WELL PUMP SIZER INSTRUCTION MANUAL Sim J. Blake 25 JUN 95 COMPUTER PUMP MODELLING PROGRAM FOR WATER WELLS PROGRAM DESCRIPTION The Well Pump Sizer allows a user to size a pump for a water well or booster application. Input consists of: H vs. Q values for a pump curve, well specific capacity static water level, motor speed, number of stages and system outlet pressure or flow rate. Results returned are: flow rate (or outlet pressure, if flow rate is specified), total dynamic head, hydraulic horsepower and pumping water level. Motor speed, number of stages, pressure and flow may be quickly and easily varied, and the operating point on the curve is graphically shown. The program requires an IBM compatible PC; the program will run without a math coprocessor, but a coprocessor is used if present and is highly recommended. A graphics adaptor is not necessary, but a VGA or EGA graphics capability is required to display pump curves and take full advantage of the program. INTRODUCTION An important aspect of obtaining the optimum efficiency out of a water well is the sizing of the pump and motor combination. Centrifugal pumps, either alone or in a stacked multi-stage arrangement, are the type of pumps which are normally used in water well & booster installations; the purpose of the Well Pump Sizer is to aid in the selection of an appropriate centrifugal pump to use in a water well. The normal process for selecting a pump consists of taking a pump performance curve of head vs. discharge, a known or assumed system discharge pressure, a known well specific yield in flow per foot of drawdown and plotting an operating point on the curve. The efficiency is then determined by comparing the operating point to the pump efficiency curve. Plotting such an operating point is an iterative process if a constant discharge pressure is to be maintained. Normally, pump curves are supplied for a small range of stages, and occasionally for a range of speeds; if operation over different ranges of speeds or number of stages than provided by the pump data is desired, the curves must be rescaled and the process must be repeated until either a good combination of stages, discharge, outlet pressure, motor speed and efficiency is found, or the pump is found to be unsuitable. Even if one does not desire to rescale pump curves, the process can get quite lengthy if a lot of pumps or a wide range of conditions are to be looked at. The Well Pump Sizer provides an alternative to the hand graphical methods used to determine pump suitability and ideal operating conditions. The program allows the user to play "what if" with a pump curve and instantly determine pump operating points by varying such parameters as number of stages, motor speed, outlet pressure, flow rate, as well as determine the optimum operating point for the condition of maximum efficiency. An ideal combination of pump operating parameters may then be quickly arrived at. THEORETICAL BASIS The program is based on the following assumptions, and must be used within certain limitations to ensure accurate results and ease of use. In any case, it would be a prudent measure to verify by hand any result of the program to be used for design purposes. A. Well Modelling The well is assumed to be pumping water, with a linear specific capacity in GPM per foot of drawdown below the static water level, and a steady state condition is assumed; i.e. drawdown does not change with time. Static water level is the distance in feet below ground level where the water lies in a non-pumping situation; pumping water level is the static water level plus drawdown, which is the flow rate divided by the specific capacity. B. Pump Curve Modelling The pump curve input consists of from four to twenty head vs. flow points where head is in feet of water, and flow is in GPM. A cubic equation is then fitted to the points with H being a function of Q; this equation is formed each time an operating point is computed and is scaled according to the following centrifugal pump affinity laws for changes in stages or motor speed: H2 = H1 x (#STAGES2/#STAGES1) x (RPM2/RPM1)2 and Q2 = Q1 x (RPM2/RPM1) The point of maximum efficiency stays in the same relative position according to these laws. The affinity laws are valid and are good estimations of actual performance as long as the changes are not extreme. Variations of two or three stages and speed changes of up to about fifty percent have been observed to agree quite well with actual pump curves. C. Calculation of Total Dynamic Head The total dynamic head represents the total head that the pump must work against; it equals the pumping water level plus the outlet pressure head plus the kinetic head V2/2G. This program ignores the kinetic term which represents the energy needed to accelerate the water from a standstill to the velocity in the pipe. Even in extreme cases, this term usually accounts for less than 1 psi; the great majority of the energy imparted to the fluid by the pump is present in the form of static head. In practice, pipe sizes are normally chosen so that velocities are below ten fps (which is a kinetic head of 1.5 ft) in the interest of minimizing frictional losses. D. Treatment of Frictional Losses Frictional losses are not taken into account in the program; piping runs from the well to the distribution system are relatively short and insignificant. Beginning at the distribution system, the operating pressure is dependent on system dynamic effects which can only be predicted by a full scale hydraulic model of the distribution system. A well or water system booster pump is faced with a situation where it must pump into a fairly constant outlet pressure which is not dependent on the flow rate of the pump. This is in contrast to a process plant situation, where the length of the pipe runs are much shorter and the operating point of the pump is dependent on velocity induced frictional losses in the pipes. For this reason, the outlet pressure does not vary with flow. E. Calculation of Flow and Outlet Pressure By default, unless the flow is varied, outlet pressure is held constant and the flow calculated through variations of other parameters. Since H = f(Q), it is necessary to use a numerical equation solving routine to solve the cubic equation for Q; this assumes a solution in between two initial guesses of zero GPM and twenty five percent past the last curve point entered (which is used to flag for out of range operation). In order for the program to converge on the correct solution, all heads must decrease with increasing flow. The program will not accept curve points entered in violation to this rule; however, the pump curve must be examined to ensure that the fitted curve does not violate the rule. F. Determination of the Maximum Efficiency Point Efficiency is defined as power output/ power input; considering the input power of the pump to be constant, the maximum efficiency will be reached at the point of highest output power. Hydraulic horsepower (pump output power) is calculated for each point on the curve (in increments of 1/2000th of the maximum flow) and the highest horsepower found and its corresponding flow rate is recorded; this flow rate is the flow at maximum efficiency. In reality, pump input power is not constant and the efficiency is dependent on the relationship between input power and output power, so the actual point of maximum efficiency may be slightly off from that calculated by the program. OPERATIONAL INSTRUCTIONS Operation consists of the following general steps: 1) Enter pump curve points, 2) Enter data specific to the well, 3) Save the data for later use, 4) Perform the evaluation. Data may be entered either by the data entry options or by a file, if one has been created; the operational steps will be explained below. in all cases, selecting a menu choice is accomplished by either typing the selection number or the first letter of the item. A. Entering Data 1. Program startup The program name is PUMP.EXE; to start the program from the A drive, type "pump" (example - A:\> pump) at the prompt. It is highly recommended that the program be installed on a hard disk. The data files should be located in the same directory that the program has been started from in order to be able to list them. After starting the program, two menu choices will appear, "File operations" and "Evaluations and results"; select "File operations". 2. File entry If a data file is present, it can be entered. In the File Operations menu, select "Retrieve data file"; the screen will display all of the files in the current directory and a prompt to enter a filename will appear. If the desired data file is on another disk or directory, it can be selected by typing in the filename prefixed with the path. Upon entering the filename, the contents of the file will be displayed on the screen, and pressing a key will bring back the File Operations menu. 3. Pump Curve Entry In order to evaluate a pump, the pump curve and well specific data must be entered. Select "Pump curve entry" and enter the number of points; at least four are required, but up to twenty may be entered. If a number out of this range is entered, the prompt to enter the number of points will appear again. After entering the number of points, prompts will appear to enter H and Q values. The first point entered is the cutoff head, it must be the highest head, and its corresponding flow should be zero or a small value. Each successive head must be smaller than or equal to the previous, and each successive flow must be greater than or equal to the previous; any deviation will result in a prompt to reenter the point. Enter the number of stages and the rpm corresponding to the pump curve, changes in stages or rpm will use these values for scaling purposes. 1Fig. 1, Typical Pump Curves Points should be chosen with care; an attempt should be made to enter points on the inflection points of the pump curve, if present. It is not normally necessary to use all twenty points available, anywhere from four to six points can do a good job if they are chosen in the right places. Once the pump curve has been entered, the "Draw pump curve" selection should be chosen, if a graphics adapter is present, a pump curve will be drawn; if the curve does not match the shape of the supplied curve, reenter the curve choosing some of the points in slightly different locations. The curve fitting routine uses a "best fit" method to draw a smooth curve through the points. The curve is a third degree polynomial, which means it can have two inflection points (changes in curve direction). 4. Well data entry Select "Well specific data entry" and enter specific capacity, standing water level and outlet pressure as prompted. If the specific capacity is not known, or the application is for a booster drawing water out of a tank, etc..., choose a large number, such as 1,000 GPM/ft. This drawdown feature can also be used to roughly simulate pipe head losses in certain applications. If the outlet pressure and the standing water level combination exceeds the cutoff head of the pump curve, a warning message is given. 5. Saving the data file Once steps 4 and 5 have been completed, the data should be saved. Select "Save data file" and enter a filename in the DOS format. A recommended filename extension is . 6. Viewing the data file Selecting "View data file" will display the current data in memory on the screen until a key is pressed. This information is displayed automatically on the graphical result screen, but this feature is useful if graphics are not supported. B. Evaluation of Data In general, certain well design parameters are normally given. Outlet pressure is normally fixed at system pressure, typically around fifty to sixty psi, hence the program holds outlet pressure constant unless specifically changed, either directly or by specifying a flow or performing an efficiency optimization. Subsequent calculations hold the new outlet pressure constant. The general object is to pump curve/number of stages/rpm combination which will operate at a specified outlet pressure and flow at maximum efficiency. When any of the parameters are changed, the present value is displayed in parentheses and selected as the default if is pressed without entering a value. 1. Calculating results Select the "Evaluation and results" menu and choose "Calculate results". If graphics is supported, a graphical result screen will appear with the pump curve in a box covering the top left quadrant of the screen. Two green lines converging on a point on the curve indicate the operating point of the pump, and a green circle indicates the calculated point of maximum efficiency. The object of the evaluation is to end up with the corner formed by the lines within the circle, while keeping other parameters at a desirable level. White numbers at the origin of the curve graph indicate the cutoff head (Hc), and the maximum flow rate (Qm). Below the curve, a table of results indicates the flow rate, total dynamic head, outlet pressure, pumping and standing water levels, percentage of the maximum efficiency (not the efficiency itself), and the hydraulic horsepower. The upper right quadrant displays the original curve points entered, and the lower right quadrant contains the polynomial equation for the pump curve. 2. Optimization for efficiency Select "Efficiency optimization" to set the flow rate equal to flow at the calculated maximum efficiency, when "Calculate results" is selected, the result screen will indicate the outlet pressure and flow rate at maximum efficiency, and the percentage of maximum efficiency will indicate 100 %. The percentage of maximum efficiency gives a relative indication of how close to top efficiency the pump is operating; the actual efficiency at any point can be easily determined by dividing the hydraulic horsepower by the input horsepower, if given, or from the supplied pump curve. The calculated efficiency point may be slightly off of the actual point of maximum efficiency depending on the variation of input to hydraulic horsepower (the program assumes a constant input horsepower), but it will be close. In any case, data from the actual efficiency curve should take precedence. 3. Changing number of stages Normally, adding or subtracting stages is the way to increase or decrease flow. Adding a stage increases the pump's head, causing it to fall back on the curve and operate at a higher flow rate at a constant outlet pressure. The stages can be changed in increments of one by selecting "Stage number change". If a "Calculate results" is performed and the total head required exceeds the head available from the pump, a warning message indicating that not enough stages are present displays, and the number of stages is automatically incremented by one. Repeated selections of "Calculate results" will add a stage until enough are present to start pumping. If the message appears, be sure to check on the number of stages present. When the pump curve is plotted on the result screen, it is scaled for the original data conditions; if the number of stages is reduced, it will be scaled down, but if the number of stages is increased, it will not be scaled up. Regardless of how the displayed curve is scaled, the results will be correct. 4. Changing motor speed Normally, three phase alternating current induction motors are used to drive pumps. Unless a variable frequency drive unit is to be used to control the motor (or an internal combustion engine or other variable speed motor is used), speed increments should be chosen corresponding to the synchronous speeds of alternating current motors with speed reduced three to five percent for slip. For example, the synchronous speed of a two pole motor is 3600 rpm, for a four pole motor it is 1800 rpm, etc.... Speed can only be varied in these increments. Speed is changed by selecting "Motor speed change". As with the case of changing the number of stages, the displayed curve will be scaled down but not up. 5. Changing outlet pressure Outlet pressure is changed by selecting "Outlet pressure change". If the warning message "Too few stages to pump anything" appears, and the addition of a stage is not desirable, the calculation may be performed by changing the outlet pressure to a lower value and resetting the number of stages to the desired level (it is automatically incremented if there are not enough stages). 6. Changing flow rate Flow rate is changed by selecting "Discharge flow rate change". Setting the flow rate causes a new outlet pressure to be calculated; the flow rate is then calculated from the new outlet pressure as a check. EXAMPLES As an example, a step by step procedure for evaluating a hypothetical pump will be given. Four example files are supplied; EX1.DAT, EX2.DAT, EX3.DAT and EX4.DAT. These are typical examples of pump curves; it is recommended that one or more of the files be retrieved and experimented with so that the operation of the program and the dynamics of pump behavior may be observed. A. Program Familiarization In this example, familiarity of the program will be gained by entering data and observing the result of varying motor speed. 1) Start the program and enter the following pump curve information. Enter <4> for the number of curve points, and enter the following points: H1 = 500, Q1 = 0; H2 = 470, Q2 = 500; H3 = 350, Q3 = 1000; H4 = 25, Q4 = 1500. Enter <5> for number of stages, and 1745 for RPM. 2) Enter the following well specific information: <65> for the specific capacity, <155> for the standing water level and <40> for the outlet pressure. 3) Save the file by selecting "Save current data file" and entering at the prompt. 4) Select "Draw pump curve" and note that the line passes through all four points, and press any key when finished. 5) Enter the Evaluation and Results menu and calculate the results. Note that the operating point is outside of the position of maximum efficiency, also observe that the flow rate is 1175 GPM. Press a key to return to the menu, perform an efficiency optimization and recalculate; note the flow rate has been set at 965 GPM and the outlet pressure is now 84 psi. 6) Change the motor speed to 1500 RPM and perform an efficiency optimization (this is useful for avoiding out of range operation when making large speed changes), then calculate. Observe that the curve has been scaled down; by default the original curve is scaled to the largest size available; if a higher RPM was chosen, the curve would not have changed size, although the shape might change slightly. The flow rate is 829 GPM and the outlet pressure is now 44 psi. B. Selecting an Operating Point In this example, the ideal operating point and number of stages of a pump will be determined. 1) Start the program and enter the following pump curve information. Enter <4> for the number of curve points, and enter the following points: H1 = 500, Q1 = 0; H2 = 470, Q2 = 500; H3 = 350, Q3 = 1000; H4 = 25, Q4 = 1500. Enter <5> for number of stages, and 1745 for RPM. 2) Enter the following well specific information: <65> for the specific capacity, <155> for the standing water level and <40> for the outlet pressure. 5) Enter the Evaluation and Results menu and calculate the results. Note that the operating point is outside of the position of maximum efficiency, also observe that the flow rate is 1175 GPM. Press a key to return to the menu, perform an efficiency optimization and recalculate; note the the flow rate has been set at 965 GPM and the outlet pressure is now 84 psi. 6) Let's say we want a flow rate of 1500 GPM to match the existing demands. We simply add a stage, perform an efficiency optimization and recalculate; we repeat this step until we are pumping over 1500 GPM, and we select the number of stages that gives us the closest flow to 1500 gallons per minute.