Rheological properties of digestate from agricultural biogas plants: An overview of measurement techniques and influencing factors

Renewable and Sustainable Energy Reviews 121 (2020) 109709

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Rheological properties of digestate from agricultural biogas plants: An overview of measurement techniques and influencing factors Nico Schneider a, *, Mandy Gerber b a b

Ruhr-Universit€ at Bochum, Lehrstuhl für Thermodynamik, Universit€ atsstr. 150, 44801, Bochum, Germany Hochschule Bochum, Institut für Thermo- und Fluiddynamik, Lennershofstr. 140, 44801, Bochum, Germany

A R T I C L E I N F O

A B S T R A C T

Keywords: Digestate Biogas Viscosity Rheological properties Anaerobic digestion Rheometer Viscometer

The main objective of this work is a comparison of measurement techniques that have been modified allowing for rheological measurements of agricultural digestate without a required pretreatment. This includes detailed in­ formation on the theoretical physical background, experimental set-up and for mixing rheometers also the calibration procedures, namely the Metzner-Otto concept/Rieger-Novak method and the Couette analogy. Furthermore, the advantages and disadvantages of rotational rheometers, torsion viscometers, mixing rheome­ ters, pipe viscometers and the so-called ball measuring system are stated. As a result, pipe viscometers are found to be applicable for field experiments, while mixing rheometers were found to be the most suitable choice for labscale experiments. Within this work, a recommendation for a possible configuration for a mixing rheometer is provided. Moreover, this article gives an overview of research works dealing with the rheological behavior of digestate from agricultural biogas plants and first identified influencing factors. Investigated samples in the featured research works all exhibit a non-Newtonian shear-thinning flow behavior and the power-law model was applied the most. The most common identified influencing factors include temperature, total solid content, feedstock, particle size and anaerobic digestion, amongst others. However, observed correlations between these factors and the flow behavior and viscosity, respectively, to date are rather qualitative then quantitative, and extensive, systematic studies have yet to be carried out in order to establish quantitative relationships in between influ­ encing factors. Based on the survey of relevant literature, recommendations for the measurement procedure and documentation of rheological measurements of digestate are provided.

1. Introduction Due to diminishing fossil fuels and an ever-growing comprehension for climate change mitigation, energy production from renewable en­ ergy sources has become utterly important within the last decades. Be­ sides wind power, geothermal and solar energy, biomass conversion is one of the mainstream technologies for the generation of sustainable energy. This also includes biochemical conversion processes like anaerobic digestion and composting, whereas the technically applied anaerobic digestion process in biogas plants has received increased attention in recent years. In order to improve the efficiency of a biogas plant, an optimal dimensioning, design and operation of the plant and its components is aspired, both in new construction as well as in Repow­ ering. For this, rheological properties describing the flow behavior and the viscosity of digestate in particular, are of great importance, in

particular for installed in-plant components such as pumps [1], heat exchangers [2] and stirrers. Here, especially the mixing of the biogas process is a common research objective in various studies [3]. Mixing ensures a uniform heat and nutrient distribution in the fermenter (digester) and enables microorganisms the access to degradable feed­ stocks [4]. Moreover, an adequate mixing avoids sedimentation as well as the formation of floating layers, and hence is beneficial for the release of biogas from digestate [5]. Mixing also prevents excessive foam for­ mation [6], which otherwise results in operational problems like plug­ ging of gas pipes, a decreased biogas yield and financial losses in the last resort [7]. A key parameter influencing mixing, and thus most of the above-mentioned effects associated with it, again is the rheological behavior of the digestate in a biogas plant. For instance, an increased viscosity leads to a reduction of flow velocities for a given rotational speed, and thus a poorer mixing [8], while a decreased viscosity can lower the energy demand of the biogas plant [9]. According to Weiland

* Corresponding author. E-mail address: [email protected] (N. Schneider). https://doi.org/10.1016/j.rser.2020.109709 Received 11 April 2019; Received in revised form 18 December 2019; Accepted 3 January 2020 Available online 10 January 2020 1364-0321/© 2020 Elsevier Ltd. All rights reserved.

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Nomenclature Latin Symbols a coefficient A coefficient b coefficient B coefficient c coefficient D diameter. [m] K consistency coefficient. [Pa sn] coefficient in Couette analogy. [ ] Kγ_ Ks Metzner-Otto constant. [ ] L length. [m] M torque. [N m] n flow behavior index. [ ] N rotational speed. [s 1] Power number. [ ] NP p exponent in Cross Model. [ ] P power. [W] r, R Radius. [m] Re mixing Reynolds number. [ ] s coefficient in Weissenberg-Rabinowitsch correction. [ ] V_ flow rate. [m3∙s 1]

ηC ρ τ τ0

Casson-viscosity. [ ] density. [kg m 3] shear stress. [Pa] yield stress. [Pa]

Subscripts a e eff H2O i o w

apparent external effective water inner outer at the wall

Abbreviations CCM corn cob mix CD cattle dung CFD computational fluid dynamics CM cattle manure CS corn silage DIN Deutsches Institut für Normung DN nominal diameter GPS whole plant silage GS grass silage HRT hydraulic retention time ISO International Organization for Standardization RLD recirculated liquid digestate after separation RS rye silage SBPP sugar beet pressed pulp TS total solid

Greek Symbols γ_ shear rate. [s 1] η dynamic viscosity. [Pa s] η0 zero-shear viscosity. [Pa s] η∞ infinite-shear viscosity. [Pa s] ηB Bingham-viscosity. [ ]

[10], up to 90% of biogas plants are equipped with mechanical stirrers for mixing purposes. However, this can account for approximately 30–55% of the total electric energy demand of a biogas plant [11], whereas its total electricity consumption commonly is 5–10% of the electricity produced [12]. In order to reduce the energy demand, and hence increase the efficiency of a biogas plant, experiments and CFD-based analytical techniques are employed to carry out parametric studies optimizing the design and operation of stirrers [13]. Both ap­ proaches require knowledge about the flow behavior and viscosity of digestate, respectively [14]. However, rheological properties data of digestate are rare [15], so that most CFD simulations are so far only been carried out rudimentarily and the used data often are assumed [16], rely on measurements of manure [17] or are based on particle-free models [18] or incorrect assumptions [19]. This is due to a limited applicability of conventional measurement systems caused by the composition of agricultural digestate, in especially large fibers and particles that, e.g., block the capillary or the gap. To remedy these deficiencies, measure­ ment systems have lately been modified allowing for rheological mea­ surements of digestate by adapting the basic principles of known rheometers. Here, especially systems offering either larger capillary di­ ameters like pipe viscometers [8,20–22] or larger gap-widths like mix­ ing rheometers [23–26] have primarily been employed for rheological measurements of agricultural digestates. However, no experimental standard method has yet been established which means that results from different studies can only be compared to a limited extent due to varying techniques and measurements conditions. To this end, the main objective of this work involves a comparison and an overview of measurement techniques that have lately been used to measure the viscosity of digestate from agricultural biogas plants. Moreover, comparing the advantages and disadvantages of the indi­ vidual methods within this study will help to identify suitable

techniques, and thus can lay the foundation for defining a standard for rheological measurements of digestate from agricultural biogas plants. In addition, previously published results for the rheological charac­ terization of digestate are summarized and influences on the flow behavior and viscosity, respectively, are presented. By this, common influencing factors can be identified which helps to clarify gaps and to further specify prospective research needs. While similar state-of-the-art studies recently have been published for wastewater, sewage sludges and comparable biomasses, this is the first study focusing on digestates from agricultural biogas plants (also see section 2.1). 2. Theoretical background 2.1. Digestate from agricultural biogas plants In literature, various notations can be found for the substance inside the fermenter of a biogas plant. While a lot of authors use digestate, others refer to it as anaerobic slurry or sludge, biogas slurry, fermenting substrate, digesting mixture of feedstocks, digester content, fermenter content or any mixture of the above mentioned. Here, digestate is the notation of choice. According to Wellinger et al. [27] digestate is the effluent after extraction of biogas via anaerobic digestion of feedstock materials. It should be noted that within the scope of this work digestate means any content taken from the fermenter at any time during the biogas process. In summary, digestate from biogas plants consists of a water-based liquid phase, a solid phase in form of feedstock residues and a gaseous phase due to gas bubbles. In this work, the focus is on digestate from agricultural biogas plants, which is not to be confused with activated sludge [28], granular sludge, municipal sludge [29], primary and sec­ ondary sludge, biosludge [30],wastewater, or sewage sludge for biogas 2

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processes originating from sewage treatment plants or related facilities, whose rheological properties have been studied in detail. Agricultural biogas plants primarily use agricultural byproducts like liquid manure, dung, harvest residues and energy crops as feedstocks being digested in a wet fermentation process. Some agricultural biogas plants solely use liquid manure as feedstock resulting in an almost particle-free digestate. However, the rheological properties of fresh and digested liquid manure as well as influencing factors on the rheology of manure have widely been characterized, e.g., by Brambilla et al. [31], El- Mashad et al. [32] and Liu et al. [33], and are therefore not part of this study. Thus, the digestate referred to in this work alongside manure usually contains large, fibrous particles due to using energy crops, which is the most important co-substrate used especially in Europe [10]. The preferred average chopping length of renewable energy crops is 50 mm [16]. However, depending on the feedstock diameters up to 80 mm (e.g., sugar beet) and lengths up to 100 mm (e.g. grass silage) can occur in the digestate [15]. 2.2. Rheology and viscosity

Fig. 1. Flow curves of a Newtonian, shear-thinning, shear-thickening, Bingham and Herschel-Bulkley fluid, respectively.

Rheology is the science of a material’s flow and deformation behavior when applied to stress. The objective of rheological measure­ ments is the determination of the degree to which the material deforms (strain), and the ratio of stress to strain for solids; and the ratio of shear stress to the rate of strain (or shear rate) for liquids, respectively [34]. The latter is called viscosity and defines the material property that de­ termines the resistance of a fluid to flow. If the shear stress is proportional to the shear rate and they exhibit a linear relationship), the fluid is ideal viscous. This can be described by Newton’s constitutive equation:

point, yield stress or yield value τ0. Below this value the fluid acts like a solid: none or only reversible (elastic) deformations occur due to an intermolecular/interparticle network of binding forces. Above the yield value irreversible deformations cause the fluid to flow [36]. Is the flow after the yield stress Newtonian, plastic fluids are referred to as ideal plastic fluids or Bingham (plastic) fluids, while they are called Herschel-Bulkley fluids or Bingham pseudoplastic fluids in the case of a shear-thinning flow behavior. Non-Newtonian fluids that are thixotropic show a decreasing viscos­ ity related to the duration of shear, even though the applied shear stress is constant. Moreover, the fluid regains its initial viscosity after a certain time without being exposed to stress. In contrast, the viscosity of rheo­ pectic fluids increases over time during constant stress. With stopping stress this effect is reversed as well. Since the viscosity of non-Newtonian fluids depends on shear rate and a flow behavior can be formulated, most researchers refer to it as rheological properties of the tested fluid, instead of talking solely about the viscosity of the fluid. If a material exhibits both viscous and elastic characteristics when being exposed to deformation it is referred to as viscoelastic. Viscoelastic materials have a hysteresis in their stress-strain curve and step constant stress causes increasing strain (creep). In addition, step constant strain causing a decrease of stress (stress relaxation) is also possible. Thus, such materials are neither fully viscous, nor fully elastic. Detailed information on the flow behavior of viscoelastic fluids can be found in Schramm [36].

(1)

τ ¼ η⋅_γ

in which the viscosity η [Pa s] is the constant proportionality coefficient between shear stress τ [Pa] and shear rate γ_ [s 1]. Hence, ideal viscous fluids are also called Newtonian fluids, whose viscosity is independent of the shear rate. In contrast, fluids are classified as non-Newtonian, if their viscosity changes with varying shear rate and thus, the relation between shear stress and shear rate is not linear. For such substances the apparent ηa or effective viscosity ηeff [Pa s] is specified, which represents one point of the viscosity curve (viscosity over shear rate) only:

ηa ð_γÞ ¼ ηeff ð_γÞ ¼

τ γ_

(2)

Fluids with a non-ideal flow behavior can be further divided in timeindependent and time-dependent non-Newtonian fluids – the latter being affected by the duration of the shear strain. A time-independent non-Newtonian fluid can be shear-thinning, shear-thickening or plastic (see Fig. 1), whereas a time-dependent non-Newtonian flow behavior can be specified as thixotropic or rheopectic [35]. The viscosity of shear-thinning fluids decreases with increasing shear rate. Shear-thinning fluids are also called pseudo-plastic. If the viscosity increases with increasing shear rate, the fluid exhibits a shear-thickening behavior, which can also be referred to as dilatant. Both effects are caused by structural changes and reorientation of particles or molecules in the fluid due to the applied shear stress. At very low shear rates these change and reorientation processes have not yet started and at very high shear rates they have already been realized as far as possible [36]. For some shear-thinning fluids this causes an ideal-viscous flow behavior at very low and very high shear rate ranges, respectively. These ranges with constant viscosity are called first and second Newtonian range or plateau, respectively. In the first Newtonian range the viscosity is referred to as zero-shear viscosity η0, whilst being called infinite-shear viscosity η∞ in the second Newtonian range. Fluids exhibiting a plastic flow behavior feature a so-called yield

2.3. Models for rheological characterization In order to illustrate the flow behavior of fluids in flow curves and viscosity curves, respectively, and to describe the relationship between shear stress or viscosity and shear rate experimentally gained data is fitted to mathematical models. These models can be referred to as flow behavior models and viscosity functions, respectively, and are used to characterize the flow properties of a fluid in order to determine its ability to perform specific functions [37]. Newton’s law of viscosity as represented in Eq. (1) describes idealviscous fluids. For time-independent non-Newtonian fluids various models and equations have been established depending on the observed flow characteristics. The most frequently applied model is the power-law model due to its simplicity. It was originally proposed by de Waele [38] and Ostwald [39], and hence is also referred to as the Ostwald-de-Waele relationship. It uses two adjustable parameters only: 3

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especially large fibers and particles that, e.g., block the capillary or the gap, necessitating a sample pre-treatment in most cases. Thus, existing measurement methods and instruments have been modified or new methods developed, which will be explained in more detail in the next sections. Nevertheless, some studies utilized conventional rotational rheometers and torsion viscometers, which will therefore be briefly explained to begin with.

(3)

τ ¼ K⋅_γn

where K is the consistency coefficient [Pa sn] and n is the flow behavior index [ ]. Combining the power-law model with Eq. (2) the following equation derives:

ηa ð_γÞ ¼ K⋅_γn

1

(4)

Thus, Eq. (4) allows for the determination of the apparent viscosity. The flow behavior index n is a measure for the degree of non-Newtonian behavior and distinguishes the type of a fluid [40]: For n < 1 a shear-thinning fluid can be described, while n > 1 results in a shear-thickening fluid. In the case of n ¼ 1 an ideal-viscous fluid is described. The disadvantage of the power-law model is its incapability to fit flow curves for fluids exhibiting zero-shear viscosities η0 and infinite-shear viscosities η∞, respectively [35]. Thus, it describes the range between both of the Newtonian plateaus only. The Cross model [41] corrects this deficiency, and thus covers the entire shear rate range:

ηa ð_γÞ η∞ 1 ¼ 1 þ ðc⋅_γÞp η0 η∞

3.1. Rotational rheometer Any rheometer utilizing a rotational movement to generate the shear rate in order to measure the viscosity is called rotational rheometer. Each rotational rheometer consists of a coaxially arranged stator and a rotor, which can be turned against each other. Different standardized geom­ etries are used in dependence of the tested viscosity range: concentric cylinders, double gap, (double) cone-plate, plate-plate or cone-cone. The gap between the two parts of the used measuring geometry contains the fluid sample. A widely-used geometry are concentric cylinders. Here, the fluid is placed in a gap between an inner cylinder (rotor) and an outer cylinder (cup). One of the two cylinders is rotated and the torque required maintaining rotation is measured. If the inner cylinder is rotated, while the outer one is stationary, the system is referred to as Searle-system. If it is the other way around, the system is called Couettesystem. Both systems are schematically shown in Fig. 2. For a given rotational speed N [s 1] and the resulting torque M [N m], shear stress and shear rate related to the surface of the inner cylinder are calculated with the following equations:

(5)

where c [s] is a constant representing the time of the transition from the first Newtonian plateau to the shear-thinning range and p a dimen­ sionless exponent. An alternative to the Cross model is presented by Bird and Carreau [42], and is called the Carreau model:

ηa ð_γÞ η∞ 1 ¼ η0 η∞ ð1 þ ðc⋅_γÞ2 Þp

(6)

τi ¼

where c and p have the same function as in the Cross model. The Bingham model established by Bingham [43] is used for plastic fluids with a yield stress τ0:

τ ¼ τ0 þ ηB ⋅_γ

γ_ i ¼ 4⋅π⋅N⋅ 2 Re

(7)

(10) R2e R2i

(11)

where L [m] is the height of the rotor, Ri is the radius of the inner cyl­ inder and Re is the radius of the outer cylinder. Hence, the viscosity is given by:

where ηB [ ] is the Bingham-viscosity, which is a calculated coefficient used for the curve fitting [35]. Based on the nature of the equation, this model can only be used for fluids that display a linear increase of shear stress with increasing shear rate once the yield stress is reached. To avoid this restriction, Herschel and Bulkley [44] presented the Herschel-Bulkley model, which combines the Bingham model and the power-law model:

τ ¼ τ0 þ K⋅_γn

M 2⋅π⋅L⋅R2i

η¼

R2e R2i M ⋅ 8⋅π2 ⋅L⋅R2e ⋅R2i N

(12)

Eq. (10) – (12) are only valid for concentric cylinder with a large gap. Equations for concentric cylinders with a small gap (Re/Ri � 1.0847) are specified in standard ISO 3219 [46]. Additional information on the measurement principles, different geometries and applications of rota­ tional rheometers can be found in Schramm [36], Tanner [40] and

(8)

Thus, this model can be used for fluids exhibiting a non-proportional relationship between shear stress and shear rate once the yield stress τ0 is surpassed. Following the power-law model, a shear-thinning flow behavior is described for n < 1, whereas a shear-thickening behavior is characterized for n > 1 and n ¼ 1 results in a Bingham-fluid. An alternate equation for plastic fluids is presented by Casson [45], and hence called the Casson model: pffiffi pffiffiffiffi pffiffiffiffiffiffiffiffi τ ¼ τ0 þ ηC ⋅_γ (9) where ηC [ ] is the Casson-viscosity and like the Bingham-viscosity a coefficient used for the curve fitting. In summary, it can be noted that using the presented models (3)–(9) in combination with Eq. (2) allows for the calculation of the apparent viscosity based on shear stress and shear rate. In literature there are several modifications of the presented models for non-Newtonian fluids, which, e.g., can be found in Tanner [40] or Mezger [35]. 3. Utilized measurement systems Conventional measurement systems like capillary viscometers, falling-body viscometers and rotational rheometers are suitable to only a limited extent, if at all, due to the nature/composition of the digestate, in

Fig. 2. Scheme of the Searle-system (a) and the Couette-system (b). 4

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Mezger [35], amongst others. In their study Deerberg et al. [47] used a rotational rheometer to characterize digestate containing corn silage and cattle manure, amongst others. However, they state that fibers and solids had to be removed before measurements in order to achieve reliable results. This is in accordance to Mbaye et al. [48] who sieved the digestate (mesh size: 7 mm) previous to measurements with a gap width of 7 mm. Instead of sieving, Tian et al. [49] grounded their samples (manure þ corn stover) with a lab-scale mill to average particle sizes of approximately 0.17 mm and 0.44 mm, respectively, with which measurements were feasible. In contrast, samples with a particle size of 4 mm could not be analyzed within their study. For rotational rheometers equipped with a concentric cylinder measuring system Jobst and Lincke [50] recommend the use only for particle sizes up to a maximum of 1.7 mm. This recommendation is tightened by Brehmer and Kraume [51] emphasizing the use for the liquid phase of digestate only. For instance, Gienau et al. [1,52] used a rotational rheometer equipped with a double gap geom­ etry for the liquid phase of agricultural digestate obtained by centrifu­ gation at 4300 min 1 for 10 min. 3.2. Torsion viscometer A special kind of instrument employing the principles of rotational rheometry are torsion viscometers which measure the torque required to rotate an immersed element in a fluid. One of the leading manufacturers is AMETEK Brookfield®, USA, explaining the name often used in liter­ ature for such devices instead: Brookfield viscometer. Here, the fluid sample usually is in a beaker or small vessel with a volume of 600 ml. The immersed element in this specific type is a spindle chosen from various geometries and designs like disc spindles, cylindrical spindles or vane spindles, amongst others. The spindle is driven through a cali­ brated spring, whose deflection is measured with a rotary transducer. A scheme of a torsion viscometer is illustrated in Fig. 3. The degree of the spring winding up indicates the fluid’s viscous drag or resistance to flow, which is proportional to the amount of torque required to rotate the spindle and related to its geometry. Thus, for a given spindle geometry and rotational speed, an increasing deflection of the spring indicates an increasing viscosity. By utilizing various spindle geometries and varying the rotational speed, a variety of viscosity ranges can be measured, which previously have been calibrated. Ac­ cording to the manufacturer, the accuracy of these viscometers is within �1%, if the required conditions (temperature, sample container size and homogeneity of the sample, amongst others) are considered [53]. However, Mezger [35] and Garuti et al. [54] point out that this method only provides device-dependent relative values of the viscosity as a function of rotational speed, due to a missing measurement of shear rates and shear stress. Thus, this method essentially enables qualitative rather than quantitative (in comparison to rotational rheometers) in­ formation of a fluid’s rheological behavior. €tz et al. [55] In their studies, Liu et al. [13], Garuti et al. [54] and Pa each used a torsion viscometer for the measurements on digestate. However, the latter emphasizes that usable results are only achieved under a strict compliance with all required conditions and that it is essential to remove impurities within the sample fluid. Furthermore, Liu et al. [13] state that the used Brookfield viscometer usually is used for Newtonian fluids. In order to adjust this equipment to the measurement of non-Newtonian fluids, Liu et al. modified the software equipped with the viscometer for data processing – details are given in their respective work [13].

Fig. 3. Scheme of a torsion viscometer.

often is referred to as mixing rheometers, mixer-type rheometers or impeller viscometer, but other designations are also possible. A typical mixing rheometer is illustrated in Fig. 4. A common stirrer geometry used for the measurement of flow properties of non-Newtonian fluids is the vane geometry [56], but other geometries are also possible. Mixing rheometers are relative measuring devices, whose theoretical approaches are based on conventional rota­ tional rheometers. In order to achieve absolute viscosity values depending on the shear rate, a calibration procedure is required. Here, two procedures can be found: the Rieger-Novak-method in combination with the Metzner-Otto concept, and the Couette analogy. 3.3.1. Metzner-Otto concept/Rieger-Novak-method Metzner and Otto [57] proposed that the shear rate γ_ [s 1] in a mixed vessel linearly depends on the rotational speed N [s 1] of the stirrer: (13)

γ_ ¼ Ks ⋅N

where Ks is a constant proportionality coefficient, which mainly depends on the used stirrer geometry [58], and thus has to be determined experimentally for each geometry of interest [59]. For this purpose, the following steps have to be carried out [60,61]: I) The torque M [N m] required to rotate a stirrer in a Newtonian fluid with known viscosity η [Pa s] and density ρ [kg/m3] at a given rotational speed N [s 1] is measured. These values are then used to calculate the power number (also known as Newton number) NP [ ], which relates the resistance force to the inertia force, and the mixing Reynolds number Re [ ], respectively:

3.3. Mixing rheometer Like torsion viscometers, the most commonly used system for rheo­ logical measurements on digestate from agricultural biogas plants basically consists of a stirrer (rotor) and a vessel (stator), in which the resulting torque at a given rotational speed is measured. This set-up

NP ¼

5

P

ρ⋅N 3 ⋅D5

¼

2⋅π⋅M ρ⋅N 2 ⋅D5

(14)

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Renewable and Sustainable Energy Reviews 121 (2020) 109709

KS ¼ N

1

⋅ γ_ ¼ N 1 ⋅

�η �n 1 1 a

K

(17)

Based on the assumptions of Metzner and Otto [57], Rieger and Novak [63–65] present a method without integrating the viscosity function of the stirred fluid. Thus, they established a method enabling the measurement of viscosities for unknown non-Newtonian fluids without having to perform rheological mea­ surements with rheometers. By measuring the resulting torque at a given rotational speed in a stirred non-Newtonian fluid, the char­ acteristic power consumption curve of the stirrer and the assignment of a power number NP to a corresponding Reynolds number Re is used to determine the apparent viscosity ηa of the fluid. This pro­ cedure parallels the steps I – IV of the Metzner-Otto concept. The apparent viscosity is directly assigned to the rotational speed of the stirrer, and thus the resulting curve represents the viscosity as a function of rotational speed, which is called apparent flow curve [66]. Combining the Rieger-Novak method and the Metzner-Otto concept, the flow curve can be transformed into a viscosity curve by using the Metzner-Otto constant KS in order to convert rotational speeds into shear rates. However, both approaches are based on the ‘matching viscosity assumption’, which can only be made neglecting inertia forces. Due to this negligence, both concepts are valid within a laminar flow region only [67]. Most authors dealing with the presented approaches rely on Metzner and Otto [57], who found flow regions to be laminar for Re < 10, while others recently expanded the region to Re < 10–100 [62,68, 69]. In order to observe a laminar flow region, measurements should be terminated with starting formation of vortexes or spouts. Many authors criticize the Metzner-Otto concept or rather the Metzner-Otto constant for not only depending on the geometry of the stirrer, but also on the flow characteristics of the fluid [70,71]. Con­ cerning this, a few studies present modified concepts embracing these issues, e.g., by including the geometry of the vessel, the density as well as rheological properties of the fluid in addition to the geometry of the stirrer [67,72–75]. Nevertheless, the Metzner-Otto concept has been applied in many publications mostly dealing with power characteristics of stirrers in nonNewtonian fluids and in studies employing mixing rheometers to determine the rheological properties of non-Newtonian fluids. For the rheological characterization of digestate Jobst and Lincke [50] used a 6-bladed stirrer with a diameter of 20 mm in a plastic measuring cup with a diameter of 133 mm and a height of 177 mm. Before measurements, a sample volume of 1.6 l was heated to the defined temperature via a water bath. According to their study, this set-up is feasible up to particles sizes of 20 mm, whereas a larger set-up (stirrer diameter: 70 mm, vessel volume: 5 l, sample volume: 3.5 l) allowed measurements for particles up to 50 mm in size. A larger set-up was also designed by Pohn et al. [26,76,77] who used a cylindrical stainless steel vessel (inner diameter: 200 mm, height: 300 mm, volume: 11 l) with a blade stirrer (diameter: 80 mm, height: 100 mm), and hence refer to it as ‘macro viscometer’. Its design is based on the ‘vane-in-a-large-cup principle’ as presented by Martínez-Padilla and Rivera-Vargas [78] and Martínez-Padilla and Quemada [69]. Heating is carried out by a welded jacket, in which tempered water is circulated. The macro viscometer was also utilized in studies by Kamar� ad et al. [12] and Stoyanova et al. [9]. The latter notes that the macro viscometer allows rheological measurements of fluids containing particles and fi­ bers with a diameter up to 15 mm and a length up to 30 mm, respectively. In their study Brehmer et al. [23] compared several stirrer geome­ tries: spiral stirrer (diameter: 118 mm), 2-bladed propeller stirrer (diameter: 136 mm), 3-bladed propeller stirrer (diameter: 131 mm), 4-bladed stirrer (diameter: 30 mm) and a 6-bladed propeller stirrer

Fig. 4. Scheme of a mixing rheometer.

Re ¼

ρ⋅N⋅D2 η

(15)

where P [W] is the required power for mixing and D [m] is the diameter of the stirrer. Plotting NP over Re represents the characteristic power consump­ tion curve of the stirrer and a functional relationship f(Re) ¼ Np can be established, which is valid for the used stirrer type and geometry only [62]. II) With the exact same set-up and geometry of vessel and stirrer, the first step is repeated with a non-Newtonian fluid with known density and viscosity curve (, e.g., determined with a rotational rheometer), and the resulting power number NP is calculated with Eq. (14). III) Metzner and Otto [57] proposed the assumption that the viscosity of a non-Newtonian fluid equals those of a Newtonian fluid, if in both cases the same characteristic power consumption is required for mixing with the same rotational speed. This sometimes is referred to as ‘matching viscosity assumption’ [60]. Based on this assumption, the inverse function f 1 of the characteristic power consumption established in I) is used to determine a corre­ sponding apparent Reynolds number Rea for the power number calculated in II). IV) The apparent viscosity ηa can then be calculated as a function of the rotational speed N transposing Eq. (15):

ηa ¼

ρ⋅N⋅D2 Rea

(16)

V) The shear rate γ_ corresponding to the calculated apparent vis­ cosity ηa is determined using the known flow behavior model of the non-Newtonian fluid previously determined with a conven­ tional rheometer. VI) Plotting corresponding shear rate γ_ over rotational speed N, the resulting slope represents the proportionality coefficient KS (Eq. (13)), which is also called Metzner-Otto constant. In case of a power-law fluid corresponding Eq. (4), Ks can be calculated as a function of the apparent viscosity ηa and the rotational speed N:

6

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(diameter: 95 mm). All stirrers were used in a vessel with an inner diameter of 160 mm and a filling height of 305 mm, and hence a filling volume of approximately 6 l, except the 4-bladed stirrer which was used in a smaller vessel (inner diameter: 143 mm, height: 180 mm, filling volume: 2.9 l). According to their findings, the stirrer geometry only slightly influences the measured flow behavior of the digestate. How­ ever, the stirrer is recommended to have a sufficient size in relation to the length of fibers in the digestate in order to provide useful results. In a study by Gienau et al. [1] a set-up was employed that included a vessel with an inner diameter of 150 mm, a total height of 260 mm, a filling height of 150 mm and hence a filling volume of approximately 2.6 l). A full blade stirrer with a height of 90 mm and a width of 70 mm was used as rotor which protruded from the level surface in order to overcome problems caused by high fiber contents. Heating was realized by a thermostat controlled water jacket. In comparison to that, Lebranchu et al. [68] used a cylindrical Plexiglas vessel with a height of 100 mm and an inner diameter of 100 mm resulting in a volume of 785 ml. The utilized stirrer was a helical ribbon with a height of 100 mm, a diameter of 98 mm and a width of 10 mm. The temperature was regulated with a heated jacket. Renpenning et al. [79] and Schimpf et al. [80] conducted measure­ ments in a temperature controlled vessel with a sample volume of 8–10 l directly used on site of a biogas plant. Further information on the set-up of the apparatus is not given. Reviol [67] used a propeller mixer which can be coaxially mounted to two different vessels. The first one has an inner diameter of 400 mm, a height of 630 mm and a volume of 60 l and is made of polyethylene. The alternative vessel is made of PMMA with a height of 492 mm, an inner diameter of 290 mm and a volume of 32.5 l [81]. In his study Reviol [67] found the Metzner-Otto concept and the Rieger-Novak method not to be sufficient due to its negligence of substance-specific characteristics. Thus, he developed the so called ‘power based concept’ which is a modified approach of a concept originally proposed by Henzler and Kauling [72]. Here, the Metzner-Otto constant is a function of the stirrer geometry as well as the power number and the Reynolds number. Detailed information on the ‘power based concept’ can be found in Reviol et al. [75,81]. Kube et al. [24] used the Metzner-Otto concept/Rieger-Novak method as an in-line approach in order to measure the viscosity directly during the operation of a biogas plant. To this end, the built-in vertical paddle stirrer of the biogas plant was modeled on a scale of 1:35 and the Metzner-Otto constant was determined in laboratory tests. The results were then transferred to the large-scale stirrer. Detailed information on either geometric proportions are not given.

and virtual system, have the same external cylinder radius Re [m], while the virtual rotor has the same height L [m] as the impeller. The basic principle of the Couette analogy includes the determination of the un­ known radius Ri [m] of the (virtual) inner cylinder with a calibration fluid, providing the same torque M [N m] as the real system for the same imposed rotational speed N [s 1] of the impeller. Once Ri has been ob­ tained, shear stress τ [Pa] and shear rate γ_ [s 1] can be calculated as a function of the radius r at any point between the (virtual) rotor and the cup (see Fig. 5) using Eq. (18) and Eq. (19), respectively:

τ¼

M 2⋅π ⋅L⋅r2

(18)

2

3 � �2n 6 4⋅π⋅ Re 7 6 n r 7 6 7 γ_ ¼ 6� �2 7⋅N 6 7 n 4 Re 15

(19)

Ri

where n is the flow behavior index [dimensionless] of the fluid. This way the shear rate is dependent on n and with it on the rheology of the fluid, which was supposed to be estimated in the first place. To solve this problem Bousmina et al. [83] showed that there is an optimal radius r* between the bob and the cup, at which the shear rate is almost inde­ pendent on the flow behavior index even in the case of large gaps. For details on the calculation of r* see Aït-Kadi et al. [82]. Hence, using r ¼ r* and n ¼ 1 in Eq. (18) and Eq. (19), respectively, the apparent viscosity ηa of a fluid with an unknown rheological behavior can then be calcu­ lated using Eq. (2). Using this method, Eq. (19) can be reduced to a linear relationship between the shear rate and the rotational speed: γ_ ¼ Kγ_ ⋅ N

(20)

where Kγ_ is a dimensionless coefficient of proportionality. According to Aït-Kadi et al. [82] and Guillemin et al. [85] this coefficient corresponds well to the Metzner-Otto constant Ks. Furthermore, they state that the Couette analogy hence offers a way to calculate Ks, instead of having to determine it in an experimental calibration procedure as described before. According to Choplin and Marchal [84] the deviation between data obtained with a Couette analogy based mixing rheometer and those determined with a conventional rheometer is about 5%. However, this value is based on rheological measurements of a food emulsion (salad dressing) and an aqueous solution (2% by weight) of carboxymethyl cellulose (CMC), which are basically free of particles. Hence, the stated error cannot be assumed for measurements on agricultural digestate, but indicates a lower limit. This is supported by a study of Hreiz et al. [86], who report a relative variation of up to 48% between measurements of non-sieved anaerobically digested cow slurry containing particles >14 mm with a mixing rheometer calibrated with the Couette analogy.

3.3.2. Couette analogy Providing the flow in a vessel to be in the laminar regime, the Cou­ ette analogy [82,83] assumes the stirrer in a mixing rheometer to be a virtual cylindrical rotor in a cylindrical cup as shown in Fig. 2. Both, real

Fig. 5. Principles of the Couette analogy adapted from Choplin and Marchal [84] and modified in this work. 7

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Renewable and Sustainable Energy Reviews 121 (2020) 109709

In their study Hreiz et al. [86] used a commercial rotational rheometer equipped with a helical ribbon impeller with a height of 54 mm and a diameter of 39 mm. The cylindrical vessel had an inner diameter of 47.5 mm, resulting in a sample volume of approximately 100 ml. Heating of the sample was realized with a Peltier device. Further information on the set-up was not given. A larger mixing rheometer based on the Couette analogy – the socalled “rheoreactor” –is presented by Montgomery et al. [25], which was built to measure the rheological properties of fibrous anaerobic slurries under anaerobic conditions. Its main components include a cy­ lindrical, hermetically sealed vessel and a stirrer with a built-in preci­ sion torque-meter as well as a rotational-speed sensor. The vessel consists of polycarbonate and polyoxymethylene and has an inner diameter of 190 mm and an inner height of 260 mm inducing a sample volume of about 6 l with approximately 15% headspace. Heating was realized by a temperature-controlled water bath. Using the rheoreactor, values of the apparent viscosity vary between approximately �14% within a 95% confidence interval, which was conducted from replicate measurements. In their study, Montgomery et al. [25] tested three different impeller types (helix, anchor and curved-vane) and found a curved-vane impeller to be most suitable for the use on fibrous slurries due to others leading to an accumulation of fibers influencing the measured torque, which is in contrast to Brehmer et al. [23] (see above). In addition, it was reported, that the measured viscosities changed over time using the rheoreactor. After starting a measurement, a short-term increase followed by a decrease of viscosity was observed, both for measurements with constant as well as intermitting mixing. The increase is explained by the release of gas bubbles at the beginning of measure­ ments and by the intensified mixing, whereas the decrease is reportedly attributed to the alignment of polymers and fibers. Thus, Montgomery et al. [25] recommend to pre-share the digestate and to do replicate measurements with a time lag applying the rheoreactor, which was also used in a study by Gruber-Brunhumer et al. [87].

from the measured data. For this purpose, the apparent shear rate γ_ wðaÞ is logarithmically plotted over the logarithmic shear stress τw and the slope of the resulting curve represents s [15,36]. Hence, the apparent viscosity can be calculated via flow rate and pressure difference in a tube by means of Eq. (2) combined with Eq. (21) – (23). Varying the pressure difference or the flow rate as well as using tube with various diameters allows adjusting different shear rates, and thus a flow curve to be determined. Further information on the approach can be found in Kokini and Dervisoglu [88], Adhikari and Jindal [89] and Secco et al. [90]. A schematic illustration of a pipe viscometer is given in Fig. 6. Chen [91] used a tube viscometer with an 8330 mm long tube and a diameter 130 mm to measure the rheological properties of beef-cattle manure. The obtained results are in good agreement well with previ­ ously published results by Chen [92] gained with a rotational viscom­ eter. However, only sieved samples (mesh size 2 mm) were measured. In order to be able to use a tube (flow) viscometer for measurements on digestate from agricultural biogas plants without removing large fi­ bers and particles, the capillary has to be enlarged to the order of magnitude of pipe diameters in technical applications. Hence, such modified tube (flow) viscometers are stated as pipe viscometers. In recent years, a few work groups have developed, designed and tested pipe viscometers allowing for the measurements of rheological properties of digestate from agricultural biogas plants without any pretreatment. Brehmer and Kraume [93] and Brehmer et al. [23] presented a pipe viscometer with a measuring section of 2500 mm length and a diameter of 43.2 mm. In their set-up 200 l digestate is stored in a tank in which an excess pressure can be generated by compressed air in a range from 0.06 to 6 bar. This establishes the flow through the pipe, and hence, varying the pressure results in flow rates between 200 and 4000 l/h. In a later work Brehmer and Kraume [51] state the biggest advantage of the described pipe viscometer being its capability to accurately measure substrates with a high TS content and long, fibrous particles, whilst the time and amount of sample required being its disadvantage. Another possible set-up is proposed by Koll [20] and Basedau et al. [15]. Here, the pipe viscometer is mounted on a trailer allowing to move the whole set-up and to carry out measurements directly at a biogas plant. A frequence-controlled eccentric screw pump pumps the digestate pulsation-free from a heated storage tank through an isolated pipe sys­ tem back to the storage tank. The system comprises four different measuring sections, which can be used individually or all at once. The nominal diameters (DN) of the pipes are DN 25, DN 32 and DN 50, respectively, each having a length of 4000 mm. The fourth measuring section consists of a pipe with a diameter of DN 150 and a length of 7000 mm. Consequently, a pressure difference range from 0.08 to 0.5 bar and with it, a shear rate range from approximately 1 to 1300 s 1 can be covered. About 350 l of digestate are needed to fill the system and ensure a constant flow rate. €nch-Tegeder et al. [22] developed and designed a pipe viscometer Mo which is implemented in an additional circuit within the pipe system of a biogas plant. Thus, an extra storage tank for the digestate is not required and degradation as well as a change in the structure of the digestate can be prevented. The viscometer consists of two measuring sections with a nominal diameter of DN 80 (length 3900 mm) and DN 100 (length 4100 mm), respectively, allowing for measurements within a shear rate range from 5 to 220 s 1 by varying the flow rate of the eccentric screw pump. This pipe viscometer set-up was also used in a study by Kress et al. [21], in which the effect of the agitation time on the nutrient distribution in a digester was investigated. In a joint project by Fraunhofer IKTS, TU Berlin and KSB AG, Ger­ many [8] a mobile pipe viscometer was developed and designed in order to conduct measurements directly on site of a biogas plant. It consists of three separate measuring sections, each with a length of 3600 mm and an inner diameter of 32 mm, 40 mm and 50 mm, respectively. The

3.4. Pipe viscometer A tube (flow) viscometer is a modified pressurized capillary viscometer (not to be confused with pressureless glass capillary vis­ cometers like Ubbelohde or Cannon-Fenske viscometers, in which the driving force is the hydrostatic pressure/gravity) [35]. Like other pres­ surized capillary viscometers the basic principle is based on the fact that a pressure difference can be measured when a fluid flows through a pipe in a laminar stationary flow. To this end, the fluid is forced through a tube of constant cross-section and precisely known dimensions, usually by pump. Subsequently, there are two options: Either flow rate V_ [m3/s] or pressure difference Δp [Pa] are fixed, and the other measured. With known dimensions of the tube, both values can be used to calculate the shear stress τw and shear rate γ_ w , respectively, at the wall of the tube with the help of the Hagen-Poiseuille law [36]:

τw ¼

Δp⋅r 2⋅L

γ_ wðaÞ ¼

4⋅V_ π⋅r3

(21) (22)

where r [m] is the inner tube diameter and L [m] is the length of the tube. While Eq. (21) is valid for both Newtonian and non-Newtonian fluids, Eq. (22) only represents an apparent shear rate γ_ wðaÞ for the latter. Here, the so-called Weissenberg-Rabinowitsch correction is used [36], which for non-Newtonian fluids relates the true shear rate at the wall γ_ w to the apparent shear rate γ_ wðaÞ calculated with Eq. (22): γ_ w ¼

γ_ wðaÞ ⋅ð3 þ sÞ 4

(23)

where s is a dimensionless coefficient which can directly be determined 8

N. Schneider and M. Gerber

Renewable and Sustainable Energy Reviews 121 (2020) 109709

Fig. 6. Scheme of a pipe viscometer adapted from Ref. [8].

digestate is pumped from a storage tank through the pipe system back to the storage tank by an eccentric pump. With the given set-up, a shear rate range from 1 s 1 to 1900 s 1 can allegedly be covered. In €nch-Tegeder comparative measurements with the pipe viscometer by Mo et al. [22] at shear rates up to 200 s 1 it was shown, that measurements with the presented set-up yield unsatisfying results for liquid digestate (after dewatering) and digestate from a secondary fermenter due to their watery consistence. However, a good agreement was found for mea­ surements of digestate from the main fermenter.

diameter of the spheres range between 8 and 18 mm. The sample volume is 500 ml. This set-up reportedly allows estimating the rheological properties of fluids containing particles up to 50 mm in size. The ball measuring system was tested by Brehmer and Kraume [93] for the use on digestate containing manure, corn silage and coarse rye meal. In comparison to other measurement devices significant de­ viations occur, due to the adhesion of particles and fibers to the surface of the ball causing an increased torque, and thus false results. Hence, the ball measuring system is not recommended for the measurement on digestate without any pre-treatment.

3.5. Ball measuring system

3.6. Comparison of measurement techniques

The ball measuring system was developed by Müller et al. [94] for the rheological characterization of semisolid dispersions with particles up to 5 mm, especially construction materials like plaster and cement. Here, a sphere (“ball”) mounted to a pin is moved through the sample on a circular path. Via measurement of the rotational speed and the resulting torque and so-called form factors converting both measured variables into shear rate and shear stress, respectively, the viscosity can be determined [95]. However, measurements are only valid during the first full rotation since the ball encounters non-sheared material in this case only. Despite this restriction, flow curves can still be recorded if a rotational rheometer controlling the rotational speed very quickly for each single measuring point is used for generating the rotation [35]. The ball measuring system consists of a cylindrical vessel with an inner diameter of 115 mm and a height of 48 mm, in which 500 ml of the sample are placed. The diameter of the sphere is 8, 12 or 15 mm depending on the viscosity range covered. A scheme of the ball measuring system is illustrated in Fig. 7. According to Schatzmann et al. [96], an improved approach based on the Metzner-Otto concept can be used for the conversion of rotational speed and torque into shear rate and shear stress, respectively, allowing the use of the device on fluids containing particles up to 10 mm in size. Pellegrino et al. [97] present the so-called sphere drag rheometer which is based on the principles of the ball measuring system. Here, the vessel has an inner diameter of 130 mm and a height of 60 mm, and the

Comparing the previously presented measuring devices, it can be concluded that every measurement system has its advantages as well as disadvantages when measuring digestate from agricultural biogas plants. An overview is given in Table 1. Conventional rotational rheometers are best suited for common rheological measurements due to precisely defined geometries allowing for absolute viscosity measurements depending on the shear rate. In addition, they offer simple handling as well as small sample sizes and are state of the art. However, the used geometries have small measuring gaps limiting the maximum grain size of particle-loaded fluids, and thus making a sample pre-treatment like sieving or grinding inevitable, which influences the measured viscosity [86]. This limitation can be reduced utilizing commercially available torsion viscometers, which however just provide device-dependent re­ sults as a function of rotational speed, resulting in qualitative rather than quantitative information of a fluid’s rheological behavior only [35]. In order to achieve shear-rate dependent viscosities mixing rheom­ eters can be employed, which were calibrated with the Metzner-Otto concept and Rieger-Novak method, respectively, or by the Couette Analogy. Here, the size of the set-up comprising stirrer and vessel can be configured in accordance to the size and length of particles and fibers, respectively. Though, an extensive calibration procedure is required and long fibers can wrap around the stirrer resulting in an increased torque, and thus distorted results. The latter can also occur in ball measuring systems, which are not only affected by fibers, but also are susceptible to an adhesion of par­ ticles to the surface of the ball. Hence, the use of ball measuring systems for untreated digestate is not recommended [51]. Since not having any rotating parts in the measuring section, a pipe viscometer offers the possibility to investigate the rheological properties of agricultural digestate without being influenced by any fibers or par­ ticles [23]. In addition, a pipe viscometer can be applied as an inline version directly into the pipe system of a biogas plant enabling instant viscosity measurements [22]. However, a lot of space and a huge sample volume are required for the set-up and the measurements, respectively. In a study by Brehmer and Kraume [51] it is shown that rotational rheometers, mixing rheometers, pipe viscometers and the ball measuring system yield comparable results for fluids containing none or very small particles. However, for fluids containing large fibers and particles only the mixing rheometer as well as the pipe rheometer

Fig. 7. Scheme of the ball measuring system adapted from Ref. [96]. 9

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Renewable and Sustainable Energy Reviews 121 (2020) 109709

Table 1 Overview of applicable volume ranges, particles sizes and shear rate ranges (if reported, references in brackets) advantages, disadvantages and applications of measuring systems used for the rheological characterization of digestate from agricultural biogas plants. Measurement system

Volume range

Applicable particle size

Shear rate range

Advantages

Disadvantages

Application

ball measuring system

0.5 l [95]

�50 mm [97]

–

- small sample volume

- liquid phase of digestate - sieved or grained digestate

mixing rheometer

0.785 l [68] – 60 l [67]

depending on vessel size, up to typical particle/fiber lenghts

depending on calibration method and torque range

- simple set-up - inline approach possible - mobil use possible

pipe viscometer

<200 l [51] <350 l [20]

depending on pipe diameter, up to typical particle/ fiber lenghts

1–1900 s 22]

- only feasible if combined with a rotational rheometer - pre-treatment required for digestate with long fibers and a large amount of particles - extensive calibration procedure - long fibers can wrap around stirrer and distort results - huge sample volume - large set-up

rotational rheometer

depending on measurement geometry and manufacturer

�1.7 mm [50]

depending on measurement geometry and manufacturer

- pre-treatment required for samples containing fibres and particles

- liquid phase of digestate - sieved or grained digestate if remaining particle size is fit for the measuring gap

torsion viscometer

600 mla

>5 mm [54]

depending on spindle geometry, usually < 100 s 1a

- only relative and device-dependent values possible [35]

- untreated digestate

a

1

[8,20,

- no rotating parts in measuring section - inline approach possible - mobil use possible - state of the art for a variety of rheological measurements - small sample volume - simple handling - simple handling - small sample volume - mobil use possible

- untreated digestate if size of set-up is sufficient in relation to the length/ diameter of particles/fibers in digestate - untreated digestate

According to manufacturer.

provided reasonable results.

total solid content, which is supported by the findings of Liu et al. [13]. In addition, Basedau et al. [15] state that K depends on temperature, which is emphasized by Liu et al. [13] reporting that K decreases with increasing temperature. However, a correlation is not given in both mentioned research works. The spectrum reported for the flow behavior index n varies between a minimum value of 0.04 and a maximum of 0.72. However, approxi­ mately 80% of the values for n range between 0.11 and 0.45 (see Table 2). According to Basedau et al. [15] n is independent of temper­ ature, whereas Liu et al. [13] state that n approaches closer to a value of 1.0 with increasing temperature. In addition to the shear-thinning behavior described by the powerlaw model, a few studies consider the digestate to have a yield stress by successfully fitting the measured data to the Bingham model (Eq. (7)) [25,49] the Herschel-Bulkley model (Eq. (8)) [24,48,49] or the Casson model (Eq. (9)) [25,49]. The reported values are presented in Table 2.

4. Rheological properties of agricultural digestate In recent years, several studies dealt with the measurement of rheological properties of digestate from agricultural biogas plants. Whereas some primarily focused on developing a suitable measurement system in order to achieve viscosity values to implement in CFD simu­ lations [26,47,68,76,77,93,98,99], others aimed at a rheological char­ acterization of digestate and possible influences on its viscosity like temperature, total solid (TS) content and particle size. An overview of the reviewed studies is given in Table 2, which includes the used mea­ surement system and the specific composition and the TS content of the agricultural digestate (if available), amongst others. 4.1. Flow behavior

4.2. Influence of temperature

Almost every study dealing with the rheological properties of digestate found it to have a non-Newtonian shear-thinning flow behavior, which is common for particle-loaded fluids and suspensions. In addition, viscoelastic behavior was reported in Refs. [8,100]. How­ ever, creep tests on digestate were conducted in these two studies only. In their study, Gienau et al. [1] found the organic compounds of digestate to correlate with its viscosity and thus, its flow behavior and state that particularly the micron sized particles contained in the digestate are responsible for its non-Newtonian behavior. However, this was only tested for the liquid phase of centrifuged agricultural digestate. In their study, Kress et al. [21] demonstrated that a reduced mixing time, and hence a reduced shear rate, led to an increase in viscosity of the digestate, which furthermore lowered the biogas release within the digester. Consequently, the non-Newtonian shear -thinning flow behavior of digestate influences the quantity of released biogas. The most frequently reported flow behavior model used for the characterization of digestate is the power-law model by Ostwald-deWaele (Eq. (3)). With regards to the consistency coefficient K values covering a range from 10 1 [Pa sn] up to 103 [Pa sn] are presented. Nevertheless, it can be seen by trend that K increases with an increasing

It is common knowledge that temperature influences the viscosity of a substance due to molecular interchange. With increasing temperature, the viscosity decreases in liquids, whilst it increases in gases. During anaerobic digestion, the agricultural digestate in a fermenter contains both a gaseous and a liquid phase, in which the latter predominates. Thus, the viscosity of digestate decreases with increasing temperature which is demonstrated in various studies [1,12,13,24,49]. However, Mbaye et al. [48] state that the temperature only has a quantitative effect on the rheological characterization of digestate, and hence that the flow behavior and models determined at different temperatures are qualitatively comparable. This is in accordance to Gienau et al. [1], who report that the shear-thinning behavior is only slightly influenced by the temperature (based on a constant slope of the viscosity curves), whereas the consistency of digestate is highly affected by its temperature (based on a decreasing consistency coefficient K with increasing temperature).

10

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N. Schneider and M. Gerber

Table 2 Overview of results found for the rheological behavior of digestate from agricultural biogas plants in several studies, in consideration of the employed measurement system, composition of digestate, TS content, temperature, shear rate or rotational speed, as well as detected flow behavior and applied models with associated parameters (if reported). Reference

Measurement system

Composition of digestatea

TS [%]

t [� C]

γ_ or N [s 1]

Flow behavior

Model

Parameter [K in Pa sn]

Results

Brehmer and Kraume [93], Brehmer et al. [23,99]

Pipe viscometer (∅ 43.2 mm)

CS, grain, CM

8.05

21.5

3–200

Shear thinning

Powerlaw

K ¼ 18.48 n ¼ 0.272

Brehmer et al. [23]

Mixing rheometer with various geometries (spiral stirrer ∅ 118 mm; 2-bladed propeller stirrer ∅ 136 mm; 3bladed propeller stirrer ∅ 131 mm; 6bladed propeller stirrer ∅ 95 mm)

- no zero-shear viscosity was detected -measurements were primarily conducted to determine the flow curve of the digestate and implement it in CFD simulations -properties of water are not suitable for designing stirrers used in agricultural biogas plants -no zero-shear viscosity was detected -flow behavior highly dependent on TS content -shape of stirrer only influences measured flow behavior slightly -stirrer needs to have a sufficient size in relation to the length of fibers in the digestate in order to provide useful results

Pipe viscometer (∅ 67.8 mm)

K ¼ 17.9 n ¼ 0.22

CS, grain, CM

8.5

21.5

0.02–10

Shear thinning

Powerlaw

Spiral stirrer: K ¼ 59.9 n ¼ 0.13

Brehmer and Kraume [100] b

Mixing rheometer Pipe viscometer (∅ 43.2 mm)

CS, CM

6.6–7.4

–

–

Shear thinning Viscoelastic

Powerlaw

2- bladed propeller stirrer: K ¼ 80.5 n ¼ 0.12 K ¼ 151.6 n ¼ 0.11 K ¼ 464.1 n ¼ 0.04 K ¼ 6–44 n ¼ 0.06–0.18

Deerberg et al. [47]

Rotational rheometer (concentric cylinders)

CM, CS, organic waste, waste water (sieved sample)

–

–

1–65

Shearthinning

–

–

Fraunhofer IKTS/TU Berlin/KSB AG [8]

Pipe viscometer (∅ 32 mm, 40 mm, 50 mm)

CS, CM

7.28

40

–

CM, CS, GS; grain meal CM; CS; GS; RS, rye grain

5.97

Shearthinning, viscoelastic

Powerlaw

K ¼ 14.32 n ¼ 0.209 K ¼ 3.35 n ¼ 0.133 K ¼ 21.58 n ¼ 0.43

Garuti et la. [54]

Torsion viscometer

Pig manure, CS, triticale silage, beet molasses, grain meal

–

42

–

Shearthinning

Powerlaw

–

Gienau et al. [1] c

Mixing rheometer (full blade stirrer)

CS, GPS, Crop, manure, dung, GS,c

3.8–12.8

0.5–4

Shearthinning

Powerlaw

K ¼ 2.11–3.67 n ¼ 0.24–0.28

Rotational rheometer (double gap)

Centrifugate of the above mentioned

20 30 40

8.5 11.8 15.1

8.22

1–10000

K¼ 0.014–0.037 n ¼ 0.74–0.76

-significant fluctuations within the rheological properties in a biogas plant monitored over several months -measurements were solely conducted to determine the viscosity of the digestate and implement it in CFD simulations -no correlation between viscosity curve and TS content could be observed -mechanical disintegration of the substrate caused a decrease in viscosity of the digestate -increase in viscosity leads to a reduction of the flow velocities forming in the fermenter and thus to a poorer mixing -viscosity decreased with increasing rotational speed -up to 37% reduced viscosity after shredding and hydrodynamic cavitation treatment of the digestate in comparison to untreated sample -temperature dependency of the consistency factor can be expressed by Arrhenius law, whereas the power-law index is not or only slightly affected by temperature. -organic compounds of digestate correlate with its viscosity -micron sized particles in the centrifugate were (continued on next page)

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Renewable and Sustainable Energy Reviews 121 (2020) 109709

Table 2 (continued ) Reference

GruberBrunhumer et al. [87] Hreiz et al. [86]

Measurement system

Mixing rheometer (rheoreactor, curved-vane impeller) Mixing rheometer (helical ribbon impeller)

Composition of digestatea

Pig manure, CS, various concentrations of microalgae biomass CD, CM (sieved and unsieved) CM

TS [%]

t [� C]

γ_ or N [s 1]

6.1

38

–

8.3

37

10 10

Sieved: 7.6

3 1

–

Flow behavior

Model

Parameter [K in Pa sn]

Shearthinning

Powerlaw

–

Shearthinning

Powerlaw

K ¼ 69.0 n ¼ 0.35 Sieved: K ¼ 8.1 n ¼ 0.32

7.6

Results found responsible for its non-Newtonian behavior -viscosity of centrifugated digestate still considerably higher than viscosity of water -addition of algal biomass leads to a decreased viscosity during anaerobic digestion -sieving (mesh size: 14 mm) leads to a decrease of viscosity -anaerobic digestion reduces viscosity

K ¼ 16.5 n ¼ 0.58

Kamara� ad et al. [12]

Mixing rheometer (Macro-viscometer)

Manure, CS, GS, grain CS, GS, RLD

7.86

39

–

Shearthinning

Powerlaw

K ¼ 18.9 n ¼ 0.132 K ¼ 6785.8 n ¼ 1.21

11.4

49

Koll [20], Basedau et al. [15]

Pipe viscometer (∅ DN 25, DN 32, DN 50, DN 100)

CS, CM, CD

7.64

39

1.3–670

Shear thinning

Powerlaw

K ¼ 16.77 n ¼ 0.1998 K ¼ 12.43 n ¼ 0.3751

CS, CM, CD

8.84

39

CS, CM, CD, silage mixd

9.94

31

K ¼ 16.49 n ¼ 0.0389

CM, CS, CCM, sugar beet CM, CS, GS, RS, CD

9.74

33

10.03

42

CM; CS; CD; CCM

10.09

38

K ¼ 23.49 n ¼ 0.2558 K ¼ 22.9 n ¼ 0.3065 K ¼ 32.09 n ¼ 0.1803

Kress et al. [21]

Pipe viscometer (∅ DN 80, DN 100)

CM, CD, horse manure, CS, GS, grain

14 � 0.2

–

Shear thinning

–

–

Kube et al. [24]

Mixing rheometer (inline, vertical paddle stirrer)

CS, RLD CS, RS, RLD GS, CS, RLD, grain CS, grain, RLD

14.5 10.7 9.7 8.0

49.0 45.0 44.4 48.0

Shearthinning

HerschelBulkley

τ0 ¼ 461 [Pa] τ0 ¼ 1015 [Pa] τ0 ¼ 903 [Pa] τ0 ¼ 361 [Pa]

Shearthinning

Powerlaw

K ¼ 4.90 n ¼ 0.32

Shearthinning

Powerlaw

K ¼ 0.125 n ¼ 0.53

Shearthinning

PowerLaw

K¼ 0.215–1.408 n¼

Lebranchu et al. [68]

Mixing rheometer (helical ribbon)

CM, cellulose (grounded)

8.8

40

Lienen et al. [101]

Rotational rheometer (concentric cylinders)

CM, org. waste (fish industry, slaughterhouse, creamery), oil (fat separator)

–

–

Liu et al. [13] e

Torsion viscometer

Corn-straw mixed with sludge inoculum from biogas plant

6.0 8.0

10, 25, 35, 55

(K, n are not reported)

–

-viscosity is strongly affected by shear rate, total solids content, temperature and particle size -faster substrate distribution after feeding at lower viscosity -mobile pipe viscometer allows for viscosity measurements directly on site -viscosity of digestate decreases with increasing hydraulic retention time (HRT) -type and composition of feedstocks have a significant influence on viscosity -no correlation between viscosity curve and TS content or HRT could be observed -reduction of mixing time in digester caused an increase in viscosity, and with it a lower gas release from the digestate -TS content most significantly influences viscosity -viscosity decreases if temperature increases -particle size impacts viscosity -measurements were solely conducted to determine the viscosity of the digestate and implement it in CFD simulations -no significant changes of the rheological characteristics were detected during a period without stirring -viscosity within a biogas plant changed over a monitoring period of 6 months -shear stress is decreased with increasing temperature and a reduced particle size; (continued on next page)

12

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Renewable and Sustainable Energy Reviews 121 (2020) 109709

Table 2 (continued ) Reference

Measurement system

Mbaye et al. [48] f

M€ onchTegeder et al. [22]

g

Montgomery et al. [25, 102] h

Composition of digestatea

TS [%]

Rotational rheometer (width gap coaxial cylinders)

Manure, grain (sieved)

5.16–6.09

Pipe viscometer (∅ DN 80, DN 100)

Mixing rheometer (rheoreactor, curved-vane impeller)

t [� C]

γ_ or N [s 1]

Flow behavior

Model

Parameter [K in Pa sn]

Results

0.206–0.332

shear stress also decreases with decreasing TS content -correlation between TS and oTS content and viscosityf -the higher the organic load, the higher the yield stress (and the viscosity) -temperature only has a quantitative effect, and hence flow behavior and models at different temperatures are qualitatively comparable -anaerobic digestion smooths the rheological behavior -viscosity depends on feedstock mixture: reducing the input of fibrous grass silage resulted in a decrease of the viscosity -viscosity increased with increasing TS content -disintegration of feedstocks leads to a decrease in viscosity -rheological patterns are more effected by the particle size with increasing TS -viscosity decreases over measurement time during constant mixing as well as intermittent mixing -replicate measurements are recommended due to the heterogeneous character of digestate and the time-dependent changes during measurements -viscosity of digestate did not change significantly within 5 days in which the same amount and type of feedstocks were fed -influence of an enzyme treatment could not be verified -mechanical disintegration of the substrate caused a decrease in viscosity of the digestate -viscosity increases right after feeding the biogas plant, but normalizes within a few hours -viscosity decreases during hydrolysis -measurements were mainly conducted to determine the viscosity of the digestate and implement it in CFD simulations -viscosity of digestates exhibiting approx. the same TS content significantly differs from each other

0.1–300

14.84–18.57

20 � 0.3

Shearthinning

Powerlaw HerschelBulkley

K ¼ 0.23–0.81 n ¼ 0.451 τ0 ¼ 3.69–18.97 [Pa] K¼ 16.60–52.96 n ¼ 0.424

Livestock manure & dung, GS, CS, grain

10.1–15.1

40.5

5–220

Shearthinning

Powerlaw

K¼ 7.53–41.92 n ¼ 0.21–0.40

Horse manure, whole-plant CS, whole-plant wheat silage

10 � 0.1

39

18–36

Shearthinning

Powerlaw

K ¼ 69–208 n ¼ 0.15–0.25 τ0 ¼ 118–166 [Pa] ηB ¼ 1.17–1.54

CS, GS, RLD, sorghum silage, solid digestate

11.2

Bingham Casson

τ0 ¼ 9.36–11.9 [Pa] ηC ¼ 0.42–0.63 –

Oechsner and M€ onchTegeder [103]

Pipe viscometer (∅ DN 80, DN 100)

Straw-based horse manure

–

–

–

–

–

–

P€ atz et al. [55]

Torsion viscometer

CM, CD, CS, GS, RS, sugar beet

7–8

–

–

–

–

–

Pohn et al. [26, 76,77] i

Mixing rheometer (Macro-viscometer)

Pig manure, CS, GS, grain, sugar beet, wheat RLD, MS, GS, leachate

9.13–9.93

40, 50

15–70

Non-Newt.

Powerlaw

K¼ 88.95–813.56 n ¼ 0.06–0.43 K¼ 2.054–172.26 n ¼ 0.45–0.72

10.6–13.09

(continued on next page)

13

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Renewable and Sustainable Energy Reviews 121 (2020) 109709

Table 2 (continued ) Reference

Measurement system

Composition of digestatea

TS [%]

t [� C]

γ_ or N [s 1]

Flow behavior

Model

Parameter [K in Pa sn]

Reviol [67], Reviol et al. [81]

Mixing rheometer (propeller impeller)

RS

–

–

–

–

Powerlaw

K ¼ 0.371 n ¼ 0.224

Renpenning et al. [79], Schimpf et al. [80]

Mixing rheometer (geometry not reported)

CS, RS

~10 - 13

–

–

–

Powerlaw

–

Stoyanova et al. [9]

Mixing rheometer (Macro-viscometer)

SBPPj, thin stillage, agricult. waste

–

35, 45, 55

~5–45

Shearthinning

–

–

Tian et al. [49]

Rotational rheometer (concentric cylinders)

Manure, corn stover

4.23–7.32

25, 35, 55

Shearthinning

Powerlaw

K ¼ 1.50–8.44 n ¼ 0.25–042 τ0 ¼ 0.21–7.08 [Pa] K ¼ 1.34–2.60 n ¼ 0.44–0.50 τ0 ¼ 2.42–11.56 [Pa] ηB ¼ 0.11–0.27 τ0 ¼ 1.47–8.71 [Pa] ηC ¼ 0.05–0.07

k

HerschelBuckley Bingham Casson

Results -viscosity of digestate from main fermenter up to 5 times higher than digestate from secondary fermenter -power based concept by Reviol as an improved alternative to the Metzner-Otto concept/ Rieger-Novak method for mixer viscometers -anaerobic digestion reduces viscosity -enzyme treatment reduces viscosity up to 18% -linear dependence between viscosity and TS content -lower viscosity in methanogenic stage of a two-stage fermenter lead to a 5-times lower energy demand for mixing in comparison to a one-stage fermenter (However, first stage of two-stage fermenter was not accounted for calculation) -reduction of feedstock particle-size as well as in­ crease of temperature causes decrease of viscosity -effect more distinct for higher TS content

a CS: corn silage; CM: cattle manure; CCM: corn cob mix; CD: cattle dung; GPS: whole plant silage; GS: grass silage; RS: rye silage; RLD: recirculated liquid digestate after separation. b Values represent the lowest and highest values, respectively, of parameter sets derived from measurements carried out once a month over a course of 7 months. c a total of 28 samples of 12 different agricultural digestate have been investigated, values represent the lowest and highest values, respectively, of all samples. K and n are reported at different temperatures for one sample (TS: 5.7%) only. d Silage mix: rape/oat/sunflower/barley. e Values represent the lowest and highest values, respectively, of parameter sets depending on particle size, TS content and temperature. f Values represent the lowest and highest values, respectively, of 4 parameter sets for each TS content range. It should be noted, that TS/oTS content was measured previous to the sieving, whereas the rheological measurements were carried out afterwards. g Values represent the lowest and highest values, respectively, of 22 parameter sets. h Values represent the lowest and highest values, respectively, of parameter sets derive from measurements carried out each hour over a course of 5 h. i Values represent the lowest and highest values, respectively, of 8 parameter sets for each TS content range. j SBPP: sugar beet pressed pulp (residue after extraction of the sugar from the chopped sugar beet). k Values represent the lowest and highest values, respectively, of 3 parameter sets.

4.3. Influence of TS content

increase in the consistency coefficient K (see section 4.1). In addition, it was observed that viscosity values and functions significantly differ from each other even though the digestates exhibit almost the same TS con­ tent [77]. This is explained by a varying composition of the particular digestate causing different particle size distributions [8] and with it a different percentage of mucilage in the digestate composition affecting the flow behavior, but not the TS content [77]. Opinions differ concerning a functional correlation between TS content and viscosity. Renpenning et al. [79] and Schimpf et al. [80] report a linear dependence between TS content and viscosity. A corre­ lation equation is however not reported. Mbaye et al. [48] state that no clear correlation was found between the yield stress and the TS content in their study. However, they report an equation allowing the

The effects of particles, solids and colloids on the rheological behavior have widely been researched for suspensions, disperse systems and emulsion in numerous studies [104,105,105] Digestate from agri­ cultural biogas plants can be classified as both a fine-particle dispersion and a coarse-particle dispersion, due to having colloids originating from manure, particles with various grain sizes as well as long fibers like blades and culms from corn silage. The sum of all dried solids in a digestate is expressed via the TS content. Thus, several studies analyzed the impact of a varying TS content on the flow behavior and the viscosity of digestate, respectively. All studies conclude that an increasing TS content leads to an increase in viscosity, which can also be seen with an 14

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Renewable and Sustainable Energy Reviews 121 (2020) 109709

calculation of the apparent viscosity ηa as a function of the water vis­ cosity ηH20 and the total solid content TS by considering the digestate as a moderately concentrated suspension: � (24) ηa ¼ ηH2O ⋅ 1 þ a ⋅ TS þ b ⋅ TS2 þ c ⋅ TS3

feedstock. In summary, altering the amount, composition or particle-size of the feedstock will lead to a change in viscosity. Thus, digestate from agri­ cultural biogas plants experiences significant fluctuations in rheological behavior over time [100,101], which is due to seasonal variations in the feedstock composition, amongst others.

where a, b and c are adjustable model parameters. They furthermore report an exponential relationship between apparent viscosity and TS content for samples with a similar ratio between organic TS content and TS content:

ηa ¼ A⋅eB⋅TS

4.5. Influence of anaerobic digestion Various studies prove an impact of anaerobic digestion and hydraulic retention time (HRT) on the viscosity of digestate: The longer the particular digestate is subject to anaerobic digestion and the higher the HRT, respectively, the lower the viscosity [15,20,25,48,55,79,86] This is supported by Stoyanova et al. [9] who demonstrated the digestate derived from the methanogenic stage of a two-stage fermenter having a less viscosity than digestate from the first stage. In addition, several studies emphasize a considerable deviation in viscosity for digestate from a secondary fermenter in comparison to digestate originating from the main fermenter [15,20,77] with Pohn et al. [77] indicating an up to 5-times higher viscosity for the latter. The influence of anaerobic digestion on the viscosity is caused by the continuing degradation process of biomass to biogas, and thus a decreasing TS content as well as reducing particle sizes with increasing HRT. However, a correlation between HRT and viscosity could not been found [20].

(25)

where A and B are constant parameters. However, it should be noted that the viscosity values fitted refer to sieved samples (mesh size: 7 mm), whereas the TS contents refer to untreated samples. Furthermore, their correlations are based on rheological measurements of green waste digestate, municipal waste digestate and organic waste digestate in addition to agricultural digestate. In contrast, other studies found no functional correlation between viscosity and TS content [8,15,20]. 4.4. Influence of feedstock and particle size Pohn et al. [77] reported varying flow behaviors for different digestates despite of exhibiting a comparable TS content, which can be attributed to the composition and the particle size distribution of the digestate, amongst others (see section 4.3). Here, the feedstock fed into the biogas plant to be degraded plays an important role. Not only the type and composition of the feedstock influence the viscosity, but also a potential pre-treatment and the amount of feedstock contribute to the rheological behavior of digestate. With regards to the former, its nature defines the amount of solids and fibers as well as particle sizes and lengths, respectively, to begin with [15]. Using substrates with smaller particles as feedstock will result in lower viscosities in comparison to a substrate with, e.g., long fibers. This is in accordance to a study by M€ onch-Tegeder et al. [22], who varied the composition of the feedstock of a biogas plant causing a change within the rheological properties of the digestate. Especially a reduction of fibrous grass silage as an input feedstock led to a decrease in viscosity of the digestate. In addition, several studies verified that a mechanical disintegration, and hence a reduction of the particle size of the feedstock, results in a €nch-Tegeder et al. [22] reported a differ­ decrease of the viscosity. Mo ence of up to 52.5% in viscosity between digestate from a biogas plant fed with untreated feedstocks and one with mechanically disintegrated feedstocks. A comparable impact is noticed by Garuti et al. [54] who found the viscosity of digestate to be reduced up to 37% after shredding and hydrodynamic cavitation treatment. The effect of the particle size on the rheological behavior of digestate is reportedly more distinct for higher TS contents, and thus a higher concentration of particles [13,22,49] In contrast, reducing the particle quantity or removing solids and fibers all together reduces the viscosity of digestate and changes the flow behavior (expressed via a shift in shape and slope of the flow curve and viscosity curve, respectively). For instance, Gienau et al. [1] found that the viscosity of the liquid phase of centrifuged digestate is 100–1000 times smaller than the viscosity of untreated digestate. Thus, a pretreatment in form of removing particles and fibers from the digestate impacts its rheological behavior and the rheological results can only limited be compared to those of untreated digestates. Besides composition and particle size, the amount of material fed to a biogas plant affects the viscosity of the digestate. Given that all mentioned factors of the feedstock remain constant, Montgomery et al. [25] demonstrated that the viscosity of digestate taken daily from the same biogas plant on five consecutive days did not change. This is in accordance to Koll [20], who showed that the same rheological behavior can be expected as long as the biogas plant is fed with the exact same

4.6. Influence of enzyme treatment A few studies dealt with the impact of an enzyme treatment on the rheological behavior of digestate. Enzymes are usually applied to the anaerobic digestion process in order to enhance the degradation of biomass, and thus improve the biogas yield. In particular, polymers in the substrate like lignocellulose are to be broken down for this purpose [10,27]. Montgomery et al. [102] observed a slight decrease in viscosity due to the addition of enzymes. However, this difference allegedly could have been caused due to inherent variations in the mixing rheometer instead. In contrast, Renpenning et al. [79] and Schimpf et al. [80] state that the digestate of an enzymes treated biogas plant exhibits a decrease in viscosity of up to 18% in comparison to an untreated biogas plant. 5. Practical implications and recommendations Based on the presented techniques with its individual advantages and disadvantages, respectively, and the initial results published for measurements on digestate from agricultural biogas plants as summa­ rized in section 4, some practical implications and recommendations can be derived both for choosing the measurement technique and for con­ ducting rheological measurements. 5.1. Measurement technique Current conventional techniques for rheological measurements feature small capillaries or measuring gaps, which limit their use for measurements on substrates containing solids and fibers with several centimeters in diameter or length. Especially for agricultural digestates this necessitates a pre-treatment like sieving in order to remove blocking substances previous to measurement. However, several studies demon­ strated that removing particles and fibers prior to measurements results in a significantly different flow behavior and viscosity in comparison to untreated digestate. Hence, the results gained with commercially available instruments like conventional rotational rheometers cannot be transferred and used for instance in CFD simulations carried out in order to design an agricultural biogas plant. It is therefore highly recom­ mended to choose an experimental set-up that actually is applicable for rheological measurements without having to alter the sample. Here, mixing rheometers and pipe viscometers were found to be the 15

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Renewable and Sustainable Energy Reviews 121 (2020) 109709

most suitable. However, the former features rotating parts to which long fibers can wrap around resulting in distorted measurements. In addition, an extensive calibration procedure is required. On the upside, a comparably small sample volume is needed and the set-up is quite simple and features relatively low investment costs. In comparison, pipe viscometers necessitate large sample volumes as well as plenty of room for the set-up, but allow for viscosity measurements of any untreated digestate. Moreover, an in-line approach directly on site of a biogas plant is also possible. Keeping the mentioned aspects in mind, it is recommended to pri­ marily choose the measurement system in dependence of the composi­ tion of the digestate including its particle and fiber sizes. Furthermore, aspects such as space and manageable sample volume have to be considered. For common lab-scale experiments a mixing rheometer can therefore be recommended, while on-site experiments could also be carried out with a preferably transportable pipe viscometer. However, the next section will only focus on the former technique, since it is the more applicable and more likely to become a reference method. Evaluating the findings from the literature research, several code­ pendent factors need to be considered and reconciled for the configu­ ration of a lab-scale mixing rheometer. To begin with, it should feature a cylindrical vessel with a volume of at least 5 l, which according to Jobst and Linke [50] allows for measurements of digestate with particles up to 50 mm in size – the preferred average chopping length of renewable energy crops (see section 2). However, a larger vessel with a working volume of 10–15 l is recommended as this allows all common particle sizes of most biomasses to be taken into account without restricting potential measurements. Furthermore, it is recommended to choose a transparent material for the vessel, such as glass or acrylic glass, in order to be able to observe the flow behavior or the particle movements, and to control potential accumulations of particles and fibers distorting the measurement. In this case, the vessel should be double-walled and have according circuit points enabling heating by circulating tempered water through this jacket. To some extent, the choice of the stirrer geometry is determined by the selected calibration method for the mixing rheometer. Here, the Metzner-Otto concept/Rieger-Novak-method is recommended, since it is more widely used and state-of-the-art, albeit mainly in areas with another research focus. Consequently, a laminar flow regime and thus a low Reynolds number range is required during measurement. To this end, a stirrer only inducing a tangential flow should be utilized. Here, an anchor impeller fulfills the requirements. When designing the stirrer, available guiding values in form of geometric relationships between stirrer and vessel as provided by most manufacturers should be taken into account. Moreover, it is recommended to realize a sufficient stirrer size in relation to the length of fibers in the digestate to be investigated. With regards to the stirring unit, a system with an integrated torque and rotational speed measurement is recommended. Otherwise, additional equipment to record these properties is necessary. With the previous-mentioned recommendations, this set-up is suffi­ cient in order to analyze and characterize the rheological behavior of agricultural digestate. However, it is not yet applicable to investigate, e. g., the impact of anaerobic digestion on viscosity or long-term changes within the flow behavior caused by a change of feedstocks. In order to be able to investigate such aspects as well, an extension of the vessel with a hermetically sealed cover is required, as for instance done by Mont­ gomery et al. [25]. Furthermore, such an extension requires adequate process measuring and control technology. All of the above recommendations should be taken into account when defining a standardized method in order to achieve comparable results across different studies. This is accompanied by the necessity that future works leading to such a standard technique should then also address the uncertainty of measurement in order to evaluate measure­ ment results.

5.2. Rheological measurements As previously shown, the greatest challenge in current research is the lack of a standardized measuring technique, leading to only a few studies explicitly dealing with an investigation of the rheological prop­ erties of digestate from agricultural biogas plants. Nevertheless, these few studies already demonstrate that the need for a standardization is not only emerging on the technical side but also on the methodical site. Here, aspects such as the measurement procedure and a corresponding documentation need to be addressed and considered at an early stage. Only this will help to obtain comparable experimental results from different studies. The overview in Table 2 shows that rheological models such as the power law model have already been successfully applied and corre­ sponding values such as the consistency coefficient K and the flow behavior index n have been fitted to the individual experimental data sets of a test series. However, these values may not be valid for appar­ ently similar cases and cannot be easily transferred to other test series. For instance, when comparing two digestates with a comparable TS content, significant differences in the rheological behavior or rather in the order of magnitude of the specific fitted parameters can be observed. This is particularly supported by studies of Pohn et al. [26] and M€ onch-Tegeder et al. [22], which demonstrated that particle quantity, particle size and the associated particle size distribution are also important parameters for the characterization of the rheological behavior (see section 4.4). Such influencing variables must therefore be investigated, specified and reported in order to be able to better estimate the comparability and transferability of results. In addition, measuring conditions and measuring ranges of, e.g., temperature and shear rate, have to be explicitly specified in order to estimate the validity of calculated parameters. The given overview also points out that the observed influences on the rheological behavior and their interrelations so far are largely of a qualitative nature rather than being clearly quantifiable. For instance, the influences of temperature and TS content on the viscosity have indeed been partly described and the caused percentual change in vis­ cosity has been expressed, but mathematical correlations between the individual measured variables have so far only been established occa­ sionally and with limitations (see section 4.3). The long-term goal in future investigations should therefore be the systematic analysis of in­ dividual influencing factors and their subsequent combination, so that predictions about the rheological behavior of any digestate would be possible on the basis of these variables and with the aid of correlations and equations, respectively. However, the challenge here is to investi­ gate these influencing factors completely separate from each other. In particular, the focus on a single parameter is quite complex, since the measurement conditions need to be kept constant, which is difficult, e. g., with regard to the origin and thus the specific composition of the digestate. For example, this could possibly be remedied by in­ vestigations focusing on the influence of various particle fractions and particle size distribution on the rheological behavior, independent of the origin and composition of the digestate. In order to make such future investigations more comparable, transparent and reproducible, initial recommendations can be derived from the studies presented in this paper. In addition to the specifications of the technical configurations, it is therefore strongly recommended to specify at least temperature, shear rate, TS content and composition of the digestate, when reporting data. With regards to the temperature, a measurement region of approximately 20 � C–60 � C should be covered in order to represent the typical psychrophilic, mesophilic or thermophilic conditions found in biogas plants. The shear rate region should at least include shear rates up to approximately 50 s 1, whereas appropriate steps are to be chosen to gain a representable data set. Here, it should be kept in mind, that the shear rate depends on the viscosity of the digestate and the maximum torque of the stirrer. Concerning the composition, the concrete percentage of the individual components should be listed and 16

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Renewable and Sustainable Energy Reviews 121 (2020) 109709

described as detailed as possible (e.g., type of manure, pre-treatment method). Moreover, the previous statements indicate that it is also necessary to specify the existing particle sizes and their respective dis­ tribution in order to fully describe the composition of digestate. It should be kept in mind that so far only a stationary state of the rheological behavior of digestate can be investigated. In order to fully represent the rheological conditions in a biogas plant, it is therefore recommended to actually carry out rheological investigations parallel to the anaerobic digestion of digestate under study. If so, the corresponding parameters (e.g., feeding intervals, organic loading rate, HRT) should as matter of course also be documented.

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Development of an in-line process viscometer for the full-scale biogas process. Bioresour Technol 2015;178: 278–84. [23] Brehmer M, Eppinger T, Kraume M. Einfluss der Rheologie auf das Str€ omungsregime in gerührten großtechnischen Biogasreaktoren. Chem Ing Tech 2012;84(11):2048–56. [24] Kube J, K€ ohnlechner M, Thurner F. Einfache Methode zur online-Bestimmung der Viskosit€ at von G€ arsubstraten in Biogasanlagen. In: Gesellschaft VDI, editor. Biogas 2011: energietr€ ager der Zukunft ; 6. Fachtagung, Fachtagung Braunschweig, 08. und 09. Juni 2011. Düsseldorf: VDI Verlag; 2011. p. 83–91. [25] Montgomery LFR, Schoepp T, Fuchs W, Bochmann G. Design, calibration and validation of a large lab-scale system for measuring viscosity in fermenting substrate from agricultural anaerobic digesters. Biochem Eng J 2016;115:72–9. [26] Pohn S, Kamarad L, Kirchmayr R, Harasek M. Design, calibration and numerical investigation of a macro viscosimeter. 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6. Conclusion This work focused on the rheological behavior and the viscosity, respectively, of digestate from agricultural biogas plants as an important parameter for designing biogas plant components (e.g., pumps, heat exchangers, stirrer) and optimizing the biogas process itself. A study on available literature demonstrated that conventional, standardized measurement systems are not feasible for these digestates, which led to a modification of different systems allowing for the aspired rheological measurements. Here, pipe viscometers are applicable for large-scale experiments such as field, while mixing rheometers were found to be the most suitable system for lab-scale experiments. Nevertheless, a standardized technique and with it an experimental set-up has yet to be defined and established in order to achieve comparable results across different studies. To this end, a suitable configuration of a lab-scale mixing rheometer was recommended as part of this work. The literature research conducted within this work showed that several studies identified some key parameters influencing its flow behavior. In general, all studies found digestate to have a nonNewtonian shear-thinning behavior. Besides that, a few studies also identified digestate to be viscoelastic, while others implied a yield stress. The power law model was applied the most, whereas some studies also successfully fitted their results to models including a yield stress. However, identified coefficients vary for either models in between studies, which almost certainly is a consequence of a different composed digestate used in the particular studies. As a result, the composition of digestate resulting from the input feedstocks is one of the key parame­ ters affecting the flow behavior, and hence the viscosity. Especially fibrous feedstocks result in higher viscous digestate, whilst smaller particle sizes lead to a decreased viscosity. Thus, a mechanical pretreatment reducing the particle sizes can help to improve the flow behavior of the digestate. Alongside particle and fiber size and length, respectively, the amount of solids (TS content) also affects the rheo­ logical behavior of digestate. Several studies document an increasing viscosity with increasing TS content. In addition, process temperature, possible enzyme treatments and the anaerobic digestion process itself have been identified as further parameters influencing the rheological behavior of digestate up to now. In summary, it can be seen that all reported parameters affecting the viscosity of digestate accompany each other and cannot easily be quantified, making numerical values gained for a specific digestate composition barely comparable to other digestates. Thus, observed correlations between the identified influences and the flow behavior to date are rather qualitative then quantitative. This emphasizes the need not only for a standardized measurement technique, but also for a standardized measurement procedure and protocol, to which some recommendations have been given in this work. Declarations of interest None.

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