Effects of layer inhomogeneities on the process of sewage sludge convective drying

Abstract Convective sewage sludge drying is often carried out in belt dryers, where the air flow is directed through the layer. In such a configuration, drying air properties, as well as the structure of the layer and its homogeneity are key factors affecting the drying process. In the present work, these factors were investigated using laboratory experiments on relatively large sludge samples with a mass of several kilograms. Drying was performed at relatively low drying air parameters (time-averaged temperatures of 65 to 80 °C and velocities of 0.44 to 0.78 m/s). The inhomogeneity of the sludge layer drying was observed by measuring the layer surface temperature with an IR camera. The reduction in layer thickness during drying was measured using an optical laser-based method. Analysis of the data included regression and fitting of the data to parametric drying curves, with the modified Nadhari drying law providing the best fit. The standard deviation of the layer surface thermograms (S) was used as a parameter that accounted for the layer homogeneity and consequently drying evenness. Higher values of S corresponded to lower drying rates and consequently longer drying times, highlighting the importance of producing layers with a homogenous structure. The measured layer thickness reduction rate indicated the overall drying intensity almost from the beginning of drying. Both the surface temperature unevenness and the layer height reduction measurement methods were demonstrated as viable approaches for real-time monitoring of the drying process with potential for application in real-scale dryers.


Introduction
Population growth, urbanization, and stricter environmental standards are leading to an increase in the number and capacity of wastewater treatment plants.As a result, the production of sewage sludge, a semisolid residue from the wastewater treatment process, continues to increase.Handling and disposal of sewage sludge is very problematic as it may contain biological, physical and chemical contaminants, including potentially toxic metals and microplastics. [1]Landfilling and agricultural reuse of sewage sludge are therefore very limited, and other sustainable disposal methods are increasingly being researched and applied. [2]Many advanced disposal methods are based on incineration, but with the addition of technologies for recovery of nutrients, mainly phosphorus. [2]Incineration usually requires a reduction in the water content of the sludge, which can be achieved by mechanical dehydration followed by convective, conductive, or radiation drying. [3]rying is also beneficial because it reduces the volume and mass of the sludge and the associated costs of handling, storage, and transportation.
Convective drying involves direct contact between hot gas and wet material and may be implemented in various forms depending on the type of dryer.Belt dryers, in which the sludge is dried in the form of a porous layer, are commonly used in industrial practice. [3,4]Studies have shown that convective sludge drying can be improved by various methods, e.g., by mixing with secondary raw materials such as sawdust, [5,6] agricultural biomass [7] or pulverized coal, [8,9] by back-mixing, [10] by adding drying accelerators [11,12] or by using additional methods such as vacuum. [13]owever, the basic convective drying process depends largely on the parameters of the drying gas, especially temperature, velocity, and humidity. [14]Modeling the influence of these factors on drying appears to be difficult due to the large variability of the drying configurations, operating conditions, and sludge properties. [15]][22] The effects related to sample size are usually not explicitly studied, but they can have significant effects on the drying process.As shown in, [23] the drying of a small sludge sample (2.5 g) and the drying of a sludge bed (250 g) were inherently different.For the larger sample, three typical drying phases were found: the adaptation phase, the constant drying rate phase, and the decreasing drying rate phase.In a smaller sample, the constant drying rate phase was not detected. [23]Further increase in the size of the sludge sample, resulting in large porous layers, could further alter the drying process, as mechanisms, specific to sludge structural changes, are manifested in large scale.Sludge shrinkage and cracking have been shown to significantly affect the porosity of the layer and its resistance to airflow. [24]The phenomenon of shrinkage has been studied in detail only on relatively small samples in the form of a bed of cylindrical extrudates. [25]By using sophisticated methods such as X-ray tomography, a complete 3D reconstruction of the material shape during drying has been realized. [25]The method was also used to study the effects of sludge-sawdust mixtures [5] and back-mixing of sludge. [10]The results showed that the total exchange surface and the object volume decreased in a quasi-linear manner relative to the moisture content of the sludge. [10]Similar results were reported in, [26] where small samples of sludge from gelatin production were measured.
The drying of sludges in industrial belt dryers involves large-scale sludge layers, which are typically not reproduced in reported research.In order to capture specific mechanisms relevant to sludge drying in real-size applications, we have initiated studies in a laboratory facility where sludge samples of several kilograms can be dried in a layer 0.5 � 0.5 m in size. [24]The setup involves gas flow passing through the sludge layer, as in real belt dryers, which means that the layer structure and its transformation during drying significantly affect the local airflow and thus the distribution of the drying rate.Consequently, the (in)homogeneity of the layer structure becomes an important factor influencing the spatial uniformity of drying and thus the quality and intensity of the overall drying process.
The inhomogeneity of sludge layers in realistic belt dryers may be inherent in the incoming sludge material or induced during the layer formation process.It may be reflected in the spatial variability of properties such as porosity, water content, and physico-chemical parameters.The development of methods to quantify and monitor the effects of layer inhomogeneity could help improve the drying process in real applications but has not yet been reported in the literature.Therefore, the drying experiments and their analysis in the present study were focusing on the effects of layer inhomogeneity.
Methods presented include fitting drying models to measured data, which is a common approach in sludge drying research, [9,16,17,21,27,28] but is usually limited to determining the coefficient values that provide the best fit.However, in the present study, an attempt was also made to relate the model coefficients to the actual operating parameters, which is rarely reported in the literature.Recently, modeling of sludge drying kinetics as a function of drying air parameters (temperature, velocity, and relative humidity) was performed by Zheng et al. [19] They obtained a good fit between the air parameters for low-temperature drying and the coefficients of the Page drying model. [29]The results showed that temperature and velocity had a greater influence in the model than relative humidity, which is also consistent with the results of L� eonard et al. [14] In addition to modeling, the presented study is based on low-cost layer monitoring methods such as the IR and video camera.In this way, a high potential for the application of the employed methodology to industrial scale dryers can be expected.

Experimental setup
The sludge drying experiments were performed in a laboratory-scale convection dryer (Figure 1), as used in the previous study [24] but with several improvements.The dryer consists of a drying chamber containing a removable perforated grate.The grate has a size of 0.5 m x 0.5 m and is equipped with 4 cm high side walls made of metal sheet.Drying air enters the chamber at the top and is extracted at the bottom.The air is circulated by a fan controlled by a variable frequency drive and a timer switch.An additional fan is installed at the top of the chamber and is used for partial extraction of moist air from the system, thus supplying fresh air to the chamber.In this way, the air relative humidity in the chamber can be controlled.The drying air is heated by two electric heaters: the main heater (2 kW power) and the intake heater (1.6 kW power).The main heater is installed at the inlet of the circulation fan and is controlled by an on/off temperature regulator, which can keep the temperature within ±0.5 � C of the set value.The intake heater is located in the fresh air intake pipe and is manually controlled.The drying air conditions in the chamber are controlled by adjusting both fan speeds and both heater powers.The measuring system limits the maximum drying air temperature to 90 � C.
The dryer is equipped with a measurement system to monitor process variables, including temperatures, relative humidities, static pressures, air flow rates, and sludge weight.All temperatures are measured with Pt100 resistance temperature detectors (RTDs, accuracy class A), air relative humidities (RH) with calibrated Honeywell HIH-4000 hygrometers (±3.5% RH accuracy) and air static pressures with Endress þ Hauser Deltabar PMD235 differential pressure transducers (±0.1% accuracy).The drying air temperatures above and below the sludge layer are measured with 4 uniformly distributed RTDs.The drying air conditions in the extraction pipe at the top of the drying chamber are additionally measured with 1 RTD and 1 hygrometer.Ambient air temperature and RH are monitored at the intake pipe (1 RTD and 1 hygrometer).Air flow rate is measured with orifice plates in three locations: upstream of the main heater (orifice 1), upstream of the extraction fan (orifice 2), and downstream of the extraction fan (orifice 3).The orifice plates are manufactured according to the ISO standard [30] and connected to the differential pressure transducers.To enable accurate air density determination, an additional RTD is installed at the orifice 3. The orifice plate installation is not according to standard [30] as sufficient upstream and downstream straight pipe sections are not provided, therefore the mass flow measurement uncertainty is estimated at 3%.The pressure drop across the sludge layer and the grate is measured with a differential pressure transducer, connected to pressure taps on the walls of the drying chamber.
On-line sludge weighing is performed with a Pavone Systems C2G1 HT high temperature load cell with a capacity of 20 kg (combined error ±0.02% of full-scale output) installed in the drying chamber under the grate.The load cell is temperature compensated up to 90 � C. According to the uncertainty propagation laws the sludge mass weighing uncertainty was calculated to be ±5.7 g. [24] Weighing of the sludge before and after drying is additionally performed on a Kern FKB 15K0.5Ascale with linearity of 1.5 g.The sludge surface temperature is measured using a FLIR T425 infrared camera (accuracy ±2 � C or 2% of reading) mounted above a zinc-selenide window on the top of the drying chamber.Thermograms are automatically recorded every minute.
The Agilent 34970 A data acquisition unit was used to measure all analog signals (temperature, RH, pressure, and weight).Data were sampled at 20-second intervals and stored on a PC using Benchlink Data Logger software.
The height of the sludge layer was monitored using an optical system based on laser illumination and video monitoring of the sludge surface (Figure 2).A line laser source was fitted outside the drying chamber and was directed at the sludge surface through a small glass window.The laser produced a thin illuminated line on the sludge surface that was automatically recorded every minute by a video camera located on the top of the drying chamber.As the height of the sludge layer decreased, the illuminated line changed position in proportion to the angle of illumination.The height of the sludge layer was later calculated based on the position of the line on the recorded images using the procedure described in Section 2.4.

Experimental procedure
The sewage sludge used for the experiments was obtained from the municipal wastewater treatment plant (WWTP) in Ig, Slovenia, with a capacity of 5000 population equivalents (PE).The sludge was a product of biological treatment (secondary sludge).It was collected at the outlet of the mechanical dewatering system (screw press) in the form of granulated material with an estimated average granule size of 5 mm.The average granule size was not measured but subjectively estimated.The sludge was loaded onto a grate (Figure 3, left) and delivered daily to the laboratory dryer site in a sealed container in quantities sufficient for 2 drying experiments.The initial moisture content of the sludge was determined from samples taken during loading at the WWTP.The average initial moisture content was 4.26 kg water per kg of dry matter or 81.0%w.b.
Before drying, the layer was leveled by hand to a height of about 40 mm, using the side walls of the grate as a guide.The prepared sludge layer was weighed on the laboratory scale and then placed in the preheated dryer.During drying, the circulation fan was automatically stopped every 5 min for up to 30 s to eliminate the drag force from the weighed data.The drying process was continued until no significant mass variation of the sludge could be detected.Then the grate with the dried sludge was removed from the dryer and weighed again on the laboratory scale.Finally, the dried sludge samples of about 100 g were taken at the end of each drying test in order to later determine the final moisture content by complete evaporation of the water from the samples at 90 � C.
The drying experiments were carried out at different drying air temperatures and velocities.The low and high temperature levels were set at 65 � C and 80 � C, respectively.These temperature levels are relevant for the full-scale convective belt dryer in Ihan, Slovenia, as well as for heat pump convective dryers. [19]The high air velocity level was selected as the maximum possible value (at full fan rotational speed), while the low velocity level was selected by setting the fan speed to 60%.This corresponded to a time-averaged air velocity of 0.78 m/s and 0.45 m/s above the layer, respectively.Air velocities were determined from measured flow rates, considering bypass flow due to air leakage between the grate and the drying chamber walls.Bypass flow rate was measured in a separate experiment by sealing the drying grate and comparing the flow rates through all 3 orifice plates.A linear relationship between the bypass flow and the pressure drop across the sludge layer was determined.
The relative humidity (RH) of the drying air was not actively controlled during drying.Instead, the extraction air fan was set to a constant speed.Therefore, the RH of the drying air evolved according to the sludge drying rate (release of moisture) and the air circulation and extraction flows (a function of both fan speed and pressure drop across the sludge layer).The time-average RH of the air above the sludge layer varied between 20% and 32% (Table 1).Previous experiments [24] using a similar setup showed that the modest variation of the extraction air flow rate and thus drying air RH did not significantly affect the drying kinetics.
The experimental program included 9 drying tests with the main parameters listed in Table 1.Drying air velocity (v), temperature (T), and RH in Table 1 are time-averaged measured values, while initial sludge mass (m 0 ), initial moisture mass percent (w 0 ), and initial moisture content (X 0 ) were determined before each test.Test 1 was specific in terms of air temperature and velocity, which were set to intermediate levels rather than high and low levels as in all other tests.Coincidentally, the sludge mass was also highest in the case of test 1.

Data reduction and drying curve modeling
The weight measured by the load cell during drying was a sum of three forces: gravity force due to the mass of the sludge, gravity force due to the grate mass and the drag force due to passing of drying air through the porous sludge layer.The grate mass was constant and simply subtracted from the measured data, while the drag force was periodically eliminated Table 1.Definition of operating conditions for all tests.The drying air parameters -velocity (v), temperature (T) and RHare time-averaged measured values.The initial sludge conditions -initial mass (m 0 ), initial moisture mass percent (w 0 ), and initial moisture content (X 0 ) were determined before each test.by turning off the circulation fan for up to 30 s and weighing at zero air flow.The drying curves typically display either the moisture content (X) or the moisture ratio (MR) as a function of time.The moisture content is defined as where m w is the water mass, m sl is the sludge mass and m dm is the sludge dry mass.The moisture ratio is a dimensionless variable and is defined as MR ¼ (X − X e )/(X 0 − X e ), where X e and X 0 are the equilibrium and the initial moisture contents, respectively.X e is often assumed to be zero, which simplifies the moisture ratio definition to: [31] MR ¼ X X 0 (2) Drying curves are usually modeled by fitting measured data to various drying laws.There is no universally applicable drying law for convective drying of sewage sludge, as shown by several studies. [9,16,17,21,27,28]herefore, several laws (Table 2) that are widely used in the scientific literature to describe the kinetics of the drying process were considered in this study. [32]The original laws of Midilli [31] and Nadhari [33] were modified by considering the initial condition of MR ¼ 1 at t ¼ 0, which eliminated one parameter in both laws.This simplification made the modified laws more comparable to the other laws containing 3 or fewer parameters without significantly reducing their predictive power.In the final analysis, the original 4-parameter laws were not considered.
Parameters in the drying laws were determined by regression analysis.The GRG nonlinear solver in MS Excel was used to minimize the sum of squared errors between the measured and predicted MR.The coefficient of determination (R 2 ), reduced chi-square (v 2 ), and the root mean square error (RMSE) were calculated for each drying law to evaluate their predictive power: where MR meas,i is the measured moisture ratio, MR pre,i the predicted moisture ratio, MR meas,ave the average measured moisture ratio, N is the number of data points and n the number of constants in the regression model.Better fit between the measured and predicted values is represented by higher values of the R 2 and lower values of the v 2 and RMSE.

Postprocessing of images
Thermograms recorded by the IR camera were imported into Matlab to produce a temperature matrix for further processing.The matrix was first multiplied by a black/white mask image to eliminate areas in the matrix, which did not correspond to the sludge surface.The resulting field of view represented approximately 60% of the total sludge surface area.The values in each matrix were then recalculated to compensate for any changes in surface emissivity (e), atmospheric transmission coefficient (s atm ), temperature of reflecting surfaces (T refl ), and atmospheric temperature (T atm ).The sludge surface emissivity was estimated to be e ¼ 0.95 based on the emissivity of the soil. [34]The atmospheric transmission constant (ATC) was calculated using the ATC calculator by Flir [35] and was always s atm ¼ 0.99.The reflection and atmospheric temperatures were defined as equal to the set temperature of the drying air above the sludge.The final step in thermogram postprocessing was to calculate the average value and standard deviation of all values, which essentially gave the average temperature and a measure of temperature variability in each thermogram, respectively.Video image processing was performed in order to determine the sludge layer height from the laser illumination.The process started with image cropping, which reduced the images to include only an area, illuminated by the laser.The laser angle (a, Figure 2) was determined from the first image by measuring the distance y 1 and the laser height above the layer.The pixel size (s) was estimated based on the recorded reference object length as s ¼ 0.25 mm.Then, each image for a given test was loaded into Matlab to produce matrices (A) of values, which represent pixel brightness.Next, the average brightness of all images (matrices) was equalized according to the following  [29] MR ¼ exp(-k t n ) k, n Wang-Singh [37] MR ¼ 1þa t þ b t 2 a, b Logarithmic [38] MR¼a exp(-k t) þb a, k, b Midilli [31] MR¼a exp(- [39] MR¼a exp(-k t)þb exp(-n t) a, k, b, n Nadhari [33] MR¼a exp(- where i represents a sequential index of the image matrix A for a given test, N is total number of image matrices in the test, m and n represent the size of matrix A, and A eq,i is the resulting matrix with equalized average brightness.To determine the average laser illuminated distance y (Figure 2), the following procedure was employed.
where term in the brackets represents element-wise product of the A eq,i matrix and grid matrix Y, which has the size of A eq,i and element values corresponding to element n-index.The n-index actually represents the y-distance, once pixel size is considered.Therefore, the result of Equation ( 8) can be seen as the average of the product of pixel brightness and its distance in the y-direction for the entire image.Finally, the reduction of sludge layer height (h 1 -h i ) is calculated as:

Uncertainty analysis
The measurement system for drying air conditions (temperature, flow rate, RH) and sludge mass consisted of sensors connected to the Agilent 34970 A data acquisition unit.The Agilent 34970 A unit features high accuracy: ±(0.004% reading þ 0.004% range) for DC voltage at 100 mV range; ±(0.002% reading þ 0.0007% range) for DC voltage at 10 V range and ± 0.06 � C for RTD between −200 and 600 � C. Its contribution to combined measurement uncertainty in all measured variables is very low when compared to the uncertainties of the sensors.The sensor uncertainties, as given in the experimental setup description (Section 2.1), can be assumed as the total measurement uncertainties for the corresponding physical quantities.The uncertainty of a variable R that depends on n independent variables x 1 , x 2 , … , x n with uncertainties dx 1 , dx 2 , … , dx n can be calculated by: The uncertainty of dependent variables X (Equation (1)) and MR (Equation (2)) was calculated to be ±0.0084 and ±0.0029, respectively, for the most unfavorable conditions (highest X and lowest X 0 values).In the calculation it was assumed that the dry matter and consequently the sludge dry mass (m dm ) was determined at the WWTP with ±0.1% uncertainty.
The uncertainty of the IR camera, used for the sludge surface temperature measurements, is specified as ±2 � C or 2% of reading.Additional uncertainties were introduced with parameters, such as sludge surface emissivity, atmospheric transmissivity, window transmissivity.These uncertainties could only be estimated, making the calculation of combined uncertainty for IR measurements unreliable.Furthermore, the study relied on analysis of surface temperature unevenness, thus measuring the (average) surface temperature level with high accuracy was not required.
The uncertainty of the layer height measurement method is difficult to estimate as the method should be calibrated and validated by performing dedicated experiments.The resolution of the method for smooth surface can be calculated as tan(a) s ¼ 0.13 mm.

Basic weighing data processing
The basic processing of the weighing data is shown in Figure 4 for a selected individual case (test 4).The weighing system continuously measured the sum of the sludge gravity force and the drag force due to the passing of drying air.During periodic stopping of the circulation fan, the drag force was eliminated and the sludge mass was determined (circular markers).In the next step of processing, the sludge mass was fitted to a drying law to produce a continuous drying curve.In Figure 4, the modified Nadhari law (Table 2) was chosen for this purpose.In addition, the pressure drop across the sludge layer is also shown, as it is an important indicator of the structural changes in the sludge layer that lead to its increased porosity.It is obvious that most of the pressure drop reduction is observed during the first half of drying.
The following analysis considers all operating points.The change in sludge mass during drying was characterized by fitting the measured data (markers in Figure 5) to various drying laws as described in Section 2.3.According to all statistical parameters (Equations (3-5)), the modified Nadhari model provided the best fit to the measured data, so it was selected as representative for all subsequent analyses.The model parameters are summarized in Table 3, while the models are represented by curves in Figure 5.
Further parameterization of the drying curves and their discussion are presented later in Section 4.3.

Sludge surface thermogram processing
The sludge surface thermograms were processed to determine the area-averaged surface temperature and its unevenness, expressed as the standard deviation of all values in the particular thermogram.The areaaveraged thermogram temperatures were closely related to air temperature and were not analyzed in detail.However, the unevenness of the surface temperature indicates the non-uniformity of the drying process and was also used as a parameter for the regression modeling.
Figure 6 presents sludge surface temperature unevenness, expressed as the standard deviation of thermograms (S), depending on the sludge moisture content (X).It is evident that in all tests, the  2 and 3) by solid curves.Table 3. Coefficients (a, k, n) and statistical parameters (R 2 , v 2 , RMSE) of the modified Nadhari drying law (curves are plotted in Figure 5).Time-averaged sludge surface temperature unevenness (S ave ) and maximum sludge surface temperature unevenness (S max ).beginning of drying (maximum X) is characterized by low values of S.Then, S values are increasing steadily until a peak value is reached (S max ), which occurs typically between X ¼ 1 and X ¼ 2. On the left-hand side of the peak, the S values approach zero value as the X is reduced to zero.The shape of S-curves is similar for all tests and is well correlated to the sludge moisture content, however, the magnitude of S can vary significantly from test to test.Generally, lower S values were attained in tests with higher drying air velocity (tests 2, 5, and 7), with the exception of test 8, where air velocity was high but S was intermediate, probably as a result of higher initial inhomogeneity of the layer.The lowest S values were actually obtained at the beginning of test 5 (X > 3.2), but here the IR camera was accidentally out of focus and the corresponding values are not representative.The highest S was measured in the case of test 9. Figure 6 includes a series of thermograms at equal intervals of X in order to demonstrate source data that was used for the calculation of S. Thermograms for tests 7 and 9 were selected since they represent cases with the lowest and highest values of S, respectively.
The temperature unevenness data were further reduced to a time-averaged value (S ave ) and a maximum value (S max ), which are shown in Table 3.The S ave value is more indicative of the complete drying process, where each measured value in time is equally weighted, while the S max value is more indicative of the drying process as a function of moisture content (Figure 6).The relationships between the temperature unevenness and drying kinetics will be discussed in more detail later.

Layer height measurements
Sludge layer height reduction (Dh), as measured by the laser illumination method, is presented in Figures 7  and 8.In all tests, the evolution of Dh (Figure 7) could be characterized by three periods: (1) a short initial period with the highest rates of Dh reduction, (2) a period of relatively constant rate of Dh reduction, and (3) a final period of constant Dh.The duration of the final period varies greatly from test to test.By far the smallest final Dh (approx.−3.8 mm) was measured in test 2, which had the highest drying rates and shortest drying time of all tests (see Figure 5), but also the lowest initial mass.These factors could contribute to specific layer structural changes during drying, that manifested as less significant Dh.However, such specifics were not noticed at the end of the drying experiment and are therefore not conclusive.All other tests resulted in the final Dh between −8 and −11.5 mm.The relative height reduction (%) with respect to the initial layer height can be only estimated since the initial layer height was not measured accurately.Based on the 40 mm estimated initial height, the final relative reduction in layer height was between 20% and 29% for all tests but test 2.
When Dh is plotted as a function of sludge moisture content (Figure 8), the three phases with different Dh gradients are still visible.However, the extent of the final phase appears much less significant, since very little moisture is removed at constant Dh.Only tests 2, 3, and 9 show significant moisture reduction at constant Dh, while in all other tests, this process appears insignificant.The central phase of Dh reduction is almost linear in some tests (e.g., test 4), while in some tests it features a change in gradient (e.g., test 7).These details could indicate changes in drying and/or sludge shrinking mechanisms, however, an indepth analysis of these processes would require more experimental data.

Layer height reduction
When interpreting the measured layer height data, the specifics and limitations of the measurement method used must be considered.First and foremost, the sludge shrinking process involves transformation of the material shape in all 3 dimensions, while the method used only records changes in one dimension.It must also be considered that the measurement method used was limited to a relatively small area of the layer.In addition, specifics such as the size of the layer, the shape of the grate, sludge material properties, granulation, etc., may affect the reshaping of the layer and the reduction of its height.Considering all these factors, it is expected that a comparison of the presented results (Figure 8) with the results obtained by other researchers who used more sophisticated methods will show remarkable differences.For example, some researchers used X-ray tomography for a full 3D reconstruction of the material shape during drying. [5,10,25]These studies, which examined sludge samples in the form of a bed of cylindrical extrudates, generally found that the decrease in sludge volume and the increase in void fraction were linearly related to the moisture content of the sludge.Results of the present study, however, indicate linear layer height reduction only within limited intervals of moisture contents.

Comparison of selected tests
The effects of various parameters on drying have been presented and discussed considering all drying tests, however, some effects are best interpreted when only selected tests are considered.For this purpose, 3 tests with very similar initial parameters (mass and moisture content of the sludge) and operating parameters (temperature and velocity level) are compared in more detail.As shown in Table 4, there was very little variation in the above parameters for tests 4, 6, and 9, but the total drying time differed significantly.The total drying time in Table 4 is expressed as the time (t 90 ), required to achieve 90% dry matter (X ¼ 0.111) per kilogram of wet sludge (m i ).
The selected tests showed a different evolution of the sludge weight (Figure 5), sludge surface temperature unevenness (S, Figure 6), and sludge layer height reduction (Dh, Figure 7).To facilitate comparison and interpretation of the results, the last two parameters are plotted again as a function of time in Figure 9.The evolution of S is represented by curves with very similar shape but different scaling.The scaling of the curve peak (S max ) seems to be correlated with the scaling (stretching) of the curve in temporal coordinate.In other words, higher S is clearly related to slower drying, except in the initial drying period, where curves almost coincide.Similar trends are shown by the Dh curves, however, the rate of drying is reflected in the rate of Dh change almost from the start of drying.After only 10 min of drying, the Dh shows the fastest drying for test 4 and the slowest drying for test 9.The shrinkage in the case of test 6 is represented by a curve that is less smooth and has higher variation in its gradient, which is probably related to specifics in the sludge layer structure.Concurrence of the S and Dh curve features (peaks, changes in gradients) is not evident in Figure 9, which means that shrinkage and temperature unevenness can hardly be correlated in the time domain.Similarly, the two phenomena cannot be correlated in dependence of moisture content X, as can be seen from Figures 6 and 8.
The thermograms in Figure 9 complement the S parameter with some additional information on sludge temperature unevenness and its relationship to the drying rate.The relatively slow drying in the case of test 9 can be clearly attributed to the presence of a cold zone in the central part of the observed surface.While the peripheral areas seem to reach the final temperature quickly, the area in the center warms up and dries slowly, affecting the overall process.Most likely, the colder zone is related to a zone of higher layer compaction or lower porosity, possibly also to a higher initial moisture content.In the case of test 4, where the sludge dried at a much higher rate, the temperature anomalies are much smaller and distributed over the entire observed area.
The presented results highlight the importance of producing a uniformly structured layer for drying in the through-flow configuration.In addition, they indicate that the S or Dh parameters could be used to monitor and control the drying process in real-scale applications where on-line weighing of the sludge layer is not practical.The Dh value at the initial drying phase could be used to predict drying rates for the entire process.Similarly, the peak S values and the time required to reach them could indicate the overall intensity of the drying process.

Drying curve parameterization
Further parameterization of the drying curves for all tests was attempted by relating the model parameters a, k, and n (Table 3) to the conditions of the experiment, considering both drying air conditions and sludge layer conditions.For convective drying processes, the effect of drying air conditions on drying kinetics is clear: drying rates are generally increased when air temperature is increased and air RH is decreased.Higher drying rates are also achieved by improving the contact of the drying air with the material, which can be achieved by favorable aerodynamic conditions (typically higher air flow rates or velocities) and material structure (i.e., layer shape and porosity).Based on these facts, several parameters were considered influential for further modeling: temperature, RH and velocity of drying air, initial mass and moisture content of the layer, pressure drop across the layer, and temperature inhomogeneity of the layer surface (expressed as standard deviation of thermograms).Time-averaged values and maximum values were considered for all quantities except the initial mass and the moisture content of the layer.The relation of the parameters a, k and n to these quantities was performed by regression, separately for each parameter.For this purpose, the exponential law (Equation ( 11)) was chosen, and the procedure used was identical to the drying law regression procedure described in Section 2.3.
where y is the dependent variable (in this case parameter a, k, or n), c i are model coefficients and x i are independent variables.Models with 2 and 3 independent variables were considered but the final comparison was done with 3-parametric models (z ¼ 3).Manual where v is the time-averaged air velocity above the layer, T is the time-averaged air temperature above the layer, S max and S ave are the maximum and timeaveraged standard deviation of thermograms, respectively, and X 0 is sludge initial moisture content.The R 2 values for the presented models in Equations (12-14) are 0.531, 0.582, and 0.489, respectively, which generally means a relatively weak explanatory power of the models.Nevertheless, they can still be used as an indication of the relationship between the operating conditions and the drying curves.First, it is important to understand the influence of the drying law parameters a, k, and n on the shape of the drying curve.Increasing any of the three parameters results in a steeper drying curve, which means higher drying rates and shorter drying times.Second, it should be noted that positive exponents in the power law Equations (12-14) mean a positive correlation between the independent variable and the model result.In this respect, the effect of drying air temperature on drying kinetics is unambiguous -an increase in air temperature increases k and n and thus accelerates drying.A clear correlation can also be seen for the initial moisture content (X 0 ), which is negatively correlated with a and thus the drying rate.It should be noted that the variations of X 0 (Table 1) were relatively small in the experiment.The effect of sludge surface temperature inhomogeneity, quantified by standard deviation, is less evident.A higher maximum standard deviation (S max ) results in higher values of a and lower values of k, while higher time-averaged standard deviation (S ave ) results in lower values of n.However, the combined effect of S max on the drying curve is negatively correlated, meaning that higher values of S max lead to lower drying rates.The effect of velocity on the drying curve is also not clearly reflected in Equations (12-14), since their exponents are both positive and negative.However, a simple calculation of the combined effect of velocity reveals that it is indeed negatively correlated with drying rate.
Considering the basic physical mechanisms of heat and mass transfer, the positive effect of air temperature on drying rate is as expected.Perhaps less clear is the effect of sludge layer temperature unevenness, as characterized by the parameters S max and S ave .Models suggest that higher surface temperature unevenness can be correlated with lower drying rate.In interpreting this correlation, it is important to keep in mind that the sludge surface temperature distribution is in fact a reflection of the heat and mass transfer process and can hardly be treated as an independent variable.It depends on the layer structure (thickness, porosity at macro and micro scale, moisture content, material properties, … ) and its interaction with the drying air.The layer structure is determined by the initial layer formation process, which inevitably leads to inhomogeneities in the sludge distribution, and by the timedependent processes during drying, such as shrinkage and cracking.This can lead to the formation of areas of higher layer compaction or lower porosity, which means higher local resistance to airflow and thus lower local air velocities and lower heat and mass transfer rates.Such anomalies are clearly reflected in the sludge surface thermograms and consequently in the S max and S ave parameters, which explains the fact that a higher evenness in sludge surface temperature, as a reflection of a uniform drying of the layer, is favorable to achieving higher drying rates.
As noted earlier, the overall effect of velocity in Equations (12-14) is negatively correlated with drying rate, which is contrary to the expected effect of velocity on drying.However, the effect of velocity in the presented models is weak, meaning that, for example, doubling the velocity hardly affects the resulting drying curve.The weak effect is also indicated by the values of the velocity exponents in Equations (12-14), which are always the smallest.In fact, eliminating velocity from these equations and regressing to 2-parameter models has a relatively small effect on the R 2 reduction.The R 2 values for Equations (12-14)  decrease from 0.531 to 0.483, from 0.582 to 0.556, and from 0.489 to 0.432, respectively.This leads to the conclusion that air velocity could be omitted as an independent variable for modeling drying curves in this case.It should be noted, however, that some influence of velocity is indirectly preserved in the models by the inclusion of thermogram unevenness (the parameters S max and S ave ).The two parameters were generally lower when the air velocity was higher, implying that the effect of velocity, as reflected in increased evenness of sludge heating and drying, was actually positive in the experiments.Other researchers report that the effect of air velocity on drying rate is both low and high, depending on the experimental conditions, especially the temperature of the drying air. [36]

Conclusions
Drying experiments were conducted with sludge layers in through-flow configuration to determine the relationships between drying rates, drying air parameters, and spatial non-uniformity of the drying process.The analysis of the methods and the results allows the following conclusions to be drawn: � The standard deviation of the sludge surface thermograms (S) was demonstrated to be an important indicator of the drying process.Higher instantaneous values of S were associated with slower drying, except in the initial drying stages.Similarly, peak values of S (S max ) and the time required to reach them were indicators of the overall intensity of the drying process.In experiments conducted at low air velocity and high air temperature, reaching 90% dry matter required 25.8 min/kg when S max was 6.6 K, while in a similar test with S max of 9.6 K, the specific drying time increased to 41.9 min/kg.� The modified Nadhari drying law provided the best fit to the measured data according to the selected statistical parameters.The coefficients of the modified Nadhari law were further modeled as functions of time-averaged parameters (drying air temperature and velocity, S, X 0 ), however, the predictive power of the models was relatively low.� Increasing the drying air velocity and producing a homogenous sludge layer were effective measures for increasing the evenness of drying, thus lowering the drying time and improving the energyefficiency of the process.� Measurement of sludge shrinkage using linear laser illumination and video recording of the illuminated surface allowed monitoring and early detection of the intensity of the drying process.The rate of drying was reflected in the rate of layer thickness reduction almost from the beginning of drying.

Figure 1 .
Figure 1.Scheme of the laboratory convective dryer.

Figure 2 .
Figure 2. Optical measuring system for layer height monitoring, consisting of a line laser and a generic HD video camera.

Figure 3 .
Figure 3. Sludge on the grate before drying (left) and after drying (right).Grate size is 0.5 m � 0.5 m.

Figure 5 .
Figure 5. Moisture ratio as a function of time for all tests.Measured data is represented by markers and fitted data (modeled according to the modified Nadhari law, Tables2 and 3) by solid curves.

Figure 6 .
Figure 6.Sludge surface temperature unevenness (standard deviation of thermograms, S) as a function of sludge moisture content with examples of thermograms for test 9 and test 7.

Figure 7 .
Figure 7. Change in sludge layer height, measured by laser illumination, as a function of time.

Figure 8 .
Figure 8. Change in sludge layer height, measured by laser illumination, as a function of moisture content.

Figure 9 .
Figure 9. Sludge surface temperature unevenness (standard deviation of thermograms, S) and sludge layer height reduction (Dh) as a function of time with selected thermograms for tests 4, 6 and 9.

Table 2 .
Drying laws used for fitting of drying curves.