Engineer N. S. MAKEROV

CALCULATION OF DIGESTION CHAMBERS

FOR SEWAGE SLUDGE

Tomsk
1928

Engineer N. S. Makerov.

Calculation of Digestion Chambers for Sewage Sludge

I. Grounds for Digesting Sludge.

The sludge separated in installations for the mechanical treatment of wastewater, in its fresh state, presents great inconveniences for its treatment, regardless of the method of its subsequent use.

A very substantial drawback of such sludge is, first, the high content of water in it, which affects its volume and weight and makes it difficult to handle in the sense of removing it beyond the limits of the treatment station.

The necessity of reducing the water content in the sludge by drying it in the open air reveals a second drawback of fresh sludge, namely that, by its nature, it is dried only with great difficulty. This property of fresh sludge is explained by the following reasons:

1) the water contained in the sludge is, for the most part, inside cells of plant origin that constitute the greater part of the suspended matter transferred into the sludge; it is as though locked inside these cells and cannot be released from them until they are destroyed;

2) fresh sludge is rich in colloids, which have the ability to swell from water and to form mucus that gives up water only with difficulty;

3) fresh sludge, when discharged onto drying beds, owing to the fact that its specific gravity is somewhat greater than the specific gravity of water (1.003–1.060), settles downward and displaces sludge water into the upper layer; having settled on the surface of the drying bed, such sludge, with its slimy particles, clogs the pores of the draining material and prevents the water standing above the layer from passing into the drainage.

In practice, the property of sludge to dry with difficulty requires more time for it to dry out; as a result, the capacity of drying beds is reduced and, consequently, a larger area of them is required. The character just described of fresh sludge, which is slimy and viscous, makes it an unfavorable material both for conveying it by gravity to the drying site through gutters or pipes and for pumping it with pumps.

A further drawback of fresh sludge is the foul odor that accompanies its drying and that does not permit operations of this kind near inhabited places.

In addition, during drying fresh sludge attracts flies, which swarm over it in masses and, of course, may become a cause of infections.

As a consequence of the above-mentioned unfavorable qualities of fresh sludge, in recent years digestion of sludge has been widely used, with the aim of depriving fresh sludge of its negative properties.

During sludge digestion, its organic matter decomposes, partly changing into a dissolved and gaseous state. Owing to this, the solid matter of the sludge is considerably reduced in volume. In addition, the water content, as a result of the decomposition of colloids and

cell membranes, which had previously retained water, is greatly reduced. If fresh sludge contains on average more than 90% water, then digested sludge contains on average only 80%. Thus, through digestion, the volume of sludge—and, consequently, its weight—is very significantly reduced¹), thereby eliminating one extremely substantial drawback of fresh sludge.

Then, after digestion, the sludge acquires the ability to dry rapidly on drained drying beds, which is facilitated by the following circumstances:

1) by its structure, after the decomposition of colloids and cellular substances, digested sludge does not retain water and readily gives it up;

2) at the moment of discharge onto the drying beds, digested sludge contains within itself bubbles of gas and therefore has a specific gravity lower than that of water; therefore, when discharged onto drying beds, such sludge floats to the surface of the sludge water; the latter thus freely drains away;

3) subsequently, the gas bubbles escape from the sludge and leave pores in it, which promote drying.

The last two circumstances are especially pronounced when sludge is discharged from the bottom of deep digestion chambers.

In practice, the property of digested sludge to dry rapidly entails the need for smaller drying areas.

Further, digested sludge has the ability, despite its lower water content, to flow more freely through troughs and pipes and to be pumped more easily than fresh sludge with its high water content. This property is acquired by the sludge as a result of the decomposition of cellular matter and colloids, whereby the decomposed substance is, as it were, in water, and not the other way around, as is the case in fresh sludge, where the water is, as it were, inside the substance. That the greater mobility and fluidity of a substance depends to a lesser degree on the water content in it and to a greater degree on its structure, Imhoff illustrates with the following interesting example: a cucumber, i.e. a solid body, contains about 95% water, whereas milk, for example, i.e. a liquid, contains on average 87% water; very fine coal sludge, even with a content of 40–50%, may still be quite liquid.

Finally, digested sludge no longer has the unpleasant odor that is characteristic of fresh sludge, and it does not attract insects. The latter properties of digested sludge make it possible to treat it near inhabited places.

II. Types of digestion chambers.

Digestion of sludge is carried out in digestion chambers of various types²), which constitute the following groups:

1. Flow-through digestion chambers:

a) single-tier, of the septic-tank type, consisting of settling basins which, owing to their large volume, permit the accumulation of sludge in them and the digestion of the latter;

¹) See the curve of the decrease in sludge weight as a function of the decrease in water content, given in the author’s article “Mechanical Treatment of Wastewater in Connection with Sludge Treatment,” published in Nos. 3–4 of Vestnik Sibirskikh Inzhenerov for 1928.

²) A characterization and evaluation of these types is given in the author’s article “Mechanical Treatment of Wastewater in Connection with Sludge Treatment,” published in Nos. 3–4 of Vestnik Sibirskikh Inzhenerov for 1928.

b) two-level, of the type of Travis and Duwidag tanks, in which the upper levels serve for the separation of suspended matter, and the lower ones—for collecting the latter and digesting it.

1. Non-flow-through two-level digestion chambers, of the type of Emscher wells. In the latter, the upper level serves for the flow of sewage and the separation of suspended matter, the lower—for collecting the sludge and digesting it.

2. Separate digestion chambers, arranged either

a) at some distance from the structures in which suspended matter is separated from the sewage, or

b) in immediate proximity to the settling devices, being separated from the latter only by thin walls (Neustadt basins, Prüss installations).

1. A combination of two-level structures (of the type of Emscher wells) and separate digestion chambers (type 3a). In this case, in the digestion chambers of the Emscher wells the digestion of the sludge is not carried through to completion; for digestion to the desired limit the sludge is conveyed into separate digestion chambers.

The calculation of the capacity of digestion chambers for all the types listed is carried out by the same methods; only the special conditions, dependent on the type of chamber and its construction and caused chiefly by differences in the thermal regime for a chamber of one kind or another, are taken into account, as well as certain other circumstances that will be clarified below.

III. Calculation of digestion chambers

4. Factors influencing the dimensions of digestion chambers.

In calculating digestion chambers, the following factors affecting their dimensions must be taken into account:

1. The quantity of fresh sludge and its character. This factor is the principal one in calculating the volume of digestion chambers. Indeed, the more sludge enters the digestion chamber, the greater, other conditions being equal, its volume must be. The character of the sludge affects the volume of the digestion chamber in the sense that the presence in the sludge of acids or toxic substances harmful to the vital activity of anaerobic microorganisms may lead to a slowing of the digestion process. This latter circumstance will affect the throughput capacity of the digestion chamber and, consequently, will require a larger volume for it.

The quantity of sludge entering the digestion chamber for treatment is, in turn, influenced by the following factors:

a) The quantity of sewage flowing through the treatment plant. The greater, other conditions being equal, the quantity of sewage flowing through the plant, the greater the quantity of sludge these waters leave behind. However, with a different character of sewage or with different operation of settling devices, one and the same sewage flow may yield far from identical quantities of sludge. The more suspended matter the sewage contains and the more perfectly the installation for separating these substances from the water operates, the greater the quantity of sludge that will be deposited per one and the same volume of water.

b) The number of inhabitants. In calculating the quantity of sludge for municipal treatment plants, it is more correct to proceed from the number of inhabitants, since the quantity of sludge per inhabitant is a more constant value than the quantity of sludge per unit volume of water under different per-capita water-consumption standards. Metcalf

and Eddy cite as an example one small town in the state of Massachusetts, where, with a change in the sewage flow from 110 liters to 426 liters per inhabitant, the quantity of sludge varied from 4.27 liters to 0.91 liters per cubic meter of sewage. The quantity of sludge per inhabitant, however, varied only from 0.29 liters to 0.41 liters.

c) Character of the sewage. Industrial wastewaters are of particular importance. It is true that, for towns with poorly developed industry, these waters are not included in the calculation. But if industrial waters constitute a significant percentage of the total sewage flow and if they carry a large quantity of sludge, then they must be taken into account separately. In this case it must be determined how great the quantity of industrial sludge is in relation to the quantity of sludge from domestic waters, and it must correspondingly be assigned per inhabitant.

d) Sewerage system. Some authors (e.g., Frank and Fries), taking into account the sludge that atmospheric waters may additionally yield per inhabitant in a combined sewerage system, consider it necessary to give digestion chambers in a combined system an additional volume in comparison with digestion chambers in a separate sewerage system. Others, however (Imhoff, more recently), believe that the sewerage system should not influence the dimensions of the digestion chamber, since through storm overflows in a combined system as much sludge is lost as through the storm-water network in a separate system.

e) Content of suspended matter in the sewage. The more suspended matter is contained in a cubic unit of sewage, the more sludge is obtained, other conditions being equal, and consequently the larger the chamber must be.

f) Operation of settling devices for retaining suspended matter. The more perfect the operation of settling devices in removing suspended matter from the sewage, the greater the percentage of suspended matter retained in the clarification structures, and the more sludge is formed, other conditions being equal. This circumstance, in turn, is influenced by the design and method of operation of the settling device.

g) Water content in the sludge. The richer the sludge is in water, other conditions being equal, the greater its volume, and consequently the greater the volume that must be given to the chamber. The water content in the sludge depends on the design of the structures in which the sludge is separated from the water. Thus, for example, settling basins give sludge with a water content from 88 to 96% and even higher; Kremer wells with sludge cylinders—considerably less: according to Dr. Kusch, the water content in the sludge from these wells falls to 85–88%, even to 83–81.5% (in the town of Hildesheim).

Imhoff gives the following data concerning the quantity of sludge as a function of the water content in it, which he recommends using in calculations.

1. In basins from which fresh sludge is removed under water—1.8 liters of sludge per person per day, with 97.5% water.

2. If fresh sludge is carefully separated from the water—0.9 liters of sludge per person per day, with 95% water.

Prüss takes 1 liter of fresh sludge per person per day with 95% water¹.

2) Degree of reduction of sludge volume during digestion. In calculating digestion chambers, attention must be paid to the circumstance—

that, when sludge digests, its volume decreases. This circumstance is explained by the fact that, during the process of digestion, the suspended substances of organic character contained in the sludge partly dissolve, partly turn into gases, and therefore the quantity of substances remaining in the solid state decreases. In addition, the character of the latter is such that they bind water to a considerably lesser degree, and therefore the water content in digested sludge is considerably less than in fresh sludge when it enters the digestion chamber.

The water content in digested sludge also depends on the construction of the digestion chambers: deep chambers give sludge with a lower water content than shallow chambers. The latter circumstance is due to the fact that in deeper chambers the sludge is under greater hydrostatic pressure.

Digested sludge contains 75–80% and up to 85% water.

Imhoff, for digested sludge, gives a standard of 0.2 liters per person per day with 80–85% water.

The degree of reduction in the quantity of sludge depends in general on various factors, such as, for example:

a) the time during which the sediment is subjected to digestion;

b) the temperature at which digestion of the sediment takes place;

c) the degree of mixing of the sludge in the digestion chamber;

d) whether fresh sediment is introduced into the digestion chamber or sediment in the period of acid fermentation;

e) the construction of the digestion chamber.

These factors will be considered in detail below in connection with other circumstances.

In practice, however, the degree of reduction in the quantity of sludge is determined by the necessary degree of digestion of the sediment. Namely, it is considered necessary and sufficient to bring the sludge to such a state that it loses its unpleasant odor and acquires the ability to dry easily in the air. This limit of digestion, called the “technical limit of digestion,” corresponds to a reduction by half of the organic dry matter and to the production of about \(3/4\) of the full possible quantity of gas.

3) Digestion time. Digestion time is an essential factor influencing the volume of the digestion chamber, since the longer the sludge remains in the chamber, the smaller the throughput capacity of the chamber and, consequently, the greater the volume that must be assigned to it.

Digestion time, in turn, depends on the following circumstances:

a) on the necessary degree of digestion, determined, as was indicated above, by the “technical limit of digestion.” The time necessary to attain this technical limit of digestion is approximately half the time required for complete digestion.

b) on the temperature. The higher the temperature of the sludge (up to a certain limit), the faster the process of digestion proceeds; the lower the temperature, the slower it is. According to Siegr, the optimal temperature for gas formation is 25° C, and for decomposition 36.5° C. Below these temperatures the processes of gas formation and decomposition slow down, and at a temperature below 6° C gas formation ceases, while decomposition, although it does occur, proceeds extremely slowly.

Figure 1 presents a diagram given by Imhoff, which shows, on the basis of a large number of experiments, the influence of temperature on the required digestion time. Two curves are shown here: one—the upper, solid curve—gives the dependence on temperature of the time for complete digestion of sludge; the other, the lower, dotted line, shows the dependence on temperature of the time required to reach the technical limit of digestion.

Fig. No. 1.

Temperature, in turn, is partly dependent on the design of the digestion chambers.

From this point of view, flow-through digestion chambers, and then non-flow-through two-tier chambers and separate digestion chambers of the Neustadt basins type and of the Prüss system, are more advantageous than separate digestion chambers arranged at a distance from the settling structures. The advantage consists in the fact that in them the temperature is maintained at a certain level owing to their being heated through the walls by the heat of the sewage water flowing through the settling chambers.

Separate digestion chambers, however, removed from the settling chambers and not heated by their heat, are in worse temperature conditions, since they depend on the temperature of the atmospheric air: in winter the temperature of digestion chambers of this kind may fall considerably.

Thus the volume of the digestion chamber can be correctly determined only when its temperature can be known in advance.

In flow-through digestion chambers, in two-tier structures, and in separate digestion chambers of the Neustadt basins type and of the Prüss system, the temperature of the digestion chambers can be predicted in advance when the temperature of the sewage waters is known, since the temperature of digestion chambers of this kind is almost equal to the temperature of the sewage waters. In this case the mean annual temperature of the digestion chamber is taken as the mean annual temperature of the sewage waters.

Below is Table I, cited by Imhoff, in which are presented the temperatures of sewage waters of various cities and the time necessary for digestion of sludge in worked-out (mature) digestion chambers of the two-tier type (and consequently, in flow-through chambers, as well as those of the Neustadt type and the Prüss system). This time is determined on the basis of the diagram shown in Fig. 1.

Table I

Time required for digestion of sludge in two-tier-type digestion chambers.

For separate digestion chambers not heated by sewage waters, determining the temperature is more difficult: it depends only to a slight degree on the initial temperature of the sludge. To a greater degree it depends on the temperature of the air. In general, the average annual temperature of digestion chambers of this kind is lower than the temperature of digestion chambers washed by sewage waters. For separate digestion chambers not heated by the heat of sewage waters, thermal insulation and artificial raising of the temperature are exceedingly important questions,¹ permitting, by maintaining the temperature of the digestion chambers at a certain level, a reduction in the time required for sludge digestion and, consequently, a reduction in the volume of the digestion chamber.

With artificial heating of digestion chambers, the required amount of heat energy will vary depending on the water content in the sludge. The more water the sludge contains, the more fuel is required to heat the digestion chamber. For example, if, when sludge with a water content of 90% is introduced into a separate digestion chamber, a certain definite amount of fuel is required to raise the temperature of the digestion chamber from 9° to 21°, i.e. by 12°, then, when sludge with a water content of 95% enters the digestion chamber, with the same amount of fuel the temperature of the digestion chamber can be raised only by 6°, i.e. from 9° to 15°. In this case the volume of the digestion chamber, as compared with the original one, according to the diagram presented in Fig. 1, must be increased twofold, or, in order to preserve the same volume, the fuel consumption must be correspondingly increased.

c) The digestion time depends on the duration of the cold season, when the digestion process, after the digestion chamber has reached its limiting low temperatures, may even stop completely. In such a case, the inflow during this period of fresh sludge and its accumulation will lead to the fact that in spring the digestion chamber will again have to pass through the entire maturation period. The maturation of digestion chambers follows a long path through acid fermentation and requires 2½ times more time than is needed for processing sludge in chambers that have already “worked in,” i.e. matured.

To avoid this, one may use artificial heating of the sludge digestion chambers, or at least, as Imhoff recommends, artificial heating of at least part of the chamber: in such an “incubator” good alkaline sludge should be maintained, which in spring could accelerate the maturation of the remaining part of the digestion chamber.

d) The digestion time depends on the degree of acidity of the sludge entering the digestion chamber.

During normal operation of a digestion chamber, fresh sludge enters a “worked-in” chamber with alkaline sludge; it is mixed, naturally or artificially, with the alkaline sludge and immediately passes into normal alkaline fermentation.

If, however, the sludge flows to the digestion chamber in a state of acid fermentation, then this sludge can be brought into a state of normal alkaline fermentation only with certain difficulties and with a loss of time.

According to Imhoff, the harm caused by the inflow of acid sludge into the digestion chamber can be eliminated either by mixing this sludge with old sludge in a proportion of 1:4, or by adding lime.

¹ On insulation and artificial raising of the temperature of digestion chambers, see the author’s article “Mechanical purification of waters in connection with sludge treatment,” published in Nos. 3–4 of Vestnik Sibirskikh Inzhenerov for 1928.

If, owing to special circumstances, the sludge entering the treatment plant is already digested or is in a state of alkaline fermentation, then the digestion time may be correspondingly reduced.

d) The digestion time depends on the perfection of the mixing of the contents of the digestion chamber; the necessity of mixing is determined by the requirements of the most rapid inoculation of fresh sludge with the bacteria of digestion and the best removal of the products of bacterial activity from the sphere in which they operate.

In this respect, the application of measures for artificial mixing is highly important, and may reduce the digestion time by half.

In the same sense, attention should be paid to the method of admitting sludge into the digestion chamber: in chambers of large area it is necessary, for the purpose of achieving the best mixing of the sludge, to strive to admit it at several points in small portions.

4) Degree of utilization of the chamber. The volume of the digestion chamber is determined as a function of the degree of utilization of the chamber, i.e., of how fully its volume is utilized. In this sense, for example, in Americanized-type Emscher wells, openings are arranged in the partitions between the compartments of the digestion chamber, serving for the uniform distribution of sludge among the compartments. For the same purpose, the direction of sewage flow in the settling chambers is periodically changed.

5) Size of the installation. The volume of the digestion chamber depends, finally, on the size of the installation, namely: in installations of small size the relative volume of the digestion chamber is taken larger than in installations of large size. This is explained by the consideration that in small installations poorer care and supervision are possible, with which untimely performance of operations of one kind or another connected with the operation of the digestion chambers is associated, and, consequently, a certain reserve of chamber volume must be provided.

B. Methods for determining the size of digestion chambers.

The abundance of those factors which influence the size of digestion chambers shows that determining the dimensions of digestion chambers is not a simple operation. Taking into account the impossibility of allowing for some of these factors in advance, it may be said that an exact calculation of the capacity of digestion chambers is generally impossible. Bearing in mind that, in determining the volume of digestion chambers, one often has to operate with many unknowns, one is satisfied only with an approximate calculation; chiefly, the experience of other cities is used—cities which, both in the character of their sewage and in other conditions, are in the same position as the city for which the structure is being designed.

In what follows, several methods for calculating digestion chambers are set forth.

1. Metcalf and Eddy, for calculating digestion chambers, recommend using the following method:

a) from analyses of sewage or from a study of its source, the quantity of suspended matter contained in a unit volume of sewage is determined.

b) the percentage of suspended matter settling in the sedimentation devices is adopted or determined.

c) it is assumed what percentage of suspended matter can rot in the digestion chamber and what percentage, consequently, remains in the digestion chamber.

d) a percentage of moisture is assumed, or else the quantity of sludge is then determined.

On the basis of these data, knowing the sewage flow and the time for which the digestion chamber is designed, the volume of the chamber can be calculated.

1. Bach indicates the following method:

a) the quantity of fresh sludge that settles during the time the sludge is stored in the digestion chamber is determined.

b) the quantity of sludge by which the total quantity is reduced as a result of digestion, settling, and dewatering is determined.

c) the difference between these quantities is determined, giving the volume of digested sludge.

But since in the digestion chamber there will be not only digested sludge that has already lain for the necessary time, but also sludge that has entered during all this time, the volume of the chamber is taken to be approximately the average between the volume of fresh sludge and the volume of digested sludge. This volume will be sufficient if the discharge of digested sludge from the digestion chamber is carried out daily in the volume in which it enters daily in the fresh state. In practice, however, sludge is discharged at somewhat longer intervals of time, determined by the subsequent treatment of the sludge (for example, by the availability of free drying beds); therefore the size of the chamber must be increased accordingly.

Example:

Suppose that in the sedimentation devices 10 cubic meters of sludge with a water content of 95% settle daily. Let the necessary digestion time be 60 days. The digested sludge, suppose, contains 80% water.

Then, if sludge with a water content of 95% and 5% dry matter has a volume of 0.5 cubic m of dry matter and 9.5 cubic m of water = 10 cubic m, then sludge with a water content of 80% and 20% dry matter will have, for a volume of 0.5 cubic m.¹) of dry matter, 2.0 cubic m of water = 2.5 cubic m. Therefore, in 60 days the fresh sludge will be \(10 \times 60 = 600\) cu. m, and the digested sludge over the same period . . . \(2.5 \times 60 = 150\) cu. m.

The average volume between the volume of fresh and digested sludge will be

\[ \frac{600 + 150}{2} = 375 \text{ cu. m.} \]

Taking the discharge of sludge from the digestion chambers as once a week, about 70 cu. m must be added to the volume obtained, i.e. the total volume of the digestion chamber must be \(375 + 70 = 445 \approx 450\) cu. m.

1. Hugo Knauer, indicating that sludge located in the digestion chamber for about 80 days loses daily about \(1/120\) of its volume, i.e. that after 80 days the sludge that settled on the first day occupies only about \(1/3\) of its initial volume, calculates the digestion chamber from the following considerations.

Let: \(s\) be the quantity of sludge entering the chamber daily.

\(n\) be the number of days for sludge digestion.

\(1/a = 1/120\) be the daily decrease of the initial volume of sludge.

Then after \(n\) days:

¹) The reduction of dry matter during digestion is not taken into account in the calculation.

The amount of sludge settling out during the first day will be expressed by the formula:

\[ s-\frac{n-1}{a}s \]

the amount of sludge settling out during the second day will be expressed by the formula

\[ s-\frac{n-2}{a}s \quad \text{etc.} \]

Summing all the amounts of sludge that have settled out over \(n\) days, we obtain the total volume of sludge, \(a\), and consequently the volume of the chamber.

\[ \begin{aligned} S&=\left(s-\frac{n-1}{a}\cdot s\right)+\left(s-\frac{n-2}{a}\cdot s\right)+\ldots+\left(s-\frac{n-(n-1)}{a}\cdot s\right)+s=\\ &=s\left[\left(1-\frac{n-1}{a}\right)+\left(1-\frac{n-2}{a}\right)+\ldots+\left(1-\frac{1}{a}\right)+1\right]=\\ &=s\left[n-\frac{(n-1)+(n-2)+\ldots+3+2+1}{a}\right]=\\ &=s\left[n-\frac{1+(n-1)}{2a}\cdot(n-1)\right]=\\ &=sn\left(1-\frac{n}{2a}+\frac{1}{2a}\right) \end{aligned} \]

Neglecting the expression \(\frac{1}{2a}\) in the parentheses, we finally obtain the formula for the chamber volume:

\[ S=sn\left(1-\frac{n}{2a}\right) \]

The volumes of digestion chambers calculated by this formula for various values of \(n\), expressed in terms of the daily portion of fresh sludge, are presented in Table II.

Table II.

capacities of digestion chambers \((S)\) as a function of digestion time \((n)\) and the daily portion of fresh sludge \((s)\).

1. According to F. Langbein, for calculating the digestion chambers of the Emscher wells on the Berlin irrigation fields at Wassmannsdorf, the following method was used:

Assuming that \(S\) cubic meters of sludge settle out daily, and that the sludge, while in the digestion chamber, decreases in volume daily by \((1/a=1/120,\) but not from the initial volume, as Knauer assumes, but from that volume which the sludge, already correspondingly reduced in volume, has each day, the following expressions may be written:

By the end of the first day the sludge will have a volume not of \(s\), but reduced by \(\frac{s}{a}\), i.e.

\[ S_1 = s - \frac{s}{a} = s\left(1-\frac{1}{a}\right)=s' \]

By the end of the second day the total quantity of sludge will have the volume:

\[ S_2=s\left(1-\frac{1}{a}\right)+s'\left(1-\frac{1}{a}\right) =s\left(1-\frac{1}{a}\right)+s\left(1-\frac{1}{a}\right)^2 = \]

\[ =s\left[\left(1-\frac{1}{a}\right)+\left(1-\frac{1}{a}\right)^2\right] \]

By the end of the third day the total quantity of sludge will have the volume:

\[ S_3=s\left[\left(1-\frac{1}{a}\right)+\left(1-\frac{1}{a}\right)^2+\left(1-\frac{1}{a}\right)^3\right] \]

By the end of the \(n\)-th day (taking the digestion time as \(n\) days), the sludge will have the volume:

\[ S_n=s\left[\left(1-\frac{1}{a}\right)+\left(1-\frac{1}{a}\right)^2+\left(1-\frac{1}{a}\right)^3+\ldots+\left(1-\frac{1}{a}\right)^{n-1}+\left(1-\frac{1}{a}\right)^n\right]= \]

\[ =s\frac{\left(1-\frac{1}{a}\right)-\left(1-\frac{1}{a}\right)^{n+1}}{1-\left(1-\frac{1}{a}\right)} =sa\left[\left(1-\frac{1}{a}\right)-\left(1-\frac{1}{a}\right)^{n+1}\right]. \]

Substituting the figures adopted for the calculation in the present case (Wassmannsdorf), namely:

\[ \frac{1}{a}=\frac{1}{120} \]

\[ n=90\ \text{days} \]

\[ s=360\ \text{cu. m.}\quad \begin{aligned} &\text{(with }90{,}000\ \text{cu. m. of daily}\\ &\text{sewage inflow and }0.4\%\text{ sludge)} \end{aligned} \]

the total volume of the digestion chambers is obtained:

\[ S_{90}=360\cdot120\cdot\left[\frac{119}{120}-\left(\frac{119}{120}\right)^{91}\right] =23{,}000\ \text{cu. m.} \]

Adopted: 24,000 cu. m.

1. Imhoff, taking into account the difficulty of calculating digestion chambers according to the quantity and properties of the sludge and according to the digestion time—since, when preparing a design, the quantity and properties of the sludge are almost never known, and since it is difficult to say in advance according to what law the content of organic matter and water in the sludge will decrease—recommends determining the volume of the digestion chamber on the basis of examples of existing installations, taking certain indicators into consideration.

On the basis of certain average data set forth below, he adopts the volume of the digestion chamber as 30 liters per inhabitant. Imhoff calls this figure the “basic” figure, corresponding to the following data: the quantity of fresh sludge entering the digestion chamber daily is 0.9 liters per person per day (with 5% dry matter and 95% water); the digestion time is 2 months; during this period the sludge decreases in volume to 0.2 liters per person per day (with 15–20% dry ...

matter and 80–85% water), and this decrease proceeds approximately along the lower curve of the diagram shown in Fig. 2.

Fig. No. 2.

Then the required size of the digestion chamber is represented by the shaded area, consisting of three parts:

\[ \begin{aligned} a &= 0.2 \times 60 = 12 \text{ liters per capita} = \text{volume of digested sludge} \\ b &= 12 \text{ liters per capita} = \text{additional volume of sludge entering during digestion.} \\ c &= 6 \text{ liters per capita} = \text{allowance for possible fluctuations.} \end{aligned} \]

\[ \text{Total } 30 \text{ liters per capita} = \text{Volume of the digestion chamber.} \]

Deviations from the average conditions indicated above entail changes in the basic figure according to the following data.

a) The basic figure of 30 liters per capita also includes sludge from ordinary industrial waters. If industrial waters produce an especially large quantity of sludge, then an appropriate addition must be made to the basic figure. Imhoff recommends, when industrial sludge is present, increasing the basic figure up to double.

b) The basic figure of 30 liters per capita is valid for a digestion time of 2 months; the latter corresponds to an average annual sludge temperature of 15° C. At any other temperatures the required digestion time changes according to the diagram presented in Fig. 1, and the basic figure must be changed accordingly. For example, at an average annual sludge temperature of 10° C, the digestion time increases to 4 months, i.e., by a factor of 2, and accordingly the volume of the chamber must be calculated on the basis of the norm

\[ 30 \times 2 = 60 \text{ liters per capita.} \]

c) The basic figure is valid for “worked-in,” mature digestion chambers, the contents of which are in alkaline fermentation, and into which fresh sludge, mixing with the old, immediately undergoes alkaline decomposition, bypassing acid fermentation. If, however, mixing of the fresh sludge, natural or artificial, is completely or partially absent, the basic figure, depending on the type of digestion chamber, increases up to \(2 \tfrac{1}{2}\) times.

d) The basic figure presupposes the entry of fresh sludge into the digestion chamber. If the sludge enters the digestion chamber in a state of acid fermentation, then the basic figure must be increased, depending on the degree of acidity of the sludge, up to double.

e) The basic figure corresponds to a certain quantity of sludge per capita, indicated above and dependent on the content in it of

of a given quantity of dry matter and water. With other qualities of sludge, the basic number must be changed accordingly.

e) The basic number of 30 liters per person presupposes full utilization of the chamber volume.

g) The basic number is valid for urban installations with a population of not less than 5,000; for small installations the basic number is increased by 1½ times.

Guided by the considerations set forth above, Imhoff establishes the following capacities for digestion chambers of various types, corresponding to an average annual temperature of wastewater of 15° C and of air of 10° C (see Table III).

Table III

Volume of digestion chambers of various types at a wastewater temperature of 15° C and an air temperature of 10° C.

6. Prüss bases the calculation of digestion chambers on the following considerations.

For a digestion chamber of a definite type and under definite temperature conditions, the decrease in the water content of sludge during digestion takes place according to a definite law, expressed by a curve of the dependence of the water content of the sludge on the digestion time.

In Fig. 3, curve I represents the decrease in the percentage water content of the sludge that occurs during digestion in the chamber of an Emscher well at a temperature of 15° C; the initial water content of the sludge is 95%. As the digestion process proceeds, the water content of the sludge decreases so that after 1½ months the sludge contains 85% water, after 3 months—80% water, and after 8 months—75% water.

Using this curve, one can construct the curve of the decrease in the volume of water (curve III), if the content of dry matter in the sludge is known at each moment of time. In the same figure, curve II shows the decrease in dry matter for an initial quantity equal to unity (0.35 mineral + 0.65 organic): after 3 months the dry matter = 0.77 (0.35 mineral + 0.42 organic), and after 8 months it is equal to 0.70 (0.35 mineral + 0.35 organic). The ordinates of this curve are plotted downward from the abscissa.

Operating with the same sludge (95% water), i.e., containing 1 part dry matter and 19 parts water, one can construct curve III, taking into account the quantity of dry matter present at each moment of time (curve II) and the water content at that time (curve I).

Then the distances between curves II and III will give, for each moment of time, the remaining quantity of sludge that will be present after the reduction of the sludge volume both through the reduction of dry matter (curve II) and through the decrease in water content (curve I).

Fig. No. 3.

Having data on the quantity of sludge at each moment in time, and taking into account the daily inflow of fresh sludge over the entire period under consideration, one can, by summing the daily ordinates, obtain the total quantity of sludge for any day and construct the curve of the volume of the digestion chamber. Curve IV is such a curve, constructed under the condition of the inflow of fresh sludge with a 95% water content, for a digestion-chamber temperature of 15° C; in this case the curve gives the volume of the digestion chamber in liters per inhabitant, assuming an inflow into the chamber of fresh sludge in the amount of one liter per person per day.

Curve IV shows that, in order to obtain sludge with an 80% water content, a digestion-chamber volume of 34 liters per person is required, and for an 85% water content—23 liters per person.

Raising the temperature to 25° C reduces the volume of the digestion chamber, according to Prüss, to 23 liters per person for digested sludge with 80% water.

Artificial mixing at 15° lowers the chamber capacity to 23 liters per person.

Simultaneous artificial mixing and raising the temperature to 25° reduce the size of the chamber to 15 liters per inhabitant, with the same water content of 80%.

1. Frank and Fries recommend, for North American conditions, using the following norms of chamber capacity per inhabitant per day when calculating digestion chambers of two-tier installations:

for the separate sewerage system . . . . 0.1 liter
for the combined sewerage system . . . . 0.2 „

where these norms correspond to a water content in the sludge of 80%; for sludge with another water content these norms must be changed accordingly.

IV. Calculation of the Additional Volume for Activated Sludge.

If the excess sludge from an activated-sludge installation is subjected to preliminary treatment by digestion together with the sediment separated from the sewage in mechanical-treatment structures, then the digestion chamber must receive an appropriate additional volume.

Imhoff recommends in such a case doubling the volume of the digestion chamber obtained by calculation for the sediment from mechanical-treatment structures alone.

He arrives at this conclusion by taking as a basis the data of Table IV on the quantity of sludge and its water content, depending on the character of the sludge, and by assuming that the reduction in the volume of the sediment during digestion follows the curves of the diagram shown in Fig. 4.

Fig. No. 4.

According to this diagram, the volume of the digestion chamber per inhabitant consists of a volume of 30 liters per person for sludge from mechanical-treatment structures and a volume of 20 liters per person for activated sludge, or in total is equal to 50 liters per person, i.e., almost twice the basic figure of 30 liters.

Table IV

Quantities of sludge and the water content in it, depending on the character of the sludge.

V. Data on the dimensions of existing digestion chambers.

The following table gives data concerning the volume of existing digestion chambers at certain installations.

Table V.

Capacities of digestion chambers at certain installations.

Calculating the average capacities of the digestion chambers by groups I, II, III, and IV, which respectively represent the Emscher wells in Germany (I), the Emscher wells in North America (II), separate Kremer digestion chambers in Germany (and Luxembourg) (III), and separate digestion chambers in North America (IV), we obtain the following table (Table VI).

Table VI.

Average capacities of digestion chambers for certain installations in Germany
(and Luxembourg) and North America.

From this table it follows above all that there is complete agreement with the considerations given above concerning temperature effects, in the sense that the digestion chambers of North American installations have larger volumes per inhabitant than the digestion chambers in Germany, namely: for the digestion chambers of Emscher wells, 50 liters as against 39 liters, and for separate digestion chambers, 66 liters as against 33 liters. As regards the difference in volumes between the digestion chambers of Emscher wells and separate digestion chambers within each country, i.e., those located in approximately identical climatic conditions, we find for the installations of North America complete agreement with the considerations stated above, namely: separate digestion chambers have a larger volume than the digestion chambers of Emscher wells (66 as against 50). But for German installations we observe, at first glance, a very strange phenomenon: the digestion chambers of Emscher wells have a larger volume than separate digestion chambers (39 as against 33), whereas, according to what was set forth above, the separate chambers ought to have had the larger volume. This apparent contradiction is explained by the following high qualities of installations with separate Kremer-system digestion chambers, which exert a favorable influence on the volume of the digestion chambers: 1) the very low percentage of water content in the fresh sludge (81.5–88%, as indicated above), 2) the insulation of the installation by an earth covering from the influence of low air temperatures, 3) the division of the digestion chamber into two compartments: preliminary and subsequent digestion.

Of course, when sludge with a higher water content enters separate digestion chambers (as is also observed with other methods of water clarification), and also in the absence of insulation, separate digestion chambers not heated by the heat of the wastewater will have larger dimensions than the digestion chambers of Emscher wells and separate digestion chambers heated by wastewater.

The separate digestion chambers for the cities of Baltimore, Birmingham, and Lüdenscheid-Friedrichstal (group V) shown in the table have an extremely large volume per inhabitant, which is explained by unfortunate design features. For example, the separate digestion chambers in Baltimore are large basins 43 meters long, 31 m wide, and 4 m deep. Naturally, when fresh sludge enters from one side of the chamber and digested sludge exits from the other, there can be no question of mixing fresh sludge with old sludge or of properly inoculating the fresh sludge with digestion bacteria; and this, as indicated above, greatly lengthens the digestion time and, of course, requires a correspondingly larger chamber volume.

Within each group, the volumes of the digestion chamber per inhabitant are subject to considerable variation, caused by differences in the temperature conditions of the wastewater, its character, the conditions of sludge mixing, etc.

The total capacity of 33 liters per person for the digestion chambers of the city of Essen-Rellinghausen (VI), which also receive surplus sludge from the activated-sludge installation, seems too low in comparison with the data given in Chapter IV; however, this is explained by the fact that the separate digestion chamber of this installation has artificial heating, and, conversely, this capacity is even exaggerated in comparison with the data of Table III for combined digestion chambers.

CONCLUSION.

In general, regardless of the method of calculation, when determining the volume of a digestion chamber it is necessary to have information on the quantity of fresh sludge retained in the settling devices¹, relating it either to a unit volume of sewage liquid and then carrying out the subsequent calculation according to water consumption, or to an inhabitant and carrying out the calculation according to population.

If the city has a sewerage system, then the determination of the quantity of sludge may be approached experimentally; in the absence of sewerage—by analogy, using data available for cities that are under the same conditions as the city for which the installation is being designed. The matter is, of course, considerably simpler if the design concerns digestion chambers at an existing treatment plant: in this case the quantity of sewage sludge retained by the settling devices can be determined by direct measurement.

It is then very important to form an idea of the final volume that the sludge will assume after digestion, and of how this reduction in volume takes place. In this respect, experimental and analogical approaches may also be used.

Finally, it is necessary to establish the digestion time required to achieve the final objective. This task, under our climatic conditions, acquires special importance owing to the low winter temperatures and the duration of the cold season, since the temperature of digestion chambers plays a decisive role in determining the digestion time, and its dependence on air temperature—especially for some types of digestion chambers—is beyond doubt.

If it is assumed that the temperature of the digestion chamber will for some time be so low that the digestion process will ceas—

stop, the calculated digestion time must be increased accordingly. In this case it is advisable to make the digestion chamber of such dimensions that it will not need to be emptied during the cold season.¹ To keep the volume of the digestion chamber as small as possible, it should be emptied in early spring, as soon as the condition of the sludge permits, leaving the necessary quantity for seeding; then, during the summer months, sludge should either be discharged periodically, or in autumn all the sludge should again be unloaded, leaving only the portion required for charging.

Under our conditions, therefore, special attention must be paid to measures of thermal insulation (in particular, also against the influence of cold groundwater) and to measures for artificial heating; moreover, in carrying out the latter, the possibility must be taken into account of using, as fuel, the gas obtained from the digestion chambers themselves.²

The calculation methods set forth above provide for determining such a volume of the digestion chamber as is sufficient for the digestion of sludge, but on the condition that the digestion chamber is already mature. Of course this volume is insufficient if the chamber volume must also provide for the entire “working-in” period; but at the same time, it goes without saying that to give the chamber an excessively large volume, required only for putting it into operation, would be inexpedient. Therefore one usually limits oneself to the volume necessary for mature chambers; to shorten the time of chamber maturation, one resorts either to “charging” them before putting them into operation with good alkaline sludge, or to adding lime to the contents of the digestion chamber, with proper mixing.

SOURCES:

H. Bach — Die Abwasserreinigung.
Imhoff. — Der Einfluss der Temperatur auf die nötige Grösse der Schlammfaulräume.
Imhoff. — Der Ruhrverband.
Imhoff. — Taschenbuch der Stadtentwässerung.
Hugo Knauer. — Kanalisation.
Kusch. — Zweistöckige Absetzbecken oder getrennte Schlammfaulbehälter?
Prüss. — Anleitung zur Berechnung von Schlammfaulräumen.
F. Sierp. — Über den Einfluss der Temperatur auf die Zersetzungsvorgänge in den Schlammfaulräumen.
Babbitt. — Sewerage and Sewage Treatment.
Materials from the author’s trip abroad in the summer of 1927.

¹ If, however, the sludge, owing to its condition, can be discharged in winter, then the cold season cannot serve as an obstacle to this; only the digested sludge should be discharged in winter not onto drying beds, but into special winter sludge ponds.

² See the author’s article: “Obtaining Gas from Sewage Sludge,” published in vol. 49, nos. 2–3, 1928, of Izvestiya STI.

1. Or on the quantity of suspended solids, in the dry state, contained in the wastewater, the percentage of their retention in mechanical-treatment structures, and the percentage moisture content of the sludge. ↩↩