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 and bottomhole pressure as a function of tubing-head pressure and formation pressure 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 wellbore flow is called stabilised if the delta pressure across wellbore is not changing over time.

The formation flow is called stabilised if the well productivity index is not changing over time.

It's important to remember the difference between constant rate formation flow and stabilised formation flow.

The stabilised formation flow may go through a gradually changing flow rate due to formation pressure change, while the productivity index stays constant.

On the other hand, the constant rate formation flow may not represent a stabilised formation flow as the bottom-hole pressure and productivity index maybe still in transition after the last rate change.

The WFP methods are not applicable if the well flow is not stabilised even if the flow rate is maintained constant.

There are two special reservoir flow regimes which are both stabilised and maintain constant flow rate: steady state regime (SS) and pseudo-steady state regime (PSS).

The steady state regime (SS) regime is reached when the flow is stabilised with the full pressure support at the external boundary.

The pseudo-steady state (PSS) regime is reached when the flow is stabilised with no pressure support at the external boundary.

In both above cases, the drawdown and flow rate will stay constant upon productivity stabilisation.

As for formation and bottom-hole pressure in PSS they will be synchronously varying while in SS they will be staying constant.

The table below is summarizing the major differences between SS and PSS regimes.

	Steady state regime (SS)	Pseudo-steady state (PSS)
Boundary	Full pressure support	No pressure support
Productivity index	constant	constant
Flow rate	constant	constant
Drawdown	constant	constant
Botom-hole pressure	constant	varying
Formation pressure	constant	varying

It's again important to avoid confusion between the termines stationary conditions (which mean that refered properties are not chaning in time) and stabilised flow conditions which may admit pressure and rate vraition.

In practice, the productivity index is usually not known at all times as there is no routine procedure to assess it.

It is usually accepted that a given formation takes the same time to stabilise the flow after any change in well flow conditions and the stabilisation time is assessed based on the well tests analysis.

Although, this is not strictly true and the flow stabilisation time depends on well-formation contact and reservoir property variation around a given well.

This is also compromised in multi-layer formations with cross-layer communication.

The conventional WFP – Well Performance Analysis is perfomed as the 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)

GLOSSARY > Well Flow Performance = WFP > wfp.png

Fig. 1. The stablised flow rate is represnted as junction point of WFP – Well Flow Performance and OPR curves.

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.

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 step 3 below
Assess formation pressure based on well tests
Simulate IPR/OPR based on the current WOR/GOR
Calculate the stabilized flow bottom-hole pressure
Gather the current bottom-hole pressure
Check up the calculation aganst the actual
Recommend the production optimisation activities to adjust bottom-hole pressure :
- adjusting the choke at surface
- adjusting the pump settings from surface
- changing the pump depth
- changing the tubing size
- changing the pump

The above workflow is very simplistic and assumes single-layer formation with no cross-flow complications.

In practise, the WFP analysis is often very tentative and production technologists spend some time experimenting with well regimes on well-by-well basis.

IPR – Inflow Performance Relation

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:

J_s(q_{\rm liq}) = \frac{q_{\rm liq}}{p_R-p_{wf}}

for oil producer with liquid flowrate (water and oil at surface conditions)

J_s(q_G) = \frac{q_G}{p_R-p_{wf}}

for gas producer with gas flowrate at surface conditions

J_s(q_g) = \frac{q_{GI}}{p_{wf}-p_R}

for gas injector with gas flowrate at surface conditions

J_s(q_w) = \frac{q_{WI}}{p_R-p_{wf}}

for water injector with water flowrate at surface conditions

where

field-average formation pressure within the drainage area of a given well:

Based on these notions the general WFP – Well Flow Performance can be wirtten in universal 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

For a single layer formation with low-compressibility fluid (like water) the PI does not depend on drwadown (or flowrate) and WFP – Well Flow Performance plot is reperented by a straight line (Fig. 1)

GLOSSARY > Well Flow Performance = WFP > IPRoil.png

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:

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.

For gas wells, condensate producers, light-oil producers, and oil producers below bubble point 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.

GLOSSARY > Well Flow Performance = WFP > IPRoil.png

Fig.2. WFP – Well Flow Performance for compressible fluid production (gas, light oil, saturated oil)

In general case of saturated oil, the PI features a complex dependance on bottom-hole pressure ( or flowrate ) which can be etstablished based on numerical simulations of multiphase formation flow.

But when field-average formation pressure is above bubble-point (which means that most parts of the drainage area are saturated oil) the PI can be farily approximated by some analytical correlations.