The deliverability of a system is its ability to deliver gas as a function of pressure. Well Deliverability tool is developed to assist oilfield operators in determining the flow rates of gas-drive wells using inflow performance relationship (IPR) and tubing performance relationship (TPR) of reservoir, wellbore and production data. The Well Deliverability tool is an integrated system that combines the following work-flows:

  • Inflow performance relationship (IPR)
  • Vertical Lift Performance / Tubing Performance relationship (VLP/TPR)
  • Operating Point Determination

The tool can be used for a wide-range of applications including, estimating optimal flow rate, sensitivity analyses, well string pressure traverse, tubing size optimization, production casing size determination etc.

Inflow Performance Relationship (IPR)


Figure I: IPR User-Interface Well Deliverability provides a simple solution for graphically visualizing the flow rate of oil/gas wells at different sand-face pressures. Using this tool, the engineer can easily simulate the change in flow rate due to change in pressure and determine the productivity index, absolute open flow and bubble point flow rate of a well; and can also save the data generated from the simulation for future review.

Production data used for the simulation can be loaded from a data repository (database, Excel spreadsheet, flat file) or manually entered into the system by the user. Well Deliverability IPR solution allows for 2 different well test types – single well test; multiple well test.

Single Well Test – In single well test, data is available for only one production instance. The basic data to be used in the simulation include:

  • Well name (completion name)
  • Reservoir pressure
  • Bubble point pressure
  • Sand-face pressure (bottom-hole pressure)
  • Flow rate
  • Gas-oil ratio

If the data is loaded from a data repository, it is important that the test date be included in the data supplied to the system. If the data is manually entered by the user, the test date is not significant in single well test IPR simulation. Once the data have been entered or loaded into the IPR system, then a numeric value (integer) can be provided in the “# of Data Points” field, to determine how many data points the simulation process should generate, before clicking the Run IPR button. By default, 100 data points are created.

The simulation calculates the Productivity Index (PI), determines the Absolute Open Flow (AOF) and estimates the Bubble Point Flow (Qb) rate of the well based on the provided data. It creates number of pressure points from zero to the reservoir pressure based on the number of data points entered. Using the PI, it computes the flow rate at each generated pressure greater than or equal to the bubble point pressure. For generated pressures less than the bubble point pressure, it uses the “Square of Pressures” method, which is widely accepted in the petroleum industry, to establish the gas flow rate. Finally, using the provided gas-oil ratio value, the oil flow rates are determined.

Multiple Well Test – in multiple well test, it is assumed that there is data for several well tests conducted on the well at different times, two of which are necessary for the IPR simulation. Which two tests are used is at the discretion of the user. The basic data to be used in the simulation include:

  • Well name (completion name)
  • Date of first test
  • First test fluid rate (gas)
  • First test sand face pressure (bottom hole pressure)
  • Date of second test
  • Second test gas rate (gas)
  • Second test sand-face pressure (bottom hole pressure)
  • Reservoir pressure
  • Gas-oil ratio

If the data is loaded from a data repository, when a well is selected from the Well Name select-list control, the IPR system responds with the lists of test dates associated to the selected well in each of the two Test Date drop-down list controls. Selecting a different date in each of the controls will populate the rate and BHP fields associated to each selected date with the corresponding rate and sand-face pressure data from the data repository. See figure below:

Multiple Well Test Parameters

Figure II: IPR – Multiple Well Test Parameter

If the data is manually entered by the user, each field should be populated accordingly.

RAI’s Well Deliverability IPR module can simulate data using either Back Pressure or Forchheimer methods.

The Method(s) check boxes allow the user to specify which method(s) should be used in the simulation. Also, “# of Data Points” provides the field for entering how many data points the simulation process should generate. 100 points are generated by default.

Once all data have been supplied to the IPR module, then clicking the Run IPR button will randomly create number of pressure points between zero and the reservoir pressure inclusive, adopt any of the selected methods in calculating gas flow rate for each generated pressure, and using the provided gas-oil ratio value, determine the oil flow rates.

The results are Inflow Performance Relationship curves:

IPR Curves

Figure III: IPR Curves

Unlike the Single Well Test, the Multiple Well Test simulation does not calculate the bubble point flow rate. It is important to note that when using multiple well test simulation, the zero value shown in the Bubble Point Flow should be ignored.

Saving Simulated IPR Data – The IPR module can be used to store simulated IPR data. In order to do this, a simulation name must be provided in the Name button, as shown below, and then clicking the Save IPR button.

Saving IPR Simulation Instance

Figure IV: Saving IPR Simulation Instance

Tubing Performance Relationship (TPR)

A very common parameter in everyday production calculations is bottom-hole pressure. In most petroleum engineering analyses, it is desired to know the bottom hole pressure (sand-face pressure) at a given well head pressure and flow-rate in a well. The Well Deliverability TPR module simplifies the determination of this frequently-used parameter whilst also providing the user with far-range of analytical results: wellbore pressure traverse, temperature gradient, and the impact of tubing configurations on flow rate. The functionality to save simulated TPR data also comes in handy.

Production data used for the simulation can be loaded from a data repository (database, Excel spreadsheet, flat file) or manually entered into the system by the user. Well Deliverability TPR solution uses the following data for the simulation process:

  • Well name (completion name)
  • Gas specific gravity
  • Inner diameter of casing/tubing
  • Roughness of tubing interior
  • Measure depth (length) of well bore
  • Angular inclination of the well to the horizontal surface
  • Tubing head pressure – pressure measured at well head
  • Tubing head temperature – temperature measured at well head
  • Sand-face temperature – temperature measured at bottom of well
  • Flow rate
  • Gas-oil ratio

If the data is in a data repository (database, spreadsheet, flat file), it can be loaded into the system, and then the Data Table option is selected from the Data Source drop-down list. In the Well Name drop-down list, the name of a well is selected, and the TPR system loads the well configuration data associated to the selected well into each of the corresponding text fields. The last field (# of Data Points) value should be manually entered. It determines how many data points the simulation process should generate. By default, 100 data points are created.

If the data is to be manually provided by the user, then the User Input option is selected from the Data Source drop-down list. In the Well Name text field and other text fields, data is entered accordingly. Below is a sample screen-capture of TPR data supplied to the system using manual entry:

TPR Parameters

Figure VI: TPR Parameters

Once user is done loading/entering data, then clicking the Run TPR button will:

  • Randomly create depth intervals from zero to measured depth of wellbore inclusive
  • Generate temperature gradient for each length interval
  • Determine pseudo-critical temperature and pseudo-critical pressure
  • Calculate pseudo-reduced pressure at well head and pseudo-reduced temperature for each wellbore length interval
  • Compute the pseudo-reduced pressure and corresponding sand-face pressure at each wellbore length interval point using a derivative of the Average Pressures/ Cullendar Smith method enumerated by Peter Ohirhian in the publication Static Behavior of Natural Gas and its Flows in Pipes
  • Calculate the corresponding gas flow rate for each computed pressure data, and finally
  • Use provided gas-oil-ratio value to derive the oil flow rate for each computed pressure data

The result of the simulation is a TPR curve and BHP (sand-face pressure) value with far-reaching applicability to the oil/gas production engineer:

TPR Curves

Figure VII: TPR Curves

Saving Simulated TPR Data – The TPR module can be used to store simulated TPR data. In order to do this, a simulation name must be provided in the Name button, as shown below, and then clicking the Save TPR button.

Saving TPR Simulation Instance

Figure IX: Saving TPR Simulation Instance

Operating Point Determination

Both the IPR and the TPR relate the wellbore flowing pressure to the surface production rate. While the IPR represents what the reservoir can deliver to the bottom hole, the TPR represents what the well can deliver to the surface. Combined, the intersection of the IPR with the TPR, called the operating point, yields the well deliverability, an expression of what a well will actually produce for a given operating condition.

RAI’s Well Deliverability’s Operating Point module equips the production engineer with the graphical tool to easily determine the intersection of IPR and TPR. It has a simple user interface that allows the user to select a saved IPR instance and a saved TPR instance to run a deliverability analyses. The analysis process is centered on combining the sand-face pressures and flow rates from each IPR and TPR instance, and generating a deliverability plot from which the operating point can be easily determined visually as shown in the figure below. Future version of the module will automatically calculate the intersection point and display it on the plot.

Operating Point Determination

Figure X: Determination of Operating Point


There are various analyses that can be performed using IPR, TPR and deliverability as tools. In the Diagnostics module, the system attempts to present to the user a simple petroleum engineering dashboard that utilizes the results from IPR and TPR simulations in sensitivity analysis and tubing size determination.


At a time when main-stream production engineering software are becoming less and less affordable to oilfield players,’s Well Deliverability tool provides an easy way to stay competitive whilst spending less. Leveraging Spotfire, Well Deliverability offers a 3-in-1 solution that combines the ease of use of Microsoft Excel with the functional power of data analytics to provide a standard, integrated, yet simple application that helps production engineers assess what the reservoir and wellbore can deliver to the surface.


Written by Theodore Etukuyo
Theodore Etukuyo holds a Bachelor's Degree in Mathematics and an Associate Degree in Petroleum Engineering Technology.