『Original by HaiChuan Translation Team: Pressure drop in fixed (single-phase tube packing) bed reactors

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English title: Pressure Drop In Fixed (Single Phase Tubular Packed) Bed Reactors. Original link: Click here. Original author: ankur2061. Translator ID: @Yaya_ITZK. Those who wish to subscribe to the articles published by the “Haichuan Translation Group” are invited to leave a message below saying “I want to subscribe” or send me a private message; I will notify everyone as soon as new articles are available. Hello everyone, today’s topic relates to the pressure drop in fixed-bed reactors. Let’s examine the factors that can cause a pressure drop in a fixed-bed reactor from a theoretical perspective. The design pressure drop should take into account the safety limit of the theoretical pressure drop. “\"Pressure drop\": For both gases and liquids, this is calculated using Euler’s equation: (ΔP/L) = K*Re*(150 + 1.75*Re)*((1 – ε) / ε)^3*(μ^2 / (ρ*Dp^3)). Here, (ΔP/L) represents the pressure drop of the bed in kPa/m or psi/ft; Re is the Reynolds number, a dimensionless value; W*Dp/(μ*(1 – ε)) represents another dimensionless quantity; and ε is the porosity, also a dimensionless value. Porosities of freshly packaged catalysts vary depending on the type of catalyst and the method of packing: For 1/16 inch (1.6 mm) cylindrical catalysts with sock-style packing, the porosity is 0.45; with compact packing, it is 0.35. For 1/20 inch (1.3 mm) and 1/10 inch (2.6 mm) catalysts using ASQ sock-style packing, the porosity is 0.47; with compact packing, it is 0.40. For 1/8 inch (3.2 mm) catalysts packed in a sheet-like manner, the porosity is 0.41. μ represents the viscosity of the gas or liquid under the given conditions, in Kg/m. (pounds/ft·hr) K = dimensional constant = 0.001 (Metric) = 1.665E-11 (USC) ρ = density of the gas or liquid under the current conditions, kg/m3 (lb/ft3) Dp = equivalent particle diameter, m (ft) W = mass flux of the liquid or gas based on the reactor cross-sectional area, kg/s·m2 (lb/hr·ft2) The equivalent particle diameter is used to calculate the column pressure drop, using the following formula: Dp = 3*D*L / (2*L + D), where Dp = equivalent particle diameter in m (ft), D = actual particle diameter in m (ft), and L = average particle length in m (ft). The “Euler” constants are 150 and 1.75, which were determined by fitting pressure drop data from various particle systems. For particles with given special shapes, using this equation and these constants can sometimes lead to significant errors in pressure drop prediction. Furthermore, errors often occur in pressure drop calculations due to the estimated porosity and equivalent particle diameter of the bed. These errors are caused by the uncertainties in particle density and particle size. Stocking method of loading: Before the 1970s, the standard method for filling catalysts in fixed-bed reactors was the stocking method of loading. During the sock-type loading process, a canvas pipe transports the catalyst from the reactor manway inlet to the bottom of the reactor catalyst bed. This canvas pipe is attached to the feed hopper or funnel at the reactor inlet; in this way, the catalyst is placed on the reactor bed using bags, preventing individual particles (especially those that are cylindrical in shape) from remaining in a stable, stationary position. Cylindrical catalysts are stacked at various horizontal and vertical positions. Cylindrical catalysts are stacked in a random direction, resulting in bridges and gaps between the catalysts. During the operation of the reactor, these bridges and gaps tend to collapse. Bed density increases as bed depth decreases. Compact packing: Since 1970, refineries, catalyst manufacturers, and catalyst loading contractors have developed compact packing equipment that can significantly reduce voids and bridging. Tight packing can increase the catalyst bed density by 17%. Furthermore, unlike sock-type addition, tight addition does not require a person to enter the reactor to distribute the catalyst evenly. Workers inside the reactor need to breathe air and wear shoes with a weight distribution to prevent them from crushing the catalyst. By introducing catalyst particles (specifically cylindrical ones) into the reactor, each cylinder can fall freely onto the catalyst surface, thereby achieving a compact packing. Before being struck by other cylindrical catalysts, an individual cylindrical catalyst is assumed to be in a horizontal, stationary position. In this case, the cylindrical catalyst tends to be placed horizontally to minimize the possibility of bridging or the formation of voids. Pressure drop caused by bed rise: In the less common upward flow operation in reactors, the pressure drop calculated from the equation above must remain below the pressure drop caused by theoretical bed rise; ideally, it should be less than 50%, and in any case not exceed 75%. The theoretical pressure drop caused by the rise of the bed is given by: (ΔP/L)BL = K*(ρp – ρ)*(1 – ε). Here, (ΔP/L)BL represents the theoretical pressure drop caused by the bed rise, in kPa/m (psi/ft). ρp is the density of the catalyst particles, in kg/m3 (lb/ft3). ρ is the density of the gas and liquid under the current conditions, in kg/m3 (lb/ft3). ε is the porosity of the bed, dimensionless. K is a dimensional constant, equal to 0.0098 for metric units and 0.00694 for USC units.

The pressure drops at the inlet of the nozzle are determined by the following formulas: ΔPe = (K*ρ*(UL – UI)^2) / 2, ΔPi = (1.3*K*ρ*UI^2) / 2, and ΔPb = (0.5*K*ρ*UL^2) / 2. Here, ΔPe represents the pressure loss due to the sudden expansion of the pipeline connecting the inlet of the distributor to the expansion section, in kPa (psi). ΔPi represents the pressure drop caused by the gas hitting the bottom of the distributor, in kPa (psi). ΔPb represents the pressure drop resulting from the gaps at the inlet of the distributor, in kPa (psi). ρ is the density of the gas and liquid under the current conditions, in kg/m3 (lb/ft3). UI is the flow velocity in the expansion section at the inlet of the distributor, in m/s (ft/sec). UL is the flow velocity in the external pipeline, in m/s (ft/sec). K is a dimensional constant, equal to 0.001 for metric units and 2.156E-4 for USC units.

The pressure drops at the sampler and the outlet nozzle are given by the following formulas: ΔPs = (2.8*K*ρ*US^2) / 2, ΔPc = (0.5*K*ρ*UL^2) / 2. Here, ΔPs represents the pressure drop due to leaks through the holes and the sampler slots, in kPa (psi). ΔPc represents the pressure drop caused by the sudden contraction at the outlet nozzle, in kPa (psi). US is the flow velocity through the holes and slots, in m/s (ft/sec). K is a dimensional constant, equal to 0.001 for metric units and 2.156E-4 for USC units