Perforation Drop and Tortuosity Related Friction (Step-Rate Analysis)

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Perforation Drop and Tortuosity Related Friction (Step-Rate Analysis)

The PERFORATION AND TORTUOSITY RELATED FRICTION (STEP RATE ANALYSIS) [F8] screen is where you provide input for FIELDPRO to calculate the friction-pressure drop due to perforations and tortuosity in the near-wellbore region. Also, data resulting from the analyses of step down flow rate tests are displayed on this screen. Modeling of perforation and tortuosity related friction is particularly important when running the fracture model with measured pressure data (e.g., running from data file or real-time data). This screen is accessible only if you choose to model the wellbore on the SIMULATION OPTIONS screen.

Note: When trying to match model-calculated net fracturing pressure to observed data, it is essential that you first remove all friction pressure from the measured data.

If perforation and tortuosity related friction are modeled correctly (i.e., removed), there will be no abrupt changes in Observed Net Pressure when there are abrupt flow rate changes, which include instantaneous shut in pressure (ISIP) measurements. The process for removing all such friction is discussed in this section.

By definition, net fracturing pressure is gauge pressure minus friction pressure (plus hydrostatic pressure if you are using surface pressure), minus closure stress. To remove all friction, you must make use of the fact that, due to energy storage considerations, net fracturing pressure in a sufficiently large hydraulic fracture cannot change abruptly. Therefore, any abrupt changes in measured pressure data that occur with abrupt flow-rate changes are due to changing friction pressure, not changes in net fracturing pressure.

The abrupt drop in surface treating pressure observed at an ISIP is the sum of perforation, near-wellbore, and wellbore friction. The abrupt change in downhole (or ‘dead-string’) pressure that is observed at an ISIP (instantaneous shut in pressure) represents the sum of perforation and tortuosity related friction. These latter two quantities, although fundamentally different, are sometimes lumped together and referred to as ‘entry’ friction.

Perforation friction is modeled by a stagnation pressure (kinetic energy) calculation where the pressure drop through the perforations varies with the square of flow velocity (where flow velocity is the total flow rate divided by total cross-sectional area of the perforations). As such, if flow rate is doubled, perforation friction increases by a factor of four.

Near-wellbore friction, on the other hand, varies roughly with the square root of flow rate. Near-wellbore friction results from flow through a tortuous, segmented region connecting the wellbore and the main body of the fracture(s). If this region maintains a constant geometry, then tortuosity related friction increases linearly with flow rate. However, the near-wellbore region generally opens wider as flow rate increases and, hence, yields a roughly square-root dependence on flow rate. As such, if flow rate is doubled, tortuosity related friction increases by a factor of about 1.4. Near-wellbore friction often varies significantly over the course of a fracture treatment.

In FIELDPRO FRACPRO, there are two relatively simple diagnostic techniques that can be used to distinguish and measure the effects of tortuosity and perforation friction. These techniques are known simply as flow rate changes and flow rate step down friction tests.



Tortuosity Related Friction

Many premature treatment screen-outs are the result of high (‘near-wellbore’) friction due to tortuosity but are often erroneously assumed to be due to insufficient pad volume or fracture width (i.e., width in the main body of the fracture). Determining the level and time dependence of tortuosity related friction using flow-rate changes, which include conducting instantaneous shut in pressure (ISIP) measurements, not only allows accurate determination of Observed Net Pressure, but it also provides a valuable diagnostic for determining near-wellbore screen-out risk and the appropriate proppant schedule.

Note: Common interpretations of perforation ‘entry’ restrictions, sometimes leading to re-perforation etc., are typically wrong: even with surface pressure measurements, so often misinterpreted, enough flow-rate changes can remedy such errors).

Initially during net pressure matching, it is best to first assume that there is no significant near-wellbore friction (which is sometimes the case). After entering the number and diameter of the perforations, the simulator should be run and Observed Net Pressure should be plotted versus time.

Indications that the simulator is predicting too little friction will manifest themselves as:

1. Upward ‘spikes’ in Observed Net Pressure for sudden decreases in flow rate; or

2. Downward ‘spikes’ in Observed Net Pressure for sudden increases in flow rate.

If you are running the model from measured Surface Pressure, then there is most likely an error in the wellbore friction calculations and the friction properties for the fluids used should be modified (e.g., on the EDIT/VIEW FLUID DATA [Shft]-[F5] screen). If you are running the model measured Bottomhole or Dead String pressure, the number and/or diameter of the perforations should be increased to the point where there are no instances where too much friction is being calculated. This procedure is described in greater detail earlier in this section.

Indications that the simulator is predicting too little friction will manifest themselves as:

1. Downward ‘spikes’ in Observed Net Pressure for sudden decreases in flow rate; or

2. Upward ‘spikes’ in Observed Net Pressure for sudden increases in flow rate.

For such instances, these effects will be accounted for using the parameters in the Tortuosity Related Friction table. If the model is running from a measured bottomhole (or dead-string) pressure, then the remaining observed friction (i.e., the amount of the abrupt pressure change) is tortuosity related friction. The parameters in the Tortuosity Related Friction table can be entered ‘manually,’ however there is also a graphical method that makes use of FIELDPRO MODULES cursor editing features to make the process easier.


You can analyze one or more flow rate changes with FIELDPRO MODULES using the following procedure:

1. Run the fracture model with a small timestep (e.g., 0.02 to 0.1 minutes) to capture the details of the flow rate and frictional changes.

2. Go to either the RESULTS GRAPHS [ALT]-[F2] screen or PROJECT EXPLORER [SHIFT]-[F3] screen, then select and configure a user-configurable plot such that Observed Net Pressure and the flow rate channel being input to the model (i.e., the channel specified on the CHANNEL INPUTS FOR MODEL [Shift]-[F6] screen) are displayed.

3. Activate cursor editing for the plot (e.g., by selecting the Cursor Editing button on the toolbar) and put the cursor on the Observed Net Pressure channel.

4. Move the cursor to a point just before the flow rate change begins (i.e., just before the upward or downward pressure spike) and mark that point by pressing [Alt]-[B] or selecting Begin. A vertical line will appear indicating the mark.

5. Move the cursor to a point just after the flow rate (i.e., just after the upward or downward pressure spike) and mark that point by pressing [Alt]-[E] or selecting End. A second vertical line will appear to indicate the mark. Because there is sometimes a small time mismatch between the flow rate and observed net pressure data, you should always verify the numerical values for both of them whenever you mark the beginning and the end of a flow rate change. Verification of the numbers is made simply by the fact that they are displayed in the System Messages area in the bottom left corner of the screen whenever marked.

6. To automatically calculate the changes in tortuosity related (‘near wellbore’) friction and flow rate and enter the relevant data into the Tortuosity Related Friction table shown on the PERFORATION AND TORTUOSITY RELATED FRICTION (STEP RATE ANALYSIS) [F8] screen, select Calculate NWB Friction. Do not select Step-Rate Analysis, since this function is used for analyzing step down flow rate tests.

7. Upon selecting Calculate NWB Friction for the first time during the analysis of any flow rate change, you will be prompted with a dialog asking you whether or not you wish to delete all entries in the Tortuosity Related Friction table. Selecting No causes the current calculated data to be added to the data currently in the Tortuosity Related Friction table located on the PERFORATION AND TORTUOSITY RELATED FRICTION (STEP RATE ANALYSIS) [F8] screen. In the table, Time will coincide with the center of the flow rate change test time span.

8. Continue this procedure for each flow rate change that you wish to analyze.


The Tortuosity Related Friction table is shown in the upper left corner of the screen. You should provide a set of table entries for each ISIP and abrupt flow-rate change of significant magnitude. The data may be entered using the flow rate change analysis procedure described above, or they may be entered manually. To aid in editing the table, you can insert a row of blank entries at the current cursor position by selecting a row number in the table and pressing [Ins]; pressing [Del] deletes the row of entries. A rule of thumb is to only use flow rate changes that are equal to 20% (or more) of the total flow rate.

If only one set of entries is made in the Tortuosity Related Friction table, tortuosity related friction is modeled as constant (for a constant flow rate) over the entire treatment, which is often sufficient when the amount of friction is small. However, the level of tortuosity related friction often changes with time during a fracture treatment. If tortuosity related friction is large initially (e.g., several hundred to several thousand psi), the tortuosity related tortuosity and/or fracture segmentation often decreases with time as more fluid (or proppant) is pumped, resulting in a better wellbore-to-fracture connection. Also, the level of tortuosity can sometimes be reduced with the use of proppant slugs, as described in SPE 25892.

For each row of entries in the Step Down Friction Data table, FIELDPRO FRACPRO solves for the coefficient, C, in the following equation:

Tortuosity Related Friction = C*(Flow Rate) to the power of b

The Near-Wellbore Friction Exponent, b, is set from the MODEL PARAMETERS screen. The default value is 0.5, which is indicative of the square root dependence that is most often seen in measured data. FIELDPRO FRACPRO interpolates linearly in time to find the value of the coefficient (C) between table entries.

Time

This is the time at which the flow-rate change or ISIP occurs.

Rate #1

Enter the magnitude of the flow rate just before the abrupt rate change or ISIP in this field.

Rate #2

Enter the magnitude of the flow rate just after the abrupt rate change or ISIP in this field.

Change In Friction

Enter the magnitude of the Observed Net Pressure change seen when going from Rate #1 to Rate #2 in this field.

Perforation Coefficient Multiplier

The calculated perforation friction is multiplied by this parameter. This parameter varies linearly between the values entered in table for the corresponding times entered in the table, however it is independent of the flow rates entered in the table. This parameter is useful in accounting for what is commonly referred to as perforation erosion.



Near-Wellbore Friction Exponent

This exponent appears in the equation used to calculate tortuosity related friction as a function of flow rate. A very important aspect of this coefficient relates to the process of distinguishing between tortuosity and perforation pressure drops.

Proppant Drag Effect Exponent

This parameter adjusts the magnitude of the proppant effect on the in-fracture drag (or friction) due to the slurry fluid. RES has found that values between 4.0 and 12.0 typically match observed data. A higher number causes greater increases in net fracturing pressure due to the pumping of proppant.



Distinguishing Torstuosity Related Friction from Perforation Friction

Tortuosity (often called ‘near-wellbore’) friction varies (roughly) with the square root of flow, while perforation friction varies with flow rate squared. The only way to distinguish friction due to tortuosity from perforation friction is by determining the flow-rate dependence of the friction pressure actually measured. FIELDPRO FRACPRO makes use of a graphical diagnostic technique called a flow rate step down friction test. Since tortuosity related friction generally varies over the course of a fracture treatment, numerous flow rate step down tests may prove useful.

Flow-rate dependence of the friction pressure can be determined by ‘stepping-down’ flow rate where one would normally be taking an ISIP (e.g., during the pad and at the end of a treatment). It is important to get data at a minimum of 3 different rates. It can also be helpful to do a small rate change at the high rate and a small rate change for the final step down to zero (i.e., shut in).

For example, suppose that you are pumping at 30 bpm. After recording the pressure at 30 bpm, quickly drop the flow rate to 28 bpm and hold it there long enough to allow the dynamics of the ‘water-hammer’ to dampen (e.g., 5 to 30 seconds). Then, after recording the pressure at 28 bpm, quickly drop the rate to 20 bpm and again hold it until the dynamics have dissipated. After recording the pressure at 20 bpm, repeat the same process from 10 bpm to 2 bpm and, finally, quickly shut the pumps down and record the ISIP. From these data, a table or plot of the (change in) friction versus flow rate (before the flow-rate change) can be constructed from which the flow-rate dependence of the measured friction can be determined. FIELDPRO FRACPRO includes features to easily (i.e., graphically) construct the table and plot for the analysis (described below).

The exact value of flow-rate achieved during each step down is not important, but it is critical to change between each flow rate as quickly as possible and to hold each flowrate as steady as possible. This is often most easily accomplished by having the service company shut down individual pumps for each step. Also, if net pressure is changing significantly during flow rate changes, you must account for this change in the friction pressure changes that you record. This should be an issue only in high leakoff scenarios with very small injection volumes.


You can analyze one or more flow rate step down friction tests with FIELDPRO FRACPRO using the following procedure:

1. Run the fracture model with a small timestep (e.g., 0.02 to 0.1 minutes) to capture the details of the flow rate and frictional changes.

2. Go to either the RESULTS GRAPHS [Alt]-[F2] screen or PROJECT EXPLORER [Shift]+[F3] screen, then select and configure a user-configurable plot such that the Measured Bottomhole Pressure and Bottomhole Slurry Rate channels are displayed. Both of these channels are FRACPRO model channels.

3. Activate cursor editing for the plot (e.g., by selecting the Cursor Editing button on the toolbar) and put the cursor on the Measured Bottomhole Pressure channel.

4. Move the cursor to a point just before the first step down begins and mark that point by pressing [Alt]-[B] or selecting Begin. A vertical line will appear indicating the mark.

5. Move the cursor to a point just after the first step down (where the pressure levels off) and mark that point by pressing [Alt]-[E] or selecting End. A second vertical line will appear to indicate the mark. When you mark a beginning or end point, the values for flow rate and observed net pressure at that point will be temporarily displayed in the System Messages area in the bottom left corner of the screen: Make sure you have selected a point with the correct flow rate.

6. To automatically calculate the changes in friction and flow rate and enter the relevant data into the Step Down Friction Data table shown on the PERFORATION AND TORTUOSITY RELATED FRICTION (STEP RATE ANALYSIS) [F8] screen, select Step-Rate Analysis. Do not select Calculate NWB Friction, since this function is used to account for tortuosity related friction only.

7. Upon selecting Step-Rate Analysis for the first time during the analysis of any flow rate step down friction test, you will be prompted with a dialog asking you whether or not you wish to delete all entries in the Step Down Friction Data table. Unless you are adding or changing a point in a previously analyzed test, you should select Yes. Selecting No will cause the current calculated data to be added to the data currently in the Step Down Friction Data table located on the PERFORATION AND TORTUOSITY RELATED FRICTION (STEP RATE ANALYSIS) [F8] screen.

8. Now position the cursor to a point just before the second step down begins (it is usually sufficient to leave the cursor at the point where the end of the first step down was marked) and mark that point by again pressing [Alt]-[B] or selecting Begin.

9. Move the cursor to a point just after the second step down and mark that point by again pressing [Alt]-[E] or selecting End.

10. Again select Step-Rate Analysis to automatically calculate the changes in friction and flow rate for the second step down and enter the relevant data into the Step Down Friction Data table shown on the PERFORATION AND TORTUOSITY RELATED FRICTION (STEP RATE ANALYSIS) [F8] screen.

11. Continue this procedure until the last step down has been marked and its results calculated. The last point must have a final flow rate of zero (or, at least, less than 1 bpm).

12. The results of the analysis can be viewed numerically and graphically, as described below.

13. If you wish to use the analysis results, the final task is to select Use Step-Down Data on the PERFORATION AND TORTUOSITY RELATED FRICTION (STEP RATE ANALYSIS) [F8] screen. This function automatically makes an entry in the Tortuosity Related Friction table (at the center of the step-down test time span) and gives you the option of changing (automatically, based on the analysis) the number of perforations.


Once you have marked and analyzed each of the step-downs in a test, the results are shown in the Step-Down Friction Analysis table near the lower right corner of the screen. The four quantities in the table are defined as follows:

Total Friction b

The estimated exponent of the total friction measured in the step down test.

Total Friction K

The estimated multiplier of the total friction measured in the step down test.

Ft=K*Q^b

here: Q - flow rate; Ft - total friction

Perforation Friction K

The perforation term multiplier in the decomposition of total observed friction into perforation and tortuosity related friction components. The flow rate term is squared and then multiplied by Perforation Friction K.

Fp=K*Q^2

here: Q - flow rate; Ft - perforation friction

NWB Friction K

The tortuosity related term multiplier in the decomposition of the total observed friction into perforation and tortuosity related friction components. NWB Friction K multiplies the square root of the flow rate term.

Ft=K*Q^0.5

here: Q - flow rate; Ft - tortuosity friction


Analyzing the friction components graphically is much easier: simply select the Friction Results Graph button on the PERFORATION AND TORTUOSITY RELATED FRICTION (STEP RATE ANALYSIS) [F8] screen to see a graph of the three friction channels (Observed Friction, Estimated NWB Friction, and Estimated Perf Friction) versus flow rate. The graph shows the relative magnitudes of the tortuosity-related and perforation friction components.

The discussion above assumes that bottomhole treating pressure is being measured. Obviously, this technique is most accurate and useful in such cases. However, this technique can be accurately used with calculated bottomhole pressure if wellbore friction is relatively small, or it is known with reasonable accuracy (e.g., pumping well-characterized fluids down a short, large-diameter wellbore), and if the total perforation or tortuosity related friction pressure is relatively large.

Perforation Data

Initially during net pressure matching, it is best to first assume that there is no significant tortuosity related friction (which is sometimes the case). After entering the number and diameter of the perforations, the simulator should be run and Observed Net Pressure should be plotted versus time.

Indications that the simulator is predicting too little friction will manifest themselves as:

  1. Downward ‘spikes’ in Observed Net Pressure for sudden decreases in flow rate; or
  2. Upward ‘spikes’ in Observed Net Pressure for sudden increases in flow rate.

For such instances, these effects will be accounted for using the Near Wellbore Friction parameters that are described later in this screen.

Indications that the simulator is predicting too little friction will manifest themselves as:

  1. Upward ‘spikes’ in Observed Net Pressure for sudden decreases in flow rate; or
  2. Downward ‘spikes’ in Observed Net Pressure for sudden increases in flow rate.

If you are running the model from measured Surface Pressure, then there is most likely an error in the wellbore friction calculations and the friction properties for the fluids used should be modified (e.g., on the INTERPOLATED FLUID DATA). If you are running the model measured Bottomhole or Dead String pressure, the number and/or diameter of the perforations should be increased to the point where there are no instances where too much friction is being calculated.


The following parameters will be shown for each of the perforated intervals that you have chosen to model on the Stimulation Flow Path screen:

  • # of Perfs - Enter the total number of perforations that you believe are taking fluid.
  • Diameter - Enter the estimated perforation diameter.
  • Perforation Pressure Drop Model:
    • Default FIELDPRO FRACPRO Model
    • FFCF Linear Gel Correlation
    • FFCF X-link Gel Correlation

These are the choices for modeling pressure losses through the perforations. The Default FIELDPRO FRACPRO Model uses a discharge coefficient (CD) of 0.814 and the formula (Crump and Conway):

ΔPperf = 0.237 * ρ * Q^2 / (D^4 * Cd^2)

Where:

  • ΔPperf = Total perforation friction, psi
  • Q = Flow rate through each perforation, BPM/perf
  • D = Diameter of perforation, in.
  • C = Discharge coefficient
  • ρ = Fluid density, lbs/gal

, while the FFCF Linear Gel Correlation (the Fracturing Fluid Characterization Facility at Oklahoma University) options use a correlation for CD. For the FFCF X-link Gel Correlation, there is also an additional term for excess pressure loss. Your choice in this field also controls the perforation model used to estimate the number of open perforations when you choose Use Step-Down Data (e.g., after performing a flow rate step down friction test).

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