Well Modeling
Well Modeling is the process of developing models (supplying input) for actual wells and using these data in Well Modeling Software to perform the analyses required by the engineer. In all of our discussions to this point, we have assumed singlephase flow of either liquid or gas. Pressure loss calculations in multiphase flow are much more complicated than those for singlephase flow. This is because in singlephase flow, the only frictional losses that occur in the system are at the fluidpipe interface. In multiphase flow, there is also the friction loss between the phases. As we have also seen in our discussion on flow regimes in tubing, there are multiple flow regimes that can occur in vertical, deviated, and horizontal wells and these can have a significant impact of energy and momentum transfer.
To quantify the pressure losses occurring in multiphase flow calculations, we must consider the physics that are occurring in each flow regime. Typically, in the oil and gas industry, for multiphase flow we evaluate the physics empirically. Table 6.05 lists the important physical data that have been observed to have a significant impact on the pressure drop in well tubing. These empirical physics are input into the well model with a MultiPhase Flow Correlation.
There are many multiphase flow correlations available and most pipe flow or nodal analysis software contains options for the most relevant correlations for crude oil and natural gas flow. The details of these multiphase flow correlations are beyond the scope of this class, so I will briefly give a general description of them and then discuss the common correlations used in the oil and gas industry.
Well Model Data
As we have already discussed, the energy balance is a steadystate equation while our flow calculations are unsteadystate problems. When we use the energy balance equation to solve unsteadystate problems, we are solving a category of physical problems called a Series of SteadyStates where the equation is derived for steadystate conditions, but we are solving it with timedependent input data.
In Table 6.05 there are color coded entries: some of the data I have listed as Static Data which implies they do not change with time or location. Other data I have listed as Dynamic Data which implies that they may change with time, location, or both.
The entries in the green cells (Table 6.05 rows 16) are the data that make up a Well Model. These data are entered into the well modeling software and are treated as fixed data for some time period or some length of tubing. For example, I have already mentioned tapered tubing strings where the diameter of the tubing may change with position. When a well model is constructed, these design changes can be implemented as part of the segmented well model.
Data or Property  Symbol  Description 

Tubing/Pipe Diameter  $${D}_{ID}$$  Dynamic data but treated as static data 
Downhole well equipment  Pumps, chokes, etc.  Static data 
True vertical depth, TVD  $$\Delta z$$  Vertical depth – depth in the true vertical direction 
Measured depth, MD  $$\Delta l$$  Measured depth – physical length of tubing 
Absolute or Relative Roughness  $$\epsilon \text{or}\epsilon /{D}_{ID}$$  Dynamic data but treated as static data 
Efficiency  $${E}_{eff}$$  Dynamic data but treated as static data 
Liquid HoldUp  $${H}_{l}$$  Dynamic data: fraction of a representative elemental volume (REV) occupied by liquid (analogous to liquid saturation in the reservoir). 
Gas HoldUp  $${H}_{g}=\left(1{H}_{l}\right)$$  Dynamic data: fraction of a representative elemental volume (REV) occupied by gas (analogous to gas saturation in the reservoir). 
Slip (or Slip Velocity)  $${v}_{s}$$  Dynamic data (difference between velocities of two different phases). 
GasLiquid Ratio  $$GLR=\frac{{q}_{g}}{{q}_{o}+{q}_{w}}$$  Dynamic data: used as input to our pressure traverse or tubing performance calculation. 
GasOil Ratio or $GOR$  $$GOR=\frac{{q}_{g}}{{q}_{o}}$$  Dynamic data: used as input to our pressure traverse or tubing performance calculation. 
Watercut or ${f}_{w}$  $${f}_{w}=\frac{{q}_{w}}{{q}_{o}+{q}_{w}}$$  Dynamic data: fraction of the water rate in the total liquid rate. Used as input to our pressure traverse or tubing performance calculation. 
WaterOil Ratio or $WOR$  $$WOR=\frac{{q}_{g}}{{q}_{o}}$$  Dynamic data: ratio of the water water rate to the oil rate. Used as input to our pressure traverse or tubing performance calculation. 
Oil, Gas, and Water PVT Properties  $$\rho ,\text{}\mu \text{,etc}\text{.}$$  Dynamic data: PressureVolumeTemperature description of all fluids. 
Well Head Pressure  $${p}_{wh}$$  Dynamic data: one of the primary knowns/unknowns of the problem. 
BottomHole Pressure  $${p}_{wf}\text{or}{p}_{ws}$$  Dynamic data: one of the primary knowns/unknowns of the problem:

Production/Injection Rate  $${q}_{o}\text{,}{q}_{l}\text{,or}{q}_{t}$$  Dynamic data: one of the primary knowns/unknowns of the problem. 
Static data may also change due to a well intervention. For example, a production engineer may decide to perform a Tubing ChangeOut Workover, where all or portions of the tubing string are removed from the well and replaced with new tubing (either the original size or a new size). When a new tubing string is used, or a new piece of downhole equipment is installed, this is considered a new well design, and a new model must be used.
I have listed some of the data in the table as “Dynamic data but treated as static data.” This is because some data that are typically assumed to be fixed with time may, in fact, change. For example, the efficiency, absolute roughness, and relative roughness may change as the tubing degrades over time due to erosion, corrosion, or wax/asphaltene/scale deposition. I have also included the tubing/pipe diameter in this category of data because severe Scale Deposition (deposition of minerals from the produced water) can be a significant issue with certain produced water compositions and can significantly reduce the effective diameter of the tubing. This is shown in Figure 6.10. This figure also illustrates why tubing changeout workovers may be performed.
I have also highlighted some entries in Table 6.05 with blue cells (rows 79.) These entries are dynamic data that typically are not of interest to most production engineers and are not entered explicitly into a well model. These data are entered implicitly into the model by the choice of the multiphase flow correlation selected by the engineer. I will discuss these dynamic data and these multiphase flow correlations in more detail later in this lesson.
The table entries highlighted with orange cells (Table 6.05 rows 1014) are entries with dynamic data that are of interest to the production engineers and are explicitly input into the well model. In actuality, only a subset of these data is required because the rates, ${q}_{o}$, ${q}_{g}$, and ${q}_{w}$, are sufficient to specify the problem. For example, the oil rate, ${q}_{o}$, the gasoil ratio, $GOR$, and wateroil ratio, $WOR$, are sufficient to specify total production. Likewise, the liquid rate, ${q}_{l}$, the gasliquid ratio, $GLR$, and watercut, ${f}_{w}$, are also sufficient to specify total production.
Finally, the table entries highlighted with yellow cells (Table 6.05 rows 1517) are entries that are either specified or calculated by the well model. As I mentioned earlier, as production engineers, we are typically concerned with two types of problems, Pressure Traverse Calculations, where we specify the flow rate and calculate the pressure drop, and Tubing Performance Calculations, where we specify one pressure and the total rate and calculate the other pressure (typically the flow bottomhole pressure, ${p}_{wf}$).