About the conception and design of anaerobic digesters in zootehnical farms

Anaerobic sludge fermentation is one of the main technological steps for treating the wastewater resulting from urban consumption in the food industry. Anaerobic fermentation ensures the sludge mineralization treatment and the fermentation gas (biogas) resulting from the process can be used for the production of thermal or electric energy. The fermentation process can take place in closed reinforced concrete tanks (digesters) having different structural forms: cylinder, tapering, ovoid depending on the type of fermentation: mesophilic or thermophilic and on the performance of sludge mixing and homogenization equipment. Fermentation tanks with a capacity of 1000-4000 m3 were designed in Romania so far, the most important being those of Bucharest wastewater treatment plant made of prestressed reinforced concrete having an ovoid shape. The present paper aims at presenting the issues related to designing the fermentation tanks of the water waste plants from urban consumption in the food industry and zoo-technical farms in a new concept in which the main fermentation tank is coupled with the fermenter for the fermentation gas storage. Consequently, hereinafter structural and functional requirements for this kind of structures are presented, together with design principles and methods that must be applied in order to fulfil the performance exigencies related to strength, stability, tightness and durability.


Functional and structural requirements
The efficiency of the anaerobic fermentation process of sludge depends mainly on the following factors: -content of organic substance in waste water; -sludge temperature: 350-400 in the case of mesophilic fermentation and 500 in case of thermophilic fermentation; -mixing and homogenization degree of sludge needed to provide bacteria in mass nourishment and constant temperature throughout the sludge mass.
Taking into account these factors, it is necessary that the tanks will be equipped with performing mixing and homogenization devices able to prevent gravitational and thermal stratification of sludge. In order to ensure a constant temperature throughout the sludge, it must be preheated to a temperature corresponding to the type of chosen fermentation. It is also necessary to daily recirculate a quantity of existent sludge with freshly preheated sludge.
From the analysis of the factors that determine the efficiency of the fermentation process, the main structural and technological requirements taken into account in the conception and design of the structure result and the following must be considered: -the structural shape must be adapted to the hydraulic homogenizing and mixing spectrum and the equipment considered; -structures must be thermal insulated to reduce heat losses and gas quantities necessary for sludge preheating.
-besides the requirements for ensuring structural strength and stability, the fermentation tanks must ensure tightness to the sludge hydrostatic pressure and fermentation gases pressure.
-the requirement of durability of minimum 50 years requires the limitation of the crack opening in terms of tightness and especially due to the corrosive attack of the fermenting gas mixed with the water vapour. In order to avoid corrosive attack, it is necessary to provide anticorrosive protection inside, taking into account the acid-sulphurous type corrosion that occurs in the upper part of the tank. -effort and deformation states must be determined taking into account both the actions modelled by force systems and the action of temperature variations taking into account sludge temperatures and maximum outdoor temperatures in the summer and winter season.
-depending on the storage capacity, it is necessary to consider the need to introduce the prestressing of concrete in order to eliminate the risk of cracking and increase the durability. farm, it resulted necessary to construct two fermentation tanks with the capacity of 1000 m 3 each, as well as some annexes separated from the tanks by tightened permanent joints.
Considering the functional requirements, the capacity of a tank, the height of the sludge column and the values of the sectional efforts, the chosen reinforced concrete structural solution has the following components: -a reinforced concrete circular matt foundation having the diameter of 17.50 m and a thickness of 40 cm; -a reinforced concrete cylindrical shell having a continuity connection with the foundation and an inner diameter of 16.00 m, a height of 6.00 m and a thickness of 30 cm; -a plastic covering tightens to the concrete cylindrical shell walls and which, because of the gas pressure resulted in the fermentation process has a spherical shape; -a floor of wood planks and beams, simply supported on the walls of the cylindrical shell and on a central interior structure sustained by a central column with the cross section 40x40 cm.
In order to ensure a favourable thermal balance, the tank was thermally insulated with expanded polystyrene applied on the cylindrical walls and extruded polystyrene under the tank foundation.
The foundation of the tanks was made on a ground with improved physical and mechanical characteristics at a depth of 2.50 m.
The distance between the two tanks is 23.60 m.
In the space between the reservoirs were made the annex constructions, in the form of reinforced concrete underground structures designated for installation and the equipment: pumping stations, preheating installations, equipment for crushing and shredding of materials.

Hypothesis for determining the efforts and deformations in the structure
Determining the state of stress and strain in the structure of a fermentation tank can be obtained by applying analytical computation or through numerical calculation methods using finite element method programs. Considering the structural system and the possibility of integrating the synthesis equations that define the state of effort in the structural elements (circular plates elastically supported and cylindrical shells), the analytical methods that allow expression of the interaction structure-stored fluid and foundation ground and define stresses and deformations through functions were chosen for computation. At the same time, there is the certainty of respecting equilibrium conditions and deformation compatibility in each structural element as well as on the boundaries of the joints between them.

Loads and loads combination
The considered fundamental load combination was taking into account: self-weights the hydrostatic pressure of the stored fluid, the pressure of the fermentation gases and the temperature variations.
The special load combination takes into consideration the hydrodynamic pressures induced by the seismic action also.
The design values of loads and their variation are shown in Figures 1, 2 and 3. where: pH = the hydrostatic pressure; 55 kN/m 2 ; pa = the active soil pressure; pg = the gas pressure; 2 kN/m 2 ; Following heat transfer calculations and taking into account a thickness of 12 cm thermal insulation at temperatures of: ti = + 45 0 C the temperature of the stored fluid; te = + 35 0 C in the summer season; -25 0 C in the winter season; the two temperature elementary fields acting on the structure are defined: Design values of the two fields considered stationary are shown in Figure 2.
+2,00 +6,00 0,00 Variation of hydrodynamic pressures [1] and their design values are presented in Figure 3 and Table 1 respectively, for the seismic zone characterized by design ground acceleration ag = 0.30g and the corner period of the elastic response spectrum Tc = 1.0s.

Analysis of the state of the efforts and deformations in the tanks structure
Determining the stress and strain state for cylindrical tanks structure, composed by cylindrical shells and circular plates can be axially symmetric treated considering the axial symmetry of the structure and of the current loads: self-weights, hydrostatic pressures, temperature variations. When comes to the action of hydrodynamic pressure induced by the occurrence of the seismic action, determining the stress and strain state of the structures must be non-symmetrically treated due to the antisymmetric nature of the hydrodynamic pressure.
The present paper presents the analytical design method used for determining axial symmetric state of stresses.
Admitting the linear elastic behaviour of the structure, the design algorithm implies the following design steps: -breaking down the structure in component structural elements by suppressing their joints and replacing the suppressed connections with corresponding system of forces thus obtaining the basic system specific to the design method; -analysis of the state of strain and deformation of the obtained cylindrical shells and circular plates subjected to bending.
Through this analysis the flexibility matrices for each structural element may be defined together with the membrane efforts for the cylindrical shell: -expressing the deformation compatibility conditions along the connecting boundary and the alteration lines, a system of algebraic equations is obtained in which the unknowns are the boundary efforts, and the coefficients of the equations are the unit displacements and the displacements determined by loads; -solving the equations system and finding the values of the sectional efforts along the joints boundaries; -computing the final efforts applying the principle of superposition of effects.
Some main computation elements necessary for applying the previous explained algorithm are presented below.

Breaking down the structure and building the basic system specific to the effort method
Considering the structure lay-out and the variation of loads the obtained basic system is shown in Figure 4.

Defining the state of efforts and deformations for cylindrical shells
According to the theory of cylindrical shells working in bending [5] [6] [2] the axial symmetric state of efforts and deformations is characterized by the sectional efforts shown in Figure 5 on an infinitesimal element.
Nx -axial stress along the cylinder generatrix direction Nθ -axial stress along a direction tangent to the circle Qx -shear force Mx, M θ -bending moments X(x) -surface loads component along the generatrix direction Z(x) -surface loads component normal to the surface The synthesis differential equation of the bending theory is obtained from the following general equations: equations of equilibrium, equivalence relationships, deformation equations, physics equations, choosing as basis unknown the displacement function w(x) in the direction of the normal to the median surface of the curved plate.
Considering the case of axial symmetrical loads and taking into account the force systems and the two elementary temperature fields T0 (x) and ΔT0 (x), acting on the curved plate, the synthesis equation has the following form: Performing in (4.1) the change of the variable ξ = x/l and denoting the product K x l = λ the equation of synthesis becomes: The general solution of the synthesis equation consists of the solution of the homogeneous equation W0(ξ) plus a particular solution depending on the loading functions type on the right hand side of the equation.
In equations (4), (5), (6) and (7) where: In the case of cylindrical shells, the particular solution wp(ξ) coincides with the membrane solution, which allows the superposition of the strains and deformations of the membrane with the strains and deformations given by the boundary forces.

Defining the state of stresses and strains in the circular plates supported on elastic foundations
The state of axial symmetric efforts and deformations in circular plates for the general case of loading -systems of forces acting in the plan or normal to the plan of the circular plates plus the two elementary temperature variations -is characterized by the sectional efforts shown in Figure 6. The state of efforts in the circular plates when loaded with a system of forces acting in its plan together with the elementary component T0 (x) of the temperature variation can be studied as a plane problem, the expressions of the efforts and the deformations of interest for the present work are presented in the following tables [3]: Table 2. Formatting sections, subsections and subsubsections.
The subject of circular plates on elastic foundations working in bending when loaded with a system of forces acting in its plan together with the elementary component T0(x) of the temperature variation can be studied using several models for the soil-element interaction.
Using the Winkler model and defining as elastic characteristic the bed coefficient (CEO) the synthesis equation of the circular plates working in bending and supported on elastic foundation is: [3] [4].
In the synthesis equation 4.6 the following notations were used: Knowing the general solution in (4.7) the expressions of sectional efforts are: • Rotation: • Expressions of sectional efforts:

Conclusions
The work presented in this article was issued in the design process of the two Nucet farm digester structures, having a capacity of 1000 cm 3 each. The fermentation tanks are in function already, proving a good structural and functional behavior.
It was proven that for axial-symmetric loads like selfweights, hydrostatic pressures, gas pressure or soil active pressure, the design analytical method presented in this paper may be used, existing the certainty of respecting the forces equilibrium conditions and deformations compatibility for the entire structure.
If the anti-symmetric loads like hydrodynamic pressure are taken into consideration, the use of presented analytical method becomes more complicated as the synthesis equation is more complex (is an 8-th order partial derivative equation).
It is concluded also that, as the reinforced concrete tanks are acted by temperature variations also, the stiffness of the cylindrical shells must be expressed corresponding to a cracked state, otherwise it exists the danger of over evaluating temperature loads.
Following the design procedure, it also resulted the fact that if larger digesters are needed having capacities over 1000cm 3 , a prestressed reinforced concrete solution it is advisable to be used rather than the solutions used for the design presented in this paper.