Risposte teoria seconda parte Separation unit operations

Part two

1) Integrated stripping-absorption processes

Scheme with indication of temperatures, pressures and heat duties for the example of the recovery of C4+ by heavy oil absorption.

A gas mixture containing light hydrocarbons (C4+ components) is fed at the bottom of an absorption column, where an absorbent solvent (heavy oil) enters from the top. The solvent selectively absorbs specific components, such as butane. The lighter components exit from the top of the absorber, while the enriched solvent containing the heavier components exits from the bottom.

To recover the absorbed C4+ components, the enriched solvent is heated and sent to the top of a stripping column. At the bottom of the stripping column, steam is injected, contacting the enriched solvent. The C4+ components are stripped from the heavy oil and exit from the top as a gas, while the heavy oil is recovered at the bottom and recycled back to the absorption column. The C4+ and steam gas mixture is condensed using cooling water, followed by separation either through distillation or settling (as hydrocarbons are non-soluble in water).

The absorption process is favored by low temperatures and high pressures, as these conditions enhance the solubility of the components in the liquid phase. In this setup, the temperature increases from the top to the bottom of the absorber:

• Top temperature Ttop = 40°C
• Bottom temperature Tbottom = 50°C

This results in a temperature difference of 10°C.

The stripping process works efficiently at high temperatures and low partial pressures to facilitate the separation of components. In this example, the pressure inside the column is slightly higher than atmospheric pressure at the top (810 mmHg) and increases towards the bottom (860 mmHg) to prevent pressure drops across the trays. Inside the column, the temperature decreases from the top to the bottom:

• Top temperature Ttop = 130°C
• Bottom temperature Tbottom = 120°C

The injected steam is superheated, entering at P = 4.5 atm and Tsteam = 143°C - 157°C. Its outlet temperature is approximately Tout = 130°C. Care must be taken to avoid condensation of steam at the bottom, as it can negatively affect the mass transfer. Thus, the bottom temperature is maintained above the steam's saturation temperature (T > Tsat). The lean solvent from the stripper is used in a heat exchanger to preheat the solvent and C4+ mixture leaving the absorber. The cooling water for condensation is around Tin = 25°C and exits at Tout = 40°C.

2) Multicomponent distillation: short-cut and rigorous method, composition and temperature profiles along the column

The rigorous method

The Naphtali-Sandholm method, introduced in 1971, is a simulation approach for multicomponent distillation columns. It enables the simultaneous solution of material and energy balances, as well as equilibrium equations, for all stages of the column.

This method is characterized by its stage-by-stage grouping of equations and their subsequent linearization. The resulting system of equations forms a tri-diagonal block matrix, which is numerically solved using the Newton-Raphson technique.

In this framework, the model equations are expressed as error functions F(j,k), where j represents the stage being analyzed and k corresponds to the specific function written for that stage, such as a balance or equilibrium equation. These error functions:

= ( − ), ,{ = ( − ), ,

As variables, Naphtali-Sandholm used the molar flow rates of the individual components:

= = ∑ ∑ = =

In this way, the congruence equations of the phases are included in the balance and equilibrium equations. The system can be solved by means of Newton-Raphson method. Rigorous model are present in ASPEN and PRO II softwares.

The short cut method

In the past, when computer simulation tools were unavailable, several approximate calculation methods were developed. Among these, the Fenske-Underwood-Gilliland method stands out as a key approach.

This method integrates the Underwood equation for calculating the minimum reflux ratio, the Fenske equation for determining the minimum number of ideal stages, and Gilliland’s correlation for estimating the actual number of ideal stages based on the reflux ratio and the minimum number of stages.

This method is applicable to systems where relative volatilities remain constant along the column and assumes constant molar flow rates in the rectifying and stripping sections. While these methods have largely fallen out of use due to advancements in computational techniques, the principles they rely on continue to be significant.

Modern shortcut methods are built on the concept of key components. Typically, only a subset of feed components appears in significant concentrations in both the distillate and residue. The lightest and heaviest of these components are identified as the light key and heavy key, respectively. The light key is defined as the lightest component present in the residue with an appreciable concentration, while the heavy key is the heaviest component present in the distillate with an appreciable concentration.

Composition and temperature profiles along the column

3) Azeotropic distillation process. Extractive distillation process

If the relative volatility of a binary mixture is near to 1, it could be present an azeotrope, in this case it is not possible to separate components with a common distillation. There are some process useful to overcome this problem:

Extractive distillation

In this process, a liquid solvent is introduced into the distillation column at a stage different from the feed to be fractionated, with the goal of breaking the azeotrope. This effect is achieved through the selective interaction of the solvent with the components of the mixture. Specifically, the solvent alters the activity coefficients of the components, thereby increasing the volatility of one component relative to the other, making it possible to separate them via distillation.

A second column is required to separate and recycle the solvent. In the chemical industry, extractive distillation is the preferred technique for separating azeotropic mixtures.

Azeotropic distillation

Similar to extractive distillation, azeotropic distillation involves adding an extra component, typically a solvent, to the process. However, the key requirement is that the solvent creates a multicomponent azeotropic mixture, usually with higher volatility, in which the pseudo-binary composition of the two components to be separated differs from the original azeotropic composition.

A classic example of azeotropic distillation is the production of pure ethanol from a water-ethanol mixture (approximately 90 mol% ethanol) using benzene as the solvent. This process is somewhat more complex than extractive distillation, as it involves not only vapor-liquid equilibria but also vapor-liquid-liquid equilibria.

4) Assumptions, derivation and significance of the Kremse-Brown-Souders equation for absorption and stripping processes

The Kremse-Brown-Souders equation represents an analytical solution to find the number of theoretical stages for absorption and stripping processes. In the case of absorption from diluted gas streams, and only in this specific situation, the concentration of component B in both phases is such that the molar ratios can be replaced by molar fractions, and the inert flow rates can be substituted with total flow rates, moreover the EL is straight.

Under these conditions, it becomes possible to analytically evaluate the number of theoretical stages. The equation for the material balance around stage j is:

( − ) = ( − )−1 +1

From the equilibrium relation: it is possible to obtain the absorption factor A:

= − −1 = →= − +1

If this equation is applied to all the ideal stages and the equations thus obtained are multiplied member by member, it results:

− =( ) −

And the addition, from the overall column balance:

) ( )( = − − −1

Equilibrium relation we get:

; that substituted in ( )= + − = −+1 − −

Permits to obtain:

This is often written as ( ) = (1 − ) + 1.

= − − +1 −

It expresses, in terms of the absorption factor and the number of stages, the ratio +1 −1 between the actual absorption (ye - yu) and the maximum possible absorption under the given conditions of the incoming fluids, i.e., ye and Xe.

The same equation is also valid for stripping, considering S as the stripping factor (S=1/A), we have:

+1− − = +1 − / − 1

No solution to the stripping problem of interest can be found for recoveries higher than 90% if the stripping factor is lower than 0.9.

5) Tray columns and packed columns: comparison, schemes including construction details, and pros/cons analysis

When selecting between packed and tray columns, it is essential to compare their characteristics.

Packed columns are particularly suited for situations where the fluid tends to foam due to the agitation of liquid by vapor. They are also preferred when the fluid is corrosive, as packing materials can be made of corrosion-resistant materials like plastics. Packed columns are ideal for operations involving high liquid and vapor flow rates, as well as for treating thermo-sensitive compounds, which require working under vacuum conditions. Moreover, packed columns are advantageous when mass transfer is controlled by the gas phase. They allow for rapid column preparation and are often more economically convenient compared to sieve tray columns.

In contrast, tray columns are better suited for treating fluids containing excess solid residues due to their simpler maintenance. They are particularly effective in processes involving strong heat development, as these systems often require cooling coils inside the column to manage heat removal. Tray columns are preferred when mass transfer is controlled by the liquid phase. They handle high vapor flows more effectively under conditions of low liquid flow rates and are ideal when multiple feed streams or withdrawals are included in the process.

The key differences between tray and packed columns also lie in performance characteristics. Packed columns, particularly those with structured packing, generally achieve lower pressure drops and higher efficiency in terms of mass transfer, as indicated by their lower HETP values. However, they are more sensitive to wetting issues and can be prone to corrosion and foaming. Tray columns, on the other hand, exhibit higher liquid hold-up and are better suited for handling suspended solids but come with higher capital costs and operational challenges in terms of pressure drop and efficiency.

In terms of construction, packed columns include several key features. They are equipped with manholes (P.U) that allow workers to perform maintenance. Liquid and vapor inlet tubes are accompanied by distributors to ensure an even distribution of liquid and vapor within the column. Redistributors are necessary when the column height exceeds 10 meters to prevent uneven mass transfer caused by vapor accumulation in the centre and liquid pooling at the boundaries.

In general columns also incorporate condensers, which can be partial or total. A partial condenser is used when the downstream process requires the distillate as a feed, while a total condenser is preferred when the distillate is the final product.

The reboiler, instead, can be thermosiphon (a,b) or Kettle (c).

The column’s skirt acts as a mechanical support and provides space for vapor to enter. Demisters are installed only for absorption or stripping processes, and the support grid serves as a mechanical structure that allows adequate vapor flow (Welded rings or plastic gri, Bars net or Structured grid).

Liquid distributors in packed columns come in various types, including perforated pipes, perforated plates, and designs with holes or chimneys. These are crucial for ensuring uniform liquid distribution across the packing material, which is essential for efficient operation.

The trays inside the columns are perforated circular plates with small holes that allow vapor to pass through while supporting liquid on the tray's surface. Under optimal operating conditions, the liquid flows down the column solely through the downcomer area. However, in less favorable conditions, liquid may pass through the holes in the plate, or vapor may flow through the downcomer section, both of which can negatively affect mass transfer efficiency.

At the end of each tray, a weir with a height “hw ” is installed to retain a certain amount of liquid on the tray, creating liquid hold-up and ensuring proper contact between the liquid and vapor phases before the liquid flows to the tray below. Additionally, the downcomer height is designed to regulate the flow of liquid onto the next tray, ensuring consistent operation throughout the column.

Over the holes different types of valves can be used, this influences the distribution of vapor in the tray.

6) Definition of NETP and HETP. Definition of NTU and HTU, and their calculation

HETP refers to the Height of the Equivalent Theoretical Plate and is commonly represented by the equation:

= ()()

Where NETP is the number of equivalent theoretical plates. The NETP can be determined using the McCabe-Thiele construction.

Unfortunately, there are no universally applicable models available in the literature to predict the value of HETP. Consequently, the aforementioned relationship can only be used for rating calculations and is not suitable for sizing the height of column packings.

Despite this limitation, the concept of HETP is valuable for assessing the efficiency of a packing section in terms of mass transfer: a lower HETP value indicates higher packing efficiency.

HTU (Height of Transfer Units) measures the height required for one transfer unit of mass transfer; a lower value indicates higher efficiency. NTU (Number of Transfer Units) represents the effectiveness of the mass transfer operation, calculated as the total height divided by HTU. Higher NTU values indicate more effective mass transfer processes.

Starting from the mass balances in the liquid and in the vapor for a packed column we have:

, = ∫ − , , = ∫ − , ,

These equation are commonly written in the form:

Where the = = = ()(), , , = =&