Fluid Properties: := 1.35 cp liquid viscosoty. m 3 density of the flowing liquid. sg:= specific gravity of the flowing liquid. Pipe System Conditions:

Transcription

1 Control Valve Selection August 17 th 1997 Andrés Felipe Ortega Montoya Chemical Engineer - Universidad Pontificia Bolivariana - Medellín, Colombia. E - Mail: aortega@janua.upb.edu.co I originally obtained this problem from the Mathcad web site. As far as I know the individual above is the original author. However, I have cleaned up the english a little and added additional documentation and comments to make the document suitable for my undergraduates. In the flow control of a process line, the degree of linearity between flow and valve stem position of any valve in the line is important if the purpose of the valve is to produce a specified flow in the system. In this document, I'm proposing a method to detere which type of control valve should be used in a pipeline system. Fluid Properties: m : 1.35 cp liquid viscosoty r : 870 kg m 3 density of the flowing liquid r : specific gravity of the flowing liquid r w Pipe System Conditions: o : 15...operating flow Dz : m...difference in elevation static elevation of the liquid (if positive, discharge is higher than suction). Ps: 0 psi...suction pressure P d : 1.5 psi...discharge pressure D: 1.5 in...pipe diameter. e : 0.3 mm...equivalent sand grain pipe roughness. L : 30 m...total pipe length. LeqD : 13...total equivalent length over diameter for the accessories in the pipe system (SLeq/D), except for the control valve. last save E:\public_html\ 1 of 10

2 pump discharge pump suction free surface pump, characterized by pump curve, Hp f() valve, characterized by stem position, x and f(x) We desire to chose a valve such that we can produce a specified flow with a specified valve setting Pump Curve equation (if there isn't a pump, H() 0. m): : o o, o The form of of a standard pump curve equation is usually parabolic : H pump ( ) a b c last save E:\public_html\ of 10

3 H p ( ) : 15 m m m here: a 10 b.005 c.006 a, b and c are coefficients specific to the pump H p ( ) m Pump Curve head on pump vs pumped flowrate Now develop an equation for the system curve. First estimate the friction factor, f, using the Hsi-Jen-Chen equation: a 5.0 b Hsi-Jen-Chen equation for the friction factor. f( Re, k) log k a b Re log k a b Re log k a b Re log k a b Re log k a b Re log k 14 + b Re This equation says that the friction factor is a function of the Reynolds number, Re, and and constant k, which turns out to be the relative roughness of the pipe, e/d last save E:\public_html\ 3 of 10

4 Now write the Bernoulli equation between the suction and discharge side of the pump P s r g v s l v + z s + f g d g p d r g + z d + v d g Dz z d z s v g kinetic energy terms neglected at the suction and discharge of the pump v p D 4 LeqD represents the accumulated L/D (equivalent length)/(pipe diameter) for the fittings P s r g P d r g + Dz f Re, e l + D D + LeqD 1 4 p D In general, the head developed within the "system" through which the pump pumps is equal to: system head (ft) discharge head (ft) + system losses (ft) - suction head (ft ) P d 4 r e L H s ( ) + Dz f, r g p D m D D + LeqD Ps : g p D...system head curve r g last save E:\public_html\ 4 of 10

5 Plot pump and system curves. The operating point of the pump lies at their intersection: o o :, o range of flows used for each curve 15 Plot showing pump operating point H p ( ) m H (m) H s ( ) 8.3 m operating point of the pump FLOWRATE Pump Head Curve System Head Curve operating point for the pump,, 33. Control Valve. The control valve must "use up" the head difference between the pump curve and system head curve to achieve a specified flow value. For the control valve, the following equation is used with Dp expressed in psi and in GPM: C v f( x) Dp C v is a unitless loss coefficient that characterizes the head loss across the valve f(x) is called the inherent characteristic of the valve. Its value is a function of the position of the valve stem, x. Both x and f(x) vary from 0 (closed valve) to 1 (open valve). Solving for C v* f(x) last save E:\public_html\ 5 of 10

6 C v f( x) ( H p ( ) H s ( ) ) r g psi ( H p ( ) H s ( ) ) r g is the difference in head between the system curve and pump curve at the desired flow. This is the head that must be "used" by the valve. In this problem we desire that should be a linear function of x. It is further desired that when x 0.5, o, then: ( x) o x 0.5 therefore: ( x) : o 0.5 x and the required value of loss coefficient, C v may be calculated as follows: ( 1) C v : ( H p ( ( 1 ) ) H s ( ( 1) ) ) r g psi C v The inherent characteristic, f(x) of some commercial valves are: Linear Trim: f l ( x) : x Equal Percentage Trim: f eq_% ( R, x) : R x 1 Parabolic Trim: f p ( x, n) : x n...where R is called the range ability and may be calculated max as R where and are the highest and max lowest flow where the valve preserves it's inherent characteristic. last save E:\public_html\ 6 of 10

7 The desired inherent characteristic for our system may be calculated as: ( x) f( x) : C v ( H p ( ( x ) ) H s ( ( x) ) ) r g psi We desire to purchase one of the aforementioned types of values with values of R and/or n such that its trim function is similar to our desired trim function, f(x). x : , R :.75 n : Valve characteristics f(x) Desired valve trim Linear Trim Equal Percentage Trim Parabolic Trim x last save E:\public_html\ 7 of 10

8 Once we select the valve, one can see the effect of the value of valve stem position, x, on the system head curve. For example, if we choose an equal percentage valve, f( x) : f eq_% ( x, R) : o o, o ( ) r Now the head produced as a result of adding the valve must be: H p ( ) H s ( ) this quantity using the basic expression for the flow through a valve. g. We can solve for C v f( x) ( H p ( ) H s ( ) ) r g psi C v f( x) 1 ( H p ( ) H s ( ) ) r g ( H p ( ) H s ( ) ) r g C v f( x) Now, add the head created by the addition of the valve to the system head curve: Hsv(, x) : H s ( ) + 1 C v f( x) lb in r g where Hsv(,x) is the system loss for a specified flow and valve stem setting last save E:\public_html\ 8 of 10

9 We can then set the value of x ( x : 0.5 ) and obtain the system head curve including the value with the specified stem position: 15 Effect of valve on system head curve 13.5 H (m) , H 1, H (GPM) Pump Head Curve System Head Curve, no valve System head curve with equal percentage control valve We can compute and plot the "installed characteristic of the valve", defined as the flow in the system as a function of the position of the valve stem, x: x : , valve stem position H p ( ) Hsv(, x) : o ( x) : root, m The root function solves for the value of necessary to satisfy the head loss for each valve setting last save E:\public_html\ 9 of 10

10 /max Valve Characteristic valve stem position, x When the valve stem is set at x 0.5 the relative flow rate,, is 0.9 of the maximum flow rate, max. When the valve is closed (x0) the flow equals zero and when the valve is open (x1) the flow equals max Bibliography. W.L. Luyben: Process Modeling, Simulation and Control for Chemical Engineers. McGraw-Hill, nd ed. New York, Constants. r w 1 gm cm 3 cp 10 poise last save E:\public_html\ 10 of 10