SPPS USER Manual 1 SPPS USER GUIDE DRAFT VERSION 6/20/2011. Please send comments to

Transcription

1 SPPS USER Manual 1 SPPS USER GUIDE DRAFT VERSION 6/20/2011 Please send comments to Brenton S. McLaury or Siamack A. Shirazi brenton-mclaury@utulsa.edu, siamack-shirazi@utulsa.edu THE EROSION/CORROSION RESEARCH CENTER THE UNIVERSITY OF TULSA

2 2 EROSION/CORROSION RESEARCH CENTER SAND PRODUCTION PIPE SAVER (SPPS) SPPS v4.2 Introduction The Sand Production Pipe Saver (SPPS) computer program has been developed by the investigators at the E/CRC. This computer program calculates sand erosion rates in the forms of pipe wall penetration rate (thickness loss of pipe in mpy or mm/year) and pipe wall thickness loss per mass of sand (thickness loss of pipe divided by mass of sand in mil/lb or mm/kg) in several pipe geometries such as elbows, tees, straight pipe, direct impingement, sudden pipe expansion, and contractions. The computer program is also capable of computing threshold flow stream velocities or production rates. Threshold velocity is a flow velocity that will produce a tolerable amount of erosion as specified by the user. General Description of SPPS Excel v4.2 Main Interface SPPS v4.2 can be downloaded from the E/CRC web site at under the Members Only section. The user will download one file titled SPPS v4.2.zip. This file needs to be unzipped and contains four files: SPPS v4.2.exe, SPPS 2D Database.xls, SavedInput.xls, and Instructions.txt. SPPS v4.2.exe is the main SPPS program that contains the user interface and code. SPPS 2D Database.xls contains CFD flow solutions necessary for the 2- D model that will be described later. SavedInput.xls is a file that can be accessed from the main SPPS program to save and retrieve user input. There is no need for the user to open either SPPS 2D Database.xls or SavedInput.xls directly. Instructions.txt contains some instructions on the installation of SPPS. Note that this version of SPPS will expire on July 1, 2012 and can not be reopened after that date. Upon opening the workbook, the sheet titled Main becomes active. The Main sheet is shown in Figure 1. This sheet displays the two main sections that are available in the program: Erosion Prediction and Threshold Prediction. The Erosion Prediction option is used to calculate either thickness loss per time or thickness loss per mass of sand. The Threshold Prediction option calculates a curve representing pairings of superficial gas and liquid velocities that result in a given penetration rate. The Erosion and Threshold Prediction options have two ways to enter the input. The first option (Input fluid properties) is to enter the fluid properties such as density and viscosity of the fluids at the pressure and temperature of interest at the location of the fitting. For this option, the gas flow rate or superficial velocity should also correspond to the actual rate of the location of the fitting. The second option (Input well conditions) is to enter the pressure and temperature at the location of the fitting and have the program calculate the fluid properties. The gas rate at standard conditions should be used for this option. The first option (entering density and viscosity) should be used if possible, since the models to predict gas and oil properties may not be valid for the well under consideration. One of the four option buttons shown in Figure 1 should be selected corresponding to the desired type of calculation, then the Go to Sheet button should be pressed. This takes the user to the appropriate sheet for performing that type of calculation. The four option buttons correspond to four different sheets within SPPS: Erosion-Input Fluid Prop, Erosion-Input Well

3 SPPS USER Manual 3 Prop, Threshold-Input Fluid Prop, and Threshold-Input Well Prop. So alternately, the user could simply select the desired sheet. Figure 1. Calculation Types Available as shown in Sheet Titles Main. The following sheets are visible to the user (these sheets are considered to be the essential sheets): Main Erosion-Input Fluid Prop(erties ) Erosion-Input Well Prop(erties) Threshold-Input Fluid Prop(erties) Threshold-Input Well Prop(erties) 1D SPPS vs Data 2D SPPS vs Data The Main sheet was previously discussed. The next four sheets correspond to the four types of calculations discussed. Sample views of the input for the Erosion-Input Fluid Prop sheet are shown in Figures 2a to 2c. The output for this sheet is shown in Figure 3. These figures show the main sections of the sheet: 1) the buttons that perform various actions, 2) the input sections, and 3) the output section. 1D SPPS vs Data and 2D SPPS vs Data contain comparisons of SPPS utilizing 1 and 2-dimensional model approaches, respectively, with data from E/CRC and literature. The data used on both sheets is identical and also serves as an experimental database.

4 4 EROSION/CORROSION RESEARCH CENTER Figure 2a. Erosion-Input Fluid Prop Sheet Input, Part 1. Figure 2b. Erosion-Input Fluid Prop Sheet Input, Part 2.

5 SPPS USER Manual 5 Figure 2c. Erosion-Input Fluid Prop Sheet Input, Part 3. Figure 3. Erosion-Input Fluid Prop Sheet Output. Features General to all Types of Calculations SPPS utilizes the spreadsheet format of Excel to allow the user to run many cases at once. This allows the user to perform sensitivity studies easily. This is accomplished by copying the

6 6 EROSION/CORROSION RESEARCH CENTER input for a case in rows below it and changing the input of interest over the desired range in a column. Each case is on a separate row. It is very important the user never delete any rows or columns in the spreadsheet. This could result in the program not running or not running properly. When running a case, the user should first select the geometry, material type, appropriate units for the variables, and options at the top of the spreadsheet. Additional information on a specific heading/variable is available if the cell contains a red marker in the upper-right corner of the cell. The user can simply, pass the mouse over the marker and the information box will appear. When selecting the geometry and material type, a form will appear after pressing the corresponding Select button. Figure 4 displays the Geometry Type form for the Erosion Prediction procedures. Figure 5 displays the Material Type form for both the Erosion Prediction and Threshold Prediction procedures. The units and options are selected by using the drop-down list in Row 6 of the different columns. In SPPS, each row represents a potential case. The user has control over the rows that are calculated. The user should type end in the Description cell in a row after the last row of input. The row where the calculations begin depends on input from the user. begin should be typed in the Description cell in a row before the first row to be considered. In this way, only the rows between begin and end will be calculated. If begin is not used, then calculations start from the first row of input (Row 8). Empty rows are ignored in the calculation. Figure 4. Geometry Type Form for Erosion Prediction Procedure.

7 SPPS USER Manual 7 Figure 5. Material Type Form. The geometry type and material type are different than the other variables. The default geometry is the type selected in the Geometry Type form (see Figure 4) and is shown in Row 6. If the geometry type cell of a case being calculated is left blank, the default value is used, but it is possible to override the default by entering the numeric code for the geometry type shown in the "Geometry Type" form. For the long radius elbow the selection is 2, but the user must specify r/d value after an underscore. For example 2_5 is a long radius elbow with r/d=5. Similarly, the default material type is the type selected in the Material Type form and is shown in Row 6. If the material type cell of a case being calculated is left blank, the default value is used, but it is possible to override the default by entering the numeric code for the material type shown in Figure 5. If Carbon Steel/Other is selected along with a 1-D geometry from the Geometry Type form, the Brinell hardness must also be given. For example, the user may enter 1_210 in the cell, where 210 is the value of the Brinell hardness. If Carbon Steel/Other is selected along with a 2-D geometry from the Geometry Type form, the Brinell hardness and the density of the material in kg/m 3 must be provided. In this case, the user may enter 1_210_7800 in the cell, where 210 is the value of the Brinell hardness and 7800 kg/m 3 is the density of the material. It is important to note that Carbon Steel/Other is the only material option that is currently available for the 2-D geometries. The following buttons appear at the top-left side of the sheets: Read Input Save Input Report RUN Delete Nonessential Sheets

8 8 EROSION/CORROSION RESEARCH CENTER The Save Input and Read Input options are available so that input for a sheet can be saved and retrieved without saving the entire SPPS file with a different name. After pressing the Save Input button, the form in Figure 6 will appear. The names provided for existing saved sheets are shown under Existing Items. To save the current sheet, the user will type in a name under Enter a name for the current input to be saved and then press Save the Current Input and Exit. A saved sheet can also be deleted by selected it from the Existing Items list and then pressing the Delete Selected Input button. To retrieve the saved sheets, the Read Input button can be pressed, and the form in Figure 7 will appear. The available saved sheets appear under Select one item from this list ; only the saved sheets of the same type as the current sheet will appear in this list. For example if the current sheet is Erosion-Input Fluid Prop, then only sheets saved while in the Erosion-Input Fluid Prop sheet will appear in the list. To import the data to the current sheet, the user will select a name from the list and then press the Read Selected Input and Exit button. It is important to note that the input currently in the sheet will be overwritten by the selected input. Figure 6. Save Input Menu.

9 SPPS USER Manual 9 Figure 7. Read Input Menu. The Report button is used to generate a report for a given case. The cases must be run before generating the report. A lowercase x should be placed in the Report column by the case(s) of interest. A sheet is created for each report selected. The report sheet has the name Report Case in Row#X where X represents the row number of the case being reported. If another report is generated with the same row number, then the name will be Report Case in Row#X(2). The user can always change the name of the report sheet if desired. In order to purge the workbook of sheets generated from reports and other features, the Delete Nonessential Sheets option can be selected. Pressing the RUN button starts the execution of the calculations. A message will appear that alerts the user that the Calculation is completed. The output section is placed to the right of the input section. The program performs a few checks on the input specified by the user. The program alerts the user to inappropriate input. If for any reason a mistake occurs during the calculation of one case, SPPS will skip this case, put a message Calculation was not successful in the Penetration Rate output column, and continue the calculation on the next case. It is recommended that the user always check the last output column where various warning messages are displayed. Erosion-Input Fluid Prop(erties) For this type of erosion calculation, fluid properties and rates are entered at the location of interest. In other words, the densities and viscosities as well as actual flow rates must be known at the location of the fitting. The liquid properties and rates can be entered for both water and oil. The program uses volume averaging when calculating the representative mixture

10 10 EROSION/CORROSION RESEARCH CENTER properties of the liquid. The gas properties are also entered. A summary of the input parameters for this calculation procedure is given below: Report - This input option creates a report with all input/output parameters. Place a lowercase x in this cell if you would like a report for this case, then press report. Before preparing the report, the case must have previously been run. Description - A user defined description of the case. This is optional. Geometry Type - The default geometry is the type selected in the Geometry Type form (see Figure 4) and is shown in Row 6. If the geometry type cell is left blank, the default value is used, but it is possible to override the default by entering the numeric code for the geometry type shown in the "Geometry Type" form. For the long radius elbow the selection is 2, but the user must specify r/d value after an underscore. For example 2_5 is a long radius elbow with r/d=5. As shown in Figure 4, there are two categories of geometries: 1-D Geometries and 2-D Geometries. As the category names imply, a one-dimensional modeling approach is used for the 1-D Geometries (elbow, long radius elbow, direct impingement, tee, plug tee, straight pipe, contraction, and sudden expansion), and a two-dimensional modeling approach is used for the 2- D Geometries (2D standard elbow and 2D direct impingement). Material Type - This is the pipe material where erosion calculation is taking place. The default material type is the type selected in the Material Type form (See Figure 5) and is shown in Row 6. If the material type cell is left blank, the default value is used, but it is possible to override the default by entering the numeric code for the material type list shown in Figure 5. For Carbon Steel/Other, the Brinell hardness must also be given. For example, the user may enter 1_210 in the cell, where 1 indicates Carbon Steel/Other and 210 is the value of the Brinell hardness. If Carbon Steel/Other is selected along with a 2-D geometry from the Geometry Type form, the Brinell hardness and the density of the material in kg/m 3 must be provided. In this case, the user may enter 1_210_7800 in the cell, where 210 is the value of the Brinell hardness and 7800 kg/m 3 is the density of the material. It is important to note that Carbon Steel/Other is the only material option that is currently available for the 2-D geometries. Pipe Roughness - This input parameter is used to calculate flow regime. For commercial steel pipes, the design value of pipe roughness is approximately ft. Pipe Diameter - This is ID of pipe. The range for acceptable pipe diameters is 0.5 to 12 inches. If your pipe diameter is larger than 12 inches, you can specify 12 inch for a conservative erosion estimate. If a pipe diameter outside this range is specified, the calculations will proceed with the diameter input by the user. The pipe diameter determines the thickness of the stagnation layer that is a region that particles have to pass through in order to strike the pipe wall. When the pipe diameter decreases, the erosion rate increases. Exit Pipe Diameter - This entry is only necessary for sudden expansions and contractions. For the sudden expansion, it is the ID of the larger diameter section after the expansion. For contractions, it is the ID of the smaller diameter section after the contraction.

11 SPPS USER Manual 11 Contraction Taper Angle - This entry is only necessary for contractions. The unit is degrees, and 90 degrees corresponds to a sudden contraction. If this entry is left blank for a contraction case, 90 degrees is the default. Particle Diameter - If the particle size varies there are two options. One option is to specify average particle size. Another option is to specify a bin size. Then, the user must specify sand rate corresponding to the bin size that is specified in each row. Then, once the calculations are completed for each bin size, then the user can simply add the erosion results to obtain the cumulative erosion rate. The range for acceptable particle diameters is 50 to 1000 microns for the 1-D geometries and 20 to 1000 microns for the 2-D geometries. Results have been compared with data ranging from 20 microns to 5 mm. The user however, can specify a particle size that is outside of the acceptable range and the calculation would yield an answer with one exception. A particle size of less than 50 microns is not allowed for 1-D geometries and simply replaced with 50 microns in the calculation if a value less than 50 microns is entered by the user. Particle Density - Erosion equations used are based on silica sand. Silica sand density is approximately 165 lb/ft 3 (2600 kg/m 3 ). Particle Sharpness - Sharp sand with angular corners is the most conservative estimate. Semirounded sand has rounded corners. Rounded-sand is similar to spherical glass beads. Sharpness factors of 1.0, 0.53, and 0.20 are applied for the sharp, semi-rounded, and rounded sand, respectively. These factors can be overwritten by placing a number between 0 and 1 in the row corresponding to the case under consideration. Particle Rate - Rate of sand in ppm is based on mass of sand per mass of mixture (fluid and sand). Volumetric concentration is the ratio of volume of sand to the volume of mixture. Mass concentration is the ratio of mass of sand to the mass of liquid or gas. If liquid is present, the calculations for ppm, mass percent, and volume percent are based only on the liquid present and the amount of gas is ignored for gas-liquid flows. The flow rate of gas is only used in calculations of particle rate when there is no liquid present. SPPS assumes a linear relation between sand rate and erosion. Based on a previous experimental study, E/CRC found this to be true for sand concentrations less than 2% by weight in liquids. Water Density (Process) - Water density at process conditions (location of fitting). This is the actual density of the water at the location of the fittings. Typical values are 62.4 lb/ft 3 or 1000 kg/m 3. Water Viscosity (Process) - Water viscosity at the location of the fitting. For saturated water viscosity range is 1.7 cp at (0 o C) to 0.24 cp (at 120 o C). At 20 o C water viscosity is about 1.0 cp. Water Rate - Water rate at the location of the fitting. Maximum acceptable liquid rate corresponds to a velocity of 15 ft/s (or m/s). This means no data is available beyond this velocity. Calculations will still be performed even if the liquid velocity is greater than 15 ft/s. Oil Density (Process) - Oil density at process conditions (location of fitting).

12 12 EROSION/CORROSION RESEARCH CENTER Oil Viscosity (Process) - Oil viscosity at the location of the fitting. Oil viscosity varies significantly with temperature. In SPPS, the recommended range for oil viscosity for calculation is 0.1 to 60 cp. Oil Rate - Oil rate at the location of the fitting. Maximum acceptable liquid rate corresponds to a velocity of 15 ft/s (or m/s). This means no data is available beyond this velocity. Calculations will still be performed even if the liquid velocity is greater than 15 ft/s. Gas Density (Process) - Gas density at process conditions (location of fitting). Gas density is a strong function of pressure and temperature. Gas Viscosity (Process) Gas viscosity at the location of the fitting. Gas Rate (process) - Gas rate at the location of the fitting. Maximum acceptable gas rate corresponds to a velocity of 300 ft/s (or m/s). This means that beyond 300 ft/s no erosion data was available. Calculations will still be performed even if the gas velocity is greater than 300 ft/s. Interfacial Tension - This is interfacial tension between gas and liquid. This parameter is only used for flow regime calculations and entrainment fraction in annular flow. Apply Regime Dependent Model - This option provides two methods that can be used to calculate erosion. One method uses the same calculation for V o, the representative particle initial velocity, for all flow regimes as seen in empirical Equations (1)-(3), V o n SL n = λ V + (1 λ) V (1) 0.11 SG VSL λ = VSG V (2) + SL V = SG n 1 exp 0.25 (3) V SL where V SL is the superficial liquid velocity and V SG is the superficial gas velocity. In order to use this model, select (2) no from the Apply Regime Dependent Model section of the input. If (1) yes is selected, then different models are applied for different flow regimes. 1 or 2 can also be entered for a case to override the default setting in Row 6. Flow Regime - In multiphase flow, the flow regime affects the calculations of flow stream velocity and erosion rates. A flow regime prediction model is available in SPPS. To use this prediction model to establish the flow regime select (1) Calculate in the Flow Regime column. However, the user can override the model by selecting one of the other options in the Flow Regime column: (2) Mist, (3) Annular, (4) Churn, (5) Slug, (6) D-Bubble, and (7) Bubbly. The default setting in Row 6 can also be overridden for cases under consideration by entering the numeric code of one of the 7 options.

13 SPPS USER Manual 13 Erosion-Input Well Prop(erties) If the user has access to the actual fluid properties at the fitting the Erosion-Input Fluid Prop(erties), discussed above, should be used. For the Erosion-Input Well Prop(erties) option, the pressure and temperature at the location of interest is entered along with flow rates at standard conditions. The program then calculates the fluid properties and actual flow rates at the fitting. The two methods for calculating erosion (based on flow regime) discussed above in the Erosion-Input Fluid Prop(erties) section are also available for this option. The additional input parameters specific to these calculations (that are not listed in Erosion-Input Well Prop(erties) above) are listed below: Water Rate - Water rate at standard conditions. Oil Density - Oil density at standard conditions. Oil Rate - Oil rate at standard conditions. Maximum acceptable liquid rate corresponds to a velocity of 15 ft/s (or m/s). This means no data is available beyond this velocity. Calculations will still be performed even if the liquid velocity is greater than 15 ft/s. Gas Rate (Standard) - Gas rate at standard conditions. Gas Molecular Weight - Gas molecular weight is used to calculate density and viscosity of the gas. Gas density is a strong function of molecular weight, pressure and temperature. Temperature - Temperature at the flowing conditions (at the fittings). Pressure - Pressure at the flowing conditions (at the fittings). Threshold-Input Fluid Prop(erties) and Threshold-Input Well Prop(erties) The input parameters for these calculations are similar to the erosion calculations discussed above in Erosion-Input Fluid Prop(erties) and Erosion-Input Well Prop(erties) sections. The primary difference is that the flow rates are not provided as input, since these are the quantities being calculated from the allowable penetration rate provided by the user as input. Another additional input is the amount of water present in the liquid phase (water cut): Water Cut - This input is the percent of water that exists in the liquid phase. This quantity is assumed to remain nearly a constant. When the fluid properties are defined, then the viscosity and density of water at the process conditions are used. On the other hand, when the well properties are defined, viscosity and density of water at the specified temperature are calculated. Allowable Penetration Rate - This is the penetration rate that can be allowed for the life of the well. Normally an allowable penetration rate of 1 mpy is recommended to account for uncertainties in the database, input parameters and stochastic nature of the erosion process.

14 14 EROSION/CORROSION RESEARCH CENTER Calculate API RP 14E Enter C Value Even though we do not recommend using API RP 14E in the presence of sand when considering erosion, it is provided as an option for comparison. To generate the API RP 14E curve, select yes from the drop-down menu and enter the C value in the row of interest. Since a range of output is produced for a given case, a new sheet is created with the name Result Case in Row#X where X represents the numerical value of the row for that case. The new sheet contains a threshold velocity map and the data used to generate the graph. A sample threshold map is shown in Figure 8. As seen in this figure, the user has the option of also showing the curve generated by applying the API RP 14E procedure. Currently only one option is available to calculate erosion for the threshold feature, and this option corresponds to the calculation of V o that is not flow regime dependent provided in Equations (1) to (3) Liquid Rate, Vsl (ft/s) Gas Rate, Vsg (ft/s) (process) E/CRC API RP 14E Figure 8. Sample Threshold Velocity Map. Models within SPPS A variety of models are used within SPPS to predict erosion rates. The models that are available depend on the type of geometry and whether multiple fluid phases (gas and liquid) are present. A discussion of the models is divided into the types of geometry as shown in Figure 3. Geometries 1 through 5 apply similar models as do geometries 21 and 22. Geometries 6, 7, and 8 (Straight Pipe, Contraction, and Sudden Expansion, respectively) each apply unique models but all were developed for single-phase carrier fluid. Geometries 1-5 (Erosion with Single-phase Carrier Fluid) The erosion calculation for these geometries is based on Equation 4. where: 1.73 L 2 D0) WV h = FM FS FP Fr / D (4) (D /

15 SPPS USER Manual 15 h = penetration rate F M, F S = empirical factors for material and sand sharpness F P = penetration factor F r/d = penetration factor for long radius elbows W = sand production rate V L = characteristic particle impact velocity D = pipe diameter D o = reference pipe diameter, 1 inch (25.4 mm) Values for F M are determined experimentally and have been determined for all materials listed in Figure 4. Values for F S can range from 0.2 to 1.0 where 0.2 is used for spherical particles (glass beads) and 1.0 is used for sharp, angular sand. Both these options are available within SPPS along with semi-rounded particles with a factor of However, the user may override these values by placing a factor in the appropriate row of the Particle Sharpness column. F P is a penetration factor that is a function of geometry. The purpose of this factor is to account for the variation in thickness loss resulting from the geometry specific erosion pattern (how spread is the erosion). F r/d is similar to F P except it was determined specifically for long radius bends from CFD predictions. It should be noted that this term was developed for single-phase carrier fluids. The diameter ratio (D/D o ) 2 term is also used to account for the difference in internal surface area that is being eroded, but in this case, the variation in eroded area results from difference in pipe size instead of geometry type. The term V L in the equation represents the characteristic particle impact velocity of particles, which must be deduced by solving a simplified particle tracking equation. E/CRC developed a method for calculating V L, which is obtained through creating a simple model of the stagnation layer representing the pipe geometry. The stagnation zone is a region that the particles must travel through to penetrate and strike the pipe wall for erosion to occur. This approach is graphically displayed in Figure 9. The severity of erosion in this zone depends on a series of factors such as fitting geometry, fluid properties and sand properties. The stagnation length increases with pipe diameter. A simplified particle-tracking model is used to compute the characteristic impact velocity of the particles; the model assumes movement in one direction with fluid velocity profile ranging from the average fluid velocity, V o, to zero at the wall. Initial particle velocity is assumed to be the same as the flow stream velocity, V o. Validity of this assumption is limited to single-phase flow when there is no-slip between the particles and fluid. Since the particle is forced to move in one direction, this is referred to as the 1-D model. Geometries 1-5 (Erosion with Multiphase Carrier Fluid) For these geometries, the erosion calculation is also based on Equation 4; however, the method to determine the representative impact velocity is different. There are two approaches used to account for multiple phases: flow regime independent and dependent models.

16 16 EROSION/CORROSION RESEARCH CENTER Flow Regime Independent Model This approach is extremely similar to the single-phase carrier fluid approach with two main differences. First, Equations 1 to 3 are used to provide the initial particle and fluid velocities instead of using the average velocity in single-phase flow. Second, the fluid properties (density and viscosity) used in the simplified particle tracking are mixture properties of the gas and liquid based on volume averaging. Stagnation Zone Equivalent Stagnation Length L Stagnation Zone Tee Particle Initial Position v o x Elbow Figure 9. Schematic Description of Stagnation Length Model Flow Regime Dependent Model The flow regime independent model does not consider the complex flow behaviors that exist in multiphase flow. The flow regime dependent model attempts to capture the physics of two-phase flow and is expected to be more reliable and general because it incorporates the important parameters of multiphase flow that are critical to erosion. Model for Annular Flow Annular flow exists at high gas velocity and low liquid velocity. Due to high gas velocity, erosion is usually higher in annular flow than other flow regimes. In gas production wells, the flow is usually annular, gas-liquid, two-phase flow. The gas flows in the core region at high velocity, the liquid flows as a thin film inside the pipe wall at a slower velocity. A schematic of annular flow is shown in Figure 10.

17 SPPS USER Manual 17 VFilm VCore.... Entrained sand and Liquid droplets in the gas core Entrained sand particles in the annular liquid film δ D- 2δ D Figure 10. Schematic of Annular Flow A fraction of the liquid is entrained in the gas core region as droplets and travels at a velocity similar to the local gas velocity. The gas core to liquid film interface is unstable and wavy with high interfacial shear stress. It is assumed that sand is uniformly distributed in the liquid phase and travels at similar velocities as the phase in which they are present. The velocities of the liquid film and liquid droplets entrained in the gas core are considered in calculating the initial particle velocities. Additionally, the mass fractions of sand in the film and in the gas core are assumed to be equal to the mass fraction of liquid in the film and gas core region. This means that the mass fraction of sand in the annular film and gas core is assumed to be the same as the mass fraction of liquid in these regions. The model for annular flow is divided into two parts to account for particles in the gas core and the liquid film. The erosion resulting from the particles in the gas core and liquid are then summed to provide the total erosion. Impact Velocity for Particles in Gas Core A two-step approach is used to determine the representative impact velocity of particles present in the gas core. The motion of a representative particle through the gas core is simplified to a one-dimensional path. A simplified Lagrangian particle tracking routine developed at E/CRC described previously is applied across the gas core. This first step is to determine the

18 18 EROSION/CORROSION RESEARCH CENTER representative velocity of a particle leaving the core region and entering the liquid film. The particle motion through the gas core is represented by the particle passing through a onedimensional flow field that has an initial velocity equivalent to the gas core velocity. The fluid properties, density and viscosity, in this region are assumed to be the mixture properties of the gas core (gas and liquid droplets). The representative length used for the particle tracking calculation is based on the diameter of the pipe. The initial particle velocity is assumed to be the liquid droplet velocity in the gas core. The particle velocity at the end of the stagnation length is assumed to represent the particle velocity at the interface of the gas core and liquid film. For many cases, the particle velocity at the interface is similar to the gas core velocity due to the differences in density between the particle and gas. However, the exchange of momentum between the gas and the particle is greater for a more dense gas causing the deceleration of the gas to slow the particles more effectively. The next step is to represent the motion of the particle through the liquid film. A two-dimensional particle tracking is applied across the liquid film. A linear fluid velocity profile is assumed, ranging from twice the average film velocity at the interface between the film and the gas core and a value of zero at the wall. The direction of the velocity is parallel to the wall, tangential velocity. The normal fluid velocity is assumed to be zero. The film thickness is determined by a method proposed by Kaji and Azzopardi (2010). The particle enters the liquid film in the direction normal to the wall with a velocity calculated with the previous particle tracking procedure in the gas core. As the particle moves through the liquid film, it develops a tangential velocity component. Upon impact, both the normal and tangential velocity components are used to determine the impact speed. This procedure provides a representative impact velocity for particles initially in the gas core. Impact Velocity for Particles in Liquid Film Several approaches have been implemented to determine the representative particle impact velocity for particles in the liquid film. The results have shown that the predicted erosion in annular flow varied little for the various approaches applied. Therefore, the representative particle impact is assumed to equal the average liquid film velocity. Calculating Erosion Rate in Annular Flow as The entrainment rate, E, is the fraction of liquid entrained in the gas core and is defined E = (Mass of liquid in the gas core) / (Total mass of liquid) Assuming the mass fraction of liquid is equal to the mass fraction of sand, then E is the fraction of sand entrained in the gas core, E = (Mass of sand in the gas core) / (Total mass of sand) The fraction of sand entrained in the liquid film, (1 - E) = (Mass of sand in the liquid film) / (Total mass of sand) The erosion rate due to sand particles in the liquid phase is calculated by using representative impact velocity of particles in the liquid film in Equation (4) and then multiplying

19 SPPS USER Manual 19 by the fraction of sand entrained in the liquid film, (1- E). The erosion rate due to sand particles in the gas phase is calculated by using the representative impact velocity for particles in the gas core in Equation (4) and multiplying by the fraction of sand entrained in the gas core, E. The total erosion rate is calculated by adding the erosion rates due to sand particles in the liquid and gas phases. The entrainment rate, E, is calculated using an expression developed by Zhang et al. (2002) as shown in Equation (5). Zhang rearranged an expression developed by Olieman (1988) in terms of dimensionless parameters. The Olieman correlation used seven different input parameters and their corresponding exponents using Harwell well data reported by Whalley. E ρ L μ L = 0.003WeSG FrSG ReSG ReSL 1 E (5) ρg μg E is the entrainment fraction; ρ L and ρ G are the densities of the liquid and gas; μ L and μ G are the viscosities of the liquid and gas; and We SG, Fr SG, Re SG and Re SL are given by WeSG = 2 ρg VSG D σ FrSG = VSG g D Re SG = ρ G V μ SG G D Re SL = ρ L V μ SL L D D is the diameter of the pipe, σ is the surface tension, and g is gravitational acceleration. The liquid film thickness, δ, is assumed to be uniform or the cylindrical gas core to be of uniform diameter, D C. The film thickness is determined based on approach proposed by Kaji and Azzopardi (2010). Also, the gas core is considered to be composed of homogeneous gas and tiny liquid droplets with no relative slip between the gas and the entrained liquid droplets. Thus, various geometric parameters can be easily expressed. The cross-sectional area of the gas-core: A C 2 = ( 1 2 δ ) A P (6) The cross-sectional area of the film: AF ( 1 δ ) AP = 4δ (7) Where A P is the cross-sectional area of the pipe and δ is the ratio of the film thickness to the pipe diameter, D. The velocity of the film can be determined from simple mass balance calculations yielding,

20 20 EROSION/CORROSION RESEARCH CENTER VFilm 2 ( 1 E) D = V (8) SL 4δ(D δ) Where V SL is the superficial liquid velocity, D is the pipe diameter, and E is the fraction of the total liquid entrained in the gas core. In this investigation, a method for calculating the droplet velocity is proposed by assuming no relative slip between the gas and liquid film. The diameter of the gas core is calculated as: D c = D - 2δ The average gas core velocity, VG 2 D VSG Dc = (9) In annular flow, droplets generate from the disturbances in the wavy liquid film surfaces near the wall, accelerate in the gas core and deposit back on to the film. The droplet acceleration in the gas core contributes to erosion due to high impact velocity of sand particles entrained in the gas core and the droplets. The droplet velocities in the gas core are less than the gas velocity, V G, due to interphase slip between the gas and droplets. The mean slip ratio, S R, is defined with the droplet velocity, V d, as R Vd VG S = (10) The droplet velocity is calculated by multiplying the gas core velocity by the above slip ratio. For annular flow at superficial liquid Reynolds number (Re L ) between 750 and 3000, experimental results of Fore and Dukler (1994) measured the average slip ratio between the droplet and gas core velocities to be approximately The droplet velocity is calculated by multiplying the average gas velocity by the slip ratio between droplet and gas velocities. Model for Very Low Liquid-High Gas Flow In this work, very low liquid-high gas flow refers to gas dominant flows where there is insufficient liquid to form a continuous liquid film around the pipe creating annular flow. Higher erosion rates are observed in gas dominant wells that can damage production equipment, piping and fittings. The erosion in very low liquid-high gas flow ranges from the erosion in gas only flow to erosion in annular flow depending on the liquid rate. To develop the erosion model for very low liquid-high gas flow, the boundaries of very low liquid-high gas must be determined. A fit was developed for very low liquid-high gas flow where the superficial liquid velocity ranges from ft/s to the local minimum erosion near the annular flow transition. The erosion in the very low liquid- high gas flow region is given by Equation (11).

21 SPPS USER Manual 21 V sl ln V sl1 ER = (ER 2 ER1) + ER1 (11) V sl2 ln V sl1 Where V = Superficial liquid velocity of interest sl V = Superficial liquid velocity of ft/s sl1 V sl2 = Superficial liquid velocity at local minimum in erosion near the transition to annular flow ER 1 = Erosion prediction for V sl1 (assuming gas only) ER = Erosion observed for V sl2 (using annular flow model) 2 In order to apply Equation (11), the value for 2 sl V must be determined. Dosila (2008) compared this local minimum to a ratio of film thickness to particle diameter, where the film thickness values for different flow conditions were calculated using the SPPS program. Figure 11 gives the value of ratio of film thickness to particle diameter for experimental data at Vsg of 95 ft/s and sand size of 150 µm in 2-inch loop for a probe at 45 0 in an elbow. This figure shows that the local minimum in erosion occurs at a film thickness to particle diameter of approximately 2. Figure 12 is a similar graph and is for the same conditions as Figure 11 except that the particle diameter is 300 µm. In this case, the local minimum in erosion occurs at a film thickness to particle diameter ratio of 0.8. Additional comparisons were made for other very low liquid-high gas conditions in the 2 and 3-inch loops. These results demonstrated the local minimum in erosion occurred at film thickness to particle diameter ratios between 0.8 and 2.0. Based on an analysis of these cases, it was decided to set the critical film thickness to particle diameter ratio at a value of 1.0.

22 22 EROSION/CORROSION RESEARCH CENTER Metal loss rate (mils/lb) Metal loss rate Calculated ratio (film thk/part dia) Vsl (ft/s) Calculated ratio (flm thk / part dia) Figure 11. Comparison of ER Probe Erosion with Ratio of Film Thickness to Particle Diameter for Sand Size of 150 µm, Vsg = 95 ft/s in 2-Inch Boom Loop. Metal loss rate (mils/lb) Metal loss rate Calculated ratio (Film thk/part dia) Calculated ratio(flm thk / part dia) Vsl (ft/s) Figure 12. Comparison of ER Probe Erosion with Ratio of Film Thickness to Particle Diameter for Sand Size of 300 µm, Vsg = 95 ft/s in 2-Inch Boom Loop.

23 SPPS USER Manual 23 Model for Slug Flow Slug flow occurs over a wide range of gas and liquid flow rates. It is the dominant flow pattern in upward inclined flow. Slug flow hydrodynamics is very complex with unique and unsteady flow behaviors. It is characterized by an alternate flow of a gas pocket, named Taylor bubble, and liquid slugs that contain numerous small gas bubbles. A thin liquid film flows downward between the Taylor bubble and the pipe wall in vertical slug flow. The Taylor bubble is assumed to be symmetric around the pipe axis for fully developed vertical slug flow. Figure 13 shows a schematic description of slug flow in vertical pipe. For fully developed slug flow, the length of the Taylor bubble is approximately in the order of 100 times the diameter of the pipe. The slug body of unit length L U is divided into two parts: the Taylor bubble of length L TB, and the liquid slug of length L LS. The Taylor bubble occupies nearly the entire pipe crosssection and propagates downstream around the wall. The average liquid velocity in the liquid slug is V LLS and the liquid holdup of the liquid slug is denoted by H LLS. Due to unsteady hydrodynamic characteristics of slug flow, it has a unique velocity, holdup and pressure distribution. Therefore, the prediction of the liquid holdup, pressure drop, heat and mass transfer are difficult and challenging. Several mechanistic models have been proposed that enable reasonable prediction of the liquid holdup in the slug, slug length, slug frequency and velocities of Taylor bubble and liquid slug. V LTB Taylor Bubble (L TB ) L SU V LLS H LLS Liquid Slug (L LS ) Figure 13. Schematic of Slug Flow in Vertical Pipe. For calculation of erosion in slug flow, it is assumed that sand is uniformly distributed in the liquid phase and the mass fraction of sand in the liquid slug is equal to the mass fraction of liquid in the liquid slug, which is given by Equation (12).

24 24 EROSION/CORROSION RESEARCH CENTER LLS H LLS VS m = (12) L H V + L H V LS LLS S TB LF F where m is the liquid mass ratio in the liquid slug (slug body), L LS is the length of the liquid slug, H LLS is the holdup in the liquid slug, V S is the velocity of the liquid slug, L TB is the length of the Taylor bubble (film zone), H LF is the holdup in the film zone, and V F is the velocity of the film. A model developed by Zhang et al. (2002) is applied to determine the parameters needed for Equation (12). This model also sets the velocity of the liquid slug equal to the mixture velocity. The density and viscosity used in the particle tracking routine are mixture properties based on the amount of liquid and gas in the liquid slug body and not the entire slug unit. The manner in which the particle impact velocity is calculated is different than for other flow regimes. In the other models, one representative particle impact velocity is calculated with the exception of the annular model which calculates two. However, the current slug model calculates many. The current model assumes that the particles at the leading edge of the liquid slug will impact at higher velocities than particles further back in the liquid slug, thus resulting in less erosion. This assumption is made since the gas pocket is in front of the liquid slug, so when the front of the liquid slug meets an obstruction like a probe or wall of a bend, there is only a relatively small amount of liquid in front of it to slow the particle impacts as shown in Figure 14. To determine the representative particle impacts, the liquid slug is divided into two zones: front of the liquid slug and the remainder of the liquid slug. The length of the front of the slug is currently set to one pipe diameter. This zone is divided into 500 lengths, and a particle impact velocity is determined for each length. For example, the representative impact velocity of a particle at the front of the liquid slug is determined using a length equivalent to 1/500 th of the pipe diameter, and the next representative particle impact velocity is determined using a length of 2/500 th of the pipe diameter. In this manner, a total of 500 different particle impact velocities are calculated for the front of the liquid slug. For the remainder of the liquid slug, one representative particle impact velocity is used and is determined using a length equivalent to a pipe diameter. This essentially defines the latest slug flow model for the bend with one exception. The latest model also assumes that the erosion is spread over the entire inner surface of the bend instead of a projected area that was previously used. The decision to spread the erosion over the entire inner surface of the bend was made based on comparisons with experimental data.

25 SPPS USER Manual 25 Figure 14. Schematic of Assumed Slug Flow Profile near a Bend. Model for Churn Flow Churn flow is somewhat similar to slug flow except churn flow is more chaotic. The liquid and gas phases have oscillatory motion and without stable and clear boundaries between the phases. As the gas velocity in slug flow increases, the liquid slug becomes shorter, breaks and mixes with the following slug. Due to this mixing phenomenon, the shape of the Taylor bubble gets distorted resulting in churn flow. Kaya (1998) defined the churn flow pattern as consisting of highly aerated slugs with repeated destruction of liquid continuity in the slug during an oscillatory motion of the slug. Churn flow is normally observed between the slug and annular flow pattern in vertical or nearly vertical upward flow. As the pipe inclination angle changes from vertical to horizontal, churn flow changes to slug flow. Churn flow does not exist in horizontal flow. A schematic of the churn flow is shown in Figure 15. There is no available mechanistic model in the literature to predict hydrodynamic behavior of churn flow due to its highly disordered and chaotic nature. Churn flow exhibits intermittent behavior, similar to slug flow. Hasan (1988) attempted to develop a separate model for churn flow by redefining the transitional velocity coefficient as Tengesdal (1988) adapted the slug flow model to churn flow with a different closure relationship for the transitional velocity of the Taylor bubble and void fraction in the liquid-phase based on experimental churn flow data of Schmidt (1977) and Majeed (1997). According to Tengesdal, under turbulent flow conditions, the maximum centerline velocity of flow can be approximated as the average mixture velocity. In churn flow, it is assumed that the sand is uniformly distributed in the liquid phase. The velocities of the liquid and sand are assumed to be the same as the mixture velocity. Therefore, the characteristic initial sand particle velocity for churn flow is assumed to be the mixture velocity and is calculated as

26 26 EROSION/CORROSION RESEARCH CENTER V o = V m = V SL + V SG (13) Mixture properties of the gas and liquid are also used to represent the fluid properties for particle tracking. Gas Bubble Liquid Phase Figure 15. Schematic of Churn Flow. Model for Bubbly and Dispersed Bubble Flows Bubble flow is characterized as small gas bubbles that are distributed in the continuous liquid phase. Bubble flow can be classified as bubbly and dispersed bubble flows based on the relative slip between the bubbles and the surrounding liquid phases. Bubbly flow exists in relatively large pipe diameters with upward vertical or inclined pipes. Due to slippage and buoyancy effects, in bubbly flow, gas bubbles tend to flow near the upper part of inclined pipes. In bubbly flow, slippage between the bubble and liquid phase is present and the bubbles are not distributed homogenously. In dispersed bubble flow, gas bubbles are uniformly distributed in the liquid phase and can be treated as homogeneous flow. Due to homogeneous distribution of gas bubbles, the mixture properties can be used in expressing dispersed bubble flow. Figure 16 represents dispersed bubble flow in a vertical pipe. In SPPS, one model for bubble flow is used to represent erosion in both bubbly and dispersed bubble flow. In bubble flow, it is also assumed that the sand is uniformly distributed in the liquid phase. The velocities of the liquid and sand in the bubble flow region is assumed to be the same as the mixture velocity. Therefore, the characteristic initial sand particle velocity for bubble flow is assumed to be the mixture velocity and can be calculated using Equation (13).

27 SPPS USER Manual 27 Gas Bubbles Liquid phase Figure 16. Schematic of Bubble Flow. Geometries 1-5 (Threshold Prediction) The threshold prediction can only be performed for these geometries. Essentially, the erosion prediction procedure utilizing the flow regime independent procedure is used in reverse to determine the gas and liquid flow rates that result in the allowable penetration rate specified by the user. Geometries (Single-phase Carrier Fluid) Like the 1-D model, the basic part of the 2- D model also assumes that flow in regions around the target wall of interest can be represented by the flow in an equivalent stagnation region. However, the 2-D model utilizes a 2-D flow field that also allows the motion of particles in two dimensions. Also unlike the 1-D model, the 2-D model calculates the impact velocity of many particles in the stagnation region instead of just one particle on the stagnation length. This is important since particles in the stagnation region may have different impact velocities. Particle tracking in 2-D space also makes it easier to incorporate the effect of turbulence. Similar to the CFD-based erosion modeling procedure, the 2-D model can also be broken into 3 main steps as described below. CFD Flow Solution The first step is to obtain 2-D flow field information. The purpose is to feed this information to the second step of this method, which requires flow field information to calculate sand particle trajectories. The basic part of the 2-D model focuses on the flow in the stagnation region. The flow information in the stagnation region comes from CFD simulations indirectly. In developing the basic part of the 2-D model, CFD simulations of the direct impingement and elbow geometries were conducted for a range of Reynolds numbers. The flow field information of these cases has been saved in SPPS database for each computational cell, which includes geometry dimensions, location of computational grids, fluid density and viscosity, fluid velocity components and their gradient, pressure and its gradient, turbulent kinetic energy and its gradient, turbulent kinetic energy dissipation rate and its gradient, and Reynolds stresses if Reynolds turbulence model (RSM) is used. For any flow condition of

28 28 EROSION/CORROSION RESEARCH CENTER interest, the 2-D model calculates its Reynolds number and interpolates among the pre-saved cases to obtain the flow field information. In the 1-D model, the type and size of geometry is accounted for by changing the stagnation length. A similar option for the basic part of the 2-D model to handle this is to change the size of the stagnation region. Yet a better way is to go beyond the concept of stagnation region by pre-saving the flow field information for different types of geometries separately. For example, the 2-D flow field information can be pre-saved for a few typical geometries, such as elbow, tee, sudden contraction, sudden expansion, straight pipe, and so on. The procedure will be the same as described in the previous paragraph. Since it is not possible to include all types of geometry in this way, one has to decide which one of the pre-saved typical geometries best resembles the actual flow geometry, then select that geometry to continue the calculation. The 2-D model in current version SPPS can handle direct impingement and standard elbow geometries. Two-Dimensional Particle Tracking The second step in the erosion calculation procedure is to calculate sand particle trajectories using the information provided in the first step. The subroutine for calculating particle trajectories is designed to handle any types of 2-D geometries. Many particles are tracked to generate statistically representative results. The particle impact information is recorded each time a particle hits the target wall. Typical particle impact information includes impact location, impact speed, and impact angle. This impact information is needed in the third step to calculate the erosion rate. The particle trajectory is determined by integrating the force balance on the particle. This force balance equates the particle inertia with the forces acting on the particle (Newton s Second Law). In Cartesian coordinates, this equation can be written as dvp FD + FP + FB + FA = (14) dt where the left side represents the resultant (total) force per unit particle mass acting on the particle and V p is the particle velocity. The major component of the force acting on a particle is the drag that is exerted on the particle by the fluid. The drag force, F D, depends primarily on the local relative (slip) velocity between the particle and the fluid and is given by F 18μ C Re ( V V ) f D r D = 2 f p (15) ρddp 24 where, V f is the fluid phase velocity, V p is the particle velocity, μ f is the molecular viscosity of the fluid, ρ p is the density of the particle, d p is the particle diameter, and C D is the drag coefficient. Re r is the relative Reynolds number, which is defined as Re r ρf Vf Vp dp = (16) μ where ρ f is the fluid density. There are additional forces on the particle, which can be included in the simulation. These additional forces account for large pressure gradients (F P ), gravity and buoyancy (F B ), and added mass (F A ). Equations (17) through (19) give mathematical representations of these terms. f

29 SPPS USER Manual 29 Pressure gradient: Gravity and buoyancy: Added mass: F A F F P 3 1 = P (17) 2 ρ p ( ρ ρ ) g p f B = (18) ρp ( V V ) 1 ρ d f f p = (19) 2 ρ dt p In the pressure gradient term given by Equation (17), P is the local pressure gradient in the carrier fluid. The gravity and buoyancy force in Equation (18) is needed when the particles and fluid have significantly different densities and when inclusion of gravitational effect is desired. The added mass force described by Equation (19) is the force required to accelerate the fluid surrounding the particle. When relative motion between the particles and the carrier fluid occurs, fluid in the immediate vicinity of the particle must also be accelerated. This results in resistive force acting on the particle and is referred to as the added mass force. There are still other forces that can be included in Equation (14). For example Saffman s lift force due to shear and forces from both centrifugal and Coriolis effects which are due to rotating frames of reference. Turbulent dispersion of particles is modeled using a stochastic approach. A Discrete Random Walk (DRW) model, or eddy lifetime model is applied to account for the interaction between particles and turbulent eddies. This model assumes that the particles travel through a succession of turbulent structures (eddies) that are present in the flow. Each individual eddy that the particle encounters is characterized by a Gaussian distributed random velocity fluctuation (u, v, and w ) and a time scale, τ e, which is called the eddy lifetime. Interaction with eddies causes particles to deviate from the trajectory as predicted by Equation (14). The values of the random velocity fluctuations that prevail during the lifetime of the turbulent eddy are sampled by assuming that they obey a Gaussian probability distribution, so that 2 u'= ζ u' (20) where ζ is a normally distributed random number, and the remainder of the right-hand side is the local rms (root mean square) value of the velocity fluctuations. For k-ε model, k-ω model and their variants, the kinetic energy of turbulence is known at each point in the flow. If the turbulence is assumed to be isotropic, the values of the rms fluctuating components in Equation (20) can be obtained as u' = v' = w' = 2k (21) 3 where k is the turbulent kinetic energy. If a non-isotropic turbulence model, such as Reynolds Stress Model (RSM) is used, the values of the rms fluctuating components in Equation (20) can be computed directly from the known Reynolds stress field:

30 30 EROSION/CORROSION RESEARCH CENTER u' = ζ u' ; v' = ζ v' ; w' = ζ w' (22) The eddy lifetime, τ e is defined as a random variation about T L : τe = -TLlog( r) (23) where r is a uniform random number between 0 and 1 and T L is the fluid Lagrangian integral time and is proportional to the particle dispersion rate. This time scale can be approximated as k T = L CL ε (24) where ε is the local dissipation rate of turbulence kinetic energy; C L is an empirical constant and is suggested to be 0.15 for k-ε model, k-ω model and their variants, and 0.30 for Reynolds Stress Model (RSM). The particle eddy crossing time, τ cross, is defined as L e τ cross = τpln 1- (25) τp Vf Vp where τ p is the particle relaxation time, defined as 4ρ d 2 p p τ p = 3μf CDRer (26) where ρ p is the density of the particle, d p is the particle diameter, μ f is the molecular viscosity of the fluid, C D is the drag coefficient, and Re r is the relative Reynolds number defined by Equation (16). In Equation (25), V f -V p is the magnitude of the relative velocity and L e is the eddy length scale, which is given by 1.5 k Le = Cμ (27) ε where C μ is a turbulence model constant. The particle is assumed to interact with the fluid phase eddy over the smaller of the eddy lifetime, τ e, and the eddy crossing time, τ cross. That implies that the interaction time τ i is dictated by either of the following possible events: 1. The particle moves sufficiently slowly relative to the fluid so as to remain inside the eddy during the entirety of the eddy lifetime. 2. The slip velocity between the particle and the fluid is sufficiently large so that the particle crosses the eddy in the particle eddy crossing time. Therefore, i ( τ, τ ) τ = min (28) When the interaction time is reached, a new value of the instantaneous velocity is sampled. Erosion Calculation e cross

31 SPPS USER Manual 31 The third step of the 2-D erosion model is to calculate the erosion rate using erosion equations and the impact information provided in the second step. An erosion equation takes the particle impact information as input and calculates the erosion rate caused by the corresponding sand particle impingement. This is done for each impingement recorded in the second step. Depending on the particle impact location, the calculated erosion rate is saved for the corresponding portion of the target wall. Knowing the erosion distribution on the target wall, one can easily read the maximum erosion rate, obtain the total erosion rate by integrating over the target wall, or do other types of calculations. SPPS provides the maximum erosion rate. There are many erosion equations available in literature. Meng and Ludema (1995) have done a comprehensive review on this topic. The E/CRC erosion equation recently proposed and validated by Zhang et al. (2007) is applied in the current work and is given by, ER = C (HB) f 0.59 F s f ( θ) V n p () θ = θ θ θ θ θ (29) where ER is the erosion ratio, defined as the amount of mass lost by the wall material due to particle impacts divided by the mass of particles impacting; HB is the Brinell hardness; F s is particle shape coefficient; F s =1.0 for sharp (angular), 0.53 for semi-rounded, or 0.2 for fully rounded sand particles; θ is the particle impact angle in radians; V p is the particle impact speed in m/s; and C and n are empirical constants, C = and n = The function f(θ) used in Equation (29) is for a corrosion resistance alloy. For other materials f(θ) must be determined by erosion testing. Also, the hardness function was developed for carbon steels. For other materials, the factor C must be modified based on empirical information. Geometries (Multiphase Carrier Fluid) Like the 1-D model, there are two approaches for calculating the erosion for a multiphase carrier fluid in the 2-D model: flow regime independent model and flow regime dependent model. Flow Regime Independent Model This approach is the same as described in the 1-D model section, except the 2-D model approach to represent the flow field, perform particle tracking, and apply erosion equation is used. Flow Regime Dependent Model Currently, there are two flow regime specific models that have been developed for the 2-D geometries: annular flow and slug flow. If the flow regime dependent model is selected and one of these two flow regimes is not predicted or specified, then the model is similar to the single-phase 2-D model except mixture properties (applying volume averaging) and mixture velocity are used. Model for Annular Flow The same models are used to characterize the annular flow structure as described in the 1-D model section. These include models for entrainment fraction and film thickness. Once again, this model is very similar to the 1-D approach. In the 1-D approach, particles originally in the

32 32 EROSION/CORROSION RESEARCH CENTER gas core were tracked across the gas core and then through the liquid film. This approach is still applied except the 2-D model approach is used to track particles across the gas core. Once the particle tracking in the gas core tracking is complete, the particles are then tracked across the liquid film. Since the 2-D model determines the particle velocities in two dimensions, this provides a more realistic boundary condition for the particles entering the liquid film. In the 1-D model, the particles were forced to enter the liquid film normal to the direction of the film velocity. Model for Slug Flow The same models are used to characterize the slug flow structure as described in the 1-D model section. This information includes liquid slug velocity, length of slug unit and liquid slug body, and fraction of liquid and particles in the liquid slug body. The same approach of calculating representative particle impact velocities for particles at various positions in the liquid slug body is applied to the 2-D model as is in the 1-D model. However, since the 2-D particle tracking routine (similar to the single-phase 2-D model) is applied for the 2-D slug model several particles are placed at each initial axial location in the slug as illustrated in Figure 17. So, the 2- D slug model is a combination of the model used to characterize slug flow behavior explained in the 1-D slug model section and the 2-D single-phase particle tracking model. Figure 17. Schematic of Particle Initial Positions in 2-D Slug Model. Geometries 6-8 (Straight Pipe / Contraction / Sudden Expansion) The models for each of these three geometries is unique. They were all developed for single-phase carrier fluid. The user may input information for multiple phases; however, the model will use mixture velocities and mixture properties based on volume averaging. The straight pipe model is a preliminary model that has not been validated with data. This model is a two part model. The first part of the model determines the probability that particles will impinge the wall after traveling across the core and then through the viscous sublayer next to the wall. The second part of the model determines the representative particle

33 SPPS USER Manual 33 impact velocity resulting from turbulence by applying a particle equation of motion near the wall. The contraction model determines the erosion on the face of the contraction utilizing a form of 2-D particle tracking not considering turbulence. Particles are released at a plane upstream of the contraction and the particle trajectories are calculated. The fluid axial and radial velocities necessary for the particle tracking are determined from a series of equations that are essentially fits to many computational fluid dynamic simulations for a variety of Reynolds numbers and contraction ratios. Particle impact information with the contraction face is used to determine the erosion rate. This sudden expansion model was developed using computational fluid dynamics simulations that were tuned to erosion data for expansions determined at E/CRC. The simulations were performed for a range of Reynolds numbers and expansion ratios. The expansion model is divided into two steps. The first step applies a two-dimensional particle routine to determine representative particle impact speed and angle to determine the erosion ratio. The second step determines the deposition rate from correlations. Combined this information provides the penetration rate. Examples Demonstrating Use of SPPS The following examples demonstrating the use of SPPS Excel v4.2 are provided: Example 1: Multiphase erosion prediction (1-D model) inputting fluid properties using flow regime independent model. Example 2: Multiphase erosion prediction (1-D model) inputting fluid properties using flow regime dependent model. Example 3: Multiphase erosion prediction (1-D model) for a range of sand sizes inputting fluid properties, Example 4: Multiphase erosion prediction (2-D model) inputting fluid properties using flow regime independent model. Example 5: Threshold velocity prediction for multiphase phase flow inputting fluid properties, Example 6: Erosion prediction in a sudden expansion. Example 1 In this example, the penetration rate in an elbow is demonstrated for multiphase flow where the calculation of V o is not dependent on flow regime. The input for this problem is shown below. The user can enter different units for the input data by selecting the appropriate unit from the drop-down menu. Note that the flow for this case is a combination of water and gas. The pipe roughness and interfacial tension will not be used in the calculation since it is set to be flow regime independent. Flow Geometry Input: Fluid/Flow Parameters: Type of Geometry: (1) Elbow Pipe (elbow) Diameter = 5.76 inches Gas velocity = m/s = 52.5 ft/s Gas Density = 52 kg/m 3 = 3.2 lb/ft 3

34 34 EROSION/CORROSION RESEARCH CENTER Gas Viscosity = cp Water Velocity (Rate) = 90 bbl/day Water Density = 994 kg/m 3 = 62.0 lb/ft 3 Water Viscosity = 1.01 cp Oil Velocity (Rate) = 300 bbl/day Oil Density = 822 kg/m 3 = 51.3 lb/ft 3 Oil Viscosity = cp Sand/ Material Input: Sand Density = 2650 kg/m 3 = lb/ft 3 Sand Size = 150 microns Sand Type (select Sharp in column Particle Sharpness ) Sand Production Rate: Assume 10 kg/day (22 lb/day) Pipe Material: Carbon Steel, Brinell hardness = 200 Model Selection: Apply Regime Dependent Model (select No) After entering the input and selecting the appropriate units, the RUN button is pressed. The output for the example appears in the output section. A report can be generated by placing an x in the Report column next to the example input and pressing the Report button. Figure 18 displays the report containing the input and the output.

35 SPPS USER Manual 35 SPPS Erosion Report Type of calculation Erosion - Input Fluid Properties Case Description Example 1 Erosion Input Data Pipe Data Sand Data Material Type Carbon Steel/Other Particle Size 150 microns BH = 200, 7800kg/m3 Particle Density 2650 kg/m3 Geometry Elbow Particle Shape Sharp Pipe Diameter 5.76 Inches Sharpness Factor 1 Sand Production Rate 10 kg/day Water Data Oil Data Velocity/Rate 90 bbl/day Velocity/Rate 300 bbl/day Density 994 kg/m3 Density 822 kg/m3 Viscosity 1.01 cp Viscosity cp Gas Data Input for Flow Regime Prediction Velocity/Rate 16 Vsg (m/s) (process) Inclination Angle 90 degrees Density 52 kg/m3 Interfacial Tension 73 dyne/cm Viscosity cp Pipe Roughness Relative roughness Additional Data Flow Regime Independent Model Output Values Erosion Rate Flow Regime mpy NA Additional Results Calculated Mixture Fluid Density Calculated Mixture Fluid Viscosity Superficial Gas Velocity Superficial Liquid Velocity kg/m cp 16 m/s m/s Figure 18. Report Generated for Example 1.

36 36 EROSION/CORROSION RESEARCH CENTER Example 2 This example is very similar to Example 1 except the flow regime dependent model is used. For this example, SPPS calculates the flow regime and then applies the appropriate erosion model. This example has all of the same input as Example 1 except for model selection and values for pipe roughness and interfacial tension are required for multiphase flow calculations, since the flow regime is being considered. Additional/Modified Input Flow Geometry Input: Fluid/Flow Parameters: Model Selection: Pipe Roughness: Relative Roughness Interfacial Tension: 73 dyne/cm Apply Regime Dependent Model (select Yes) Flow Regime (select (1) Calculated) Figure 19 displays the report containing the input and the output for Example 2.

37 SPPS USER Manual 37 SPPS Erosion Report Type of calculation Erosion - Input Fluid Properties Case Description Example 2 Erosion Input Data Pipe Data Sand Data Material Type Carbon Steel/Other Particle Size 150 microns BH = 200, 7800kg/m3 Particle Density 2650 kg/m3 Geometry Elbow Particle Shape Sharp Pipe Diameter 5.76 Inches Sharpness Factor 1 Sand Production Rate 10 kg/day Water Data Oil Data Velocity/Rate 90 bbl/day Velocity/Rate 300 bbl/day Density 994 kg/m3 Density 822 kg/m3 Viscosity 1.01 cp Viscosity cp Gas Data Input for Flow Regime Prediction Velocity/Rate 16 Vsg (m/s) (process) Inclination Angle 90 degrees Density 52 kg/m3 Interfacial Tension 73 dyne/cm Viscosity cp Pipe Roughness Relative roughness Additional Data Flow Regime Dependent Model Output Values Erosion Rate Flow Regime mpy Mist Flow (Calculated) Additional Results Calculated Mixture Fluid Density Calculated Mixture Fluid Viscosity Superficial Gas Velocity Superficial Liquid Velocity kg/m cp 16 m/s m/s Figure 19. Report Generated for Example 2.

38 38 EROSION/CORROSION RESEARCH CENTER Example 3 This example is very similar to Example 2 except calculation are performed for a range of sand sizes to account for particle size distribution. Figure 20 contains the sand distribution for this example. Nine cases are run to represent the nine bin sizes. The average size within a given bin is used as input for the sand size as shown in Figure 21. Table 1 lists the sand sizes used as input and the respective weight percent < >425 Weight Percent in Range (%) Sand Size Range (microns) Figure 20. Sand Size Distribution for Example 3. Figure 21. Sand Size Input for Example 3.

39 SPPS USER Manual 39 Table 1. Sand Size Distribution used for Example 3. Sand Size (microns) Weight Percent The output section obtained after running the cases is shown in Figure 22. The rows specific to Example 3 are 13 to 21. The information in rows 28 to 37 below the initial output were added after the output was generated. The penetration rate values for each sand bin size was copied to rows below in column BV. Values for the sand weight percent for each bin size was added in the bottom rows for column BZ. Since the same sand rate (10 kg/day) is entered for all 9 cases, the bottom rows of column CB weights the penetration results according to the weight percent, so the bottom rows of column CB are the products of multiplying columns BV and BZ. The penetration rate accounting for the sand size distribution is the sum of the values in the bottom rows of column CB, which is about 25.3 mpy.

40 40 EROSION/CORROSION RESEARCH CENTER Figure 22. Output for Example 3.