Definition
WFP – Well Performance Analysis analysis is a comparative analysis between:
the formation fluid deliverability (the ability of reservoir to produce or take-in the fluid) which is called WFP – Well Flow Performance
and
wellbore fluid deliverability (the ability of well to lift up or lift down the fluid) and which is called OPR or TPR or VFP (equally popular throughout the literature)
It is based on correlation between surface flowrate q and bottomhole pressure p_{wf} as a function of tubing-head pressure p_s and formation pressure p_R and current reservoir saturation.
In general case, the WFP – Well Flow Performance is set individually for each well.
Application
- Setting up the required production or injection regime for each well upon the current formation pressure, reservoir saturation and production target specified by FDP
- Generating WFP – Well Flow Performance tables as input for 3D simulations
Technology
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.
The conventional WFP – Well Performance Analysis is perfomed as the
\{ p_{wf} \ {\rm vs} \ q \} cross-plot with two model curves:
- IPR – Inflow Performance Relation – responsible for resevroir deliverability (see below)
- OPR – Outflow Performance Relation ( also called TPR – Tubing Performance Relation and VFP – Vertical Lift Performance ) – responsible for well deliverability (see below )
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. |
Given a tubing head pressure p_s 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. |
Workflow
- Check the current production rate against the production target from FDP
- If the diffference is big enough to justify the cost of production optimization (see point 8 below) then proceed to the next step
- Assess formation saturation in pay zones based on well tests
- Assess formation pressure based on well tests
- Calculate the stabilized flow bottom-hole pressure
- Gather the current bottom-hole pressure
p_{wf}
- Check up the calculation aganst the actual
p_{wf}
- Recommend the production optimisation activities to adjust bottom-hole pressure
p_{wf}:
- adjusting the choke at surface
- adjusting the pump settings from surface
- changing the pump depth
- changing the tubing size
- changing the pump
- adjusting the choke at surface
The above workflow is very simplistic and assumes single-layer formation with no cross-flow complications.
IPR – Inflow Performance Relationship
IPR – Inflow Performance Relation represents the relation between the bottom-hole pressure p_{wf} and surface flow rate q during the stabilised formation flow:
(1) | p_{wf} = p_{wf}(q) |
which may be non-linear.
The IPR analysis is closely related to well PI – Productivity Index J_s which is defined as below:
| for oil producer with liquid flowrate q_{liq} = q_O + q_W (water and oil at surface conditions) | ||
| for gas producer with gas flowrate
q_G at surface conditions | ||
| for gas injector with gas flowrate
q_{GI} at surface conditions | ||
| for water injector with water flowrate q_{WI} at surface conditions |
where
p_R | field-average formation pressure within the drainage area V_e of a given well: p_R = \frac{1}{V_e} \, \int_{V_e} \, p(t, {\bf r}) \, dV |
Based on these notions the general WFP – Well Flow Performance can be wirtten in universal form:
(6) | p_{wf} = p_R - \frac{q}{J_s} |
providing that q has a specific meaning and sign as per the table below:
- | for producer |
+ | for injector |
q=q_{\rm liq}=q_o+q_w | for oil producer |
q=q_g | for gas producer or injector |
q=q_w | for water injector or water-supply producer |
For a single layer formation with low-compressibility fluid (like water) the PI does not depend on drwadown (or flowrate) J_s = \rm const and WFP – Well Flow Performance plot is reperented by a straight line (Fig. 1)
Fig.1. WFP – Well Flow Performance plot for low-compressible fluid production (water, undersaturated oil) |
This is a typical WFP – Well Flow Performance plot for water supply wells, water injectors and oil producers above bubble point.
The PI can be estimated using the Darcy equation:
(7) | J_s = \frac{2 \pi \sigma}{ \ln \frac{r_e}{r_w} + \epsilon+ S} |
where \sigma = \Big \langle \frac{k} {\mu} \Big \rangle \, h = k \, h\, \Big[ \frac{k_{rw}}{\mu_w} + \frac{k_{ro}}{\mu_o} \Big] – water-based or water-oil-based transmissbility above bubble point
,\epsilon = 0.5 for steady-state SS flow and \epsilon = 0.75 for pseudo-steady state PSS flow.
For gas wells, condensate producers, light-oil producers, and oil producers below bubble point P_{wf} < P_b the fluid compressibility is high, formation flow in well vicinity becomes non-linear (deviating from Darcy) and free gas slippage effects inflict the downward trend on WFP – Well Flow Performance plot (Fig. 2).
It can be interpreted as deterioration of near-reservoir zone permeability with fluid velocity is growing.
Fig.2. WFP – Well Flow Performance for compressible fluid production (gas, light oil, saturated oil) |
In general case of saturated oil, the PI J_s features a complex dependance on bottom-hole pressure p_{wf} ( or flowrate q) which can be etstablished based on numerical simulations of multiphase formation flow.
But when field-average formation pressure is above bubble-point p_R > p_b (which means that most parts of the drainage area are saturated oil) the PI can be farily approximated by some analytical correlations.
OPR – Outflow Performance Relationship
OPR – Outflow Performance Relation also called TPR – Tubing Performance Relation and VLP – Vertical Lift Performance represents the relation between the bottom-hole pressure p_{wf} and surface flow rate q during the stabilised wellbore flow under a constant Tubing Head Pressure (THP):
(8) | p_{wf} = p_{wf}(q) |
which may be non-linear.
Fig 3. OPR for low-compressible fluid |
Fig 4. OPR for compressible fluid |
Sample Case 1 – Oil Producer Analysis
Fig. 5. WFP for stairated oil |
Fig. 6. WFP for stairated oil |
Sample Case 2 – Water Injector Analysis
Sample Case 3 – Gas Producer Analysis
References
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