35.2.1.1.1 Filtration Principles

In cake filtration, the resistance to flow increases with time as the cake builds on the filter medium. Initially the only resistance to flow is provided by the filter medium; however, as the cake builds, the cake itself becomes a resistance that must be overcome by the fluid being removed. If the filtration is performed at a constant pressure, the flow rate will decrease monotonically during the filtration. This is called a constant pressure filtration. In a less common constant rate filtration, the pressure drop is increased gradually to afford a constant flow rate.

In general, the rate of filtrate flow in a pressure‐driven filtration can be depicted as shown in Figure 35.2. The rate of filtrate flow (q) is directly proportional to the driving force, pressure differential (ΔP = P₁ − P₂) and inversely proportional to the length (L) of the cake (which in turn is a function of the amount of cake filtered).

For the same amount of filtered slurry, an increase in the filtration area (A) would provide more surface area for the filtrate flow and a reduction in the cake height L. An increase in the filtrate viscosity would adversely affect the filtration rate. Hence, the filtrate flow can be given as follows:

(35.1)

where

• q = dV/dt = filtration flow rate (m³/s)
• ΔP_Cake = pressure drop across the cake (Pa)
• A = filtration area (m²)
• μ = filtrate viscosity (Pa·s)
• L = filtration length or cake height (m)

Equation (35.1) is called Darcy's law [1] with a proportionality constant k defined as the cake permeability:

(35.2)

where

• k = permeability of the cake (m²)

The term (L/k) is equivalent to the cake resistance (R_c) faced by the fluid flow during filtration:

(35.3)

where

• R_c = cake resistance (m⁻¹)

However, in addition to the cake resistance, the flow also faces the medium resistance (R_m = L_m/k_m). These resistances can be presented as resistances in series in determining the rate of filtration (rate at which volume of filtrate is collected) [2]

(35.4)

where

• ΔP is the combined pressure drop (Pa) across the cake and the filter medium.

Specific cake resistance (α) is then given by

(35.5)

where

• C = concentration of slurry (kg/m³)
• V = volume of filtrate collected (m³)

Specific cake resistance (m/kg) is an intrinsic property of the material being filtered and is a function of the particle size, cake porosity, particle density, and shape [3].

At time zero, the term (αCV/A) is zero as the filtration has not been initiated (V = 0), and there is no cake built up, and hence there is no resistance due to the cake (R_c = 0). The total resistance at this time is due to only the medium resistance (R_m). As the filtration proceeds (V > 0), the cake starts to build up, and the value of R_c in Eq. (35.4) increases, thereby resulting in a corresponding increase in the overall resistance and further decreasing the rate of filtration. After a certain point of filtration, R_c dominates and R_m becomes negligible. In general terms, R_c originates from the packing of the particles as the cake forms, restricting the space available for the fluid to flow through. The fluid must then flow through the spaces between the particles with increasing friction, which in turn, for the same pressure drop, results in a decrease in the filtrate flow rate.

Combining Eqs. (35.4) and (35.5) and rearranging,

(35.6)

Integrating Eq. (35.6) from the start of filtration (t = 0, V = 0) to an arbitrary time t at which a volume V of filtrate has been collected, we obtain

(35.7)

Equation (35.7) can be further rearranged as

(35.8)

The term V/At in Eq. (35.8) corresponds to the volume of the filtrate filtered through unit area in unit time and is denoted as the average filtration flux or simply the filtrate flux. Note that the average filtration flux is an inverse function of the amount of the cake collected (CV = M).

In some cases, the flow itself influences the packing of the solid particles that may result in an increased resistance. In a filtration process this will be experienced as a change in the specific cake resistance with increased pressure (flow), and the cake is then said to be compressible. Specific cake resistance in the case of compressible cakes may be represented by an average‐specific cake resistance in the following equation:

(35.9)

where

• α₀ and n are empirical constants.
• n is called the compressibility index of the cake.

For incompressible cakes, α is independent of ΔP, and the compressibility index n is 0. If the cake is compressible (dependent on pressure), then n is greater than 0. Typical pharmaceutical cakes have a compressibility index in the range of 0.2–1.

The average filtrate flux profiles of compressible and incompressible cakes are illustrated in Figure 35.3 as a function of the pressure drop across the cake. As seen in the figure, in the case of incompressible cakes (n = 0), an increase in the pressure drop results in a corresponding increased filtrate flow, while in moderately compressible cakes (0 < n < 1), the filtrate flow monotonically increases but with decreasing slope, and in highly compressible cakes (n > 1), the flow reaches a maximum and starts to decline as the pressure is increased further. This is mainly because of the fact that in the case of highly compressible cakes, after a certain point an increase in pressure compresses the cake, filling the interstitial spaces between the particles, thereby reducing the space available for the filtrate to flow through the cake.

Derivation of Eqs. (35.4) through (35.8) assumed that solid particles are deposited on the filter cake and there is no migration of particles across the surface of the cake.

Figure 35.4 shows the profile of a typical pressure drop seen across the cake and medium from the initiation (t = t₀) to the completion of filtration (t = t_f).

At t = t₀, there is no cake, and hence the overall pressure drop is only due to the medium resistance, and at t = t_1/2, the overall pressure drop is due to the combination of cake and medium resistances with cake resistance contributing to the majority of the pressure drop. At the end of the filtration, the overall pressure drop is mainly due to the cake resistance with minimal contribution from the medium. The linearity and the precise slopes of the profiles of the pressure drops depend on the compressibility of the cake.

From Figure 35.4, at

(35.10)

As a result of the increasing resistance over time, the filtration flux decreases over time. The profile of the average filtration flux as a function of total cake formation (mass of cake over unit area of filtration, M/A) and specific cake resistance can be estimated for a given applied pressure differential and viscosity by using Eq. (35.8) as shown in Figure 35.5. A significant reduction in the flux occurs during the initial period of filtration as the cake resistance begins to dominate over the medium resistance. The profiles in Figure 35.5 are estimated for filtration at pressure 20 psi, viscosity of 1.2 cP, and R_m 1 × 10⁶ m⁻¹ as an example case.

It is also evident from the figure that reporting the average filtration flux to compare the filtration performances of two different slurries could be misleading, as those two streams could result in the same filtration flux but for different levels of cake formation. A comparison of just the filtration fluxes (e.g. from Buchner funnel filtration) can be performed as long as the filtration pressure and the M/As are similar. Typical ranges for the ratio M/A seen in the laboratory (left‐most gray region) and pilot plant (right‐most gray region) are also given in Figure 35.5 for better understanding. Table 35.1 gives a general guidance of the filtration performance in terms of specific cake resistance.

35.2.1.2.1 Centrifugation Principles

In a small‐scale centrifuge with a lower rotational speed, the liquid surface usually takes the shape of a paraboloid [5]. However, in large‐scale industrial centrifuges, due to high rotational speed, the centrifugal force dominates the force of gravity and the liquid surface takes a cylindrical shape, and it is coaxial with the axis of rotation (horizontal or vertical depending on the centrifuge). Figure 35.7 depicts a typical scenario inside a vertical axis centrifuge. As seen in the figure, the outer layer of cake (of radius r_i) and the outer layer of the liquid (of radius r₁) are cylindrical in shape and are coaxial with the axis of rotation of the basket (of radius r₂).

The pressure drop across the cake and liquid layer is [3]

(35.11)

where

• ω = angular velocity of the basket (rad/s)
• ρ = slurry density (kg/m³)

Combining Eqs. (35.6) and (35.11) and substituting for ΔP,

(35.12)

Equation (35.12) has been derived with the following assumptions:

1. The filtration area does not change with the cake formation.
2. The liquid layer is on top of the cake layer at all times.
3. Gravitational force is negligible when compared with the generated centrifugal force.
4. Medium resistance is constant throughout the filtration.

Similar to pressure filtration, for compressible cakes, α increases with an increase in the centrifugal force.

The centrifugal force F_G created by rotating the centrifuge is given by the following equation:

(35.13)

where

• F_g = gravitational force of the Earth
• G = centrifugal gravity = ω² × r₂
• g = Earth's gravity

G values can be determined using the radius of the bowl and the rotational speed as shown in Figure 35.8.

35.2.1.2.2 Filtration as a Multistage Process

Filtration of a slurry to form a cake, either by pressure filtration or centrifugation, can also be modeled as a multistage process including stages such as the formation, the consolidation, and the immobilization of the cake bed. Discussion of this more sophisticated approach is beyond the scope of this chapter. More information about this approach is available in the literature [6, 7].

35.2.1.3.1 Spontaneous Nucleation vs. Seeded Crystallization

Figure 35.9 shows the comparison of two crystals produced from the same pharmaceutical intermediate but through different crystallization conditions. The spontaneously nucleated batch (Figure 35.9a) has a significant portion of fines with a needlelike morphology and a high aspect ratio, while the seeded batch (Figure 35.9b) has a thicker rodlike morphology and comparatively low aspect ratio. In this case, the modification in crystallization reduced the filtration time significantly. The specific cake resistance measured for the needles (Figure 35.9a) was 6.9 × 10¹⁰ m/kg, while the specific cake resistance for the rods (Figure 35.9b) manufactured with an improved crystallization was 9.0 × 10⁹ m/kg.

35.2.1.3.2 Distillative Crystallization vs. Antisolvent Crystallization

In this example, the crystallization was changed from a distillative crystallization (DC) to an antisolvent crystallization (AS) with a different solvent system. This change in crystallization did not affect the crystal behavior significantly (see Figure 35.10), and the estimated specific cake resistances were 1.37 × 10¹¹ m/kg and 0.4 × 10¹¹ m/kg. However, a significant decrease in the viscosity of the mother liquor (from 2.4 to 0.45 cP) and in the solid concentration (from 126 to 27 mg/ml) between these two crystallizations played a major role in influencing the filtration performance in this example. The impact of these variables on the filtration time could be explained by Eq. (35.7) as below.

Since there is very minimal effect of R_m on filtration time, the medium resistance term in Eq. (35.7) could be ignored, and the filtration times (t₁ and t₂) for these two cases are given as follows:

Since the values of ΔP and A were the same for both the cases, the ratio of t₁ and t₂ is

By substituting M for CV, the ratio of the filtration times (t₁/t₂) of both filtrations to filter the same amount of cake (M₁ = M₂) is then given by

Note that when M₁ = M₂, V₁/V₂ can be replaced by C₂/C₁, as has been done here. Substitution of the values for viscosity, cake resistance, and concentration in the above expression provides an estimate of the time ratio between the two filtrations:

The profiles of the cake formation and the filtrate received over time for both filtrations are given in Figure 35.11. As seen in the figure, the slurry crystallized from the DC took approximately 117 seconds to filter, while the one from the AS took only approximately 35 seconds to filter a similar amount of cake.

35.2.2.1.1 Pressure Filtration

35.2.2.1.1.1 Buchner Funnels

Buchner funnel filtration is one of the simplest and most widely used forms of laboratory filtration. It is named after the chemist Ernst Buchner who invented the Buchner funnel and Buchner flask. It is vacuum driven and can be used in a scale ranging from a few tens of milligrams to a few kilograms. Figure 35.12a shows a picture of a Buchner funnel filtration setup. The funnel is made of porcelain, glass, or plastic (Figure 35.12b). The filter media, typically a filter paper or a filter cloth, is kept on the perforated plate to retain the solid. In the case of a sintered glass funnel, the fritted surface acts as the filter medium. The usage of the Buchner funnel is mainly driven to implement a separation and they are rarely used to collect scale‐up parameters; however, with some care, they can provide a first approximation to the filtration properties of the cake. After completing the isolation, cake washes can be performed by adding the solvent on the wet cake and starting the filtration.

35.2.2.1.1.2 Leaf Filters

Leaf filters are relatively larger‐scale filters compared with Buchner funnel filters. Their use is driven by the need to characterize slurry filtration properties and requires detailed measurement of the filtration profile, i.e. rate of filtrate collection. Figure 35.13 shows a few examples of leaf filters of different materials of construction. Leaf filters consist of three parts: a bottom portion with flow valve, a middle stem portion, and a top lid portion. The bottom portion has the provision to place the filter medium, the middle stem portion holds the slurry, and the top portion closes the stem portion. After connecting the bottom portion (with filter medium of desired pore size) to the stem portion, the slurry is poured into the stem. The top lid portion is then connected to the stem. The chosen pressure set point is attained usually through compressed nitrogen/air. Cake washes can also be performed in a similar fashion. Filtration is performed at multiple pressures to fully characterize the cake properties such as the specific cake resistance and the compressibility index. Refer to Example Problem 35.2 for clarity.

35.2.2.1.2 Centrifugation

The pharmaceutical industry uses various types of centrifuges. This section provides an example of a vertical axis, batch mode centrifuge (Figure 35.14a). It uses a perforated basket (Figure 35.14b) rotating on a vertical axis to produce a centrifugal force on the slurry that is fed to the basket through the feed pipe. The perforated basket is lined with a filter bag of desired pore size. This filter bag retains the solid particles as wet cake, while the filtrate passes through the filter medium. The filtrate flows out of the basket through the perforations and gets collected outside through the outlet valve. Cake washes can then be performed through similar steps by feeding the wash solvent to the basket.

35.2.2.2.1 Filter Dryer

Filter dryers are one of the most robust isolation equipment used in the pharmaceutical industry. As the name implies, it encompasses the filtration and the drying unit operations into a single piece of equipment. Figure 35.15 shows the cross‐sectional representation of a filter dryer. The mode of operation for filtration is similar to that of the leaf filter. The required differential pressure is generated by introducing either pressure upstream of the filter medium or vacuum downstream. Typical operation would include equipment setup (fitting a filter cloth of appropriate pore size and material of construction and performing leak checks), loading the slurry, deliquoring the mother liquor, loading the wash, deliquoring the wash, drying, and discharging. Filter dryers are usually fitted with an agitator that can be lowered or raised as needed. The presence of an agitator makes filtering and cake washing more efficient as the agitator aids in mixing the cake uniformly. Agitation also helps in smoothing the cake in case of crack formation that otherwise could cause channeling of the wash solvents resulting in inefficient cake washing. Filter dryers are also fitted with a jacket to facilitate heating in the drying step. Provision of a jacket also allows for performing filtrations at different temperatures. After completing the filtration and washing steps, the cake can be dried in the same equipment, and the dry cake can be discharged through the discharge port with the help of the agitator. There is typically an offset between the lowest position of the agitator and the filter cloth in order to avoid lifting or rupturing the cloth. This offset often results in residual cake (denoted as “heel”) left on the cloth after the discharge. The heel could potentially slow down the filtration of the next batch. Heel removal is discussed in a later Section 35.2.3.2.1.

35.2.2.2.2 Centrifugal Filter

Centrifuges can be used either continuously or in batch mode. The pharmaceutical industry prefers batch centrifuges from a regulatory standpoint as it gives an option of stopping the unit operation in case the product specification fails at some point. This section provides examples of batch centrifuge filters.

35.2.2.2.2.1 Peeler Centrifuge

Peeler centrifuges are available with a horizontal or vertical axis of rotation. The mode of discharge is through a mechanical peeling action. Figure 35.16 shows the cross‐sectional representation of a peeler centrifuge. Typical operation involves equipment setup (fitting a filter bag of appropriate pore size and material of construction, performing leak checks), initiating the spinning, loading the slurry, deliquoring the mother liquor, loading the wash, deliquoring the wash, peeling, discharging, and removing the heel before initiating the next load. Isolation starts as soon as the slurry is loaded, as the basket is already spinning, yielding the necessary centrifugal force for the separation. After the liquid layer goes below the cake surface, cake washing can be initiated. After completely deliquoring the wash solvents, the cake is peeled off using a hydraulically activated peeler. The peeled solids are then discharged through a chute for the next unit operation. Often, there is an offset between the peeler's closest position and the cloth, resulting in a residual heel. Depending on the available equipment train, either the discharge chute could be connected to a dryer, and the material discharged directly to the dryer, or the cake could be discharged into drums and transported to the dryer for further processing. The operating parameters of the peeler centrifuge such as the load size and the spin speed are adjusted according to the process requirements. For example, a lower spin speed may be chosen to isolate a compressible cake and to prevent the formation of a highly compressed cake, the heel of which might be difficult to remove.

35.2.2.2.2.2 Inverting Bag Centrifuge

Inverting bag centrifuges are horizontally or vertically rotating centrifuges incorporating an automatic discharge. Figure 35.17 shows the schematic representation of a horizontally rotating, inverting bag centrifuge. The order of operation in this centrifuge is very similar to the peeler centrifuge except for the mode of discharge. In this case, after completing the filtration and washing, the filter bag is stroked forward by a hydraulically controlled piston, turning the bag inside out, allowing the solids to be discharged. The filter bag is secured to the basket wall at the front end, preventing it from completely detaching from the basket. These centrifuges offer an efficient and faster cake removal as the bag is turned inside out.

35.2.2.2.3 Non‐Agitated Filter Dryers

These are similar to filter dryers except that they are not fitted with agitators. Figure 35.18 shows a schematic representation of a non‐agitated filter dryer in closed and cross‐sectional views. The absence of an agitator may necessitate manual mixing of the cake during washing and drying, for content uniformity. In case of crack formation in the cake, the lid needs to be opened to manually smooth the cake. For this reason, operating a non‐agitated filter dryer requires more personal protection (such as full suit, face shield, supplied breathing air, etc.) for the operator to avoid material exposure. Non‐agitated filter dryers are usually fitted with a jacket.

35.2.3.1.1 Buchner Funnel Filtration: First‐Order Approximation

As mentioned earlier, Buchner funnel filtration is performed when there is no requirement for extensive data collection. It is possible only to record the total amount of filtrate collected (V) and the total time (t) to complete the filtration at a single differential pressure (vacuum driven either through a vacuum pump or house vacuum). An average filtrate flux could be calculated from V, t, and the filtration area. The average filtration flux (L/m²h) obtained from a Buchner funnel filtration is sufficient to estimate the average‐specific cake resistance () by using Eq. (35.8) as a first‐order approximation. An approximate R_m could be used for this calculation. Eq. (35.8) can be rearranged as follows:

(35.14)

where

• M = CV = mass of dry solids (kg)

The pilot plant filtration performance (filtration flux and cycle time) can then be calculated by using the estimated and the pilot plant operating parameters such as differential pressure (ΔP), filtration area (A), and batch size (M). Since, in typical pharmaceutical separations, the medium resistance is negligible when compared with the cake resistance, estimation of specific cake resistance through this approach by using an approximate low R_m is fairly reasonable. It should be noted that has been estimated from a single data point obtained by conducting filtration at a single pressure. Hence, it is not possible to calculate the compressibility index of the cake through this approach.

35.2.3.1.2 Leaf Filtration: Usage of t/V at a Single Pressure

With the help of balances equipped with automated data collection, the instantaneous filtrate volume at a particular time interval could be collected during leaf filtration experiments at multiple pressures. However, in cases of limited material availability, data from filtration at a single pressure may be used to calculate the cake properties more accurately when compared with Buchner funnel filtration. Equation (35.7) can be rearranged as follows:

(35.15)

From the t vs. V data, t/V can be plotted against V to obtain a straight line, the slope of which is μαC/2A²ΔP and the intercept is μR_m/AΔP. With all the other parameters such as μ, C, A, and ΔP known, α and R_m can be calculated. Pilot plant filtration performance can then be estimated using the similar approach described earlier. Compressibility index cannot be calculated through this set of data.

35.2.3.1.3 Leaf Filtration: Usage of t/V at Multiple Pressures

Inverse filtration rate (t/V) data at multiple pressures is the most complete data set required to calculate the cake properties including the compressibility index. Equation (35.9) can be modified as

(35.16)

After calculating α and R_m for the individual differential pressures as explained above, ln(α) can be plotted against ln(ΔP) to obtain a straight line. The slope of this straight line is the compressibility index (n) and the intercept is ln(α_o).

Even though this approach is more complete and reliable, the previous two approaches can also be beneficial in cases of limited data.

35.2.3.1.4 Leaf Filtration: Filtration over Heel/Cake Washes

Cake washes are typically performed when the cake is already deposited and the clean solvent is filtered through the deposited cake to displace the mother liquor. In often cases, crystal slurry is also filtered over the heel from the previous batch. Pilot plant performances of these cases can also be predicted by using similar equations. Equation (35.8) can be given as

(35.17)

where

• , in the case of slurry filtration over a clean filter cloth.
• , in the case of slurry filtration over a heel.
• , in the case of a cake wash.

In the case of a cake wash, the term M (= CV) in Eq. (35.17) is zero as the concentration of API in wash solvent is zero.

35.2.3.1.5 Laboratory and Pilot Plant Centrifuge Filtration

A similar set of data is collected from laboratory and pilot plant centrifuges as the pressure filtration. Spin speed (rpm) and feed rate (kg/h) are the only two parameters required in addition to the data set of t vs. V collected from a leaf filter at multiple pressures. Spin speed can be collected through the motor of the centrifuge, and the feed rate can be collected through a mass flow meter, radar, or load cell.

t vs. V data from leaf filtration is sufficient for estimating the specific cake resistance as discussed previously. In addition to α, for modeling a centrifuge operation in the pilot plant, the slurry feed rate and the centrifuge spin speed need to be optimized for the following constraints: (i) to minimize centrifuge vibration, (ii) to maintain uninterrupted filtration for completing a load, (iii) to evenly distribute the cake, (iv) to minimize compression of the cake (in the case of compressible cakes), and (v) to prevent the formation of the standard wave. In simplified terms, Eq. (35.12) can be used for this purpose in a similar fashion as described for pressure filtration.

35.2.3.2.1 Heel Removal

The formation of a heel may be an unavoidable problem in cake filtration in most of the equipment, except in cases such as inverting bag centrifuges. As discussed earlier in this chapter, the offset between the agitator or peeler and the filter medium results in the formation of a heel. The next load/batch could be filtered over the heel from the previous load/batch as long as it does not adversely affect the filtration performance, but the heel would become the primary filtration medium for the next load. For compounds with low toxicology profiles, a manual removal of the heel is a viable option. However, for compounds with high potency/toxicology profiles, removal of a heel in filter dryers/centrifuges needs an additional unit operation involving the dissolution of the cake in a solvent and passing the solution through the filter cloth. In modern‐day centrifuges, there are provisions such as blowing compressed nitrogen from behind the cloth to remove the heel. Another possible solution in a centrifuge is to loosen the heel by rewetting it with wash solvent and discharging it.

35.2.3.2.2 Filter Medium Blinding

The filter medium may play an important role in determining the filtration performance. At the beginning of the filtration process, the filter medium retains the solid particles while allowing the filtrate to pass through. The cake that is formed on the medium as a result then does most of the filtration. However, in some cases it has been observed that the filtration performance on a used filter medium is significantly different from that on a new one. This behavior could be observed even in the absence of heel over the medium. This is called “filter medium blinding” [4]. It results from clogging of the pores by the solid particles, thereby preventing the free movement of the filtrate through the pores as originally observed in a new medium. Due to this blinding, the initial medium resistance for the next batch/load might rise. Figure 35.20 shows the effect of filter cloth blinding on the medium resistance. From this figure, it is clear that the filter medium resistance increased gradually over the number of filtration cycles.

It is generally not possible to remove blinding through mechanical agitation or by passing compressed gas (nitrogen or air) through the medium, as it could result in permanently damaging the medium, rendering it unfit for use for the next batch/load. A typical solution for this problem is to use a solvent to dissolve off the entrained solid particles.

35.2.3.2.3 Cake Cracking

In many cases, mostly after the deliquoring step, cake cracking is observed. In cases where a complete removal of the mother liquor (along with the unreacted starting material, reagents and by‐products) is relied upon by washing the wet cake, cake cracking may pose a detrimental effect on the quality of the batch. Cracking of the cake results in the formation of various channels. When washed with solvents without reslurrying the cake, the wash solvents tend to pass through these channels (paths of least resistance), leaving many parts of the cake unwashed. Cake cracking becomes more frequent when the average porosity of the cake is high [8], resulting in the formation of channels. The presence of cracks could be identified by (i) visual inspection through the sight glass, (ii) monitoring the filtrate flow (an abnormally fast deliquoring could be a sign of cracking), and (iii) measuring the purity of the cake, and the presence of a washable impurity in the cake could be another sign of an inefficient washing possibly due to channeling. This problem is commonly solved in the pharmaceutical industry by smoothing the cake before initiating the wash sequence. This smoothing action eliminates the channels allowing the wash solvent to filter/wash through the cake more uniformly.

35.2.3.2.4 Compressible Cake

Compressible cakes may adversely affect the filtration performance if high pressures (pressure filtration) or high spin speeds (centrifugal filtration) are used. In addition to slow filtration, difficulty in discharging the wet cake and formation of hard agglomerates are other possible detrimental effects of a highly compressed cake.

35.2.3.3.1 Volume Considerations for Cake Washes

In principle, the volume of displacement wash required to displace the mother liquor should be estimated by the cake height and the coaxial mixing that occurs at the front end of the wash as it traverses the cake in a plug flow. Generally, however, the risk of channeling is too high, and as a rule of thumb, the solvent volume should be equal to at least thrice the volume of wet cake. In general terms, a reslurry wash requires more solvent than a displacement wash. If the isolation is performed in multiple loads, the cake wash volumes should be adjusted accordingly. This is true for both pressure filtration and centrifugation.

35.2.3.3.2 Uniform Washing

To facilitate an efficient cake wash, care should be taken to ensure a uniform wash of the entire cake bed. Even though there are various approaches (such as spray balls, mists, or weirs) available to spray the solvent evenly across the surface of the cake, care should be taken to ensure that the cake surface is adequately smoothed to prevent (i) more solvent stagnating on troughs and (ii) channeling of the wash solvent through cracks formed across the bed. These two factors might cause uneven washing of the cake, increasing the likelihood of inefficient washing of some parts of the cake.

In‐process controls could be put in place to ensure the complete removal of the impurities and mother liquor. Possible controls include parameters such as purity, color, and pH. However, the accuracy of these methods is directly related to the uniformity of the wash.

35.3.1.2.1 Jacket Warm‐Up Period

The period between A and B is called the warm‐up period and accounts for the time taken for the system to heat up toward the target set point of the jacket temperature controller. At this point, drying will proceed as solvent saturating the surface of the solids is vaporized. Under reduced pressure, this vapor‐phase solvent would be continuously removed through the dryer vent. In the case where reduced pressure is not used, a continuous gas flow (i.e. sweep) through the dryer is utilized to ensure that vaporized solvent is removed through the dryer vent with the inert carrier gas (e.g. nitrogen). Under vacuum conditions, the cake will often cool down to below its original temperature due to the energy transfer associated with the solvent enthalpy of vaporization. In this case, the cake temperature will increase back to the jacket set point temperature when drying is essentially complete and all the solvent has been vaporized.

35.3.1.2.2 Constant Rate Period

The period between B and C is typically characterized by a constant drying rate (as can be seen from the second and third drying curves in Figure 35.22). The drying mechanism during this period is dominated by heat transfer, and the drying rate is usually limited by the rate of heat transfer to the system. During this period, solvent that has saturated the surface of the solids is rapidly vaporized. The driving force during this constant rate period is the temperature difference between the dryer jacket set point and the temperature of the solvent being removed (at the system pressure). The drying rate can hence be increased by either increasing the jacket temperature set point or decreasing the pressure (i.e. to decrease the boiling point). It is important to note that the rate of solvent removal is also dependent on the size of the vacuum pump. If the pressure setting is too low, the rate of solvent vaporization may exceed the capacity of the vacuum pump to remove solvent from the system. In this case, the system settles at a higher pressure than the desired set point, and the drying rate is determined by the vacuum pump flow rate rather than the heat transfer rate. For the drying rate to be controlled by the heat transfer rate, the vacuum pump must be appropriately sized for the system so that it imposes no limitations on solvent removal from the dryer. As would be expected, the drying rate is also affected significantly by the surface area available for heat transfer. As the cake dries, this area is reduced; however, agitation of the cake exposes “fresh” solvent to the heated surface and increases the area for heat transfer. Hence, agitation of the cake allows for an increase in the area available for heat transfer.

35.3.1.2.3 Falling Rate Period

At the point C, solvent is no longer abundant on the solid surface: i.e. the surface becomes unsaturated, and the drying rate begins to fall. This point is typically called the critical moisture content. Note that the term “moisture” derives from historical convention when early drying studies were carried out with water, but the concept of a critical transition point applies to any solvent system. The critical moisture content is a property of the material being dried that also depends on the thickness of the material and the relative magnitudes of the internal and external resistances to heat and mass transfer. In some cases, it could also be a function of the total surface area of the solid phase and hence the particle size [3]. It is important to take into account possible variations in the value of the critical moisture content during scale‐up of a drying process.

During the period from C to E, heat transfer no longer becomes the limiting mechanism for drying. Instead, mass transfer becomes the dominant mechanism limiting the rate of solvent removal from the heated surface. As a result, the drying rate is typically observed to fall as depicted in the second and third drying curves of Figure 35.22. In some cases, the decrease in the rate of drying can become significant and lead to extremely long drying times. At some point during the falling rate period, the solvent present on the surface is depleted, and solvent present inside the internal structure of the solids remains (either as a solvate or an occluded solvent that may not be removable). The drying rate is then determined by the movement of this internal solvent to the heated surface for vaporization. This transition is given at point D and can sometimes be seen by plotting the drying rate versus the solvent content as shown in the third drying curve of Figure 35.22. It is important to note that this solvent migration is extremely difficult to model and may not be a feature clearly visible on many drying curves.

35.3.3.4.1 Long Drying Times

Long drying times can cause significant bottlenecks in the overall process and is most often a result of a prolonged period under the mass transfer limited mechanism. Drying times can be improved by ensuring that most of the drying operation is carried out under heat transfer‐limited conditions and that both the driving force and the heat transfer area available are maximized as much as possible (within the constraints of product stability and equipment limitations). From Eq. (35.19), it can be seen that the difference between the jacket temperature and the product temperature provides the driving force for heat transfer and the heat transfer coefficient is equally as important. Static dryers such as a vacuum oven often do not provide enough surface area for heat transfer, whereas drying in agitated dryers can provide the benefits of increased surface area for heat transfer. Note that certain solvents such as water can be difficult to remove regardless of the equipment used, leading to longer drying times. Estimation of the critical moisture content in the lab and simulation of the drying process with a model can be helpful to ensure that appropriate operating conditions are used in the plant to achieve optimal drying cycle times.

An approach that is often used in manufacturing to reduce drying times is to flow an inert gas such as nitrogen through the drying cake. This strategy utilizes convection to remove residual solvent from the wet solids as the inert carrier gas passes through the cake. A strategy for scaling up this approach was proposed by Birch and Marziano [19], using a simplification of the Carman–Kozeny equation for flow through particulate beds [19]. In their work, they showed that the pressure drop across the cake is proportional to the specific gas flow rate (i.e. per unit cross‐sectional area) multiplied by the depth of the cake. The proportionality constant is a function of the void fraction of the solid bed, the particle diameter of the solids, and the viscosity of the solvent being removed. It can be determined by lab experimentation and assumed to have the same value on a larger scale if the physical properties of the solid being isolated and the wash solvent remain the same. The pressure drop needed to maintain a specific gas flow rate on scale can then be calculated for the larger‐scale bed depth to achieve the same rate of solvent removal [19]. Some important considerations when using a nitrogen blow‐through operation are that (i) a strong vacuum from the bottom/outlet side of the cake may be needed to ensure that the system is under enough reduced pressure to ensure vaporization of the solvent, (ii) there may be a constraint on the maximum operating pressure in the headspace of the dryer if the cake is susceptible to compression, and (iii) intermittent cake smoothing may be required to prevent channels from forming that could result in the inert gas bypassing the majority of the drying cake [20].

35.3.3.4.2 Agglomeration/Balling

Solid particles can sometimes aggregate to form hard agglomerates with solvent trapped inside (also known as balling). This problem is most often seen in agitated dryers and is generally worse in filter dryers. Agglomeration is often caused by agitating the cake too aggressively while it still contains a significant amount of solvent. Since agglomeration is a phenomenon that is not well understood and there are no specific guidelines on how to avoid the issue during drying, a general approach is to avoid agitation in the initial stages of the drying. One factor that may be important for avoiding the formation of agglomerates is the solubility of the product in the individual solvents that are being removed. Sometimes the cake has been washed with a mixture of solvents prior to drying and if there is enough solubility in one of these solvents by itself, the product could become partially dissolved that could lead to fusion of the crystals by the formation of solid bridges between them as the solvent is removed. One approach to avoiding agglomeration is therefore to adjust the solvent composition of the final cake wash to avoid the potential enrichment of highly soluble solvents during the drying operation. Agglomeration has been found to occur when the drying rate is high and the shear rate is relatively low [21, 22], indicating that there is a higher risk for agglomeration if agitation is applied during the initial stages of drying when the process is heat transfer controlled as opposed to mass transfer controlled. Indeed, there is often a critical amount of solvent, known as the “sticky point,” at which the tendency to form agglomerates may be maximal [12]. This is due to the presence of solvent capillary forces strong enough to cause particles to agglomerate together if agitation is applied, in a similar fashion to how particles stick together in a wet granulation process. Birch and Marziano ([19]) showed that the “sticky point” can be determined experimentally using mixer torque rheometry, since the torque required to maintain a constant rotational speed during agitation will increase as binder solvent is added to the solids until it is at a maximum value when the agglomerates are strongest (i.e. at the “sticky point”) [19]. The magnitude of the torque at this point is also an indication of the hardness of the agglomerates that are formed. However, a potentially more reliable estimate of agglomerate hardness (along with the extent of agglomeration) can be obtained by sieving samples of the solids [19]. Birch and Marziano [19] also showed that the “sticky point” depends upon the size of the particles present in the cake, with smaller particles requiring more solvent to bind them together due to higher specific surface area [19]. Once the “sticky point” has been determined, a drying protocol needs to be designed to avoid the application of agitation while the solvent content of the cake is above the “sticky point.” Since this could result in undesirably long drying times, the application of a nitrogen blow‐through operation (as described earlier) is typically used instead of agitation until the solvent content is below the “sticky point” [19, 20].

35.3.3.4.3 Particle Attrition

If the product crystals are sensitive to shear, agitation of the cake can lead to particle breakage and attrition. In these cases, maintaining a specified particle size during drying can then become a challenging aspect of the drying operation. Equipment selection and careful consideration of how the agitation will be operated are critical for ensuring particle size integrity. Based on the geometry of the equipment and how the agitator interacts with the cake, the force exerted on the particles should be considered. Particles are likely to experience less force in a tumble dryer as opposed to a filter dryer or conical dryer. When the use of a tumble dryer is not an option, lab studies to determine the maximum shear that the particles can endure before breakage becomes a problem can be carried out. The plant agitation protocol could then be scaled up based on maintaining a lower tip speed than the critical value. However, it is important to note that the ranges of tip speeds achievable in the lab often do not overlap with those achievable in the plant. Particle attrition has been shown to occur when the drying rate is low and the shear rate is high [21, 22], indicating that there is a higher risk for particle attrition if continuous agitation is applied during the later stages of drying when the drying rate is limited by mass transfer.

Remy et al. [10] correlated the impact of agitated drying on powder properties with the amount of work done by blades on the cake, which is determined by the normal stresses (hydrostatic pressure) and the bulk friction coefficient of the cake (affected by the degree of wetness). The publication demonstrated an experimental setup that allowed for the determination of the cake's bulk friction coefficient that in turn could be used to estimate the work exerted on the cake in different large‐scale equipment. From a laboratory setup, the impact on the powder properties at scale‐relevant conditions could then be evaluated.