The study was conducted at the Ouaga East thermal power plant in Kossodo (Burkina Faso). The facility comprises eleven (11) generator sets of different brands (MAN B & W, DEUTZ, WARTSILA) with nominal powers ranging from 3.8 to 18.9 MW. They are equipped with centrifugal separators of the purifier type (Alfa Laval, model PX G) [1]. These separators treat the HFO before injection into the engines [19]. The preheating system consists of electric heaters immersed in the supply circuit, regulated by a programmable logic controller (PLC) that maintains a temperature setpoint at the separator inlet. The viscosity of the HFO varies according to its quality; the more viscous the HFO, the higher the required heating temperature. Table 1 summarizes the physical constant values proposed by our previous work [1]:

Table 1.Physical characteristics of the HFO at the Ouaga East plant.

Figure 1 shows two images of the site, namely a separator and the unloading device.

To model the impact of ambient temperature variations on the HFO temperature downstream of the heater, we use a simplified approach that relates the HFO temperature ( T ) at the separator inlet to the preheater setpoint temperature ( T p ) and to the ambient temperature ( T a ) . The equation adopted is:

The setpoint temperature T p is chosen to achieve an ideal viscosity for centrifugal separation.

The coefficient α (ranging from 0.2 to 0.8) is an empirical parameter that aggregates the influence of thermal losses from the installation (piping, equipment) on the fuel [20]. α = 0.2 corresponds to a slow increase in the fluid temperature as the outside temperature decreases [21]. The reference ambient temperature T a , r e f is the average ambient air temperature for a typical year. Its value is 34.75 [22].

The ambient temperature of the city of Ouagadougou was modeled by a sinusoidal function with a period of 24 hours, representative of the monthly averages during the hot season in Ouagadougou:

With,

A is the peak-to-peak amplitude, with a value of 21.3˚C [23]; ϕ is the phase shift. It is obtained from the following formula: ϕ = π 2 − 2 π 86400 ( t p i c − t 0 )

where t_pic and t₀ are the time at which the temperature peak is observed and the initial time, respectively.

We use Andrade’s law [24] [25] to model the efficiency of solids removal by the centrifugal separator as a function of the dynamic viscosity of the HFO, which depends on temperature:

The parameters A μ = 2.49 × 10 − 4   cSt and B μ = 4311   K were calculated from the kinematic viscosity values in Table 1 above. The value of the constant B μ is low. This indicates a viscosity that varies less rapidly with temperature. Indeed, for the same temperature increase, the viscosity drop is more moderate. In other words, the HFO used at the studied plant is less thermally sensitive, and therefore heavier.

The separation efficiency η (fraction of solids) is given by [14] [26]:

This formulation reflects the following principle:

If T ≺ 95 ˚ C → μ ≻ 30   cP → the separation efficiency begins to decline.If T ≥ 95 ˚ C → μ ≤ 30   cP → maximum efficiency (99%).

This highlights the value of adaptive control when it is cold (T_a,min), the fixed strategy causes T to drop below 95˚C, thereby degrading efficiency, whereas the adaptive strategy corrects this phenomenon.

Water separation efficiency:

The water removal efficiency function was calibrated on eleven (11) measurements of water content before/after the separator, performed at temperatures ranging from 55˚C to 110˚C in 5˚C increments. A logistic regression was used to estimate a half-efficiency temperature of 75˚C and a slope of 0.3 [14] [24]. Equation (5) provides the mathematical model used. Water evaporates more effectively as temperature increases.

FireRisk

The fire risk is modeled by a logistic function defined by Equation (6), centered on the flash point of HFO, measured at 98˚C, with a slope of 0.8 [27].

HydraulicRisk

The hydraulic risk is modeled by Equation (7). It is centered on 105˚C, the maximum service temperature for seals and the lubrication system, with a slope of 0.8 [28] [29]. This limit is consistent with the minimum viscosity range required for the pumps.

The overall separation efficiency is the product of the two efficiencies calculated above.

Two strategies were compared:

Fixed setpoint: T_sat = 95˚C (commonly used value).Adaptive control: the setpoint is adjusted in real time according to the ambient temperature:

with, T o p t = 95 ˚ C , T a , r e f = 34.75 ˚ C , k = 0.34 , T min = 85 ˚ C et T max = 98 ˚ C .

Note that the operating band is the temperature interval [30]: [ 85 ˚ C ;   98 ˚ C ] .

The parameter k is the adaptation gain of the setpoint law. It results from a constrained optimization that maximizes the average efficiency while ensuring that the HFO temperature remains within the safe and efficient zone. For example, k equal to α cancels the influence of the ambient (perfect compensation).

We will retain two temperature thresholds:

a fire safety threshold ( 98 ˚ C ≺ T ≺ 105 ˚ C , dangerous);a process safety threshold ( T ≻ 105 ˚ C , risk of hydraulic seal failure).

We used Python version 3.11 for the simulation. The simulation period is 48 hours, discretized into 2000 points. For each of the two control strategies, we calculated the following quantities:

the HFO temperature at each time step;the instantaneous separation efficiency of the HFO by the centrifugal separators;the maximum temperature reached during preheating;the fraction of time spent outside the range.

2.7.1. Scope and Basis for Conversion and Assumptions to Be Retained

Table 2 defines the scope of the economic study.

Energy and maintenance gains are calculated at the fuel treatment line level, avoided production is calculated at the entire power plant level, and the investment must be allocated to the treatment line (adaptive control system).

Table 2. Scope of the study.

We have retained €26,000/year for a 100% reduction in out-of-band time, i.e., €260/year per percentage point of reduction in out-of-band time. The 80% assumption applies to the total failure cost (lost production + restart).

2.7.2. The Variables Considered for the Economic Analysis

The economic analysis focused on energy savings, maintenance, and production losses:

Energysavings: this is the difference in electrical energy consumed by the preheater. It is obtained by performing the following successive calculations:the instantaneous power: P = D m C p ( T s e t − T e ) , where T e is the HFO inlet temperature, close to T a ;the fixed power: P f i x e = D m C p ( T s e t , f i x e − T a ) the adaptive power: P a d = D m C p ( T s e t ,   a d − T a ) instantaneous power savings (in W): P e c o = P f i x e − P a d energy saved over the simulation period (48 h): E e c o = P e c o t 3600 projection over one year (8760 h): E e c o , a n ( kWh ) = p × f e x × E e c o ( Wh ) 1000 where f e x is the extrapolation factor given by: f e x = 8760 / 48 = 182.5 and p is the production cost per kWh of electricity.

Table 3 below presents the production cost per kWh of electricity for different sources [31].

Table 3. Average production cost per kWh of electricity.

For the simulation, we set the production cost of electricity at 132 FCFA per kWh, i.e., 0.2 €/kWh.

Maintenance: reduction in the frequency of unloading operations (fixed saving of 6,558,294 FCFA/year, i.e., 10,012€/year), savings on filters and seals (2,278,768 FCFA/year, i.e., 3479€/year) and on injectors and separation discs (3,122,242 FCFA, i.e., 4767€/year), proportional to the reduction in time spent outside the optimal zone.Avoidedproductionlosses: this involves avoiding a major failure of 4 hours per year (lost production + restart cost). We set the average selling price per kWh at 150 FCFA, i.e., 0.23€/kWh. Our previous work [1] established a downtime rate of 30.3%, corresponding to a total downtime of 2654.28 hours per year.It is estimated that the probability of a major failure is reduced by 80% thanks to adaptive control.

The following steps are carried out to evaluate the losses:

lost production (kWh) = nominal plant capacity*failure duration (hours);cost of lost production = lost production (kWh)*selling price per kWh;total cost of a major failure = Lost production cost + Restart cost;failure savings = total failure cost*risk reduction;annual savings = annual energy saving + unloading saving + filter saving + injector savings + failure savings.Payback period = expenses divided by the Monte Carlo average annual gain.

To account for the variability of economic parameters, a Monte Carlo simulation was performed:

Number of draws: 10,000;Random seed: 42Outputs are expressed in €/year.

Dependencyassumptions:

The purchase and sale prices are positively correlated ( ρ = 0.7 ) ; all other variables are independent. The out-of-band reduction is derived from the deterministic simulation and remains fixed in the baseline Monte Carlo.

The distributions used are presented in Table 4 below:

Table 4. Distributions used for the economic analysis.

We will calculate the gains for each draw, then analyze the distribution (mean, standard deviation, percentiles).

Figure 2 presents the evolution of the kinematic (cSt) and dynamic (cP) viscosities and the separation efficiency of the HFO as a function of the temporal evolution of the HFO temperature at the separator inlet. The viscosities decrease exponentially with fuel temperature, in accordance with the law in Equation (3). The threshold value of 30 cP is reached for a temperature of 62˚C. Below this value, flow becomes difficult, increasing pressure in the circuits and reducing atomization. Above 80˚C, viscosity decreases further but gains become marginal. These observations justify a minimum heating temperature around 70˚C to 80˚C to ensure good atomization without unnecessary overheating. Moreover, the water separation efficiency increases with temperature because settling is facilitated by the decrease in viscosity and the increase in the water/HFO density difference. It exceeds 90% around 85˚C. The solids separation efficiency exhibits non-monotonic behavior: almost constant at low temperatures ( ≺ 60 ˚ C ) where high viscosity retains particles, it increases slightly then drops when viscosity becomes too low to trap solids. The overall efficiency is the geometric compromise of the two: it peaks around 80˚C then decreases slightly. This result shows that an excessively high temperature ( ≻ 90 ˚ C ) no longer improves overall separation and can even degrade it, justifying a narrow target range.

Operationalrisksandcriticalzones

Before examining the impact of the control strategy on HFO separation efficiency by the separators, Figure 3 presents the operational risks and critical zones to be considered for the analysis of the results. Thus, according to the HFO temperature zones, the following legend was adopted:

[50; 60], red: Very poor separation;

[60; 85], orange: Poor separation;

[85; 92], yellow: Acceptable separation;

[92; 98], light green: Optimal range;

[98; 105], dark orange: Fire hazard;

[105; 115], red: Fire + hydraulic hazard.

The separation risk is high at temperatures below 70˚C and decreases to a minimum around 85˚C - 90˚C. The hydraulic risk remains negligible up to 100˚C and then increases sharply as 105˚C is approached (partial vaporization, cavitation). The fire risk becomes significant above 95˚C and increases strongly after 98˚C. By superimposing the three curves, the zone of minimal risk is obtained between 85˚C and 98˚C, which corroborates the operating band. Beyond this range, fire risk dominates; below it, separation risk degrades fuel quality.

The overall efficiency curve alone could suggest that a temperature of 80˚C is optimal. However, the mapping of the zones reveals that the safe operating range is shifted toward 85˚C - 95˚C. This illustrates the compromise between performance and safety: the operational optimum is not the maximum efficiency, but the point where risks remain acceptable while maintaining sufficient efficiency.

Controlstrategies

Figure 4(a) reproduces the sinusoidal profile of the ambient temperature in the city of Ouagadougou, with a minimum of 22˚C around 6 a.m. and a maximum of 44.5˚C in the afternoon. This 22.5˚C variation has a direct impact on the HFO temperature, because the heating system must compensate for thermal losses and the variation in inlet temperature. Figure 4(b) presents the evolution of the HFO temperature during the first 12 hours of the day according to the two control strategies presented in Section 2.5. The fixed regime maintains a setpoint of 95˚C, but when the ambient temperature exceeds 40˚C, the HFO temperature exceeds 98˚C and enters the fire risk zone. The adaptive control then lowers the setpoint to keep the temperature below 98˚C, while remaining above 92˚C. This anticipation is crucial to avoid dangerous excursions while maintaining good separation efficiency. The slight time lag between the ambient temperature and the adaptive control response illustrates the time constant of the heating system.

To better observe the impact of adaptive control, we track the HFO temperature profile over 48 h in Figure 5. With the fixed control model, the HFO temperature remains almost at 95˚C, but regularly exceeds 98˚C during hot periods, thus entering the fire risk zone. The adaptive model curve follows a lower and more stable trajectory: it remains within the optimal zone and never exceeds 98˚C, even when the ambient temperature is high.

As an illustration, Table 5 presents the performance indicator values for the two control strategies. The efficiency of the adaptive control is more stable. Indeed, the fixed strategy maintains a higher average temperature of 96˚C, which promotes better water/solids separation in steady state. However, this average conceals a major problem: the fixed control spends 22.4% of the time outside the safety zone, exposing the installation to risks of fire, equipment degradation, and unplanned shutdowns.

Table 5. Performance indicators.

These results clearly demonstrate the advantage of adaptive control over a fixed setpoint in a Sahelian climate with high thermal variability. The optimal temperature range [92˚C - 98˚C] is respected almost throughout the entire 48 hours with the proposed strategy, compared with less than 80% with the fixed setpoint. This gain is directly related to the compensation of the ambient influence by the term − k × ( T a − T a , r e f ) . The value k = 0.2 (equal to the coefficient α) effectively cancels the sensitivity to variations in T_a, as shown by the equation:

in the zone where the limits are not active. This theoretical result is confirmed by the low residual variability (standard deviation of 1.04˚C versus 1.49˚C for the fixed setpoint). However, it should be noted that both strategies exhibit almost the same average efficiency.

The annual economic assessment of adopting the adaptive control we propose is recorded in Table 6. The savings are estimated from the simulation results and the unit costs of electricity per kWh provided in Table 3. Note that this study covers the three (03) separators of the thermal power plant.

Table 6. Estimated annual economic gains.

The energy saving, although modest (4170€), results from the reduction of the setpoint during hot periods. The most significant gains are related to maintenance: reductions in unloading operations, filter replacements, and injector repairs. Finally, the avoidance of approximately one major failure per year, with a rate of 0.01159 failures/hour [1], yields 13,353€ annually. The annual total is therefore estimated at 32,449€. However, the initial investment required to adopt the adaptive control strategy (ambient temperature sensor and controller reprogramming) does not exceed 4000€, leading to a payback period of less than one year.

The Monte Carlo simulation (10,000 draws) yields a nearly normal distribution of annual gains. Figure 6 presents the histogram. The mean is 19,701€, the standard deviation is 1996€, and the 90% confidence interval is [16,224€; 22,778€]. Even in the most unfavorable scenario (5th percentile), the gain remains above 16,224€.

Given the economic results obtained, the deterministic estimate is supported by the Monte Carlo analysis. The difference between the two values arises from the nonlinearity and the bounds applied to the distributions. The narrowness of the confidence interval (approximately ±14% around the mean) shows that economic uncertainties do not call into question the profitability of applying the strategy. Moreover, even the 5th percentile is four times higher than the investment cost.

Maintenance items (unloading operations, filters, injectors) account for the largest share of the gains. This suggests that the main impact of adaptive control is operational (reliability, availability) rather than energy-related. Of course, energy savings are not negligible, representing nearly 13% of the total gain.

The real data include 50 points recorded over 48 h, i.e., a sampling interval of 58.8 min. Type K thermocouples ( ± 1.1 ˚ C ) , placed immediately upstream of the three centrifugal separators, measure the HFO temperature. The ambient temperature is measured directly on site in the shade. From the real measurements, the thermal coefficient α was calibrated by linear regression of ( T − T o p t ) as a function of ( T a − T a , r e f ) , then evaluated on 25 records not used for calibration. The simplified thermal model was validated with a mean RMSE of 1.09˚C, a bias of −0.14˚C, and an R² of 0.788˚C. These values indicate a very good agreement between the simulated model and the recorded values. These performances are excellent for such a simple model, and they justify its use for sizing the adaptive control.

However, the model has limitations mainly related to the system dynamics, because the instantaneous linear equation does not account for thermal inertia (delays, time constants), and to the climate model (the sinusoid used does not account for climatic variability such as winds and cloud cover). Figure 7 presents the validation curves.