Method for calculating the viscous performance of pumps based on their water performance characteristics and new dimensionless parameters for controlling and monitoring viscosity, flow and pressure

Abstract

This article describes a dimensionless relationship between volumetric flow, head and kinematic viscosity in pump operation and a method for using the dimensionless relationship to predict the viscous performance of a pump from water performance characteristics. Using the described dimensionless relationship, called the Ketan viscous head number, the described method determines a viscous head correlation that allows accurate prediction of pump performance at any given speed, flow and viscosity. Thus, the described Ketan viscous head number and method allow prediction of pump performance in viscous applications from water performance characteristics without the need to physically test the pump in the viscous application.

Description

[0001] Cross-application of related applications

[0002] This application claims priority to U.S. application serial number 16 / 582,684, filed on September 25, 2019, entitled "METHOD OF CALCULATING VISCOUS PERFORMANCE OF A PUMP FROM ITS WATER PERFORMANCE CHARACTERISTICS AND NEW DIMENSIONLESS PARAMETER FOR CONTROLLING AND MONITORING VISCOSITY, FLOW AND PRESSURE," which is commonly assigned with the present application and is incorporated herein by reference in its entirety. Background Art

[0003] Centrifugal pumps have been developed and used for centuries to handle viscous fluids. The performance of a centrifugal pump is affected by many factors such as the viscosity, speed, stage size, flow rate and hydraulic design of the pump. Typically, the pump is tested in water at atmospheric conditions and its performance at a fixed speed is used to select the pump and the number of stages. Predicting the performance of a pump in a viscous application is very difficult because the performance depends on the speed, viscosity and flow rate of the pump. For a given viscous application, the pump is typically tested in various viscous fluids at a range of speeds and its test data is interpolated. This testing process has been found to be lengthy and expensive. In addition, interpolating and modeling the performance used in the application is complex and introduces inaccuracies in the performance predictions. BRIEF DESCRIPTION OF THE DRAWINGS

[0004] Reference is now made to the following description in conjunction with the accompanying drawings, in which:

[0005] Figure 1 is a graph of the normalized flow rate of a pump in water at a given RPM versus the normalized Ketan viscous head number;

[0006] Figure 2 It is a graph of the normalized flow rate of a pump in various viscous fluids at a given RPM and the normalized Ketan viscous head number;

[0007] Figure 3 is a flow chart of an embodiment of a method for predicting the performance of a given pump in a fluid of interest having a desired viscosity at a desired RPM;

[0008] Figure 4 is a graphical representation of a performance curve for an exemplary pump;

[0009] Figure 5 is a flow chart of an embodiment of a method for modeling performance characteristics of a pump in a viscous application;

[0010] Figure 6 is a block diagram of an embodiment of a computer system implemented according to the principles of the present disclosure; and

[0011] Figure 7 is an exemplary viscous application of an electric submersible pump (ESP). DETAILED DESCRIPTION

[0012] Electric submersible pumps have been used to pump oil out of formations since the 1930s. An ESP is a multistage centrifugal pump with a few to hundreds of stages that runs at variable speeds (e.g., from 1500 revolutions per minute (RPM) to 8000 RPM) and can pump hundreds to hundreds of thousands of barrels per day (BPD). The selection of pump sizing for a given viscous application involves selecting the stage type, number of pump stages, (optional gas separators), seals (protectors), and motors.

[0013] In viscous applications, especially offshore, the performance prediction of ESPs is particularly important and requires a higher level of accuracy than conventional prediction tools can provide. This is due to the fact that offshore applications are expensive to operate and small differences in sizing and prediction of the appropriate pump type can result in millions of dollars in losses.

[0014] In order to determine the proper size of a pump stage for a viscous application, it is necessary to understand its performance in a variety of viscosities. Typically, a pump with several stages is built and tested in a test facility over a desired viscosity and speed range before the pump is sized and deployed in an actual application. The test results are used to predict the performance of the pump in an actual application such as an offshore oil production application, and the predictions are used to correctly size the pump and its motor before deployment. Since viscosity and speed can vary greatly from application to application, this build-test-analyze-model-predict process is not only costly and time-consuming, but also inaccurate.

[0015] Presented herein is a dimensionless relationship between volume flow, head, and kinematic viscosity that simplifies the prediction of viscous pump performance. The presented relationship is referred to in this disclosure as the Ketan viscous head number and is expressed as equation (1):

[0016] Ketan Viscous Head Number = q / h*v Equation (1), where q is the volume flow rate, h is the head, and v is the kinematic viscosity.

[0017] Head is a function of pump flow, speed, stage size, and hydraulic design; flow is affected by pump speed, stage size, and hydraulic design; and kinematic viscosity is a fixed fluid property.

[0018] The Ketan viscous head number can also be expressed in different ways, such as by the following equations (2) and (3):

[0019] (q*ρ) / (p*v)=mass flow rate / (pressure*kinematic viscosity) Equation (2),

[0020] (q*ρ) / (h*μ)=mass flow / (head*absolute viscosity) Equation (3), where ρ is density, p is pressure, and μ is absolute viscosity.

[0021] The Ketan viscous head number represents a measure of the performance condition of a pump: the ratio of flow rate to the head obtained at a given viscosity. In other words, it is the ratio of volumetric or mass flow rate to head or pressure at a fixed internal resistance or viscosity.

[0022] The Ketan viscosity head number can be calculated using equation (1) using the published water performance characteristics of a given pump at a fixed speed (RPM). The water performance characteristics of a given pump are typically available from the manufacturer of the pump and are provided in the form of a pump curve that is plotted against flow, head, and brake horsepower (BHP) at a fixed speed (e.g., RPM). Typically, water pump performance characteristics for ESP pumps are published at 50 Hz (2917 RPM) and / or 60 Hz (3500 RPM), depending on the primary application of the pump.

[0023] Figure 1 A relationship 100 is shown between the normalized flow rate 110 of a pump in water at a given RPM and the normalized Ketan viscous head number 120. The relationship 100 varies with changes in pump design and is also a function of the specific speed of the pump. The relationship 100 can be used to predict the viscous performance of a pump at different RPMs and in different fluids. The relationship 100 is hereinafter referred to as the Ketan viscous head number correlation.

[0024] The normalized flow rate 110 on the x-axis is determined using the water performance characteristics of the pump. For a given RPM, the flow rate from the water performance characteristics is normalized using a reference point, such as the flow rate at the best efficiency point (BEP). The BEP refers to the point in the pump curve where the efficiency is the highest. For normalization, each of the flow rates can be divided by the BEP flow rate.

[0025] The normalized Ketan viscous head number 120 on the y-axis is determined using the water performance characteristics of the pump. The Ketan viscous head number is first calculated using equation (1) and the flow, viscosity, and head from the water performance characteristics. Since the flow and head are from the water performance characteristics, the viscosity is 1 centipoise. The calculated Ketan viscous head number is then normalized using the Ketan viscous head number at a reference point, such as the BEP. Similar to the normalized flow 110, each Ketan viscous head number in the Ketan viscous head number 120 is divided by the Ketan viscous head number at the BEP for normalization.

[0026] Figure 2 Shown in Figure 1 The relationship between each normalized flow rate 210 and the normalized Ketan viscosity head number 220 of the same pump at the same RPM but different viscosities in FIG200. Different from Figure 1 The relationship 100 in FIG. 1 and the relationship 200 are for fluids other than water. The fluids include a first fluid having a viscosity of 6 centipoise (hollow square), a second fluid having a viscosity of 9 centipoise (hollow triangle), a third fluid having a viscosity of 19 centipoise (solid rectangle), a fourth fluid having a viscosity of 35 centipoise (hollow diamond), a fifth fluid having a viscosity of 50 centipoise (X), a sixth fluid having a viscosity of 90 centipoise (hollow circle), a seventh fluid having a viscosity of 100 centipoise (solid square), an eighth fluid having a viscosity of 140 centipoise (solid triangle), a ninth fluid having a viscosity of 244 centipoise (+), and a tenth fluid having a viscosity of 541 centipoise (X).

[0027] As shown, although the fluid and its viscosity are different, its viscous head number correlation, that is, the relationship between its normalized flow rate and its normalized Ketan viscous head number remains unchanged. Thus, the Ketan viscous head number correlation of a pump in water at a given RPM, for example Figure 1 and 2 The 100 and 200 in the figure can be used to predict pump performance in viscous applications.

[0028] Figure 3 1 shows a flow chart of an embodiment of a method 300 for predicting the performance of a pump in a fluid of interest at a desired RPM. The method 300 or at least a portion thereof may be performed by Figure 5 The method 300 is executed by a computer system such as 500 in the embodiment of the present invention. The series of instructions that cause the processor of the computer system to execute the method 300 when executed can be stored in a computer readable medium such as a CD-ROM, a floppy disk, a flash drive or other types of data storage. The method 300 starts at step 305.

[0029] At step 310, the parameters of the application in which the pump will operate are defined. The parameters may include: the fluid of interest (desired viscosity) in which the pump will operate, the desired flow rate (the rate at which the operator wants to move the fluid of interest), and the desired speed (the RPM at which the operator wants the motor to operate the pump), as well as the desired pump (depending on the application, the pump may have different diameters and different numbers of stages - the stage at which the operator wants to operate the pump).

[0030] At step 320, a water performance characteristic of the pump at a fixed RPM is received. The fixed RPM may be one of the RPMs at which the manufacturer of the pump publishes and provides the water performance characteristics of the pump, such as 3500 RPM, 2917 RPM, and / or 1750 RPM. The water performance characteristic may be in the form of a performance curve plotted against flow, head, and BHP at a certain RPM. The BEP water performance characteristic of the pump may be indicated in the performance curve, and if not indicated, the BEP water performance characteristic may be interpolated from the curve. It should be understood that throughout this disclosure, it is assumed that the viscosity of water is 1 centipoise and the room temperature is 20°.

[0031] At step 330, the specific speed of the pump (i.e., the desired pump) is calculated. The specific speed of the pump is calculated using the BEP water performance characteristics of the pump at a fixed RPM received at step 320. The specific speed is a number that characterizes the impeller type in a pump in a unique and consistent manner. The determination of the specific speed is independent of the size of the pump and can be useful when comparing different pump designs. The specific speed is calculated using equation (4):

[0032] Ns = (n*q^0.5) / (h^0.75) Equation (4), where Ns = specific speed, n = pump shaft speed (rpm), q = flow rate at best efficiency point (BEP) (m3 / hour, liters / second, liters / minute, m3 / minute, US gpm, Imperial gpm), h = head (m, ft).

[0033] Based on the specific speed, the flow type of the pump can be estimated. The specific speed range of radial flow is about 500 to about 1500-1700, the specific speed range of mixed flow is about 1500-1700 to about 7000-8000, and the specific speed range of axial flow is about 7000-8000 to about 20000.

[0034] At step 340, the water performance characteristics of the pump at the desired RPM are calculated. If the desired RPM is different than the RPM of the published performance curve, then the similarity law is used. In the illustrated embodiment, the water performance characteristics of the pump at the desired RPM include the BEP water performance characteristics of the pump at the desired RPM. The calculation uses the similarity law and the water performance characteristics of the pump at a fixed RPM. The similarity law states:

[0035] Flow rate at desired RPM = Flow rate at fixed RPM * (desired RPM / fixed RPM);

[0036] Head at desired RPM = Head at fixed RPM * (desired RPM / fixed RPM)^2; and

[0037] BHP at desired RPM = BHP at fixed RPM * (desired RPM / fixed RPM)^3.

[0038] Similarity laws are used to calculate the performance of water from one speed to another. Similarity laws are also used to design new pumps based on existing pumps. It should be understood that the similarity laws described above do not apply to viscous applications such as fluids other than water because viscosity affects various losses such as leakage and friction losses that are not proportional to speed.

[0039] Using the example values ​​provided above, the pump example has a BEP flow rate of 1974 BPD at 2333 RPM, a BEP head of 24.88 ft. at 2333 RPM, and a BEP BHP of 0.531 HP at 2333 RPM.

[0040] At step 350, a Ketan head number correlation of the pump in water at a desired RPM is developed. In the illustrated embodiment, a Ketan head number correlation of the pump in water at a desired RPM is developed based on the water performance characteristics of the pump at the desired RPM. Figure 1 and 2 As described, the normalized flow rate and the normalized Ketan viscous head number are first determined before developing the Ketan viscous head number correlation.

[0041] The normalized flow rate of the pump at the desired RPM is determined by normalizing the individual flow rates of the pump in water at the desired RPM using a reference flow rate at the desired RPM. In the illustrated embodiment, the reference flow rate is the BEP flow rate at the desired RPM, and the normalized flow rate is determined by dividing the individual flow rates of the pump at the desired RPM by the BEP flow rate. It should be understood that flow rates other than the BEP flow rate, such as near zero flow rate or near maximum flow rate, may also be used for normalization of flow rate.

[0042] The normalized Ketan head number of the pump at the desired RPM is determined by normalizing the Ketan head number of the pump in water at the desired RPM using the Ketan head number of the reference flow rate of the pump in water at the desired RPM. As discussed above, the Ketan head number is the ratio of the flow rate to the corresponding head at a fixed viscosity. Thus, each Ketan head number is calculated by dividing each flow rate by the corresponding head, considering that the viscosity of water is 1.

[0043] Once the Ketan head number is calculated for each flow rate, the Ketan head number can be normalized by dividing by the reference Ketan head number. In the illustrated embodiment, the reference Ketan head number is the Ketan head number for the reference flow rate (i.e., the BEP flow rate). Although not explicitly shown, if the normalized flow rate and Ketan head number of the pump are plotted, it will form a graph similar to Figure 1 and 2 The curves of the relationship 100 and 200.

[0044] At step 360, the BEP flow and BEP head of the pump in the fluid of interest at the desired RPM are calculated. In the illustrated embodiment, the BEP flow and BEP head of the pump in the fluid of interest at the desired RPM are calculated based on flow and head correction factors related to the viscosity and RPM relationship and the BEP water performance characteristics of the pump at the desired RPM.

[0045] A flow correction factor for the BEP flow of the pump in the fluid of interest at a desired RPM is derived from the correlation of the BEP flow ratio, which is the ratio of the BEP flow at a desired viscosity and a given RPM to the BEP flow of water at a given RPM, with varying RPM and viscosity. Similarly, a head correction factor for the BEP flow of the pump in the fluid of interest at a desired RPM is derived from the correlation of the BEP head ratio (i.e., the ratio of the BEP head at a desired viscosity and a given RPM to the BEP head of water at a given RPM) with varying RPM and viscosity. Once the correction factors are derived, the BEP flow and BEP head of the pump in the fluid of interest at a desired RPM are calculated by multiplying the BEP flow and BEP head correction factors by the water BEP flow and water BEP head at the desired RPM, respectively.

[0046] At step 370, the performance of the pump in the desired application is predicted. The desired application is represented by the parameters that have been defined in step 310. In the illustrated embodiment, using the desired flow defined in step 310, the head of the pump in the fluid of interest at the desired flow and the desired RPM is determined.

[0047] As a first step, a normalized expected flow rate of the pump in the fluid of interest at the desired RPM is calculated based on the BEP flow rate of the pump in the fluid of interest at the desired RPM from step 360 and the desired flow rate from step 310. More specifically, the normalized expected flow rate of the pump in the fluid of interest at the desired RPM is calculated by dividing the desired flow rate by the BEP flow rate of the pump in the fluid of interest at the desired RPM.

[0048] Once the normalized expected flow rate of the pump in the fluid of interest at the expected RPM is calculated, the normalized Ketan head number corresponding to the normalized BEP flow rate of the pump is calculated using the Ketan head number correlation from step 350. From the Ketan head number correlation, the normalized Ketan head number (Ketan head coefficient) can be interpolated.

[0049] The head of the pump in the fluid of interest at the desired flow rate and the desired RPM is calculated based on the desired flow rate of the pump in the fluid of interest at the desired RPM, the BEP flow rate and BEP head of the pump in the fluid of interest at the desired RPM, and the normalized Ketan viscosity head number. The head of the pump can be calculated using equation (5):

[0050] Where Q cp1，速度1 is the desired flow rate at the desired velocity and desired viscosity; Q cp1，速度1，BEP is the BEP flow rate at the desired velocity and desired viscosity; h cp1，速度1 is the desired head at the desired speed and desired viscosity; h cp1，速度1，BEP is the BEP head at the desired speed and the desired viscosity. Method 300 ends at step 375 .

[0051] It should be understood that the method 300 is applicable not only to centrifugal pumps, but also to other types of pumps that can be used to handle viscous fluids, such as positive displacement pumps, rotary pumps, and metering pumps. It should also be understood that in addition to oil well production, the method 300 can also be used in other oilfield applications such as mud pump performance control and monitoring and chemical injection applications in oil wells, for example, viscosity, scale inhibition, sand control, and in some cases, it can be used in non-mining applications such as the medical field for blood flow control and monitoring (e.g., measurement of drug transfer rate), and in the chemical and petrochemical industries for controlling and monitoring the injection and mixing of chemicals to achieve appropriate chemical reactions.

[0052] To illustrate how method 300 works in a real application, method 300 has been performed with actual values ​​for an ESP pump example. In the example, an operator may want to find out the head of a SJ2800 pump when it moves 300 cP of fluid at 700 BPD and 2333 RPM. These desired parameters are defined in step 310.

[0053] The water performance characteristics of the SJ2800 pump at 3500 RPM or 60 Hz are received in step 320. The received characteristics are shown as Figure 4Received performance curve 420 and efficiency curve 430 are for an SJ2800 pump in water with a specific gravity of 1.00 at room temperature and atmospheric pressure. Performance curve 420 shows the change in head in ft. at 3500 RPM with respect to the change in flow in BPD. The efficiency curve indicates the water BEP characteristics at 3500 RPM, such as a BEP flow of 2961 BPD and a BEP head of 56 ft.

[0054] In step 330, the specific speed of the pump instance is calculated using the BEP flow and BEP head. When calculated with the appropriate unit conversion, the specific speed of the pump is 1589 BPD. Since the specific speed is between 500 and 1500-1700, the pump is most likely of radial flow type.

[0055] In step 340, the water performance characteristics of the pump instance at 2333 RPM are calculated. The calculated flow rate is shown as Figure 4 At 2333 RPM, the BEP flow of the pump example is 1974 BPD and the BEP head is 24.88 ft. Using the water performance characteristics of the pump example at 2333 RPM, a Ketan viscosity head number correlation is developed in step 350 for the pump example in water at the desired RPM.

[0056] In step 360, the BEP flow and BEP head of the pump instance in the fluid of interest (300 cP) at 2333 RPM are calculated. To do this, correction factors for the BEP flow and BEP head are first derived. The correction factors are derived from the relationship between the BEP flow and BEP head ratio and the varying RPM and viscosity, and in the example, the correction factors are 0.4678 and 0.9244, respectively. Using these correction factors, the BEP flow of the pump instance in the fluid of interest at 2333 RPM is 923.232 (1974*0.4678) BPD, and the BEP head of the pump instance is 23 (24.88*0.9244) ft. The BEP flow is the product of the water BEP flow at 2333 RPM and the correction factor for the BEP flow, and the BEP head is the product of the water BEP head at 2333 RPM and the correction factor for the BEP head.

[0057] In step 370, the performance of the pump instance defined in step 310 in the application is determined, i.e., the head of the SJ2800 pump moving the fluid of interest at 700 BPD and 2333 RPM. As described above in step 370, the head of the SJ2800 pump in the viscous application is determined using the expected flow rate, the BEP flow rate and BEP head of the SJ2800 pump in the fluid of interest at 2333 RPM, and the normalized BEP flow rate of the pump in the fluid of interest at 2333 RPM.

[0058] 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 from step 310 (i.e., 700 BPD) by the BEP flow rate of the pump in the fluid of interest at 2333 RPM (i.e., 923.232) and is therefore 0.758. Using the normalized BEP flow rate of the pump in the fluid of interest at 2333 RPM and the Ketan viscous head number correlation from step 350, the normalized Ketan viscous head number (Ketan viscous head coefficient) corresponding to the normalized BEP flow rate of the pump in the fluid of interest at 2333 RPM is calculated. The normalized Ketan viscous head number is 0.708.

[0059] Substituting the BEP flow and BEP head of the SJ2800 pump in the fluid of interest at 2333 RPM, the expected flow, and the normalized Ketan viscosity head number into equation (5), the head of the pump instance in the fluid of interest at 700 BPD and 2333 RPM is calculated. 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 results can be verified by curve 460 representing the performance characteristics of the pump instance in the fluid of interest at 2333 RPM.

[0060] Figure 5 1 shows a flow chart of an embodiment of a method 500 for modeling performance characteristics of a pump in a viscous application. The method 500 may be performed by Figure 6 The method 500 is executed by a computer system such as 600 in the embodiment of the present invention. The series of instructions that cause the processor of the computer system to execute the method 500 when executed can be stored in a computer readable medium such as a CD-ROM, a floppy disk, a flash drive, or another data storage device. The method 500 starts at step 505.

[0061] At step 510, the operating parameters of the pump are used to form a dimensionless number. The operating parameters of the pump include head, flow, speed, viscosity, stage, BHP, and efficiency, and the operating parameters are arranged in a dimensionless form, such as the dimensionless relationship described above, i.e., the relationship between flow, head, and viscosity for the Ketan Viscous Head Number.

[0062] At step 520, dimensionless numbers are used in ratio terms to model the performance characteristics of the pump under various operating conditions. The ratio terms contain the ratio of each operating parameter to the corresponding operating parameter at a reference point. The reference point can be any point in the performance curve such as a BEP point, a point near zero flow, and / or a point near maximum flow. The method 500 ends at step 525.

[0063] Figure 6shows that a viscous performance prediction method has been built and configured to perform such Figure 3 300 or Figure 5 6. In the illustrated embodiment, system 600 includes processor 620, interface 640, and memory 660. It should be understood that system 400 has been simplified for illustrative purposes and may not show some components that may be present in an actual system.

[0064] Processor 620 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 interface 640 and memory 660 .

[0065] Interface 640 is a user interface and / or network interface card configured to receive the water performance characteristics of a given pump. As discussed above, the water performance characteristics of a given pump are typically provided by the manufacturer 680 of a given pump. Interface 640 can be a communication interface configured to communicate data, i.e., transmit and receive data. In this way, interface 640 can include necessary logic, ports, terminals, connectors, etc., to communicate data. Ports, terminals, connectors can be conventional sockets for communicating data via a communication network.

[0066] The memory 660 is a computer memory such as a read-only memory (ROM), a programmable ROM (PROM), an erasable PROM, a dynamic random access memory (DRAM), a static random access memory, and a flash memory. The memory 660 is configured to store the water performance characteristics and other calculated performance characteristics of a given pump received from the processor 620. The memory 660 may also be configured to store computer executable instructions to direct the operation of the processor 620 when the processor is activated. The operating instructions may correspond to one or more algorithms that predict the performance of a given pump in a fluid of interest at a desired RPM.

[0067] Figure 7 A viscous application of an electric submersible pump (ESP) is shown. In the application shown, an ESP assembly 700 is placed at the bottom of a well in a subsea underground oil well. The ESP assembly 700 can also be used for onshore operations. The ESP assembly 700 includes a speed controller 705, an ESP motor 720 (e.g., a DC motor), and an ESP pump 755.

[0068] In the illustrated embodiment, the speed controller 705 is placed in a cabinet 740 within a control room 735 on an offshore platform 745 such as an oil rig. The speed controller 705 is configured to adjust the speed of the ESP motor 720 to increase well productivity. In the illustrated embodiment, the ESP motor 720 is a two-pole, three-phase squirrel cage induction motor that operates to rotate the ESP pump 755. The ESP motor 720 is located near the bottom of the ESP assembly 700, just above the downhole sensor deep in the well. A power cable 715 extends from the speed controller 705 to the ESP motor 720. The length of the power cable 715 can be up to 12,000 feet.

[0069] ESP pump 755 may be a multi-stage centrifugal pump, each stage comprising an impeller and a diffuser. Prior to deployment, the ESP pump 755 may be configured to be a multi-stage centrifugal pump, each stage comprising an impeller and a diffuser. Figure 5 500) using the viscosity performance prediction method (such as Figure 3 300) predicts the performance of the ESP pump 755. Based on the prediction, the ESP pump 755 can be controlled to move the fluid of interest, such as oil or other hydrocarbons, through the production pipeline 730 to the storage tank on the offshore platform 745.

[0070] In some embodiments, pump 755 can be a horizontal pump, a screw pump, or an electric submersible screw pump. A motor seal section and an inlet section can extend between motor 720 and pump 755. Well casing 725 can separate ESP assembly 700 from well formation 760 and / or seawater. Perforations in casing 725 can allow the fluid of interest to enter underground casing 725 from formation 760.

[0071] Portions of the above-described apparatus, system, or method may be embodied in or performed by various analog or digital data processors, wherein the processor is programmed or stores an executable program of a sequence of software instructions to perform one or more of the steps of the method. The processor may be a programmable logic device such as a programmable array logic (PAL), a general array logic (GAL), a field programmable gate array (FPGA), or another type of computer processing device (CPD). The software instructions of such a program may represent an algorithm and be encoded in a machine-executable form on a non-transitory digital data storage medium such as a magnetic or optical disk, a random access memory (RAM), a magnetic hard disk, a flash memory, and / or a read-only memory (ROM) to enable various types of digital data processors or computers to perform one, more, or all of the steps of one or more of the above-described methods or the functions, systems, or apparatus described herein.

[0072] Portions of the disclosed examples or embodiments may involve a computer storage product having a non-transitory computer-readable medium having program code thereon for performing various computer-implemented operations embodying a portion of an apparatus, device, or performing steps of a method described herein. As used herein, non-transitory refers to all computer-readable media other than transient, propagating signals. Examples of non-transitory computer-readable media include, but are not limited to: magnetic media such as hard disks, floppy disks, and magnetic tapes; optical media such as CD-ROM disks; magneto-optical media such as floppy disks; and hardware devices such as ROM and RAM devices that are specifically configured to store and execute program code. Examples of program code include both machine code (such as code produced by a compiler) and files containing higher-level code that can be executed by a computer using an interpreter.

[0073] In interpreting the present disclosure, all terms should be interpreted in the broadest possible manner consistent with the context. Specifically, the terms "comprises" and "comprising" should be interpreted as referring to elements, components or steps in a non-exclusive manner, thereby indicating that the mentioned elements, components or steps can exist, be used, or be combined with other elements, components or steps not explicitly mentioned.

[0074] Those skilled in the art to which this application relates will appreciate that other and further additions, deletions, substitutions and modifications may be made to the described embodiments. It should also be understood that the terms used herein are only for the purpose of describing specific embodiments and are not intended to be restrictive, because the scope of the present disclosure will be limited only by the claims. Unless otherwise defined, all technical terms and scientific terms used herein have the same meaning as those of ordinary skill in the art to which the present disclosure belongs. Although any method and material similar to or equal to the method and material described herein may also be used to practice or test the present disclosure, a limited number of exemplary methods and materials are described herein.

[0075] Aspects disclosed herein include:

[0076] A. A method for predicting the performance of a pump in a fluid of interest at a desired RPM, the method comprising: receiving a water performance characteristic of the pump at a fixed RPM; using the water performance characteristic of the pump at the fixed RPM to determine a Ketan viscosity head number of the flow rate of the pump in water at the desired RPM, the Ketan viscosity head number representing the ratio of the flow rate to the corresponding head at a fixed internal resistance and the desired RPM; using the water performance characteristic of the pump at the desired RPM to determine a viscous head correlation between a normalized flow rate of the pump in water at the desired RPM and a normalized Ketan viscosity head number corresponding to the normalized flow rate; and using the viscous head correlation to predict the performance of the pump in the fluid of interest at the desired RPM.

[0077] B. A system for predicting the performance of a pump in a fluid of interest at a desired RPM, the system 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 a Ketan viscosity head number of the flow rate of the pump in water at a desired RPM using the water performance characteristics of the pump at a fixed RPM, the Ketan viscosity head number representing the ratio of the flow rate to the corresponding head at a fixed internal resistance and the desired RPM; determine a viscous head correlation between a normalized flow rate of the pump in water at the desired RPM and a normalized Ketan viscosity head number corresponding to the normalized flow rate using the water performance characteristics of the pump at the desired RPM; and use the viscous head correlation to predict the performance of the pump in the fluid of interest at a given RPM.

[0078] C. A method for modeling the performance characteristics of a pump in a viscous application, the method comprising: forming a dimensionless number using operating parameters of the pump; and using the dimensionless number in a ratio term to model the performance characteristics of the pump under various operating conditions.

[0079] Each of aspects A, B and C may have one or more of the following additional combinations of elements. Element 1: It further includes calculating the water performance characteristics of the pump at the desired RPM using similarity 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 best efficiency point (BEP) water performance characteristics of the pump at the fixed RPM. Element 2: Wherein the water performance characteristics of the pump at the desired RPM are calculated by using: flow rate at the desired RPM = flow rate at the fixed RPM * (the desired RPM / the fixed RPM); head at the desired RPM = head at the fixed RPM * (the desired RPM / the fixed RPM)^2; and BHP at the desired RPM = BHP at the fixed RPM * (the desired RPM / the fixed RPM)^3. Element 3: It further includes calculating the BEP flow rate of the pump in the fluid of interest at the desired RPM based on a flow correction factor derived from the relationship of the BEP flow ratio to the varying RPM and viscosity, and calculating the BEP head of the pump in the fluid of interest at the desired RPM based on a head correction factor derived from the relationship of the BEP head ratio to the varying RPM and viscosity. Element 4: Wherein the flow correction factor for the BEP flow rate of the pump in the fluid of interest at the desired RPM is further derived from the desired RPM and the viscosity of the fluid of interest. Element 5: Wherein the head correction factor for the BEP head of the pump in the fluid of interest at the desired RPM is further derived from the desired RPM and the viscosity of the fluid of interest. Element 6: It further includes defining the desired flow rate of the pump, the desired RPM, the fluid of interest, and the desired stage based on the viscous application for which the pump will be used. Element 7: It further includes calculating the specific speed of the pump at the desired stage using the BEP water performance characteristics of the pump at the fixed RPM. Element 8: wherein the BEP water performance characteristic of the pump at the fixed RPM is provided by a water performance curve of the pump. Element 9: wherein the determining the viscous head correlation comprises determining the normalized flow rate of the pump in the water at the desired RPM by normalizing the flow rate of the pump in the water at the desired RPM using a reference flow rate of the pump in the water at the desired RPM. Element 10: wherein the determining the viscous head correlation further comprises determining the normalized Ketan viscous head number by normalizing the Ketan viscous head number using a Ketan viscous head number corresponding to the reference flow rate of the pump in the water at the desired RPM.Element 11: wherein the reference flow rate of the pump is selected from the group consisting of: a BEP flow rate of the pump in the water at the expected RPM, a near zero flow rate, and a near maximum flow rate. Element 12: wherein the predicting the performance of the pump includes calculating a head of the pump in the fluid of interest at the expected flow rate and the expected RPM using the viscous head correlation, the BEP flow rate of the pump in the fluid of interest at the expected RPM, the BEP head of the pump in the fluid of interest at the expected RPM, and a normalized BEP flow rate of the pump in the fluid of interest at the expected RPM. Element 13: The calculating of the head of the pump in the fluid of interest at the desired flow rate and the desired RPM includes: calculating the normalized BEP flow rate of the pump in the fluid of interest at the desired RPM based on the desired flow rate and the BEP flow rate of the pump in the fluid of interest at the desired RPM; calculating a normalized Ketan viscous head number corresponding to the normalized BEP flow rate of the pump in the fluid of interest at the desired RPM using the viscous head correlation; and calculating the head of the pump in the fluid of interest at the desired flow rate and the desired RPM based on the desired flow rate, the 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 viscous head number corresponding to the normalized BEP flow rate of the pump in the fluid of interest at the desired RPM. Element 14: It further includes changing the size of the pump based on the performance of the pump in the fluid of interest at the desired RPM. Element 15: wherein the operating parameter of the pump comprises at least one of head, flow, speed, viscosity, diameter, brake horsepower, and efficiency. Element 16: wherein the ratio term comprises a ratio of each of the operating parameters to the corresponding operating parameter at a reference point. Element 17: wherein the reference point is a point in a performance curve and is selected from the group consisting of: a best efficiency point, a point near zero flow condition, and a point near maximum flow.

Claims

1. A method for predicting the performance of a pump in a fluid of interest at a desired RPM, the method include: receiving water performance characteristics of the pump at a fixed RPM; determining a Ketan head number for the flow rate of the pump in water at a desired RPM using the water performance characteristics of the pump at the fixed RPM, the Ketan head number representing a ratio of the flow rate to the corresponding head at a fixed internal resistance and the desired RPM; determining a viscous head correlation between a normalized flow rate of the pump in water at the desired RPM and a normalized Ketan viscous head number corresponding to the normalized flow rate using the water performance characteristics of the pump at the desired RPM; as well as The performance of the pump in the fluid of interest at the desired RPM is predicted using the viscous head correlation.

2. The method according to claim 1, further comprising calculating the water performance characteristics of the pump at the desired RPM using a similarity law 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 a best efficiency point (BEP) water performance characteristic of the pump at the fixed RPM.

3. The method of claim 2, wherein the water performance characteristics of the pump at the desired RPM are calculated by using: The flow rate at the desired RPM=the flow rate at the fixed RPM*(the desired RPM / the fixed RPM); The head at the desired RPM=the head at the fixed RPM*(the desired RPM / the fixed RPM)^2; and The BHP at the desired RPM=the BHP at the fixed RPM*(the desired RPM / the fixed RPM)^3.

4. The method of claim 1, further comprising calculating the BEP flow rate of the pump in the fluid of interest at the desired RPM based on a flow correction factor derived from the relationship between the BEP flow rate ratio and "varied RPM and viscosity", and calculating the BEP head of the pump in the fluid of interest at the desired RPM based on a head correction factor derived from the relationship between the BEP head ratio and "the varied RPM and viscosity", wherein the BEP flow rate ratio is a ratio of the BEP flow rate at a desired viscosity and a given RPM to the BEP flow rate of water at a given RPM.

5. The method of claim 4, wherein the flow correction factor for the best efficiency point (BEP) flow of the pump in the fluid of interest at the desired RPM is further derived from the desired RPM and the viscosity of the fluid of interest.

6. The method of claim 4, wherein the head correction factor for the best efficiency point (BEP) head of the pump in the fluid of interest at the desired RPM is further derived from the desired RPM and the viscosity of the fluid of interest.

7. The method of claim 1, further comprising defining a desired flow rate for the pump, the desired RPM, the fluid of interest, and a desired level based on a viscous application for the pump.

8. The method of claim 1, further comprising calculating a specific speed of the pump at a desired stage using a Best Efficiency Point (BEP) water performance characteristic of the pump at the fixed RPM.

9. The method of claim 8, wherein the best efficiency point (BEP) water performance characteristic of the pump at the fixed RPM is provided by a water performance curve for the pump.

10. The method of claim 1, wherein the determining the viscous head correlation comprises determining the normalized flow rate of the pump in the water at the desired RPM by normalizing the flow rate of the pump in the water at the desired RPM using a reference flow rate of the pump in the water at the desired RPM.

11. The method of claim 10, wherein the determining the viscous head correlation further comprises determining the normalized Ketan viscous head number by normalizing the Ketan viscous head number using a Ketan viscous head number corresponding to the reference flow rate of the pump in the water at the desired RPM.

12. The method of claim 11, wherein the reference flow rate of the pump is selected from the group consisting of: a best efficiency point (BEP) flow rate of the pump in the water at the desired RPM, a near zero flow rate, and a near maximum flow rate.

13. The method of claim 1, wherein said predicting the performance of said pump comprises calculating a head of said pump in said fluid of interest at an expected flow rate and said expected RPM using said viscous head correlation, a best efficiency point (BEP) flow rate of said pump in said fluid of interest at said expected RPM, a best efficiency point (BEP) head of said pump in said fluid of interest at said expected RPM, and a normalized best efficiency point (BEP) flow rate of said pump in said fluid of interest at said expected RPM.

14. The method of claim 13, wherein said calculating the head of a pump in said fluid of interest at said desired flow rate and said desired RPM comprises: calculating the normalized best efficiency point (BEP) flow rate of the pump in the fluid of interest at the desired RPM based on the desired flow rate and the best efficiency point (BEP) flow rate of the pump in the fluid of interest at the desired RPM; calculating a normalized Ketan viscous head number corresponding to the normalized best efficiency point (BEP) flow rate of the pump in the fluid of interest at the desired RPM using the viscous head correlation; and The head of the pump in the fluid of interest at the expected flow rate and the expected RPM is calculated based on the expected flow rate, the best efficiency point BEP flow rate of the pump in the fluid of interest at the expected RPM, the best efficiency point BEP head of the pump in the fluid of interest at the expected RPM, and the normalized Ketan viscosity head number corresponding to the normalized best efficiency point BEP flow rate of the pump in the fluid of interest at the expected RPM.

15. The method of claim 1, further comprising varying a size of the pump based on the performance of the pump in the fluid of interest at the desired RPM.

16. A system for predicting the performance of a pump in a fluid of interest at a desired RPM, the system include: an interface configured to receive water performance characteristics of the pump at a fixed RPM; as well as a processor coupled to the interface and configured to: determining a Ketan head number for the flow rate of the pump in water at a desired RPM using the water performance characteristics of the pump at a fixed RPM, wherein the Ketan head number represents a ratio of the flow rate to the corresponding head at a fixed internal resistance and the desired RPM; determining a viscous head correlation between a normalized flow rate of the pump in water at the desired RPM and a normalized Ketan viscous head number corresponding to the normalized flow rate using the water performance characteristics of the pump at the desired RPM; and The performance of the pump in the fluid of interest at the desired RPM is predicted using the viscous head correlation.

17. The system of claim 16, wherein the processor is further configured to calculate the water performance characteristics of the pump at the desired RPM using a similarity law 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 a best efficiency point (BEP) water performance characteristic of the pump at the fixed RPM.

18. The system of claim 17, wherein the water performance characteristics of the pump at the desired RPM are calculated by using: The flow rate at the desired RPM=the flow rate at the fixed RPM*(the desired RPM / the fixed RPM); The head at the desired RPM=the head at the fixed RPM*(the desired RPM / the fixed RPM)^2; and The BHP at the desired RPM=the BHP at the fixed RPM*(the desired RPM / the fixed RPM)^3.

19. The system of claim 16, wherein the processor is further configured to: calculating the best efficiency point BEP flow rate of the pump in the fluid of interest at the desired RPM based on a flow correction factor derived from the relationship between the best efficiency point BEP flow rate ratio and "varying RPM and viscosity", wherein the best efficiency point BEP flow rate ratio is the ratio of the best efficiency point BEP flow rate at the desired viscosity and given RPM to the best efficiency point BEP flow rate of water at a given RPM; and The best efficiency point BEP head of the pump in the fluid of interest at the desired RPM is calculated based on a head correction factor derived from the relationship between the best efficiency point BEP head ratio and "the varying RPM and viscosity".

20. The system of claim 19, wherein the flow correction factor for the best efficiency point (BEP) flow of the pump in the fluid of interest at the desired RPM is further derived from the desired RPM and the viscosity of the fluid of interest.

21. The system of claim 19, wherein the head correction factor is further derived from the desired RPM and the viscosity of the fluid of interest.

22. The system of claim 16, wherein the processor is further configured to define a desired flow rate for the pump, the desired RPM, the fluid of interest, and a desired level based on a viscous application for the pump.

23. The system of claim 16, wherein the processor is further configured to calculate a specific speed of the pump at a desired level using a Best Efficiency Point (BEP) water performance characteristic of the pump at the fixed RPM.

24. The system of claim 23, wherein the best efficiency point (BEP) water performance characteristic of the pump at the fixed RPM is derived from a water performance curve for the pump.

25. The system of claim 16, wherein the processor is further configured to determine the normalized flow rate of the pump in the water at the desired RPM by normalizing the flow rate of the pump in the water at the desired RPM using a reference flow rate of the pump in the water at the desired RPM.

26. The system of claim 25, wherein the processor is further configured to determine the normalized Ketan viscous head number by normalizing the Ketan viscous head number using a Ketan viscous head number corresponding to the reference flow rate of the pump in the water at the desired RPM.

27. The system of claim 26, wherein the reference flow rate of the pump is selected from the group consisting of: a best efficiency point (BEP) flow rate of the pump in the water at the desired RPM, a near zero flow rate, and a near maximum flow rate.

28. The system of claim 16, wherein the performance of the pump is predicted by calculating the head of the pump in the fluid of interest at an expected flow rate and the expected RPM using the viscous head correlation, the best efficiency point (BEP) flow rate of the pump in the fluid of interest at the expected RPM, the best efficiency point (BEP) head of the pump in the fluid of interest at the expected RPM, and the normalized best efficiency point (BEP) flow rate of the pump in the fluid of interest at the expected RPM.

29. The system of claim 28, wherein said calculating the head of a pump in said fluid of interest at said desired flow rate and said desired RPM comprises: calculating the normalized best efficiency point (BEP) flow rate of the pump in the fluid of interest at the desired RPM based on the best efficiency point (BEP) flow rate of the pump in the fluid of interest at the desired RPM; calculating a normalized Ketan viscous head number corresponding to the normalized best efficiency point (BEP) flow rate of the pump in the fluid of interest at the desired RPM using the viscous head correlation; and The head of the pump in the fluid of interest at the expected flow rate and the expected RPM is calculated based on the normalized best efficiency point (BEP) flow rate of the pump in the fluid of interest at the expected RPM, the best efficiency point (BEP) head of the pump in the fluid of interest at the expected RPM, and the normalized Ketan viscosity head number corresponding to the normalized best efficiency point (BEP) flow rate of the pump in the fluid of interest at the expected RPM.

30. A method for modeling the performance characteristics of a pump in a viscous application, the method include: forming a dimensionless number using an operating parameter of the pump; as well as The dimensionless number is used in a ratio term to model the performance characteristics of the pump under various operating conditions, wherein the modeling includes determining a Ketan viscous head number for the flow rate of the pump in water at a desired RPM and using the water performance characteristics of the pump at the desired RPM to determine a viscous head correlation between a normalized flow rate of the pump in water at the desired RPM and a normalized Ketan viscous head number corresponding to the normalized flow rate.

31. The method of claim 30, wherein the operating parameter of the pump comprises at least one of head, flow, speed, viscosity, diameter, brake horsepower, and efficiency.

32. The method of claim 30, wherein the ratio term comprises a ratio of each of the operating parameters to a corresponding operating parameter at a reference point.

33. The method of claim 32, wherein the reference point is a point in a performance curve and is selected from the group consisting of: a best efficiency point, a point near a zero flow condition, and a point near a maximum flow.

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