Structure and Sludge-Water Mixing of Anaerobic Reactor

Abstract

Complete sludge-water mixing reaction is a common mode of operation for anaerobic reactors. However, sludge-water mixing must be carried out at low mixing intensities or flow velocity in order to maintain stable anaerobic colonies in the anaerobic sludge and thus achieve high anaerobic biochemical reaction efficiencies. In this chapter, the Continuous Stirring Tank Biochemical Reactor (CSTBR) was defined in terms of the sludge-water mixing time scale t¯ and the biochemical reaction time scale T (t¯ << T) for the analysis of sludge-water mixing reaction of anaerobic reactor, it tends to CSTR when t¯ → 0. Upflow Anaerobic Sludge Blanket (UASB) reactors and Internal Reflux Packed-Bed Anaerobic Reactors (IRPAR) with confined anaerobic sludge can mix sludge and water with lower mixing intensities to achieve the CSTBR mode, the corresponding velocity can be as low as 0.4–5.0 m/h. This chapter analyses the structural and operational characteristics of these two types of anaerobic reactors, and presents the corresponding sludge-water mixing calculation models and the operation conditions required to achieve the CSTBR mode. Such mixing model analysis is an effective way of designing structural of anaerobic reactors and controlling operation.

1. Introduction

1.1 Anaerobic reactor

The anaerobic reactor is a biochemical reactor that efficiently carries out anaerobic biochemical degradation of organic matter. The biochemical reaction of organic matter degradation by anaerobic colonies in an anaerobic reactor is carried out by the activity of microbial symbiont, which includes a complex process consisting of many species of bacteria and a number of intermediate steps. If the organic matter is made up of complex organic compounds. It first needs to be hydrolyzed into simple organic matter, which is then fermented by acid-producing bacteria to produce volatile acids, which are then converted into acetate and hydrogen by specialized hydrogen-producing acetic acid-producing bacteria. Finally, methanogenic bacteria convert the acetate and hydrogen into methane. This related, complex process is shown in Figure 1.

Figure 1.

Anaerobic biochemical reaction block diagram.

As can be seen from the tandem reaction route in Figure 1, the anaerobic degradation process can proceed efficiently when the microorganisms in each sequence utilize the organic intermediates at the same rate as these intermediates are produced. Anaerobic biodegradation of organic matter can almost always be carried out spontaneously as soon as reaction conditions are suitable.

Anaerobic reactors have been used for anaerobic biodegradation of organic matter in water for a long time. An obvious problem recognized in early studies was that by simply increasing the amount of anaerobic sludge in an anaerobic reactor without good sludge-water mixing, the increase in reaction efficiency of the anaerobic reactor was limited. Subsequent studies have shown that using, for example, refluxed gas released from the anaerobic reaction or refluxed effluent to agitate the sludge-water and increase the strength of the sludge-water mixing also failed to significantly improve the reaction efficiency of the anaerobic reactor. It was not until Lettinga et al. developed the UASB anaerobic reactor in the 1970s and the development of the fixed-fill bed anaerobic reactor in the same generation. These types of anaerobic reactors have a higher anaerobic biochemical reaction efficiency than the previous anaerobic reactors that consisted of air bubbles or mechanical agitation of the sludge in suspension. The study of these anaerobic reactors and their engineering applications has gained much attention because of their well-shaped sludge morphology and the conditions conducive to sludge-water mixing. Speeces describes the special clustering of anaerobic microorganisms in granular sludge and biofilms as reducing the distance of metabolic material transfer and thus optimizing the collaboration between microorganisms [1]. It can be seen that in addition to the amount of anaerobic sludge and the state of sludge-water mixing, the morphology of the anaerobic sludge present, the stability of the anaerobic colonies within the sludge, and the solid phase mass transfer distance all influence the reaction efficiency of the anaerobic reactor. The morphology of the anaerobic sludge and the composition and stability of the internal biological community must be maintained while the sludge-water in the anaerobic reactor is adequately mixed. As a result, anaerobic reactors cannot use general mechanical or similar mixing methods to mix sludge-water simply by increasing the mixing intensity to avoid high shear flows destroying the anaerobic sludge morphology and the composition of its internal biological community. This makes sludge-water mixing in anaerobic reactors rather special and needs to be focused on both the structural design of the anaerobic reactor and the operating process, as well as the mixing pattern to mix sludge-water at low mixing intensities. This chapter will analyze ways to improve the efficiency of the sludge-water mixing reaction in terms of anaerobic reactor structure, operation, sludge properties, sludge-water mixing pattern, and mixing intensity. This will assist in the engineering design and operational control of anaerobic reactors to improve the efficiency of anaerobic biochemical degradation of organic matter.

1.2 Continuous stirred tank biochemical reactor (CSTBR)

According to the basic theory of mixed reactors, there are three mixing modes of reactors used for mixing reactants, mode of continuous stirring tank reaction (CSTR), mode of diffusion mixed reaction, and mode of push-flow reaction. Due to the long reaction time and complexity of the biochemical degradation of organic pollutants, the CSTR mode is more often used in biochemical reactors of wastewater treatment.

Figure 2 shows a model of an ideal CSTR. By definition, the reactants are instantaneously mixed in the reactor, with complete homogeneous mixing at time t = 0 and equal reactants concentrations at any point or a uniform concentration distribution in the reactor.

Figure 2.

Schematic diagram of CSTR reactor.

Let the reactor volume V, the input and output flow Q, the hydraulic retention time T, T = V/Q, the initial concentration of inert tracer C_0, and the output concentration C(t). In accordance with the mass balance equation, it is obtained that

$$\frac{\mathrm{C}\left(\mathrm{t}\right)}{{\mathrm{C}}_0}={\mathit{exp}}^{\left(-\frac{\mathrm{t}}{\mathrm{T}}\right)}$$E1

In practical engineering, regardless of the mixing method, the time t > 0 for homogeneous mixing in a reactor deviates to varying degrees from the ideal model in Figure 2. The concentration in a reactor can tend to be homogeneous, or the reactor tends to CSTR when t → ∞. In designing a mixed reactor, the time t, when the mixing process tends to mix homogeneity, is much less than the reaction time T, t << T, the reactor can be approximated as a CSTR. As shown in Figure 3, increasing the mixing intensity of a mixing process with diffusion mode, its Peclet number decreases the output line E(t) of the tracer of instantaneous source tends to that of CSTR for a shorter time t. Therefore, suitable mixing methods can be selected or constructed according to the reaction time T and mixing time $\overline{\mathrm{t}}$ in to save energy or meet other constraints required by the reactants. For example, anaerobic reactors require a low mixing intensity to complete the sludge-water mixing reaction.

Figure 3.

E(t) curve of the actual complete mixing reactor.

By mixing the water through a turbulent flow field generated by high-intensity mechanical agitation, the reactor can approach CSTR indefinitely. Short reaction times and small volumes or mixing scales are easy for mixing with higher-intensity mechanical agitation to achieve CSTR. The biochemical degradation of organic matter has a slow reaction rate, takes longer to complete, and the volume and mixing space scale of the reactor is larger. If the biochemical reactor converges to CSTR at a time $\overline{\mathrm{t}}$ << T relative to the biochemical reaction completion time or hydraulic retention time T, the mixing time $\overline{\mathrm{t}}$ can be ignored, allowing the biochemical degradation of organic matter to proceed in a complete mixed state. The shorter the mixing time $\overline{\mathrm{t}}$, the closer it is to CSTR, but at too short a mixing time $\overline{\mathrm{t}}$ is unnecessary compared to the long biochemical reaction time T. For biochemical reaction tanks with large volumes and mixing space scale, the mixing mode should be constructed according to the time scale T of biochemical degradation of organic matter and mixing time scale $\overline{\mathrm{t}}$, so as to obtain a biochemical reactor approximating to CSTR, $\overline{\mathrm{t}}$ << T. This type of reactor is defined as a Continuous Mixing Tank Biochemical Reactor (CSTBR), according to the sludge-water mixing time scale t and the biochemical reaction time scale T, $\overline{\mathrm{t}}$ << T.

Analysis of the large-scale turbulent mixing of the oxidation ditch and aeration basin can help to understand the mixing time scale $\overline{\mathrm{t}}$ in a CSTBR. The aerobic-activated sludge allows the simultaneous mixing of sludge and water at higher turbulent intensities due to its high flocculation capacity. The mixing of small-scale turbulent eddies in the oxidation ditch and aeration tank tends to be instantaneous compared to the longer time taken to complete the biochemical reaction, so the mixing of small-scale turbulent eddies in the mixing process can be ignored, and only the mixing of large-scale time-averaged flows needs to be considered to analyze the mixing completion time t. Accordingly, Yang developed a dynamic mixing model of an oxidation ditch and an aeration tank to analyze the mixing processes and proved that the oxidation ditch tends to CSTR with a combination of two mixing modes: discontinuous mixing in circulation and one-dimensional continuous dispersing mixing, while the aeration tank tends to CSTR with discontinuous diffusion mixing [2]. Model calculations show that for the same biochemical reaction time T = 12.0 h, the mixing time $\overline{\mathrm{t}}$ increases from $\overline{\mathrm{t}}$ = 2.5 min for a small volume of V = 500.0 m³ to $\overline{\mathrm{t}}$ = 2.8 h for a large volume of V = 25,000 m³ for oxidation ditches and aeration tanks with treatment of 1000–50,000 m³/d and volumes of V = 500–25,000 m³. Figure 4 shows the model calculated mixing output E(t) curves for the instantaneous point sources of tracers in the oxidation ditch and aeration basin. As can be seen from Figure 4, the mixing reaction process in these two types of biochemical reactors is almost equivalent. In practice, the mixing is assumed to be complete in both the oxidation ditch and the aeration tank. The all-mixing completion time $\overline{\mathrm{t}}$ = 2.5 min ∼ 2.8 h satisfies the CSTBR condition, $\overline{\mathrm{t}}$ << T. Obviously, too short mixing completion time is unnecessary. For oxidation ditches with smaller volumes, the mixing time $\overline{\mathrm{t}}$can be increased by reducing the roughness of the ditch wall and the water flow velocity in the ditch; when the ditch volume is too large, the roughness of the ditch wall can be increased to shorten the mixing time $\overline{\mathrm{t}}$, making $\overline{\mathrm{t}}$ << T. For aeration tanks, the aeration air rate can be adjusted to preset the mixing completion time $\overline{\mathrm{t}}$.

Figure 4.

Output pattern of oxidation ditch and aeration tank.

Unlike in oxidation ditches and aeration tanks where sludge-water can be mixed at a high turbulent intensity. As anaerobic sludge lacks sufficiently strong flocculation capacity, anaerobic bacteria communities are easily destroyed by shear stresses in the flow. Thus, high-intensity mixing of sludge-water does not necessarily increase the efficiency of the anaerobic degradation reaction of organic matter. In the analysis of sludge-water mixing in anaerobic biochemical reactors, both the scale of the anaerobic sludge and the stability of the anaerobic bacteria community need to be considered, requiring greater control of the sludge-water mixing process.

2. Methodology

2.1 Anaerobic sludge

Before discussing sludge-water mixing in anaerobic reactors, the properties of anaerobic sludge are analyzed. The main body of anaerobic sludge is made up of clustered aggregations of anaerobic microorganisms. These microorganisms adhere to each other synergistically, forming a highly structured and stratified symbiosis. For example, in anaerobic sludge, in the outer layer, it is the fermenting bacteria that are clearly dominant; while in the deep inner layer, the bacteria that degrade propionate are dominant. One important way to improve the biochemical reaction efficiency of an anaerobic reactor is to use large amount of sludge. However, it may also reduce the efficiency of sludge-water mixing, which is not conducive to anaerobic biochemical reactions.

The early anaerobic reactors were simple in construction. The reactor is generally a reaction tank with an inlet and an outlet and a gas collection port. The anaerobic reactor relies on the bubbles released from the anaerobic reaction to naturally mix the sludge and water, namely, biogas stirred anaerobic reactor. Sometimes, a mechanical stirring device is set up to disturb the deposited sludge and suspend it to participate in the sludge-water mixing reaction.

In the interior of these anaerobic reactors, the anaerobic sludge can migrate unrestrictedly within the reaction zone. In practice, anaerobic sludge of uncertain geometry and distribution can be clearly observed. The sludge can either float in larger blocks with geometries even larger than 100.0 mm or more, or it can break up into fine particles and remain suspended in the water. In addition, sludge can float on the water surface or be deposited on the bottom of the tank and collected in large sludge masses. The sludge-water mixing at any spatial location exhibits a stochastic character. This type of anaerobic reactor is defined as an unconfined sludge anaerobic reactor. The average agitation intensity of its bubbles is not high, and the sludge-water mixing reaction is inefficient and the time to complete the sludge-water mixing reaction is longer [3].

To date, no studies have been carried out on the strength of anaerobic sludge in relation to sludge-water mixing. Speeces’s study noted that dense anaerobic sludge can be obtained in practice, but that the high intensity of turbulent shear flow can destroy the composition of bacterial aggregates in anaerobic sludge and that recovery can take weeks or months. The application of mechanical mixing of sludge-water requires a high mixing intensity just to keep the anaerobic sludge in suspension. Furthermore, apart from energy consumption considerations, the resulting complete sludge-water mixing does not necessarily increase the efficiency of the anaerobic reaction. Therefore, this mode of sludge-water mixing is rarely used in engineering now.

The geometry of the anaerobic sludge affects the efficiency of the anaerobic reaction. Larger sludge sizes can limit the anaerobic reaction rate due to the long transfer distance within the sludge, while smaller sludge sizes are not conducive to the formation of symbiotic biomass in the sludge, which is also detrimental to the anaerobic reaction. Using VFA, which is susceptible to anaerobic degradation, as an indicator, Speeces concluded that the unrestricted mass transfer distance for molecular diffusion within the anaerobic sludge is no greater than 1.0 mm and that at this scale, complete biopolymers are also obtained at the same time. For example, hydrogen-producing and hydrogen-using bacteria can both be in the same bacterial aggregate and the transfer of H₂ will not be a limiting factor in carrying out the methanation reaction. Speeces recommends an average sludge particle diameter of around 2.0 mm.

In UASB reactors and anaerobic reactors with fixed biofilms, the anaerobic sludge is confined to a local scale or fixed to the surface of the packed media and does not migrate with the flow. The geometrical scale of the anaerobic sludge can be controlled in the unrestricted mass transfer range. As in the UASB reactor, the anaerobic sludge particles are confined to the sludge bed with a sludge particle size of 2.0–4.0 mm, which is close to the unrestricted mass transfer distance within that of the Speeces recommended. This type of anaerobic reactor is defined as a confined-sludge anaerobic reactor [4]. With the appropriate sludge distribution, the confined sludge anaerobic reactors can achieve a complete sludge-water mixing reaction state through water mixing at a low mixing intensity, according to the condition of CSTBR.

2.2 Anaerobic reactor construction

The construction of the anaerobic reactor should be designed to achieve: (1) complete sludge-water mixing $\overline{\mathrm{t}}$ << T, operating in a CSTBR mode; (2) a low enough mixing intensity; and (3) a stable biological flora and unrestricted mass transfer scale in the solid phase sludge.

The configuration of the various types of anaerobic reactors currently in use is shown in Figure 5. The sludge bed of UASB reactor, packed bed, permeation in anaerobic reactor shown are all confined sludge areas, where the sludge is fixed or confined to a localized area, which is conducive to sludge-water mixing with low mixing intensity in CSTBR mode for presetting the sludge-water mixing state, by organizing the water flow pattern and shaping and distribution anaerobic sludge through the structural design.

Figure 5.

The various types of anaerobic reactors.

In the anaerobic baffled reactor (ABR), although the anaerobic sludge is isolated in the reaction compartments and cannot migrate with the flow at the full reaction zone scale, it can migrate with the flow in the isolation compartments, and the sludge-water in each reaction compartment is mixed by bubble agitation. The ABR anaerobic reactor is not a confined sludge anaerobic reactor due to its large isolation compartments. The sludge moving space scale is of the same order of magnitude as the full mixing space scale.

Other anaerobic reactors, including fluidized bed and mechanically stirred anaerobic reactors are unconfined sludge anaerobic reactors, in which the anaerobic sludge moves within the reactor with the water flow. Complete sludge-water mixing reactions in fluidized beds and mechanically stirred anaerobic reactors require high flow velocity and mixing intensities. To date, there is still no effective method for analyzing or presetting the morphology of sludge and the state of sludge-water mixing in such anaerobic reactors. However, there are some lessons to be learned.

For anaerobic reactors with biogas-stirred, the construction is simple, and almost no internal structural design is required. Due to the uncertainty of the gas production of the anaerobic reaction, the anaerobic sludge-water mixing reaction is uncontrollable. All that can be achieved in current engineering applications is to apply a mixing model, which is posteriori, to analyze the state of sludge-water mixing and the volumes involved in the mixing reaction based on the monitoring of operational data.

3. Key results

3.1 UASB reactor

Figure 6 shows the internal structure of a UASB anaerobic reactor [5]. The main structure of which consists of five parts: (1) the sludge bed reaction area formed by the high-density accumulation of anaerobic sludge particles in the lower part of the reactor; (2) the sludge blanket; (3) the water distribution area at the bottom; (4) the three-phase separator; and (5) the gas collection chamber.

Figure 6.

Schematic diagram of UASB reactor.

In Figure 6, the height of the sludge bed is H₁, and the volume is V₁; The sludge blanket with height H₂ and volume V₂, on the upper part of the sludge bed, below the three-phase separator; the sludge separating area above the inlet of the three-phase separator, with a height of H₃ and a volume of V₃.

The water enters the reactor from the bottom water distribution zone. After anaerobic biochemical degradation of the organic pollutants in the sludge bed reaction zone, it flows into the upper sludge blanket zone and out through the three-phase separator. All sludge particles overflow from the sludge bed with the rising water flow and bubbles are separated in the V₂, V₃ zone, and the three-phase separator and settled back into the sludge bed, while the gases are collected in the gas collection chamber. The sludge bed is the main reaction zone where the organic matter is degraded. In the V₂ and V₃ zone, small amounts of suspended sludge particles are present, and the anaerobic biochemical degradation of organic matter continues, but in smaller quantities.

As can be seen from Figure 6, sludge-water mixing in the UASB reactor occurs in the sludge bed reaction zone V₁ and water in the upper zone (V₂ + V₃) with upwelling bubble agitation. The two mixing zones are adjacent to each other, but the mixing patterns are different. The maximum mixing volume that may participate in a UASB reactor is (V₁ + V₂ + V₃).

According to the study by Pol et al. [6], settling velocities of granular sludge of approximately 60 m/h are common, whereas the superficial upflow velocities in UASB reactors are usually kept below 2.0 m/h in practice. Therefore, the mixing in the sludge bed can be analogous to the diffusion of a seepage flow in general porous medium with dense sludge granular. The sludge blanket (V₂ + V₃) is stirred unstably by biogas at a small spatial scale, and the volume V_C involved in complete mixing cannot be preset，V_C ≤ (V₂ + V₃). Fortunately, the amount of suspended anaerobic sludge particles in this zone is small [7], and it is possible to disregard sludge-water mixing or ignore the amount of organic matter degraded and only analyze the mixing of the water.

Following the different sludge-water or water mixing patterns in these two mixing zones, mixing model equations can be developed, respectively [4]. Assuming that the anaerobic sludge particles in the sludge bed are distributed homogeneously, the sludge-water mixing process in the UASB can be simplified to a series-connected water advective diffusion unit V₁ with mixing unit Vc, where the water is stirred by biogas bubbles.

The water entering the sludge bed from the bottom is uniformly distributed and flows through the sludge bed in the form of seepage. The organic matter is biochemically degraded by the anaerobic sludge while the water diffusive mixing in the sludge bed, and the two processes interact with each other. However, If the anaerobic biochemical degradation reaction in the sludge bed operates in a CSTBR mode when the complete time scale t_P of the diffusive mixing is sufficiently small, t_P << T, or at the time t, t < t_P, before mixing homogenization, the influence of biochemical degradation of organic matter can be disregarded, and only inert tracers are required to analyze the diffusive mixing process of the water. For anaerobic sludge particles of homogeneous distribution, the mixing of sludge-water and mixing of water is completed simultaneously in the sludge bed.

As shown in Figure 6, u = q/A, where u is the velocity of seepage flow, q is the influent, and A is the section area. Let C (y, t) be the tracer concentration distribution in sludge bed, y ∈ (0, H₁). Analogous to the diffusion of a seepage flow, the one-dimensional concentration equation of the tracer in the sludge bed is as follows:

$$\frac{\mathrm{\partial C}\left(\mathrm{y},\mathrm{t}\right)}{\mathrm{\partial t}}+\mathrm{u}\frac{\mathrm{\partial C}\left(\mathrm{y},\mathrm{t}\right)}{\mathrm{\partial y}}={\mathrm{E}}_{\mathrm{y}}\frac{{\partial }^2\mathrm{C}\left(\mathrm{y},\mathrm{t}\right)}{\partial {\mathrm{y}}^2}$$E2

where E_y - diffusion coefficient of the sludge bed.

The sludge blanket (V₂ + V₃) is stirred unstably by biogas, and the volume involved in complete mixing cannot be preset. V_C is the volume involved in complete mixing, V_C ≤ (V₂ + V₃) and letting C (t) be the tracer concentration in V_C, then the tracer concentration equation of V_C can be written

$$\frac{\mathrm{dC}\left(\mathrm{t}\right)}{\mathrm{dt}}=\frac{{\mathrm{V}}_{\mathrm{c}}}{\mathrm{q}}\left(\mathrm{C}\left({\mathrm{H}}_1,\mathrm{t}\right)-\mathrm{C}\left(\mathrm{t}\right)\right)$$E3

where C (${\mathrm{H}}_1,\mathrm{t})$- tracer concentration of sludge bed at y = H₁ and time t.

Applying Eqs. (3) and (4) to simulate the diffusive transport process of the instantaneous tracer at the location of the inlet cross-section, the E(t) output curve, and the concentration distribution of the tracer, the time t_P for the completion of sludge-water mixing in the UASB reactor can be obtained to analyze the state of sludge-water mixing.

Let the tracer mass M be injected instantaneously at the inlet section. The initial boundary conditions of Eq. (3) of the sludge bed are.

$$\mathrm{C}\left(0,0\right)=\mathrm{M\delta }\left(\mathrm{y}\right)$$E4

where δ(y) is a Dirac function.

$$\mathrm{C}\left(\mathrm{y},0\right)=0,\mathrm{y}\in \left(0,{\mathrm{H}}_1\right)$$E5

$$\frac{\mathrm{\partial C}\left(0,\mathrm{t}\right)}{\mathrm{\partial y}}=0$$E6

The initial boundary conditions of Eq. (4) are.

$$\mathrm{C}\left(0\right)=0$$E7

$$\mathrm{C}\left(\mathrm{t}\right)=\mathrm{C}\left({\mathrm{H}}_1,\mathrm{t}\right)$$E8

If V_C is known, based on the model Eqs. (2) and (3), and the initial boundary conditions (4) and (6), the E(t) output curve of the UASB inlet instantaneous tracer injection can be numerically calculated using the difference method.

Figure 7 shows the vertical distribution of tracer concentrations in the UASB reactor at moments t_i, i = 1, 2,…,10, obtained from the model analysis. As the mixing time increases, the peak tracer concentration gradually decreases and the sludge-water mixing area in the sludge bed becomes homogeneous. The concentration in the upper bubble natural mixing zone is shown at the end of the fold on the left side of the curve. Before the sludge-water in the sludge bed is uniformly mixed, the tracer concentration in the bubble agitation zone is lower than the tracer concentration in the outflow from the top of the sludge bed, and the concentration on the boundary surface at the top of the sludge bed decreases transversely. After homogeneous mixing, the tracer concentration in the bubble agitation zone is greater than that in the outflow from the top of the sludge bed, and the concentration variation in the two zones on the decomposition surface at the top of the sludge bed tends to be smooth. According to Yan and Yang’s model, the sludge-water mixing in the sludge bed is considered complete when the peak concentration C = 2$\overline{\mathrm{C}}$, $\overline{\mathrm{C}}$—the average concentration of tracer in the sludge bed. In Figure 7, the time of complete mud-water mixing is t4 and the peak concentration of tracer is located in the central region of the sludge bed; when t₄ << T₁, the sludge bed operates as a stand-alone CSTBR, T₁—the hydraulic residence time of the sludge bed. And the upper bubble mixing region is the CSTR for the water mixing with a mixing volume of V_C.

Figure 7.

Vertical concentration distribution curve of tracer.

Figure 8 shows the E(H₁, t) output curves for the tracer at the top of the sludge bed and the E(t) output curves for the tracer in the upper bubble mixing zone obtained from the UASB model calculations and analysis. The left side shows the high sludge bed expansion condition and the right side shows the low sludge bed expansion condition. In the high expansion sludge bed condition, the volume of the upper bubble mixing zone (V₂ + V₃) and the volume of water involved in mixing are small, E(H₁, t) is close to the E(t) output curve, and the UASB reactor can be simplified to a CSTBR operating unit; in the low expansion sludge bed condition, E(H₁, t) deviates from the E(t) output curve, and the UASB reactor can be simplified to a CSTBR of sludge bed operates in tandem with a CSTR of water with a mixing volume of V_C in its upper part. The tracer concentration peaks at high sludge bed swelling conditions are smaller than those at low sludge bed swelling conditions, and the sludge-water mixing is better.

Figure 8.

UASB output concentration and cumulative mass output curve.

In a computational analysis of the sludge-water mixing process in a group of UASB reactors, Yan and Yang used the UASB tracer test data from the Pena test on engineering scale to determine the diffusion coefficient of the sludge bed, E_y = 0.00006 ∼ 0.00012 m²/h. The value of E_y is larger when the upward water flow velocity is larger, and the sludge bed expands and is smaller when the upward water flow velocity is smaller. The variation of E_y is not significant and is stable at 10⁻⁴ orders of magnitude.

Here present the key elements of a computational analysis of sludge-water mixing in a UASB reactor [2]. The sludge bed height H₁ = 1.0 ∼ 2.5 m, an upward flow velocity u = 0.4 ∼ 0.8 m/h, a hydraulic residence time T₁ = 3.1 ∼ 3. 8 h, and a mixing completion time t₄ = 1.0 ∼ 1.9 h, t₄ << T₁.The sludge bed operates as a CSTBR, with low upward flow velocity u and mixing intensity.

As V_C is generated by the agitation of bubbles released from the anaerobic reaction, its value cannot actually be determined in advance. However, there are two extremes in the operating conditions of the UASB reactor. The sludge-water mixing process can be calculated without prior determination of the V_C. This can be used to analyze sludge-water mixing characteristics of UASB reactor.

1. Sludge bed with high expansion condition, H₂ = 0, (V₂ + V₃) is much smaller than V1, at this time can ignore the upper involved in the volume of water mixing V_C, calculate and analyze the state of sludge-water mixing in the sludge bed. Under these conditions, the sludge bed has the longest diffusion mixing time and flow, the percolation diffusion coefficient is also larger, and the sludge-water mixing state is the best.

2. The sludge bed with low expansion condition, where H₂ and (V₂ + V₃) are maximum, but taking V_C = 0, (V₂ + V₃) operates in a push-flow mode. At this condition, the sludge bed has the shortest seepage diffusion mixing time and flow and also has a smaller percolation diffusion coefficient due to the denser sludge particle build-up, which results in the worst mud-water mixing conditions in the sludge bed. When (V₂ + V₃) is operated in push-flow mode, the end of the E (H₁, t) curve at the top of the sludge bed does not produce a descending fold when the boundary concentration of the sludge bed outflow is higher. As can be seen from Figure 7, the sludge-water mixing time calculated for this condition will be greater than the mixing time for the normal condition of V_C > 0. This condition occurs at the beginning of the UASB start-up operation when gas production is low.

From these two extreme operating conditions, the possible sludge-water mixing states in the UASB reactor can be approximated, while the other general operating conditions have sludge-water mixing states in between. In general operation, 0 < V_C < (V₂ + V₃). To obtain an accurate V_C during UASB reactor operation, a tracer test is required, and V_C can be calculated by model analysis of E(t) curve of tracer output.

The model analysis determines the seepage diffusive mixing of the sludge bed and the mixing of the upper water volume to complete the vertical mixing of sludge-water in the UASB reactor in CSTBR mode. The horizontal sludge-water mixing operation is ensured by a uniform water distribution system at the bottom of the sludge bed, resulting in a uniform horizontal concentration distribution in each section of the UASB. The uniformity of water distribution at the bottom of the sludge bed directly impacts the sludge-water mixing in the sludge bed. There is already more technical and engineering experience in this aspect. A more reliable water distribution system for UASB reactors is the small resistance distribution system. Although the accuracy of the water distribution uniformity is not as good as with large resistance distribution systems, its large cross-sectional flow paths make them less likely to block and easier to clear.

The morphological shaping of sludge particles and their scale control also are key factors in the control of sludge-water mixing. The shape and size of the sludge particles, as well as the compactness and homogeneity of the accumulation, have a direct impact on the seepage and diffusion processes in the sludge bed. Numerous biological factors—may influence the formation of sludge particles Speece [1], in addition to the usual COD concentration: alkalinity, organic acids, hydrogen partial pressure, multiple trace elements, methanogen types, lipids, and nitrogen and calcium. The formation of sludge particles appears to be a very complex biological process. However, once the sludge particles in the sludge bed have been initially formed, they can be hydraulically graded to leave the sludge particles with good settling and conformational scales. This results in a uniformly stacked sludge bed with the right size of anaerobic sludge particles. A range of 9.0–55.0 m/h is the recommended flow velocity for hydraulic classification by Speece [1].

The larger sludge bed expansion height H₁ and lower upward flow velocity u facilitate sludge-water mixing, allowing the UASB to operate in a CSTBR mode. However, a higher sludge bed expansion height will not be conducive to maintaining a uniform sludge particle distribution and releasing air bubbles between particles inside the sludge bed, it will also cause the sludge-water mixing reaction to deviate from CSTBR. Too low a flow velocity may result in compaction of the sludge bed, which is not conducive to seepage diffusive mixing. As a general rule of thumb, UASB reactors have an upward flow velocity of u = 1.0–5.0 m/h and a sludge bed height of H₁ = 1.5–3.0 m. Limits the height of the sludge bed and the upward flow rate, which also limits the amount of sludge and the volumetric load of organic matter in the UASB reactor.

3.2 Internal reflux packed-bed anaerobic reactor (IRPAR)

Internal reflux is widely used in biochemical treatment processes to promote mixing of the water and improve the efficiency of the biochemical reactions. In many cases, internal reflux is provided to facilitate the mixing of water, although it may be mainly required to meet other process operating conditions. For example, in aerobic or anaerobic biofilters, internal reflux is used to increase the flow velocity to flush out excess or aged biofilm growing on the surface of the filter media; in fluidized beds, internal reflux is used to increase the water flow velocity to fluidize suspended bioparticles and also to mix the water; in filled bed anaerobic reactors, internal reflux is used to increase the mixing intensity of bubbling between the pores of the filler and the mixing of the water and is desired to obtain a completely mixed anaerobic reactor.

In Figure 9, the anaerobic reactor IRPAR is equipped with an internal reflux system [7]. The substrate was fed in at the bottom of the reactor through a conical inlet followed by a distribution plate. The effluent was withdrawn from the top for recirculation and disposal.

Figure 9.

Model of IRPAR.

Here the water and sludge-water mixing processes in an IRPAR are analyzed, and the convergence to a CSTR biochemical reactor as a CSTBR is demonstrated under set conditions. This analysis and demonstration were done by Yan and Yang.

Figure 9 shows the model of an IRPAR. C₀ is the influent concentration, and C(H, t)is the effluent concentration at time t. The height and the volume of the packed bed reaction zone are H and V, and the reflux ratio is R, R > > 1. The influent q and the reflux Q, Q = Rq, are mixed instantaneously at Point A and uniformly distributed to the bottom with concentration C(0, t). The hydraulic retention time is T, T = V/q, and the reflux cycle time is T_L = V/Q.

For the fillers with pore sizes much smaller than the mixing scale of the anaerobic reaction zone, the sludge-water mixing proceeds with reflux water and influent traversing the surface of the biomembrane in each cycle. As shown in Figure 9, the mixing of water occurs at three scales of mixing: (1) large-scale transport of water flowing from the upper outflow to the bottom inflow, and then traversing the surface of the biomembrane attached to the filler in the reactor; (2) small-scale mixing of the biogas and the rising water; and (3) the microscale molecular diffusion within the biomembrane on the filler. The large spatial and time scales of the reflux transport are close to H and T_L, respectively. The small mixing scale of the rising flow and biogas is close to the scale of the filler pores. The mixing scale within the biomembrane is close to the membrane thickness, which is much smaller.

Figure 9 ignores the flow time of the internal circulation pipeline. Let C (y, t) be the concentration distribution of the tracer, y ϵ (0, H); $\overline{\mathrm{C}}$ (k) is the average tracer concentration in the reactor at time t = kT_L, k = 0, 1, 2, . . ., Eq. (3) was derived:

$$\overline{\mathrm{C}}\left(\mathrm{k}\right)=\frac{1}{{\mathrm{T}}_{\mathrm{L}}}{\int }_{\mathrm{k}{\mathrm{T}}_{\mathrm{L}}}^{\left(\mathrm{k}+1\right){\mathrm{T}}_{\mathrm{L}}}\mathrm{C}\left(\mathrm{H},\mathrm{t}\right)\mathrm{dt}$$E9

According to Eq. (6), the average output concentration in T_L is equal to the average concentration $\overline{\mathrm{C}}$ (k) in the reactor. The average concentration $\overline{\mathrm{C}}$ (k), k = 0, 1, 2, …, can be obtained by mathematical induction

$$\frac{\overline{\mathrm{C}}\left(\mathrm{k}\right)}{\overline{\mathrm{C}}\left(0\right)}={\left(1-\frac{1}{\mathrm{R}}\right)}^{\mathrm{k}}$$E10

where $\overline{\mathrm{C}}$ (0) - initial average concentration in the reactor and k = 0. According to Eq. (8), furthermore, as R → ∞, the average concentration $\overline{\mathrm{C}}$ (k) achieved in a CSTR at t = kT_L, can be obtained as follows:

$$\frac{\overline{\mathrm{C}}\left(\mathrm{k}\right)}{\overline{\mathrm{C}}\left(0\right)}={\mathrm{e}}^{-\frac{\mathrm{k}}{\mathrm{R}}}$$E11

The cycle time T_L can be defined as a mixing time scale of the IRPAR. The essence of internal reflux mixing is large-scale transport, and it cannot change the tracer concentration distribution C (y, t). Only the small-scale mixing of biogas and the rising water flow can encourage uniform mixing of the water.

The discontinuous discrete distribution of the mean tracer transport concentration on the mixing time scale T_L is obtained from Eq. (10) and shown in Figure 10. The CSTR continuous output curve is also given in the figure. From Figure 10, it can be seen that after R > 10, the concentration output curve of the anaerobic reactor has been able to discretely converge to the continuous concentration curve of the CSTR as a CSTBR. A simple derivation shows that the rising flow velocity in the reactor with internal reflux is u_L = (R + 1)u, u being the rising flow velocity in the absence of reflux or when R = 0. For u = 0.5 ∼ 5.0 m/h, and taking R = 20, u_L = 10.5 ∼ 105 m/h, T_L/T = 21. At this point, the mixing time scale T_L << T, and the ability to mix sludge-water at low flow velocity and mixing intensities is close to CSTR on the time scale T_L, as a CSTBR. Taking a larger R-value and reducing T_L can be closer to CSTR or be a CSTBR, but will make u_L too large for the stability of the microbial symbionts in the anaerobic sludge membrane.

Figure 10.

E(t) curve of the CSTR and the internal reflux anaerobic reactor.

Consider the steady-state anaerobic degradation reaction of organic pollutants with only internal reflux transport. The concentration difference ΔC of organic pollutants formed between the bottom section and the upper outlet section is

$$△\mathrm{C}=\frac{{\mathrm{C}}_0-\mathrm{C}\left(0,\mathrm{t}\right)}{\mathrm{R}}$$E12

From Eq. (12), letting R → ∞ or T_L → 0, Eq. (13) was obtained

$${\mathrm{C}}_0+\mathrm{Tr}=\mathrm{C}\left(\mathrm{H},\mathrm{t}\right)$$E13

where r is biochemical degradation rate of pollutants.

Eq. (13) is the concentration equation of a steady-state CSTR. Therefore, considering the homogeneous distribution of the anaerobic biomembrane, even without considering the unstable small-scale mixing of biogas and rising water flow, and only using a sufficiently large internal reflux ratio R, R > > 1, an equivalence between the sludge-water mixing reaction in the internal reflux anaerobic reactor and the complete mixing and reaction of the CSTR can be achieved, and the microscale molecular diffusion of the biomembrane is processed synchronously.

In accordance with the conditions set by the internal reflux sludge-water mixing model, the pore size of the filler media and the pore space between the filler media in a packed bed anaerobic reactor should be sufficiently small, much smaller than the mixing space size of the anaerobic reactor, and evenly distributed. In addition to economic considerations, the specific surface area, roughness, biological inertia, mechanical strength, and suitable shape and void space of the filler material should be considered. The particle size and inter-particle void size of the filler is a key consideration, with Speece recommending a particle size of around 15 mm. Speece’s research shows that the depth of the packed bed has no significant effect on operation, but the recommended packing height is 2.0 m [1]. Although the smaller filled bed height increases the area of lateral water distribution and the difficulty of uniform water distribution, smaller u_L, and mixing intensity can be obtained.

Filled bed anaerobic reactors rely on the mixing of water at point A in Figure 9 and uniform water distribution at the bottom of the packed bed to ensure a uniform lateral distribution of concentration in the packed bed. Similar to the UASB reactor, the water distribution at the bottom of the packed bed in a packed bed anaerobic reactor uses a small resistance distribution system to help prevent blockages in the water distribution system and to facilitate cleaning and maintenance.

In some aerobic or anaerobic biochemical reactors with filled media and internal reflux, when the particle size of the filled media is much small and evenly distributed, the sludge-water mixing process in large-scale internal reflux is isomorphic. A large-scale sludge-water mixing model similar to that of the IRPAR can be used to analyze the operating mode of sludge-water mixing in internal reflux and the conditions for achieving a CSTBR, such as biofilters and biological contact aerobic or anaerobic biochemical reactors.

4. Conclusion

According to anaerobic sludge properties, sludge-water mixing in anaerobic reactors operating in complete mixing mode should all take place at low mixing intensities or water flow velocity in order to maintain a stable anaerobic biota in the anaerobic sludge and thus improve the efficiency of the anaerobic biochemical reaction. In this chapter, the CSTBR was defined in terms of the sludge-water mixing time scale $\overline{\mathrm{t}}$ and the biochemical reaction time scale T ($\overline{\mathrm{t}}$ << T), which is used to analyze the sludge-water mixing characteristics of anaerobic reactors and tends to CSTR as $\overline{\mathrm{t}}$ → 0. Both the UASB reactor and the IAPRA reactor are confined sludge anaerobic reactors and have different mixing patterns. However, both can achieve CSTBR mode with low mixing intensity and simultaneous sludge-water mixing. According to the structural characteristics and mixing patterns of these two types of anaerobic reactors, corresponding sludge-water mixing calculation models can be established to analyze the working conditions and corresponding operational parameters to achieve the CSTBR mode.

1. The UASB reactor consists of a sludge-water mixing reaction unit that operates as a CSTBR and a unit of water mixing unit that operates as a CSTR in series mode. The UASB reactor can be simplified to a single-stage CSTRB anaerobic reactor when the sludge bed expansion height is large and the volume of the upper part of the water involved in the natural mixing of the bubbles is small. The sludge-water mixing reaction can reach the CSTBR at a low mixing intensity, which corresponds to flow velocity as low as 0.8 m/h in a UASB of engineering scale.

2. IAPRA mixes sludge-water with a internal reflux of large space scale, and the mixing time scale is the internal reflux period T_L. The sludge-water mixing reaction reaches CSTBR when T_L << T. The sludge-water mixing intensity is lower, and the corresponding water flow velocity can be as low as below 5.0 m/h for a CSTBR mode.