WFP – Well Performance Analysis analysis is a comparative analysis between:
and
It is based on correlation between surface flowrate and bottomhole pressure as a function of tubing-head pressure and formation pressure and current reservoir saturation.
Ideally, the well flow model for WFP – Well Flow Performance analysis should be performed individually for each well but even typical for a given asset can.
Most reservoir engineers exploit material balance thinking which is based on long-term well-by-well surface flowrate targets (whether producers or injectors).
In practice, the flowrate targets are closely related to bottomhole pressure and associated limitations and require a specialised analysis to set up the optimal lifting (completion, pump, chocke) parameters.
This is primary domain of WFP – Well Flow Performance analysis.
WFP – Well Flow Performance is performed on stabilised wellbore and reservoir flow and does not cover transient behavior which is one of the primary subjects of Well Testing domain.
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The conventional WFP – Well Performance Analysis is perfomed as the cross-plot with two model curves:
The intersection of WFP – Well Flow Performance and OPR curves represent the stabilized flow (see Fig. 1)
Fig. 1. The stablised flow rate is represnted as junction point of WFP – Well Flow Performance and OPR curves. | Fig. 2. The dead well scenario. |
Given a tubing head pressure the WFP Junction Point will be dynamic in time depending on current formation pressure (see Fig. 2) and formation saturation (see Fig. 3).
Fig. 2. A sample case of stablised flow rate as function of formation pressure. | Fig. 3. A sample case of stablised flow rate as function of formation water saturation and corresponding production water-cut. |
The above workflow is very simplistic and assumes single-layer formation with no cross-flow complications.
In practise, the WFP – Well Flow Performance analysis is often very tentative and production technologists spend some time experimenting with well regimes on well-by-well basis.
IPR – Inflow Performance Relation represents the relation between the bottom-hole pressure and surface flow rate during the stabilised formation flow:
p_{wf} = p_{wf}(q) |
which may be non-linear.
The IPR analysis is closely related to well PI – Productivity Index which is defined as below:
| for oil producer with liquid flowrate (water and oil at surface conditions) | |
| for gas producer with gas flowrate at surface conditions | |
| for gas injector with gas flowrate at surface conditions | |
| for water injector with water flowrate at surface conditions |
where
field-average formation pressure within the drainage area of a given well: |
Based on above defintions the general WFP – Well Flow Performance can be wirtten in a general form:
p_{wf} = p_R - \frac{q}{J_s} |
providing that has a specific meaning and sign as per the table below:
for producer | |
for injector | |
for oil producer | |
for gas producer or injector | |
for water injector or water-supply producer |
The Productivity Index can be constant or dependent on bottom-hole pressure or equivalently on flowrate .
In general case of multiphase flow the PI features a complex dependance on bottom-hole pressure (or equivalently on flowrate ) which can be etstablished based on numerical simulations of multiphase formation flow.
For undersaturated reservoir the numerically-simulated WFP – Well Flow Performances have been approximated by analytical models and some of them are brought below.
These correlations are usually expressed in terms of or as alternative to .
They are very helpful in practise to design a proper well flow optimization procedure.
These correaltions should be calibrated to the available well test data to set a up a customized WFP – Well Flow Performance model for a given formation.
For a single layer formation with low-compressibility fluid (water or dead oil) the PI does not depend on drawdown (or flowrate) and WFP – Well Flow Performance plot is reperented by a straight line (Fig. 1)
Fig.1. WFP – Well Flow Performance plot for constant productivity (water and dead oil) |
This is a typical WFP – Well Flow Performance plot for water supply wells, water injectors and dead oil producers.
The PI can be estimated using the Darcy equation:
J_s = \frac{2 \pi \sigma}{ \ln \frac{r_e}{r_w} + \epsilon+ S} |
where – water-based or water-oil-based transmissbility above bubble point ,
for steady-state SS flow and for pseudo-steady state PSS flow.
The alternative form of the conatsnt PI WFP – Well Flow Performance is:
\frac{q}{q_{max}} = 1 -\frac{p_{wf}}{p_R} |
For gas producers, the fluid compressibility is high and formation flow is essentially non-linear, inflicting the downward trend on the whole WFP – Well Flow Performance plot (Fig. 2).
Fig. 2. WFP – Well Flow Performance for dry gas producer or gas injector into a gas formation |
The popular dry gas IPR correlation is Rawlins and Shellhardt:
\frac{q}{q_{max}} = \Bigg[ \, 1- \Bigg( \frac{p_{wf}}{p_R} \Bigg)^2 \, \Bigg]^n |
where is the turbulent flow exponent, equal to 0.5 for fully turbulent flow and equal to 1 for laminar flow.
The more accurate approximation is given by LIT (Laminar Inertial Turbulent) IPR model:
a \, q + b \, q^2 = \Psi(p_R) - \Psi(p_{wf}) |
where – is pseudo-pressure function, is laminar flow coefficient and is turbulent flow coefficient.
It needs two well tests at two different rates to assess or .
But obviously more tests will make assessment more accruate.
For saturated oil reservoir the free gas flow inflict the downward trend of WFP – Well Flow Performance plot similar to dry gas (Fig. 3).
Fig. 3. WFP – Well Flow Performance for 2-phase oil+gas production below and above bubble point |
The analytical correlation for saturted oil flow is given by Vogel model:
\frac{q}{q_{max}} = 1 - 0.2 \, \frac{p_{wf}}{p_R} - 0.8 \Bigg(\frac{p_{wf}}{p_R} \Bigg)^2 \quad , \quad p_b > p_R > p_{wf} |
For undersaturated oil reservoir the WFP – Well Flow Performance model will depend on the bottom-hole pressure.
When it is higher than bubble point then formation flow will be single-phase oil and production will follow the constant WFP – Well Flow Performance.
When bottom-hole pressure goes below bubble point the near-reservoir zone free gas slippage also inflicts the downward trend at the right side of WFP – Well Flow Performance plot (Fig. 3).
It can be interpreted as deterioration of near-reservoir zone permeability when the fluid velocity is high and modelled as rate-dependant skin-factor.
Fig. 3. WFP – Well Flow Performance for 2-phase oil+gas production below and above bubble point |
The analytical correlation for undersaturated oil flow is given by modified Vogel model:
\frac{q}{q_b} = \frac{p_R - p_{wf}}{p_R - p_b} \quad , \quad p_R > p_{wf} > p_b |
q = (q_{max} - q_b ) \Bigg[ 1 - 0.2 \, \frac{p_{wf}}{p_b} - 0.8 \Bigg(\frac{p_{wf}}{p_b} \Bigg)^2 \Bigg] + q_b \quad , \quad p_R > p_b > p_{wf} |
For 3-phase water-oil-gas flow the IPR analysis is perfomed on oil and watr components (see Fig. 4.1 and Fig. 4.2).
Fig. 4.1. Oil WFP – Well Flow Performance for 3-phase (water + oil + gas) formation flow | Fig. 4.2. Water WFP – Well Flow Performance for 3-phase (water + oil + gas) formation flow |
OPR – Outflow Performance Relation also called TPR – Tubing Performance Relation and VLP – Vertical Lift Performance represents the relation between the bottom-hole pressure and surface flow rate during the stabilised wellbore flow under a constant Tubing Head Pressure (THP):
p_{wf} = p_{wf}(q) |
which may be non-linear.
Fig 3. OPR for low-compressible fluid |
Fig 4. OPR for compressible fluid |
Fig. 5. WFP for stairated oil |
Fig. 6. WFP for stairated oil |
Joe Dunn Clegg, Petroleum Engineering Handbook, Vol. IV – Production Operations Engineering, SPE, 2007
Michael Golan, Curtis H. Whitson, Well Performance, Tapir Edition, 1996
William Lyons, Working Guide to Petroleum and Natural Gas production Engineering, Elsevier Inc., First Edition, 2010
Shlumberge, Well Performance Manual