Orifice flows can lie
- 1. Orifice Flows Can Lie Orifice flow measurement not only needs compensation for temperature and pressure but also correction for inaccurate calculations. This article will simplify those calculation into a ready to use formula. Orifice flow meters are one of the most commonly used flow measurement devices used in the industry. They are cheap, easy to maintain, easily replaceable and generic. Typically the accuracy of these meters is within +/- 2% of measured value which is mostly acceptable to clients. But this accuracy is contingent on the calculation behind flow measurement using orifice, specifically flow correction for temperature and pressure changes. A flow meter reading can be completely off if wrong compensations are used. Let’s understand how flow is measured by an orifice. Orifice is simply a flow restriction with known behavior i.e. the performance or orifice w.r.t. flow can be defined quantitatively by using empirically established equations. Certain flow causes certain delta P under given conditions. In practical applications, the delta P produced across the orifice due to flow through it is used to estimate the flow. These calculations require temperature, pressure and density amongst other parameters and constants. The transmitters in plant uses design values of T, P and density (rho) to do these calculations whereas, in actual, the flowing conditions are often different. It is important to know how to correct the flow displayed on control board/DCS. This is what the article will talk about in a practical perspective. An abridged version of orifice equation goes like, (1) For gasses, we can write (2) (3) Where, V = Actual volumetric flow (Am3/hr) Rho = flowing density (kg/m3) Remember, the delta P measured by transmitter remains fixed for a given flow and conditions, it’s just the conversion of delta P to flow using equations that can be done differently to arrive at correct or incorrect values. The flow transmitter does these calculations by using the values fed into it, which are the design values. The required correction is to change the T, P, rho used in these calculations from design to flowing values. Since delta P is same, the uncorrected and corrected flows are related. Using previous equation, we get (4) Rearranging, we get (5) Where, subscript “old” refers to the design value being used in calculations and “f” means the properties at actual flowing conditions. Also, from ideal gas equation, we know (6) Where again, subscript “d” stands for design conditions (considered in orifice and flow meter datasheet). Using the two previous equations, the observed reading can be corrected to get actual reading. This is commonly done by a flow compensation feature in modern digital systems in DCS. The values of T and P needs to be imported to the calculation block configured in DCS and the flow value shown on control board/panel is then the compensated value. F Flow Compensation PT TTFT Flow Orifice Delta P based flow transmitter Pressure and Temperature transmitter Fig. 1: T and P compensation in Flow Transmitters Tushar Goel Chemical Engineer IIT (BHU), Varanasi
- 2. Above shown configuration is one of the most commonly used flow compensation system at the battery limit flows of plant for accurate measurement of import and export streams. Actual volumetric flow vs Normal volumetric flow But this is just the beginning of corrections and compensations. Many clients prefer their flow measurements represented on a standard or normal conditions for easy comparison. This makes it easy to communicate the flow values by eliminating the need to tell P and T every time the flow value is reported. Typically the normal conditions are 0 deg C and 1 atm i.e. the flow reported in Nm3/hr is always at 273.15 K and 1.033 kg/cm2a. where, Flowing Pressure (Pf) and Flowing Temperature (Tf) are expressed in units of kg/cm2 (g) and °C. As one can see, once again the use of T, P arises to covert the flows from actual to normal conditions. If flowing conditions (Tf, Pf) are not provided to the calculation block, design conditions will be used by default, which is again bound to give wrong flow values. Correcting the uncorrected flows represented at normal conditions (Nm3/hr) One of the tedious tasks for a process engineer is to correct the uncompensated and uncorrected DCS reading into correct flow measurements. The calculation to convert Am3/hr to Nm3/hr was done by DCS by using design T and P while actually the flowing T and P are different. This needs to be corrected. Below flowchart explain the process of doing the calculations. Let us consider an example: Td = 10 deg C Pd = 2.2 kg/cm2g Rhod = 3.8597 kg/m3 MWd = 28.03 Tf = 20 deg C (measured by instrument) Pf = 2.7 kg/cm2g (measured by instrument) MWf = 22.8 (as provided by laboratory sample analysis) Flow as shown on DCS screen = 4000 Nm3/hr which is uncorrected and uncompensated. Converting the Nm3/hr to Am3/hr (uncorrected) = 4000 ∗ ( 1.033 1.033+2.2 ) ∗ ( 10+273.15 273.15 ) = 1324.86 Am3/hr (uncorrected) Now, we know (7) 𝑟ℎ𝑜_𝑜𝑙𝑑 𝑟ℎ𝑜_𝑛𝑒𝑤 = (2.2 + 1.033) 2.7 + 1.033 ∗ 20 + 273.15 10 + 273.15 ∗ ( 28.03 22.8 ) So we get, rhoold/rhonew = 1.104717 Now using the correction formula from eq. (5) And finally converting the Am3/hr to Nm3/hr based on actual flowing conditions, we get The correct flow is 4688.83 vs 4000 Nm3/hr as shown on DCS screen which equals to 17% error in measurement. The above calculations are summarized in the following single formula for correction of gas flows reported in Nm3/hr: Convert the measured Nm3/hr to Am3/hr based on Design conditions The DCS system has incorporated a calculation which converts the Am3/hr to Nm3/hr based on DESIGN CONDITIONS. But the conditions have changed to FLOWING CONDITIONS, so you would like to undo those calculations. Correct this Am3/hr by using the orifice correlation. Convert the Corrected Am3/hr back to Nm3/hr based on actual flowing conditions The Am3/hr that we got in previous step was calculated based on ΔP observed across orifice. The conversion of ΔP to Am3/hr also involves T & P and Mol. Wt. Since these values have changed, we need to correct this conversion of ΔP to flow. Once the corrected Am3/hr based on actual MW, T and P is obtained, we need to convert it to Nm3/hr. This conversion has to be done based on FLOWING CONDITIONS and not the design conditions.