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Category: Calculation

How to Easily Estimate the Time Needed for the Vessel to Collapse

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In this post, I want to share to you how to easily estimate the time needed for the vessel to collapse. The equation involves several simple and basic equation, such as conservation principle and adiabatic compression equation. Let’s dig into the example.

There is a thermally insulated vessel initially at atmospheric pressure and partially filled with water. The vessel is fed with additional water at a constant flow rate of 2 m3/h. The air contained in the vessel headspace is compressed as the additional water is fed. The vessel can withstand a maximum pressure of 3 atm absolute. Read More

How to Calculate Partial Volume of Horizontal Vessel with Ellipsoidal Heads

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In this post, I want to share with you how to calculate partial volume of horizontal vessel with ellipsoidal heads. Basically, the horizontal vessel consists of cylinder and two heads. Thus, the total volume will be:

Total volume = volume of liquid in two heads + volume of liquid in cylinder
Total volume = 1/6 π K1 D3 + 1/4 π D2 L

Where:

K1 = 2 b/D

b, D, and L are function of vessel geometry. Please see figure below. Read More

How to Estimate Time Required for Heating or Cooling

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In this post, I want to share how to estimate time required for heating and cooling.

The contents of a large batch reactor or storage tank frequently need to be heated or cooled. In this circumstance, the physical properties of the liquor may change throughout the process, as well as the overall transfer coefficient. When estimating the amount of time needed to heat or cool a batch of liquid, it is frequently possible to assume an average value for the transfer coefficient. Steam condensing, either in a coil or some type of hairpin tube heater, is a common method for heating the content of storage tank.

It is reasonable to assume that the overall transfer coefficient U is constant in the context of a storage tank filled with liquor having mass m and specific heat Cp and heated by steam condensing in a helical coil. The rate of heat transfer is given by: If T s is the temperature of the condensing steam, T1 and T2 are the initial and final temperatures of the liquor, A is the area of the heat transfer surface, and T is the temperature of the liquor at any time t, then:

The time t for heating from T1 to T2 can be determined using this equation. If the steam condenses in a reaction vessel’s jacket, the same analysis may be applied.

Heat losses during the heating or, for that matter, cooling operation are not considered in this analysis. The heat losses increase naturally as the temperature of the vessel’s contents rises, and at a certain point, the heat supplied to the vessel equals the heat losses, making further increases in the temperature of the vessel’s contents impossible.

By increasing the rate of heat transfer to the fluid, for example, by agitating the fluid, and by minimizing heat losses from the vessel by insulation, the heating-up time can be shortened.

The amount of agitation that can be achieved in a large vessel is constrained, thus one attractive alternative is to circulate the fluid through an external heat exchanger.

Let’s see example below on how to estimate time required for heating or cooling. Read More

Preliminary Sizing of Hydrocyclones

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In this post, I want to share how to do preliminary sizing of hydrocyclones. In previous post, hydrocyclones are utilized for solid-liquid separations. The centrifugal force is produced by the motion of the liquid in this centrifugal device, which has a stationary wall. Like a gas cyclone, the gas cyclone operates on much the same principles. Hydrocyclones are inexpensive, reliable separators that work with particle sizes ranging from 4 to 500 micron. Figure below shows hydrocyclones typical proportion geometry.

Hydrocyclone typical proportion
Hydrocyclone typical proportion

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Basic Sizing Equation for Sedimentation Centrifuges

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In this post, I want to share basic sizing equation for sedimentation centrifuges. Based on previous post, sedimentation centrifuges used to separate materials based on the density difference between the solid and liquid phases. They are usually used to produce cleared liquid.

Basic sizing equation for sedimentation centrifuges use the term sigma (Σ). The sigma is used to describe a performance of a centrifuge regardless of the physical characteristics of solid-fluid system. The sigma value is equivalent to the cross-sectional area of a gravity settling tank with the same clearing capacity. The sigma value is often expressed in cm2.

The sigma theory is a description of how centrifuge performance is described. It offers a way to compare sedimentation centrifuge performance and to scale up from laboratory and pilot scale experiments. Read More

How to Estimate Thermal Conductivity of Liquid

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Thermal conductivity of a material is a measure of its ability to a particular material conduct heat. In the international system of units (SI), thermal conductivity is measured in watts per meter-kelvin (W/(m.K)). In imperial units, thermal conductivity is measured in BTU/(h·ft·oF).

Thermal Conductivity of Solids

Solid composition, shape, structure all affect how well it conduct heat. Many handbooks provide thermal conductivity of solids for frequently used engineering materials.

Thermal Conductivity of Liquid

Equation below can be used to estimate thermal conductivity of liquid.

Estimate thermal conductivity of liquid
Estimate thermal conductivity of liquid

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How to Estimate Density of Liquid Mixture

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In this post, I want to share how to estimate density of liquid mixture. This calculation is very simple yet useful for process engineers.

Density of liquid mixture can be estimated from density of pure components in the mixture. Many handbooks have a large database of density of pure liquids. Density of most organic liquids usually lies between 800 and 1000 kg/m3, except than those containing a halogen or other “heavy atom”.

Density at normal boiling point can be obtained from the molar volume. Read More

Material Balances involving Unsteady-State Process

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In previous posts, I shared how to calculate material balances of several cases. Those calculation involve steady-state condition. In steady-state process, the accumulation is zero. The streams flowrate and composition are also did not vary with time. The calculation are more complex if these conditions are not met. The unsteady-state behaviour of a process is important when considering the process start-up and shut-down, and the response to process upsets.

Unsteady-state material balances are solved by setting up balances over a small increment of time, which results in a set of differential equations that describe the process. These equations can be solved analytically for simple problems. Computer-based methods would be employed for more difficult problems.

Example below is an example of general approach used to solve un-steady state problem. Read More

Material Balances Calculation Involving Purge Process

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Bleeding off a portion of the recycle stream is important in a production process to avoid the accumulation of undesirable material. For instance, if inert components from a reactor feed are not separated from the recycling stream in the separation units, they would build up in the recycle stream until they made up the whole stream. To keep the inert level within reasonable level, some of the stream would need to be purged. Normally, a continuous purge would be employed. Assuming steady-state circumstances:

Loss of inert in the purge = Rate of feed of inerts into the system

The concentration of any component in the purge stream will be the same as that in the recycle stream at the point where the purge is taken off. Consequently, the relationship shown below can be used to calculate the necessary purge rate:

[Feed stream flowrate] × [Feed stream inert concentration] =

[Purge stream flowrate] × [Specified (desired) recycle inert concentration]

Let’s see example below. Read More