the dependent variable.

• Diagnostics and residual analysis: residuals were analyzed for normality (Anderson-Darling test), independence (Durbin-Watson statistic), and homoscedasticity (Breusch-Pagan test). Outliers and influential points were assessed using standardized residuals and Cook’s distance.

• Model performance: coefficients of determination (R² and adjusted R²) and Root Mean Square Error (RMSE) were calculated to evaluate explanatory power and predictive accuracy.

2.3 Model validation

The proposed regression model was validated through:

• Temporal validation: model coefficients estimated using data from January-July 2022 were tested against operational data from August-December 2022.

• Comparative validation: predicted energy losses were contrasted with those obtained from the Darcy-Colebrook equation, enabling assessment of the model’s ability to reproduce theoretical expectations.

• Operational validation: the model’s predictions were further assessed against real events, such as energy loss increases prior to pigging operations.

Using the validated regression model, Figure 3, the increase in energy loss was monitored throughout the year. The model successfully identified the tendency of energy loss accumulation, supporting the decision-making process for pigging operations. Finally, the t-test was applied to quantify the increase in flow after pigging, and the associated production gains were statistically confirmed.

Figure 3
Graphical representation of the proposed methodology/model. Source: Carvalho (2025).

3. Results and discussion

The results presented here were originally obtained in the author's master's dissertation (Carvalho, 2023).

After generating the energy loss data history, it was possible to observe that the points of sections 1 (EB4-PMS5), 2 (PMS5-PMS6), 3 (PMS6-PMS7), 4 (PMS7-PMS8) and 5 ( PMS8-EB5) compose the energy loss of section 1. Thus, when the Bernoulli equation is applied, they presented similar behavior, but different values due to the variation of the geometric dimension, as can be seen in Figure 4 and Figure 5.

Figure 4
Energy Loss EB4 - EB5. Source: Carvalho (2023).

Figure 5
Energy Loss EB4 - PMS5. Source: Carvalho (2023).

Bernulli's equation applied to slurry pumping systems consists of determining the energy loss at two points. The pressure measurements and geometric dimension were collected at the initial point EB4 and then the difference with the corresponding measurements at the final point was determined, that is, EB5 for Figure 4 and PMS5 for Figure 5. Subsequently, this The pressure difference was divided by the specific mass of the pulp, resulting in the meters of slurry column (msc) obtained.

In Table 1, it is possible to observe the average energy loss of the stretches of section 1, applied in the same period shown above, in meters of slurry column (mcp):

Table 1
Average energy loss of sections in section 1.

Segment	EB4 PMS5	PMS5 PMS6	PMS6 PMS7	PMS7 PMS8	PMS8 EB5	EB4 EB5
Energy loss(mcp/m)	0.006204	0.004852	0.004562	0.004318	0.005252	0.004974

As the loss increases, it is assumed that there is material deposition on the line and, consequently, this indicates the need for cleaning with the PIG's. However, when analyzed individually, the trend of the graphs may show a need for cleaning in which there is no material deposition.

The energy loss is directly related to the velocity and flow rate of the slurry in the line, so if there is an increase in the pumped flow, the energy loss follows this trend, but material deposition does not necessarily occur in the line, but greater interaction of the particles with the pipe wall causing friction.

Therefore, it is necessary to follow the evolution of energy loss as a function of flow. For this, the Darcy-Colebrook equation was initially used to determine the expected energy loss for the pipeline according to its characteristics and according to the variation in flow velocity.

When analyzed section by section with up to 40 km in length, the equation showed a coherent relationship with the actual energy loss of the system. In Figure 6, the values of the actual energy loss (blue color) and the calculated energy loss (orange color) are shown: notice that both are superimposed, demonstrating that the actual energy loss curve is within the expected limits for a given pumping speed.

Figure 6
Relationship between actual energy loss and the Darcy-Colebrook equation in the EB4 to PMS5 segment. Source: Carvalho (2023).

However, when applied to section 1 in its entirety (Figure 7), it showed a certain discrepancy due to the increase in the length of the pipe and the large variation in roughness and internal diameter, variables of the Darcy-Colebrook equation. For this calculation, the means of these variables were used (Table 2 and Figure 8).

Table 2
Variation of roughness in section 1.

Segment	EB4 PMS5	PMS5 PMS6	PMS6 PMS7	PMS7 PMS8	PMS8 EB5
e (mm)	0,2101	0,1463	0,1309	0,0750	0,1210

Figure 7
Actual vs. Darcy-Colebrook Energy Loss (EB4-EB5). Source: Carvalho (2023).

Figure 8
Significant variation in internal diameter along section 1. Source: Carvalho (2023).

Observing Figure 7, it is possible to interpret that the energy loss is controlled, since the actual loss points (blue color) are below the Darcy-Colebrook equation points (orange color). This inconsistency occurs due to the use of the average of the variables for a large length of pipeline, thus providing a wrong analysis that can show an increase in energy loss or even cause a reduction in the diameter of the pipeline due to excessive incrustation and lack of cleaning.

Thus, a linear regression model was proposed, considering the real variables of the process. Operational data were collected in moments of stability, that is, in periods without limitations due to maximum pressure, and in periods without deposition of material on the line (after the passage of the cleaning PIG or without a tendency to increase the energy loss), and periods that the operation was stable and process variables such as flow, pressure and concentration were controlled. These data were collected every two hours, over a period of 7 months, in the year 2022.

To determine the regression, the Minitab software was initially used to calculate the degree of correlation of the surveyed variables with the energy loss. The flow was the only variable that presented statistically direct correlation, with a range of 0.735, that is, a strong correlation according to the Pearson correlation coefficient. This analysis was carried out with the aim of determining whether the data sample used was within the desired characteristics, disregarding instrumental errors.

From the linear regression analysis, Equation (3) was reached, which correlates the energy loss (J) with the flow rate (Q).

(3) $$J=\mathrm{0,000638}+\mathrm{0,000007Q}$$

Where: J = Linear energy loss (mcp/m); Q = Flow rate (m³/h).

Applying the calculated equation in the graph of the actual energy loss Figure 9, there can be observed a relationship adherent to reality.

Figure 9
Energy loss as a function of linear regression EB4 - EB5. Source: Carvalho (2023).

After determining the equation, used throughout the year 2022, it showed a good performance by indicating the tendency to increase the linear energy loss and adapting to the actual loss. In Figure 10, one can observe the bars that signal the passage of cleaning PIG's to control energy loss in moments of trends, as well as the effectiveness of cleaning due to the drop in loss after the PIG's campaigns.

Figure 10
Energy loss control. Source: Carvalho (2023).

Following the reduction in linear energy loss due to sequential PIG passage, an increase is observed in the graph of Figure 11. This increase is associated with the increase in the flow due to the reduction of the obstruction in the line, resulting, consequently, in an energy loss due to friction. In the present context, this energy loss due to friction is not considered harmful to the system, since it is accompanied by production gains.

Figure 11
Flow rate increase after the PIG. Source: Carvalho (2023).

When performing a statistical comparison between the flow before and after the passage of the cleaning PIG, a two-sample t-test was applied using Minitab software to evaluate whether the difference in mean flow rates was statistically significant. The analysis considered 255 samples for the condition "before PIG" and 316 samples for "after PIG".

The average flow rate before the PIG passage was 628.32 m³/h (standard deviation = 4.65 m³/h), while after the PIG passage, it increased to 640.31 m³/h (standard deviation = 6.65 m³/h). The calculated difference in means was 11.98 m³/h, with a 95% confidence interval ranging from 11.05 m³/h to 12.91 m³/h.

Since the confidence interval does not include zero and the p-value was < 0.001, the null hypothesis (which assumes no difference between the means) was rejected. This confirms that the increase in flow after the cleaning PIG is statistically significant.

Therefore, a specific increase of 11.98 m³/h in flow rate was observed after the passage of the cleaning PIG. Considering a slurry specific mass of 2,220 kg/m³ and a solids concentration of 69.45%, this corresponds to an estimated production gain of 13,299 dry metric tons per month. The monthly gain was calculated using Equation (4):

(4) $$\text{Gain}=11.98\times 2.22\times 0.6945\times (24\times 30)=\mathrm{13,299}\text{tms}/\text{month}.$$

4. Conclusions

The analysis of particle behavior in pipelines is a complex and highly variable process, especially in operations involving iron ore slurry. The complex physical properties of the slurry and operational pumping variables hinder accurate energy loss prediction.

The models currently used to determine energy loss are normally applied in pipeline projects, but they do not take into account important variables during operation, limiting their effectiveness. Each model has its particularities, and it is up to the engineer to determine which one best suits the conditions of the process in question.

Furthermore, in the case of long-distance pipelines, averaging the process variables in the equations does not always reflect the actual condition of the pipeline, which can lead to inconsistent results or even situations that do not correspond to reality. The Darcy-Colebrook model has shown good performance in pipelines with lengths of up to 40 km and low variation in roughness, but this is a restricted condition that does not apply to most pipelines.

The proposed model is based on the desired conditions for the operation, taking into account the history of the pipeline. Process variables are applied indirectly, as they represent actual operating conditions. The advantage of this model is its practicality in calculations, but it is necessary to have at least one year of pipeline operation history. The equation obtained through linear regression is specific to Samarco’s Pipeline 2; however, the methodological framework is transferable. By combining operational stability data with regression analysis, this study advances beyond traditional theoretical models, offering a replicable tool for real-time monitoring of energy loss in slurry pipelines. This novelty lies in transforming historical operational data into a predictive instrument for maintenance planning and production optimization.

From the data obtained by analyzing the energy loss curve and the critical operating speeds, it was possible to obtain specific gains in the production of 13,299 tms/month. In addition, it was possible to preventively control energy loss, based on slurry concentration and flow parameters, and corrective programming of cleaning campaigns with PIGs. These actions improved operational efficiency and optimized resource utilization.

• Funding information
  There are no funders to report for this submission.

Data availability

The authors state that this manuscript is based on the Master's Dissertation of Igor Moreira de Carvalho, entitled "Proposta de um método para monitoramento e controle da perda de carga em minerodutos com base em variáveis operacionais do processo: um estudo de caso," presented in 2023 at the Federal University of Minas Gerais, in the Graduate Program in Mechanical Engineering (PPGMEC-UFMG), with all data available at the following link: https://repositorio.ufmg.br/items/dd91cbb8-bade-4852-8e29-e00f600d1fa5 .

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Edited by

• Associate Editor
  Jório Coelho

Publication Dates

• Publication in this collection
  03 Apr 2026
• Date of issue
  2026

History

• Received
  03 July 2025
• Accepted
  12 Oct 2025