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European Biosolids and Organic Resources Conference 15-16 November, Edinburgh, Scotland

MIXING OPTIMIZATION OF GAS-MIXED ANAEROBIC DIGESTION USING CFD

Dapelo, D.1 and Bridgeman, J.1

1Department of Civil Engineering, University of Birmingham, UKCorresponding Author Email: [email protected]

Abstract

In this paper, an Euler-Lagrange model for computational fluid dynamics was employed to simulate a full-scale gas-mixed digester. A novel method to assess mixing quality was described. The method defines a passive tracer to assess the relative mixing quality of different system configurations by comparing the respective tracer distributions. The method was used to assess the effectiveness of four different mixing strategies. Better mixing quality and less mixing time can be achieved by switching biogas injection between two different nozzle series at regular time intervals, and smaller time intervals resulted to be more effective in reducing the mixing time.

Keywords

Anaerobic Digestion, CFD, Lagrangian, Mixing, Non-Newtonian, Sludge, Tracer

Introduction

Every day, over 10 billion litres of wastewater are treated in UK in more than 9,000 wastewater plants (WaterUK, 2012). A number of stages in the wastewater process result in sludge production: in 2010—2011, the wastewater plants in the UK produced about 1.5 million tonnes of sewage sludge (WaterUK, 2012). The whole wastewater treatment process, including sludge treatment and disposal, is an energy-intensive operation. Data returned by the EU Member States suggest energy consumption exceeds 23,800 GWh per annum, and further increases of 60% are forecast in the next 10-15 years, primarily due to tightened regulation of effluent discharges. Predictions show that by 2030 the world will have to produce 50% more food and energy and provide 30% more water, while mitigating and adapting to climate change. Therefore, the “explicit link between wastewater and energy” must be addressed.

Mesophilic anaerobic digestion is the most widespread technology for sludge treatment (Bridgeman, 2012). Sludge is mixed with anaerobic bacteria at temperatures between 22 and 41 ◦C, and biodegradable material is broken down into more stable compounds. One of the most interesting aspects of anaerobic digestion is that biogas, which is prevalently methane, is produced during the process. Biogas, in turn, is increasingly harnessed as a renewable energy by means of combined heat and power technology (Bridgeman, 2012). According to (Owen, 1982) mixing is responsible for about 17—73% of the total energy consumption of an industrial digester, and yet, current practice in digester design is still rooted in “rule of thumb rather than science” (Dapelo and Bridgeman, 2015). Therefore, the only practicable strategy to reduce the energy consumption of a digester consists of reducing the level of mixing without compromising, and indeed enhancing, biogas production.

Although mixing is fundamental for the success of full-scale anaerobic process, recent experimental (McMahon et al., 2001; Stroot et al., 2001; Ong et al., 2002; Gómez et al., 2006; Ward et al., 2008) and CFD-based research (Bridgeman, 2012; Wu, 2012; Sindall et al., 2013) show that overmixing can damage the process of digestion, and in any case has a detrimental effect on the economics of an

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anaerobic digestion plant. However, there is no consensus on how to assess mixing and, consequently, how to define overmixing. The reason is that traditional mixing assessing approaches based on average shear rate magnitude have been proved unsuccessful in the case of anaerobic digestion. (Bridgeman, 2012) reported laboratory-scale digesters producing biogas regularly despite the average shear rate was one order of magnitude lower than the traditional minimum value of 50—80 1/s suggested in (Tchobanoglous et al., 2010). Furthermore, (Dapelo and Bridgeman, 2015) reproduced the design of a real, working full-scale gas-mixed digester, and found that the average shear rate was below 1 1/s in all the cases. Other work on the same design (Dapelo, 2016) shows that assessment of average shear rate is not able to ascertain the eventual benefit of unconventional mixing strategies, such as alternating biogas injection between two different nozzle series at regular time interval in gas-mixed digesters. Therefore, it is necessary to define a new criterion to assess mixing in anaerobic digestion.

In this paper, a novel method to compare the mixing quality of different system configurations is described. An Euler-Lagrangian CFD model to simulate gas mixing in anaerobic digestion introduced in (Dapelo et al., 2015) is used to reproduce the behaviour of the full-scale digester described in (Dapelo and Bridgeman, 2015). In this setup, biogas is collected from the top of the tank and injected back into the sludge through a series of nozzles placed at the bottom of the tank. The bubbles rise through buoyancy, thus transferring part of their momentum to the surrounding sludge. This momentum exchange gives rise to motion and flow patterns within the sludge, thus ingenerating mixing. A passive tracer is defined, and its behaviour tracked over time. The relative quality of mixing of different system configurations is assessed by comparing the tracer distributions at a given time.

Assessment of Mixing Through a Passive Tracer

Passive Tracer

The passive tracer was modelled through the introduction of a scalar field c assuming values within the continuous interval [0, 1] and reproducing the concentration of a solute compound within the liquid phase. The field c obeys a convection-diffusion equation with zero diffusivity:

(∂ t+u⃗ ⋅∇ )c=0 , ( 1 )

where u⃗ is the liquid phase velocity field.

Assessment of Mixing

The assessment of mixing through the analysis of the scalar field c can be performed in the following way. At an initial time, the tracer is “inoculated” inside the domain. Mathematically, this meaning defining c = 0 in the entire domain, and c = 1 in one (or few more) regions of size much smaller than the whole domain. Then, the behaviour of the tracer is evaluated in the successive times. If the system is well mixed, the tracer assumes an approximately constant non-zero value through the domain, regardless of the actual value it. On the contrary, tracer values of different orders of magnitude coexisting together in a poorly mixed system. In the extreme case of totally non-mixed system, the tracer assumes the value c = 0 everywhere apart from the inoculation sites, where c = 1.

The degree of uniformity of the tracer can be assessed as follows. The interval of values I ≡ [0 ,1 ] that c can assume is divided into several sub-intervals I 1,…, IN such that I 1∪…∪ IN=I . For each

sub-interval Ii, the relative occupancy αi is defined as follows:




α i= ∫ ¿ i ¿❑(c ( x⃗ ) )d3 x ¿∫ d3 x

, ( 2 )

where the rectangular function ¿ i¿❑(c ) is defined as:

¿ i¿❑ (c )={1 , c∈ Ii ;0 , c∉ I i .( 3 )

This definition implies that ∑i=1

N

αi=1 . When the tracer field c becomes uniform (and hence the

system becoming well mixed), one single occupancy α i becomes much larger than all the others,

regardless of its particular value, but with the exclusion of the one referring to the lowest value of c. In this latter case, in fact, the tracer has not been able to spread through the domain. Then, given two different system configuration, described respectively by the two sets of relative occupancies αi and βi and with the same subdomain decomposition I 1 ,…, IN , the first configuration is better mixed than

the second if max i≠ 1α i>max j ≠1β j .

CFD Modelling

Sludge Rheology

In CFD work, the power-law model has been proved as an effective approximation of the non-Newtonian sludge rheology (Wu and Chen, 2008; Bridgeman, 2012). In such model, the viscosity μ depends on the shear rate magnitude S through a dimensionless power index n and a consistency index K (Pa sn):μ=K Sn−1 . ( 4 )

The power-law coefficients depend on the total solid content (TS) and the temperature (Achkari-Begdouri and Goodrich, 1992), but the temperature can be considered as fixed at 35 oC due to the necessity of maintaining mesophilic conditions, and hence the only relevant parameter is the TS content. Table 1 reports the values of the power-law coefficients in function of the TS. As sludge density differs by less than 1% from water density at 35 oC (994 kg/m3), a constant value of 1,000 kg/m3 was adopted for the sake of simplicity.

Table 1: Sludge rheology at 35 oC, from (Achkari-Begdouri and Goodrich, 1992)

Total solid (%)

Consistency coeff. (Pa sn)

Power-law index (–)

Shear rate range (1/s)

Viscosity range (Pa s)

Density (kg/m3)

2.5 0.042 0.710 226—702 0.006—0.008 1,000.365.4 0.192 0.562 50—702 0.01—0.03 1,000.787.5 0.525 0.533 11—399 0.03—0.17 1,001.009.1 1.052 0.467 11—156 0.07—0.29 1,001.3112.1 5.885 0.367 3—149 0.25—2.93 1,001.73




Computational Model

Sludge in gas-mixed anaerobic digestion is a multiphase fluid, composed of a liquid phase and a gaseous, bubbly phase. The bubbles are much smaller than the digester size, and are prevalently arranged in vertical narrow plumes rising above the nozzles. On the other hand, the detailed analysis of the single bubbles’ motion is not required, as the aim of the study presented here was to reproduce the flow patterns of the liquid phase at the digester’s length scale and then to use the information on flow patterns to ascertain the grade of mixing. In this modelling situation, an Euler-Lagrangian model is preferable (Andersson et al., 2012).

An Euler-Lagrange model for gas-mixing in anaerobic digestion was developed and validated in (Dapelo et al., 2015), and subsequently, was employed to study flow and viscosity patterns and average shear rate in a full-scale application (Dapelo and Bridgeman, 2015). The Navier-Stokes equations with a power-law viscosity are solved in conjunction with the equations of motion of the single bubbles, while a two-way coupling is obtained by adding a momentum-exchange term to the equations (Dapelo et al., 2015). Bubble drag and lift forces were reproduced with the models described in (Dewsbury et al., 1999) and (Tomiyama et al., 2002) respectively. The underlying assumptions are: (i) spherical bubbles, (ii) pointwise bubbles, (iii) no bubble-bubble interaction, and (iv) at each timestep, overall number of bubbles present in the system smaller than 104 (Dapelo et al., 2015).

Meshing

The modelled digester is the same as in (Dapelo and Bridgeman, 2015), and can be approximately described as a cylinder above an inverted frustum. Twelve nozzles are placed along a circle at the inclined bottom of the tank, at regular intervals. The geometry of the digester is summarised in Table 2 (courtesy of Peter Vale and Severn Trent Water Inc.)

Table 2: Geometry of the digester, from (Dapelo and Bridgeman, 2015)

External diameter Dext 14.63 mDiameter at the bottom of the frustum Dint 1.09 mCylinder height h 14 mFrustum height h0 3.94 mDistance of the nozzle from the axis Rnoz 1.75 mDistance of the nozzle from the bottom hnoz 0.3 mMaximum gas flow rate per nozzle Qmax 4.717 103 m3/sMixing time tmix 15 min/h

Due to the symmetry of the problem, only a wedge comprising an angle of π/6 radians around the symmetry (y) axis of the digester, with appropriate periodic conditions on the facets was considered for the simulations. The nozzle lied onto the radial symmetry plane (xy) of the domain. A grid of 98,420 cells, depicted in Figure 1, was already proved to be able to reproduce detailed flow patterns faithfully in (Dapelo and Bridgeman, 2015), and therefore was used in the work described here. The computational work was undertaken at the BlueBEAR high performance computing facility in the University of Birmingham. Each simulation was run in parallel on two dual-processor 8-core 64-bit 2.2 GHz Intel Sandy Bridge E5-2660 worker nodes with 32 GB of memory, for a total of 32 nodes.




Figure 1: Mesh geometry, from (Dapelo and Bridgeman, 2015)

In (Dapelo and Bridgeman, 2015; Dapelo et al., 2015), the Launder-Gibson Reynolds-stress turbulent model (Gibson and Launder, 1978) reproduced the non-symmetric Reynolds stress tensor originating from bubble-liquid momentum transfer at a contained computational expense, and therefore it was employed in the work presented here. Following (Dapelo and Bridgeman, 2015; Dapelo et al., 2015), the timestep for the (transient) simulations was defined dynamically with an algorithm aimed at keeping the maximum Courant number just below a specified value of 0.2. Let i be a generic cell, Li its linear dimension and ui the velocity magnitude at that cell and Δt the timestep; then the Courant number Coi at the cell i is defined as:

Coi=ui ΔtLi. ( 5 )

The maximum Courant number Co, is defined as the maximum of Coi over i. After a starting value of Δt of 10-5, the timestep was corrected to keep Co slightly below the limit of 0.2.




As in (Dapelo and Bridgeman, 2015), a preliminary series of first-order simulations was run from a configuration in which neither fluid phase motion nor bubbles were present. The value of c was set to 0 everywhere apart from four small squares, where it was set to 1. The coordinates of these squares are reported in Table 3. The initial conditions for the other quantities were set as in (Dapelo and Bridgeman, 2015): 4.95 10−4 m2/s3 for the turbulent energy dissipation field ε, zero for pressure p, velocity u⃗ and Reynolds stress tensor R. In Table 4, the complete set of boundary conditions is reported.

Table 3: Coordinates of the squares where c is set to 1 as initial condition

Square id. 1st corner xyz (m) 2nd corner xyz (m)First (6.8, 7.8, -0.2) (7.0, 8.0, 0.2)Second (6.8, 6.8, -0.2) (7.0, 7.0, 0.2)Third (5.8, 7.8, -0.2) (6.0, 8.0, 0.2)Forth (5.8, 6.8, -0.2) (6.0, 7.0, 0.2)

This first-order series was stopped after a computational time of 10 s, which was considered as sufficient to have a fully developed bubble plume. The last timesteps were used as initial conditions for the main, second-order simulations, while the previous timesteps were discarded. The main simulations were run for a computational time of 890 s, for an overall time of 15 min. Binary files of the system configurations were collected every 10 s during the main runs. Computational runtime and observed timestep resulted similar to what observed in (Dapelo and Bridgeman, 2015), namely below 24 hours, and between 0.0013 and 0.14 seconds respectively.

The differencing schemes used were the same as in (Dapelo and Bridgeman, 2015): linear for interpolations, limited central differencing for the Gradient operator, linear for the Laplacian, Van Leer for all the other spatial operators, first-order Eulerian scheme for the time derivative in the preliminary runs and second-order backward for the main runs.

Table 4: Boundary conditions

Top p Constant zerou⃗ Slipε SlipR Slipc Slip

Wall / Bottom p Adjusted such that the velocity flux is zerou⃗ Constant zeroε Wall functionR Wall functionc Zero gradient

Simulation Strategy

The computational model requires four parameters as input data: bubble diameter, injected gas flow rate and the two power-law coefficients of Equation ( 4.

As discussed in (Dapelo and Bridgeman, 2015), it is currently impossible to set a value for the bubble diameter confidently due to the lack of experimental data in the literature about bubbles inside a digester. However, (Dapelo and Bridgeman, 2015) performed CFD simulations with three different




bubble sizes (2, 6 and 10 cm), and showed that the shear rate dependence over total solid and mixing input power had similar trends for all the bubble sizes taken into consideration, and therefore they were able to conclude that bubble size is irrelevant to the purpose of assessing mixing quality. On the other hand, a smaller bubble size for the same injected gas flow rate means a higher number of bubbles simultaneously present in the system. For this reason, a larger bubble size is preferable in order to keep the number of bubbles low and better meet the model assumption (iv) of number of bubbles simultaneously present in the system smaller than 104. Consequently, the bubble size was set to 10 cm in the work presented here.

(Dapelo and Bridgeman, 2015) assessed the average shear rate for different values of injected flow rate, and concluded that the shear rate is optimized for Q = 0.5 Qmax. Hence, this value was used for the simulations described here. The power-law parameters were determined from Table 1 once that a value for the TS had been chosen. (Dapelo and Bridgeman, 2015) investigated the values of TS of 2.5, 5.4 and 7.5%, and found that higher values of TS gave rise to less intense velocity flow patterns. The spreading of the tracer is directly linked to the intensity of the velocity flow patterns through Equation ( 1 ), and hence it is reasonable to suppose that a higher TS value gives rise to a more difficult spreading of the tracer. As the aim of the work reported here was to determine how the gas injection strategy can improve mixing through an analysis of the tracer diffusion, it seemed reasonable to consider the situation where the tracer spreading resulted more difficult, and hence the TS value of 7.5% was adopted. Higher values of TS were considered as they do not occur in gas-mixed digesters.

Four gas injection strategies were analysed. In the first run, injection was operated through the original nozzle series, at the distance Rnoz = 1.75 m from the symmetry axis. The second run was performed with biogas being injected from a new nozzle series, placed at the distance Rnew = 5.49 m from the symmetry axis. In the third run, injection was switched between the original and the new nozzle series every minute, starting from the old series. Finally, in the forth run, the same was done as in the third run, but the interval between switching from one nozzle series to the other was brought to 5 minutes.

Results and Discussion

In each of the four runs described above, the scalar field c was evaluated every minute starting from the first minute. In all the cases, the interval I was divided into six dub-intervals following a logarithmic scale Figures Figure 2, Figure 3, α1 drops considerably if compared to the levels of the original nozzleseries; in particular, it ceases to be the largest relative occupancy after 12 minutes. Furthermore, α1 drops continuously through the whole run, thus indicating that biogas injection still brings benefit in terms of mixing when mixing time increases. Therefore, it makes sense to mix for longer times when the new nozzle series is taken into consideration, contrarily to the case of the original nozzle series. However, a section of the domain which is not reached by the tracer still survives even after 15 minutes, and conversely, α6 remains constant through the whole run, thus indicating that some areas are still unmixed at the end of the run. and The action of switching between the two nozzle series (As regards the new nozzle series (Figure 3), α1 drops considerably if compared to the levels of the original nozzle series; in particular, it ceases to be the largest relative occupancy after 12 minutes. Furthermore, α1 drops continuously through the whole run, thus indicating that biogas injection still brings benefit in terms of mixing when mixing time increases. Therefore, it makes sense to mix for longer times when the new nozzle series is taken into consideration, contrarily to the case of the original nozzle series. However, a section of the domain which is not reached by the tracer still survives even after 15 minutes, and conversely, α6 remains constant through the whole run, thus indicating that some areas are still unmixed at the end of the run.) dramatically increases the quality ofmixing. After around 3 minutes, the system reach the same level of mixing that was displayed in the




case of injection through the new nozzle series after 15 minutes. Furthermore, α1 and α6 vanish after around 6 minutes, thus indicating that the tracer has reached every part of the domain. report the variation of the relative occupancies against time.

Figure 2: Original nozzle series

When biogas injection occurs from the original nozzle series (Figure 2), the relative occupancy of the first interval α1 drops slowly up to around 7 min, and then remains stationary. In any case, α1 remains b far the largest relative occupancy, whereas a small area with the highest concentration (α6) remains practically unchanged. In other words, this injection strategy can achieve mixing only on a modest fraction of volume whilst leaving the vast majority of the domain untouched. In particular, biogas injection cannot bring any beneficial effect after seven minutes.

Figure 3: New nozzle series

As regards the new nozzle series (Figure 3), α1 drops considerably if compared to the levels of the original nozzle series; in particular, it ceases to be the largest relative occupancy after 12 minutes. Furthermore, α1 drops continuously through the whole run, thus indicating that biogas injection still brings benefit in terms of mixing when mixing time increases. Therefore, it makes sense to mix for longer times when the new nozzle series is taken into consideration, contrarily to the case of the original nozzle series. However, a section of the domain which is not reached by the tracer still survives even after 15 minutes, and conversely, α6 remains constant through the whole run, thus indicating that some areas are still unmixed at the end of the run.




Figure 4: Nozzle series switched every 1 min

The action of switching between the two nozzle series (As regards the new nozzle series (Figure 3), α1 drops considerably if compared to the levels of the original nozzle series; in particular, itceases to be the largest relative occupancy after 12 minutes. Furthermore, α1 drops continuously through the whole run, thus indicating that biogas injection still brings benefit in terms of mixing when mixing time increases. Therefore, it makes sense to mix for longer timeswhen the new nozzle series is taken into consideration, contrarily to the case of the original nozzle series. However, a section of the domain which is not reached by the tracer still survives even after 15 minutes, and conversely, α6 remains constant through the whole run, thus indicating that some areas are still unmixed at the end of the run.) dramatically increases the quality of mixing. After around 3 minutes, the system reach the same level of mixing that was displayed in the case of injection through the new nozzle series after 15 minutes. Furthermore, α1 and α6 vanish after around 6 minutes, thus indicating that the tracer has reached every part of the domain.

Figure 5: Nozzle series switched every 5 min

Switching every 5 minutes (Figure 5) instead of every minute brings to a similar level of mixing but in more time – 15 minutes instead of 10. In particular, α1 and α6 vanish after around 11 minutes instead of 6.

Conclusions

A method based on the analysis of the distribution of a scalar tracer to assess mixing in CFD simulations was described for the first time. Such method was applied to numerical simulations of gas mixing in anaerobic digestion, and the relative effectiveness of four gas injection strategies was assessed.

Traditional strategies based on injecting from only one nozzle series were found to be not completely satisfactory, as the tracer could not reach every part of the domain. In particular, the tracer could not




reach the majority of the domain when biogas was injected from the original nozzle series, and mixing operation resulted to be ineffective after around 7 min.

Strategies based on switching gas injection between two different nozzles series were found to increase the quality of mixing dramatically in terms of uniformity of the tracer distribution, and at a much faster time.

A diminution of the time interval before switching between two nozzle series was found to bring no effect in terms of uniformity of the tracer distribution, but allowed to reach similar distributions in less time – specifically, the time saving was comprised between 1/2 and 2/3. It is then advantageous to keep the switching time short.

When the time interval before switching between two nozzle series, the tracer reached every part of the domain after about 6 minutes.

Acknowledgements

The details of the digester geometry were kindly provided by Peter Vale and Severn Trent Water Ltd., whom the authors gratefully acknowledge. The computational work reported in this paper was undertaken using the Blue- BEAR high performance computing facility at the University of Birmingham, UK. The authors are grateful for the facility and support provided by the University.

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