METHOD FOR CALCULATING THE VISCOSITY PERFORMANCE OF A PUMP FROM ITS WATER PERFORMANCE CHARACTERISTICS AND A NEW DIMENSIONLESS PARAMETER FOR CONTROLLING AND MONITORING VISCOSITY, FLOW, AND PRESSURE

Abstract

This paper introduces a dimensionless relationship between volumetric flow rate, head, and kinematic viscosity in pump operation and a method that uses this dimensionless relationship to predict a pump's viscosity performance from the water's performance characteristics. Using the presented dimensionless relationship, called the Ketan viscosity head number, the method determines a viscosity head correlation that allows for the accurate prediction of pump performance at any given speed, flow rate, and viscosity. The Ketan viscosity head number and the method presented thus allow for the prediction of pump performance in a viscosity application based on water performance characteristics without physically evaluating the pump in that application.

Description

METHOD FOR CALCULATING THE VISCOSITY PERFORMANCE OF A PUMP FROM ITS WATER PERFORMANCE CHARACTERISTICS AND NEW DIMENSIONLESS PARAMETER FOR CONTROLLING AND MONITORING THE VISCOSITY, FLOW AND PRESSURE BACKGROUND OF THE INVENTION Centrifugal pumps have been developed and used for centuries in handling viscous fluids. The performance of a centrifugal pump is affected by several factors, such as viscosity, speed, stage diameter, flow rate, and the pump's hydraulic design. Generally, a pump is evaluated in water under atmospheric conditions, and its performance at a fixed speed is used to select the pump and the number of stages. Predicting a pump's performance in a viscous application is very difficult, as performance depends on pump speed, viscosity, and flow rate. For a given viscosity application, a pump is typically evaluated in various viscous fluids over a range of speeds, and the test data is interpolated. This analysis has proven to be a lengthy and expensive process.Furthermore, interpolating and modeling performance for use in an application is complex and introduces inaccuracies in performance prediction. Ref. 330682 BRIEF DESCRIPTION OF THE FIGURES Reference is now made to the following descriptions taken in conjunction with the accompanying figures, where: Figure 1 is a graph of a relationship between normalized flow rates and normalized Ketan viscosity head numbers for a pump in water at a given RPM; Figure 2 shows graphs of relationships between normalized flow rates and normalized Ketan viscosity head numbers for a pump in various viscous fluids at a given RPM; Figure 3 is a flow diagram of one modality of a method for predicting the performance of a given pump in a fluid of interest having a desired viscosity at a desired RPM; Figure 4 is an illustration of performance curves for an example pump; Figure 5 is a flowchart of one modality of a method for modeling the performance characteristics of a pump in a viscosity application; Figure 6 is a block diagram of one type of computer system implemented according to the principles described; and Figure 7 is an example viscosity application of an electric submersible pump (ESP). zr l ίηη / ζζηζ / Ε / γίΛΐ DETAILED DESCRIPTION OF THE INVENTION Electric submersible pumps (ESPs) have been used to pump oil from underground formations since the 1930s. An ESP is a multistage centrifugal pump with a few to hundreds of stages operating at varying speeds, for example, from 1,500 revolutions per minute (RPM) to 8,000 RPM, and can pump from a few hundred to a few hundred thousand barrels per day (BPD). Selecting a pump size for a given viscosity application includes choosing a stage type, the number of pump stages, (optional gas separator), seal (shield), and motor. Predicting the performance of an ESP in viscosity applications, especially in marine applications, is particularly important and requires greater accuracy than that provided by conventional prediction tools. This is because operating a marine application is very expensive, and even a small difference in sizing and predicting the correct pump type can result in losses of several million dollars. To determine the appropriate size of a pump stage for a viscosity application, it is necessary to know its performance at various viscosities. Generally, a pump with few stages is built and tested at desired viscosity and speed ranges in a testing facility before being sized and used in the specific application. The test results are used to predict the pump's performance in the specific application, such as a marine production application, and this prediction is used to select the appropriate size of the pump and its motor before use. This process of building, testing, analyzing, modeling, and predicting is not only very expensive and time-consuming but also imprecise, as viscosities and speeds can vary widely depending on the specific application. This document introduces a dimensionless relationship between volumetric flow rate, head, and kinematic viscosity that simplifies the prediction of pump viscosity performance. The relationship presented is referred to throughout as a Ketan viscosity head number and is expressed as Equation (1): Ketan viscosity head number = q / h*v Equation (1), where q is a volumetric flow rate, h is a head and v is a kinematic viscosity. The head is a function of flow rate, speed, stage diameter, and hydraulic design of the pump; the flow rate is affected by the speed, stage diameter, and hydraulic design of the pump; and kinematic viscosity is a fixed fluid property. The Retan viscosity head number can also be represented in different ways as shown in Equations (2) and (3) below: (q*p) / (p*v) = mass flow rate / (pressure * kinematic viscosity) Equation (2), (q*p) / (h*p) = mass flow rate / (head * absolute viscosity) Equation (3) , where p is a density, p is a pressure and μ is an absolute viscosity. The Retan viscosity head number represents a measurement of a pump's performance condition: a ratio of flow rate to head at a given viscosity. In other words, it is a ratio of volumetric or mass flow rate to head or pressure at a fixed internal resistance or viscosity. The Retan viscosity head number can be calculated using the published water performance characteristics of a given pump at a fixed speed (RPM) using Equation (1). The water performance characteristics of a given pump are generally available from the pump manufacturer and are provided as a pump curve, plotted against flow rate, head, and brake horsepower (BHP) at a fixed speed, e.g., 1 RPM. In general, the water pump performance characteristics of an ESP pump are published at 50 Hz (2917 RPM) and / or 60 Hz (3500 RPM) depending on the pump's primary application. Figure 1 illustrates a relationship between normalized flow rates and normalized Ketan viscosity head numbers for a pump in water at a given RPM. This relationship varies with changes in pump design and is also a function of the specific pump speed. It can be used to predict pump viscosity performance at different RPMs and in different fluids. Relationships beyond this are referred to as the Ketan viscosity head number correlation. The normalized flow velocities 110 on the x-axis are determined using the pump's water performance characteristics. The flow velocities from the water performance characteristics are normalized by using a flow velocity at a reference point, for example, the best efficiency point (BEP), for a given RPM. The BEP refers to a point on a pump curve where efficiency is highest. For normalization, each of the flow velocities can be divided by the BEP flow velocity. The standardized viscosity head numbers of Ketan 120 viscosity head numbers at the shaft are determined using the pump's water performance characteristics. Using Equation (1) and the flow rates, viscosity, and heads from the water performance characteristics, the Ketan viscosity head numbers are first calculated. Since the flow rates and heads are derived from the water performance characteristics, the viscosity is 1 centipoise. The calculated Ketan viscosity head numbers are then normalized using a Ketan viscosity head number at the reference point, e.g., BEP. Similar to the normalized flow rates 110, each of the Ketan 120 viscosity head numbers is divided by the Ketan viscosity head number at the BEP for normalization. Figure 2 illustrates 200 relationships between the various standardized flow rates 210 and the standardized Ketan viscosity head numbers 220 for the same pump at the same RPM, but at different viscosities in Figure 1. Unlike the 100 relationship in Figure 1, the 200 relationships are for fluids other than water. The fluids include a first fluid having a viscosity of 6 centipoise (empty square), a second fluid having a viscosity of 9 centipoise (empty triangle), a third fluid having 19 centipoise (solid rectangle), a fourth fluid having 35 centipoise (empty diamond), a fifth fluid having 50 centipoise (X), a sixth fluid having 90 centipoise (empty circle), a seventh fluid having 100 centipoise (solid square), an eighth fluid having 140 centipoise (solid triangle), a ninth fluid having 244 centipoise (+) and a tenth fluid having 541 centipoise (£). As shown, while fluids and their viscosities differ, their viscosity head number correlation—that is, the ratio between their normalized flow rates and the normalized Ketan viscosity head numbers—remains the same. Therefore, a Ketan viscosity head number correlation for a pump in water at a given RPM, for example, 100 and 200 in Figures 1 and 2, can be used to predict pump performance in a viscosity application. Figure 3 illustrates a flowchart of one modality of Method 300 for predicting pump performance in a fluid of interest at a desired RPM. Method 300, or at least a portion of it, can be performed by a computer system, such as 500 in Figure 5. A series of instructions that, when executed, cause a computer system's processor to perform Method 300 can be stored on a computer-readable medium, such as a CD-ROM, a floppy disk, flash memory, or other data storage device. Method 300 begins at step 305. In step 310, the application parameters for the pump are defined. These parameters may include: the fluid of interest (desired viscosity) in which the pump will operate, a desired flow rate (the flow rate at which the operator wants the fluid of interest to move), a desired speed (the RPM at which the operator wants to operate the pump motor), and a desired pump (the pump may have a different diameter and number of stages depending on the application and the stage at which the operator wants to operate the pump). In step 320, the pump's water performance characteristics at a fixed RPM are received. The fixed RPM may be one of the RPMs, such as 3500 RPM, 2917 RPM, and / or 1750 RPM, at which the pump manufacturer publishes and provides the pump's water performance characteristics. The water performance characteristics may be in the form of a performance curve plotted with respect to flow rate, head, and BHP at a given RPM. The pump's BEP water performance characteristics may be indicated on the performance curve, and if not indicated, the BEP water performance characteristics may be interpolated from the curve. It should be understood throughout the description that the water is assumed to have a viscosity of 1 centipoise and an ambient temperature of 20°C. In step 330, the specific pump speed is calculated, i.e., the desired pump speed. The specific pump speed is calculated using the pump's BEP water performance characteristics at a fixed RPM, which are obtained in step 320. A specific speed is a number that uniquely and consistently characterizes the type of impeller in a pump. A specific speed is determined independently of the pump size and can be useful for comparing different pump designs. The specific speed is calculated using Equation (4). Ns = (n*qA0.5) / (ύL0.75) Equation (4), where Ns = specific speed, n = rotational speed of the pump shaft (rpm), q = flow rate (m3 / h, 1 / s, 1 / min, m3 / min, US gpm, UK gpm) at the best efficiency point (BEP), h = head elevation (m, ft). From the specific speed, the pump's flow type can be estimated. The specific speed for radial flow ranges from around 500 to around 1500-1700, the specific speed for mixed flow ranges from around 1500-1700 to around 7000-8000, and the specific speed for axial flow ranges from around 7000. 8000 to around 20000. In step 340, the pump's water performance characteristics at the desired RPM are calculated. If the desired RPM differs from the RPM on the published performance curve, then affinity laws are used. In the illustrated mode, the pump's water performance characteristics at the desired RPM include the pump's BEP water performance characteristics at the desired RPM. The calculation uses affinity laws and the pump's water performance characteristics at the fixed RPM. The affinity laws state that: flow rate at desired RPM = flow rate at fixed RPM * (desired RPM / fixed RPM); printhead at desired RPM = printhead at fixed RPM * (desired RPM / fixed RPM)A2; and BHP at desired RPM = BHP at fixed RPM * (desired RPM / fixed RPM)Λ3. Affinity laws are used to calculate water flow rates from one velocity to another. They are also used to design a new pump based on an existing one. It is understood that the affinity laws described above do not apply to viscosity applications, for example, for fluids other than water, because viscosity affects various losses, such as seepage and friction losses, which are not proportional. Desired RPM with the BEP flow rate. It is understood that flow rates other than the BEP flow rate, such as a flow rate close to zero or a flow rate close to the maximum, may also be used for normalizing flow rates. The normalized Retan viscosity head numbers for the pump at the desired RPM are determined by normalizing the pump's Retan viscosity head numbers in water at the desired RPM using a Retan viscosity head number for the pump's reference flow rate in water at the desired RPM. As mentioned earlier, a Retan viscosity head number is a ratio of a flow rate to a corresponding head at a fixed viscosity. Since the viscosity of water is 1, each Retan viscosity head number is calculated by dividing each flow rate by a corresponding head. Once the Retan viscosity head numbers are calculated at various flow rates, they are normalized by dividing them by a reference Retan viscosity head number. In the mode shown, the reference Retan viscosity head number is a Retan viscosity head number for the reference flow rate, which is the BEP flow rate. Although not explicitly shown, if the normalized flow rates and pump Retan viscosity head numbers are mapped, they would form a curve similar to the 100, 200 ratios in Figures 1 and 2. In step 360, a BEP flow rate and pump BEP head in the fluid of interest are calculated at the desired RPM. In the mode shown, the pump BEP flow rate and pump BEP head in the fluid of interest at the desired RPM are calculated based on the flow rate and head correction factors with respect to viscosity and RPM ratio, and the pump's water performance BEP characteristics at the desired RPM. The flow rate correction factor for the pump's BEP flow rate in the fluid of interest at the desired RPM is derived from a correlation of the BEP flow rate ratio, which is the ratio of a BEP flow rate at the desired viscosity and a given RPM to a BEP flow rate of water at the given RPM, with RPM and viscosity changing. Similarly, the head correction factor for the pump's BEP flow rate in the fluid of interest at the desired RPM is derived from a BEP head ratio correlation, i.e., the ratio of a BEP head at the desired viscosity and a given RPM to a BEP head of water at the given RPM, with RPM and viscosity changing.Once the correction factors are derived, the BEP flow rate and pump BEP head in the fluid of interest at the desired RPM are calculated by multiplying the BEP flow rate and BEP head correction factors by the BEP water flow rate and BEP water head at the desired RPM, respectively. In step 370, the pump performance is predicted for a desired application. The desired application is represented by the parameters defined in step 310. In the mode shown, using the desired flow rate defined in step 310, the pump head in the fluid of interest is determined at the desired flow rate and desired RPM. As a first step, a desired normalized pump flow rate in the fluid of interest at the desired RPM is calculated based on the pump's BEP flow rate in the fluid of interest at the desired RPM from step 360 and the desired flow rate from step 310. More specifically, the desired normalized pump flow rate in the fluid of interest at the desired RPM is calculated by dividing the desired flow rate by the pump's BEP flow rate in the fluid of interest at the desired RPM. Once the desired normalized pump flow rate in the fluid of interest at the desired RPM is calculated, a normalized Ketan viscosity head number corresponding to the normalized BEP pump flow rate is calculated using the Ketan viscosity head number correlation from step 350. From the Ketan viscosity head number correlation, the normalized Ketan viscosity head number (Ketan viscosity head factor) can be interpolated. The pump head in the fluid of interest at the desired flow rate and RPM is calculated based on the desired pump flow rate in the fluid of interest at the desired RPM, the BEP flow rate and the pump's BEP head in the fluid of interest at the desired RPM, and the normalized Ketan viscosity head number. The pump head can be calculated using Equation (5): _ O cPL speed 1 hcPL speed L EKP h cPl speed 1= -------------------------------------------------------O cPL speed l EKP vis eos head factor Ketan r—Λ'_ / c\ oxEquation (5), QCpi. where Qcpi, velocity i is the desired flow rate at desired velocity and viscosity; Qcpi, velocity i, bep is the BEP flow rate at desired velocity and viscosity; hCpi, velocity i is the desired head at desired velocity and viscosity; hCpi, velocity i, bep is the BEP head at desired velocity and viscosity. Method 300 ends at step 375. It is understood that Method 300 can be applied not only to a centrifugal pump, but also to other types of pumps, such as a positive displacement pump, a rotary pump, and a metering pump, which can be used to handle a viscous fluid.It is also understood that in addition to well production, the 300 method can also be used in other oilfield applications, such as in the control and monitoring of mud pump performance, and the application of chemical injection in the oil well, for example, for viscosity, scale inhibition, sand control, and in some instances, it can be used in generic applications, such as in the field of medicine for the control and monitoring of blood flow, for example, a measurement of transfer rate in medicine, and in the chemical and petrochemical industry for the control and monitoring of injection, and for the mixing of chemicals to obtain suitable chemical reactions. To demonstrate how Method 300 works in a specific application, Method 300 has been implemented using concrete numbers from an example ESP pump. In this example, the operator might want to determine the flow rate of an SJ2800 pump when it is moving fluid at 300 cP, 700 BPD, and 2333 RPM. These desired parameters are defined in Step 310. The water performance characteristics of the SJ2800 pump at 3500 RPM or 60 Hz are received at stage 320. The received characteristics are shown as a performance curve 420 and an efficiency curve 430 in Figure 4. The received characteristics are for an SJ2800 pump in water at ambient temperature and atmospheric pressure with a specific gravity of 1.00. The performance curve 420 shows head variations in feet with respect to changes in flow rates in BPD at 3500 RPM. The efficiency curve indicates the BEP water characteristics at 3500 RPM, such as a BEP flow rate of 2961 BPD and a BEP head of 17.06 m (56 ft). In step 330, the specific speed in the pump example is calculated using the BEP flow rate and the BEP head. When calculated with the appropriate unit conversion, the pump's specific speed is 1589 BPD. Since the specific speed is between 500 and 1500-1700, the pump likely has a radial flow type. In step 340, the water performance characteristics of the pump example at 2333 PM are calculated. The calculated flow rates are shown as a curve 440 in Figure 4. At 2333 RPM, the BEP flow rate for the pump example is 1974 BPD and the BEP head is 7.58 m (24.88 ft). Using the water performance characteristics of the example pump at 2333 RPM, the correlation of the Ketan viscosity head number for the pump example in water at the desired RPM is developed in step 350. In step 360, the BEP flow rate and BEP head of the pump example in the fluid of interest (300 cP) at 2333 RPM are calculated. To do this, the BEP flow rate and BEP head correction factors are first derived. These are derived from BEP flow rate and BEP head ratios with varying RPM and viscosity, and in the example, they are 0.4678 and 0.9244, respectively. Using these correction factors, the BEP flow rate of the pump example in the fluid of interest at 2333 RPM is 923.232 (1974 * 0.4678) BPD, and the BEP head of the pump example is 23 (24.88 * 0.9244) feet. The BEP flow rate is a product of the BEP flow rate of water at 2333 RPM and the correction factor for the BEP flow rate, and the BEP head is a product of the BEP head of water at 2333 RPM and the correction factor for the BEP head. In step 370, the pump performance for the application defined in step 310 is determined; that is, the SJ2800 pump head moving the fluid of interest at 700 BPD and 2333 RPM. As described above with step 370, the SJ2800 pump head for the viscosity application is determined using the desired flow rate, the BEP flow rate, and the BEP head of the SJ2800 pump in the fluid of interest at 2333 RPM, and a normalized BEP flow rate of the pump in the fluid of interest at 2333 RPM. The normalized BEP flow rate of the SJ2800 pump in the fluid of interest at 2333 RPM is calculated by dividing the desired flow rate, i.e., 700 BPD of stage 310, by the pump's BEP flow rate in the fluid of interest at 2333 RPM, i.e., 923.232, and is therefore 0.758. By using the normalized BEP flow rate of the pump in the fluid of interest at 2333 RPM and the correlation of the viscosity head number of For the Ketan stage 350, a normalized Ketan viscosity head number (Ketan viscosity head factor) is calculated corresponding to the normalized BEP flow rate of the pump in the fluid of interest at 2333 RPM. The normalized Ketan viscosity head number is 0.708. By setting the BEP flow rate and BEP head of the SJ2800 pump in the fluid of interest at 2333 RPM, the desired flow rate and the normalized Ketan viscosity head number in Equation (5), the pump head example in the fluid of interest at 700 zr l ίηη / ζζηζ / E / γίΛΐ is calculated BPD and 2333 RPM. The head of the SJ2800 pump in the fluid of interest at 700 BPD and 2333 RPM is calculated to be 24.39 ((700*23) / (932.232*0.708)). The result can be verified from a 460 curve that represents the performance characteristics of the example pump in the fluid of interest at 2333 RPM. Figure 5 illustrates a flowchart of one modality of Method 500 for modeling the performance characteristics of a pump in a viscosity application. Method 500 can be implemented using a computer system, such as 600 in Figure 6. A series of instructions that, when executed, cause a computer system's processor to perform Method 500 can be stored on a computer-readable medium, such as a CD-ROM, floppy disk, flash memory, or other data storage device. Method 500 begins at step 505. In step 510, the pump operating parameters are used to form a dimensionless number. The pump operating parameters include head, flow rate, speed, viscosity, stage diameter, BHP, and efficiency, and are arranged in dimensionless form, such as the dimensionless ratio mentioned above, which is between flow rate, head, and viscosity for the Ketan viscosity head number. In step 520, the dimensionless number is used in a ratio term to model the pump's performance characteristics for various operating conditions. The ratio term includes a ratio of each operating parameter to a corresponding operating parameter at a reference point. The reference point can be any point on a performance curve, such as a BEP point, a point near zero flow rate, and / or near maximum flow rate. Method 500 ends in step 525. Figure 6 shows one embodiment of a computer system that has been built and configured to carry out a viscosity performance prediction method, such as 300 in Figure 3 or 500 in Figure 5. In the embodiment shown, system 600 includes a processor 620, an interface 640, and memory 660. It is understood that system 400 has been simplified for illustrative purposes and may not show some of the components that may be present in a real system. The 620 processor is a processing unit, such as a central processing unit and / or a graphics processing unit, configured to predict the performance of a given pump in a fluid of interest at a desired RPM. The processor is coupled to the 640 interface and the 660 memory. The 640 interface is a user interface and / or network interface card configured to receive the water performance characteristics of a specific pump. As mentioned previously, the water performance characteristics of a specific pump are typically provided by the pump manufacturer. The 640 interface can be a communication interface configured to transmit and receive data. As such, the 640 interface may include the necessary logic, ports, terminals, connectors, etc., for data communication. The ports, terminals, and connectors can be standard receptacles for communicating data over a network. Memory 660 is a type of computer memory, such as read-only memory (ROM), programmable ROM (PROM), erasable PROM, dynamic random-access memory (DRAM), static random-access memory, and flash memory. Memory 660 is configured to store the performance characteristics of the water received from the pump and other calculated performance characteristics from the 620 processor. Memory 660 can also be configured to store executable computer instructions to direct the operation of the 620 processor when it boots from there. These operating instructions might correspond to an algorithm or algorithms that predict the performance of a given pump in a fluid of interest at a desired RPM. Figure 7 shows a viscosity application of an electric submersible pump (ESP). In the application shown, an ESP 700 assembly is placed at the bottom of an underground oil well beneath the ocean. The ESP 700 assembly can also be used for onshore operations. The ESP 700 assembly includes a 705 speed controller, an ESP 720 motor (for example, a DC motor), and an ESP 755 pump. In the configuration shown, the speed controller 705 is installed in a cabinet 740 inside a control room 735 on an offshore platform 745, such as an oil platform. The speed controller 705 is configured to adjust the speed of the ESP 720 motor to increase well productivity. In the configuration shown, the ESP 720 motor is a two-pole, three-phase squirrel-cage induction motor that drives the ESP 755 pump. The ESP 720 motor is located near the bottom of the ESP 700 assembly, directly above the deep-hole sensors within a well. Se zr l ίηη / ζζηζ / E / γίΛΐ extends a power cable 715 from the speed controller 705 to the ESP motor 720. The power cable 715 can be up to 3657.6 m (12,000 ft) long. The ESP 755 pump can be a multi-stage centrifugal pump that includes an impeller and a diffuser in each stage. Before its use, the performance of the ESP 755 pump is predicted using a viscosity performance prediction method, such as 300 in Figure 3, by means of a computer system, such as 500 in Figure 5. Based on the prediction, the ESP 755 pump can be controlled to move the fluid of interest, such as oil or other hydrocarbons, through a production pipeline 730 to storage tanks on board the offshore platform 745. In some configurations, the 755 pump may be a horizontal surface pump, a progressive cavity pump, or an electric progressive cavity submersible pump. A motor joint section and inlet section may extend between the 720 motor and the 755 pump. A 725 well casing may separate the 700 ESP assembly from the 760 well formation and / or seawater. Perforations in the 725 casing may allow the fluid of interest from the 760 formation to enter the underground 725 casing. A portion of the apparatus, systems, or methods described above may be implemented in various modes or carried out by different analog or digital data processors, where the processors are programmed or stored with executable programs of software instruction sequences to perform one or more of the steps of the methods. For example, a processor may be a programmable logic device, such as a programmable logic array (PAL), a generic logic array (GAL), a field-programmable gate array (FPGA), or another type of computer processing device (CPD).The software instructions of the programs may represent algorithms and be encoded in machine-executable form on non-transient digital data storage media, for example, magnetic or optical disks, random access memory (RAM), magnetic hard disks, flash memory and / or read-only memory (ROM), to allow various types of digital data processors or computers to perform one, multiple or all of the stages of one or more of the methods, or functions, systems or devices described above herein. The examples or modalities described herein may refer to computer storage products with a non-transient, computer-readable medium containing program code to perform various computer-implemented operations that constitute a part of an apparatus or device, or perform steps in a method set forth herein. The term "non-transient" as used herein refers to all computer-readable media except transient and propagating signals. Examples of non-transient, computer-readable media include, but are not limited to: magnetic media, such as hard disks, floppy disks, and magnetic tape; optical media, such as CD-ROMs; magneto-optical media, such as floppy disks; and hardware devices specifically configured to store and execute program code, such as ROM and RAM devices.Program code examples include machine code, such as that produced by a compiler, and files containing higher-level code that can be executed by the computer using an interpreter. When interpreting the description, all terms should be interpreted as broadly as possible in accordance with the context. In particular, the expressions "comprises" and "comprising" should be interpreted as referring to elements, components, or stages in a non-exclusive manner, indicating that the mentioned elements, components, or stages may be present, used, or combined with other elements, components, or stages that are not expressly mentioned. Persons in the mid-level trade to which this application relates will appreciate that additions, deletions, substitutions, and modifications other than those described in the embodiments are possible. It should also be understood that the terminology used herein is for the purpose of describing only particular embodiments and is not intended to be limiting, as the scope of this description is limited only by the claims. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by a person in the mid-level trade to which this invention pertains. Although any methods or materials similar or equivalent to those described herein may also be used in the practice or analysis of this description, only a limited number of the exemplary methods and materials are described herein. The aspects described herein include: A. A method for predicting the performance of a pump in a fluid of interest at a desired RPM, comprising: receiving water performance characteristics of the pump at a fixed RPM; determining Ketan viscosity head numbers for the flow rates of the pump in water at a desired RPM by using the water performance characteristics of the pump at the fixed RPM, the Ketan viscosity head numbers representing ratios of flow rates to heads corresponding to a fixed internal resistance and the desired RPM; determining a viscosity head correlation between the normalized flow rates of the pump in water at the desired RPM and the normalized Ketan viscosity head numbers corresponding to the normalized flow rates by using the water performance characteristics of the pump at the desired RPM;and predict pump performance in the fluid of interest at the desired RPM using viscosity head correlation. B. A system for predicting the performance of a pump in a fluid of interest at a desired RPM, comprising: an interface configured to receive water performance characteristics of the pump at a fixed RPM; and a processor coupled to the interface and configured to: determine the Ketan viscosity head numbers for the pump flow rates in water at a desired RPM by using the water performance characteristics of the pump at a fixed RPM, wherein the Ketan viscosity head numbers represent the ratios of the flow rates to the corresponding heads at a fixed internal resistance and the desired RPM;Determine a viscosity head correlation between the normalized flow rates of the pump in water at the desired RPM and the normalized Ketan viscosity head numbers that correspond to the normalized flow rates by using the water performance characteristics of the pump at the desired RPM; and predict the pump performance in the fluid of interest at the determined RPM by using the viscosity head correlation. C. A method for modeling the performance characteristics of a pump in a viscosity application, comprising: forming a dimensionless number by using operating parameters of the pump; and using the dimensionless number in a ratio term to model the performance characteristics of the pump for various operating conditions. Each of aspects A, B, and C may have one or more of the following additional elements in combination. Element 1: further comprising calculating the water performance characteristics of the pump at the desired RPM using affinity laws and the water performance characteristics of the pump at a fixed RPM, and the water performance characteristics of the pump at the fixed RPM include the water performance characteristics of the pump at the best efficiency point (BEP) at the fixed RPM. Element 2: wherein the water performance characteristics of the pump at the desired RPM are calculated using: a flow rate at the desired RPM = flow at the fixed RPM * (the desired RPM / the fixed RPM); a head at the desired RPM = a head at the fixed RPM * (the desired RPM / the fixed RPM)^2; and a BHP at the desired RPM = a BHP at the fixed RPM * (the desired RPM / the fixed RPM)^3. Element 3: which also includes calculating a flow rateElement 4: wherein the flow rate correction factor for the pump's BEP flow rate in the fluid of interest at the desired RPM is derived from the desired RPM and viscosity. Element 5: wherein the head correction factor for the pump's BEP flow rate in the fluid of interest at the desired RPM is derived from the desired RPM and viscosity of the fluid of interest. Element 6: further comprising defining a desired flow rate, the desired RPM, and the fluid of interest.and a desired pump stage based on a viscosity application in which the pump will be used. Element 7: further comprising calculating a specific pump speed at a desired stage by using the pump's BEP water performance characteristics at the fixed RPM. Element 8: wherein the pump's BEP water performance characteristics at the fixed RPM are provided from a pump water performance curve. Element 9: wherein determining the viscosity head correlation includes determining the normalized pump flow rates in water at the desired RPM by normalizing the pump flow rates in water at the desired RPM using a reference pump flow rate in water at the desired RPM. Element 10: wherein determining the viscosity head correlation further includes determining the normalized Retan viscosity head numbers by normalizing the numbers ofRetan viscosity heads are calculated using a Retan viscosity head number corresponding to the pump's reference flow rate in water at the desired RPM. Example 11: wherein the pump's reference flow rate is selected from the group consisting of a BEP flow rate, a flow rate close to zero, and a flow rate close to the pump's maximum in water at the desired RPM. Element 12: wherein predicting pump performance includes calculating a pump head in the fluid of interest at the desired flow rate and RPM using viscosity head correlation, a pump's BEP flow rate in the fluid of interest at the desired RPM, a pump's BEP head in the fluid of interest at the desired RPM, and a normalized pump's BEP flow rate in the fluid of interest at the desired RPM. Element 13: calculating the pump headThe process of calculating the pump's normalized BEP flow rate in the fluid of interest at the desired flow rate and RPM includes: calculating the pump's normalized BEP flow rate in the fluid of interest at the desired RPM based on the desired flow rate and the pump's BEP flow rate in the fluid of interest at the desired RPM; calculating a normalized Ketan viscosity head number corresponding to the pump's normalized BEP flow rate in the fluid of interest at the desired RPM using viscosity head correlation; and calculating the pump head in the fluid of interest at the desired flow rate and RPM based on the desired flow rate, the pump's BEP flow rate in the fluid of interest at the desired RPM, the pump's BEP head in the fluid of interest at the desired RPM, and the normalized Retan viscosity head number corresponding to the pump's normalized BEP flow rate.Element 14: further comprising changing the pump size based on the pump performance in the fluid of interest at the desired RPM. Element 15: wherein the pump operating parameters include at least one of the following: a head, a flow rate, a speed, a viscosity, a diameter, a brake horsepower, and an efficiency. Element 16: wherein the term ratio includes a ratio of each of the operating parameters to a corresponding operating parameter at a reference point. Element 17: wherein the reference point is a point on a performance curve and is selected from the group consisting of a best efficiency point, a near-zero flow condition point, and a point near the maximum flow rate. It is hereby stated that, as of this date, the best method known to the applicant for putting the aforementioned invention into practice is the one that is clear from the present description of the invention.

Claims

1. A method for predicting the performance of a pump in a fluid of interest at a desired RPM, characterized in that it comprises: receiving water performance characteristics of the pump at a fixed RPM; determining Ketan viscosity head numbers for the pump flow rates in water at a desired RPM by using the water performance characteristics of the pump at the fixed RPM, the Ketan viscosity head numbers representing the ratios of the flow rates to the corresponding heads at a fixed internal resistance and the desired RPM; determining a viscosity head correlation between the normalized flow rates of the pump in water at the desired RPM and the normalized Ketan viscosity head numbers corresponding to the normalized flow rates by using the water performance characteristics of the pump at the desired RPM;and predict the pump performance in the fluid of interest at the desired RPM using the viscosity head correlation.

2. The method according to claim 1, characterized in that it further comprises calculating the water performance characteristics of the pump at the desired RPM using affinity laws and the water performance characteristics of the pump at the fixed RPM, and the water performance characteristics of the pump at the fixed RPM include the water performance characteristics of the pump at the best efficiency point (BEP) at the fixed RPM, and optionally wherein the water performance characteristics of the pump at the desired RPM are calculated using: a flow rate at the desired RPM = flow at the fixed RPM * (the desired RPM / the fixed RPM); a head at the desired RPM = a head at the fixed RPM * (the desired RPM / the fixed RPM)A2; and a BHP at the desired RPM = a BHP at the fixed RPM * (the desired RPM / the fixed RPM)A3.

3. The method according to claim 1 or 2, characterized in that it further comprises calculating a pump BEP flow rate in the fluid of interest at the desired RPM based on a flow rate correction factor derived from a connection of a BEP flow rate ratio with changing RPM and viscosity, and calculating a pump BEP head in the fluid of interest at the desired RPM based on a head correction factor derived from a connection of a BEP head ratio with changing RPM and viscosity.

4. The method according to claim 3, characterized in that the flow rate correction factor for the pump's BEP flow rate in the fluid of interest at the desired RPM is further derived from the desired RPM and a viscosity of the fluid of interest, or the head correction factor for the pump's BEP head in the fluid of interest at the desired RPM is further derived from the desired RPM and a viscosity of the fluid of interest.

5. The method according to any of the preceding claims, characterized in that it further comprises defining a desired flow rate, the desired RPM, the fluid of interest, and a desired pump stage based on a viscosity application in which the pump will be used.

6. The method according to any of the preceding claims, characterized in that determining the viscosity head correlation includes determining the normalized pump flow rates in water at the desired RPM by normalizing the pump flow rates in water at the desired RPM by using a reference flow rate of the pump in water at the desired RPM and, optionally, determining the normalized Ketan viscosity head numbers by normalizing the Ketan viscosity head numbers by using a Ketan viscosity head number corresponding to the reference flow rate of the pump in water at the desired RPM.

7. The method according to any of the preceding claims, characterized in that predicting pump performance includes calculating a pump head in the fluid of interest at a desired flow rate and desired RPM using viscosity head correlation, a pump BEP flow rate in the fluid of interest at the desired RPM, a pump BEP head in the fluid of interest at the desired RPM, and a normalized pump BEP flow rate in the fluid of interest at the desired RPM, and optionally wherein calculating the pump head in the fluid of interest at the desired flow rate and desired RPM includes: calculating the normalized pump BEP flow rate in the fluid of interest at the desired RPM as a function of the desired flow rate and the pump BEP flow rate in the fluid of interest at the desired RPM;Calculate a normalized Ketan viscosity head number that corresponds to the normalized flow rate zr l ίηη / ζζηζ / E / γίΛΐ of the pump BEP in the fluid of interest at the desired RPM by using the viscosity head correlation; and calculate the pump head in the fluid of interest at the desired flow rate and the desired RPM as a function of the desired flow rate, the pump BEP flow rate in the fluid of interest at the desired RPM, the pump BEP head in the fluid of interest at the desired RPM and the normalized Ketan viscosity head number that corresponds to the normalized flow rate of the pump BEP in the fluid of interest at the desired RPM.

8. The method in accordance with any of the preceding claims, characterized in that it further comprises changing a pump size based on the pump performance in the fluid of interest at the desired RPM.

9. A system for predicting the performance of a pump in a fluid of interest at a desired RPM, characterized in that it comprises: an interface configured to receive water performance characteristics of the pump at a fixed RPM; and a processor coupled to the interface and configured to: determine the Ketan viscosity head numbers for the pump flow rates in water at a desired RPM by using the water performance characteristics of the pump at a fixed RPM, wherein the Ketan viscosity head numbers represent the ratios of the flow rates to the corresponding heads at a fixed internal resistance and the desired RPM;Determine a viscosity head correlation between normalized pump flow rates in water at the desired RPM and the normalized Ketan viscosity head numbers corresponding to the normalized flow rates using the pump's water performance characteristics at the desired RPM; and predict the pump performance in the fluid of interest at the desired RPM using the viscosity head correlation.

10. The system according to claim 9, characterized in that the processor is further configured to calculate the water performance characteristics of the pump at the desired RPM using affinity laws and the water performance characteristics of the pump at the fixed RPM, and the water performance characteristics of the pump at the fixed RPM include the water performance characteristics of the pump at the best efficiency point (BEP) at the fixed RPM, and optionally wherein the processor is further configured to: calculate a BEP flow rate of the pump in the fluid of interest at the desired RPM as a function of a flow rate correction factor derived from a connection of a BEP flow rate ratio with changing RPM and viscosity;and calculate a pump BEP head in the fluid of interest at the desired RPM based on a head correction factor derived from a connection of a BEP head ratio with changing RPM and viscosity.

11. The system according to claim 9 or 10, characterized in that the processor is further configured to calculate a specific pump speed at a desired stage by using BEP water performance characteristics of the pump at the fixed RPM.

12. The system according to any of the preceding claims 9, characterized in that the processor is further configured to determine the normalized pump flow rates in water at the desired RPM by normalizing the pump flow rates in water at the desired RPM by using a reference pump flow rate in water at the desired RPM and, optionally, wherein the processor is further configured to determine the normalized Ketan viscosity head numbers by normalizing the Ketan viscosity head numbers by using a Ketan viscosity head number corresponding to the reference pump flow rate in water at the desired RPM.

13. The system according to claim 12, characterized in that the reference flow rate of the pump is selected from the group consisting of a BEP flow rate, a flow rate close to zero, and a flow rate close to the maximum of the pump in water at the desired RPM.

14. The system according to any of the preceding claims 9, characterized in that the pump performance is predicted by calculating a pump head in the fluid of interest at a desired flow rate and desired RPM using viscosity head correlation, a pump BEP flow rate in the fluid of interest at the desired RPM, a pump BEP head in the fluid of interest at the desired RPM, and a normalized pump BEP flow rate in the fluid of interest at the desired RPM.

15. The system according to claim 14, characterized in that calculating the pump head in the fluid of interest at the desired flow rate and desired RPM includes: calculating the normalized BEP flow rate of the pump in the fluid of interest at the desired RPM as a function of the BEP flow rate of the pump in the fluid of interest at the desired RPM; calculating a normalized Ketan viscosity head number corresponding to the normalized BEP flow rate of the pump in the fluid of interest at the desired RPM by using viscosity head correlation;and calculate the pump head in the fluid of interest at the desired flow rate and desired RPM based on the normalized BEP flow rate of the pump in the fluid of interest at the desired RPM, the BEP head of the pump in the fluid of interest at the desired RPM, and the normalized Ketan viscosity head number corresponding to the normalized BEP flow rate of the pump in the fluid of interest at the desired RPM.

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