MIXING OPTIMIZATION OF GAS-MIXED ANAEROBIC DIGESTION USING CFD

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, UK
Corresponding 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
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
Organised by Aqua Enviro
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:
( + ⋅ ) = 0 , ( 1 )
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 ≡ [0, 1]
that c can assume is divided into several sub-intervals 1, … , such that 1 ∪ …∪ = . For each
sub-interval Ii, the relative occupancy αi is defined as follows:
= ∫ Π (( )) 3
∫ 3 , ( 2 )
Π () = { 1 , ∈ ; 0 , ∉ .
( 3 )
This definition implies that ∑ =1 = 1 . When the tracer field c becomes uniform (and hence the
system becoming well mixed), one single occupancy 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 1, … , , the first configuration is better mixed than the
second if max≠1 > max≠1 .
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):
= − . ( 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
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 m
Diameter at the bottom of the frustum Dint 1.09 m
Cylinder height h 14 m
Frustum height h0 3.94 m
Distance of the nozzle from the axis Rnoz 1.75 m
Distance of the nozzle from the bottom hnoz 0.3 m
Maximum gas flow rate per nozzle Qmax 4.717 103 m3/s
Mixing 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:
Co =
. ( 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 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 zero
ε Slip
R Slip
c Slip
Wall / Bottom p Adjusted such that the velocity flux is zero
Constant zero
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 ( + ⋅ ) = 0 , ( 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 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 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
of the run.
Figure 4) 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 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.
As regards the new nozzle series (
of the run.
The action of switching between the two nozzle series (As regards the new nozzle series (
of the run.
Figure 4) 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.
References
Achkari-Begdouri, A. and Goodrich, P. R. (1992) Rheological properties of dairy cattle manure.
Bioresour. Technol., 40, 149–156. doi: 10.1016/j.biortech.2004.06.020.
Andersson, B., Andersson, R., Håkansson, L., Mortensen, M., Defence, N., Sudiyo, R. and van
Wachem, B. (2012) Computational Fluid Dynamics for Engineers. Cambridge University Press.
Bridgeman, J. (2012) Computational fluid dynamics modelling of sewage sludge mixing in an
anaerobic digester. Adv. Eng. Softw., 44(1), 54–62. doi: 10.1016/j.advengsoft.2011.05.037.
Dapelo, D. (2016) Gas mixing in anaerobic digestion. University of Birmingham. Available at:
http://etheses.bham.ac.uk/6879/.
Dapelo, D., Alberini, F. and Bridgeman, J. (2015) Euler-Lagrange CFD modelling of unconfined gas
mixing in anaerobic digestion. Water Res., 85, 497–511. doi: 10.1016/j.watres.2015.08.042.
Dapelo, D. and Bridgeman, J. (2015) Computational Fluid Dynamics Modelling of Unconfined Gas
Mixing of Wastewater Sludge in a Full Scale Anaerobic Digester. in Kruis, J., Tsompanakis, Y., and
Topping, B. H. V. (eds) Proc. Fifteenth Int. Conf. Civil, Struct. Environ. Eng. Comput. Stirlingshire, UK:
Civil-Comp Press. doi: 10.4203/ccp.108.270.
Dewsbury, K., Karamanev, D. and Margaritis, a. (1999) Hydrodynamic characteristics of free rise of
light solid particles and gas bubbles in non-Newtonian liquids. Chem. Eng. Sci., 54(21), 4825–4830.
doi: 10.1016/S0009-2509(99)00200-6.
Gibson, M. M. and Launder, B. E. (1978) Ground effects on pressure fluctuations in the atmospheric
boundary layer. J. Fluid Mech., 86, 491–511. doi: 10.1017/S0022112078001251.
Gómez, X., Cuetos, M. J., Cara, J., Morán, a. and García, a. I. (2006) Anaerobic co-digestion of
primary sludge and the fruit and vegetable fraction of the municipal solid wastes. Conditions for mixing
and evaluation of the organic loading rate. Renew. Energy, 31(12), 2017–2024. doi:
10.1016/j.renene.2005.09.029.
McMahon, K. D., Stroot, P. G., Mackie, R. I. and Raskin, L. (2001) Anaerobic codigestion of municipal
solid waste and biosolids under various mixing conditions-II: Microbial population dynamics. Water
Res., 35(7), 1817–1827. doi: 10.1016/S0043-1354(00)00438-3.
Ong, H. K., Greenfield, P. F. and Pullammanappallil, P. C. (2002) Effect of mixing on biomethanation
of cattle-manure slurry. Environ. Technol., 23, 1081–1090.
Owen, W. F. (1982) Anaerobic Treatment Processes. in Energy wastewater Treat. Englewood Cliffs,
NJ: Prentice-Hall, Inc.
Sindall, R. C., Bridgeman, J. and Carliell-Marquet, C. (2013) Velocity gradient as a tool to characterise
the link between mixing and biogas production in anaerobic waste digesters. Water Sci. Technol.,
67(12), 2800–2806. doi: 10.2166/wst.2013.206.
Stroot, P. G., McMahon, K. D., Mackie, R. I. and Raskin, L. (2001) Anaerobic codigestion of municipal
solid waste and biosolids under various mixing conditions-I. digester performance. Water Res., 35(7),
1804–1816. doi: 10.1016/S0043-1354(00)00439-5.
Tchobanoglous, G., Burton, Franklin, L. and Stensel, H. D. (2010) Wastewater Engineering. Metcalf &
Eddy, Inc.
Tomiyama, A., Tamai, H., Zun, I. and Hosokawa, S. (2002) Transverse migration of single bubbles in
simple shear flows. Chem. Eng. Sci., 57(11), 1849–1858. doi: 10.1016/S0009-2509(02)00085-4.
Ward, A. J., Hobbs, P. J., Holliman, P. J. and Jones, D. L. (2008) Optimisation of the anaerobic
digestion of agricultural resources. Bioresour. Technol., 99(17), 7928–7940. doi:
http://water.wuk1.emsystem.co.uk/home/news/press-releases/indicators2010-11/water-uk---
sustainability-report-2010-11.pdf\nfiles/1080/Water UK_2012_Sustainability Indicators 2010-2011.pdf.
Wu, B. (2012) Integration of mixing, heat transfer, and biochemical reaction kinetics in anaerobic
methane fermentation. Biotechnol. Bioeng., 109(11), 2864–2874. doi: 10.1002/bit.24551.
Wu, B. and Chen, S. (2008) CFD simulation of non-Newtonian fluid flow in anaerobic digesters.
Biotechnol. Bioeng., 99(3), 700–711. doi: 10.1002/bit.21613.

Documents

MIXING OPTIMIZATION OF GAS-MIXED ANAEROBIC DIGESTION USING CFD