...

Definition

WFP – Well Performance Analysis analysis is a comparative Сomparative analysis between:

• the formation the reservoir fluid deliverability (the ability of of reservoir to produce or take-in the fluid) which is called WFP – Well Flow PerformanceInflow Performance Relation (IPR)

and

• wellbore fluid deliverability (the ability of of well  to lift up or lift down the fluid) and which is called OPR or TPR or VFP (equally popular throughout the literaturecalled Lift Curves (LC) (also called  Vertical Lift Performance (VLP) or Tubing Performance Relation (TPR) )

It is based on correlation between surface flowrate 

Application

...

• Setting up the  required 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

• FDP 
  
  
• Generating Lift Curves (LC) tables as input for Reservoir Flow Modelling (RFM)
  
  

Technology

...

AnchorStabilisedStabilisedMost reservoir engineers exploit material balance thinking which is based on long-term well-by-well surface flowrate targets  (whether producers or injectors).

...

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 behaviour which is one of the primary subjects of Well Testing domain.

...

...

.

The

...

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

...

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

...

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.

...

...

...

...

...

...

...

...

...

...

...

...

...

...

...

...

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 

• IPR – Inflow Performance Relation (IPR) – responsible for resevroir reservoir deliverability (see below)
  
  

• OPR – Outflow Performance Relation ( also called TPR – Tubing Performance Relation and VFP – Vertical Lift Performance Lift Curves (LC) – responsible for for well deliverability  (see below )

Anchor
JP JP

The intersection of WFP – Well Flow Performance and OPR curves represent the stabilized flow IPR and Lift Curves represent the Stabilised wellbore flow (see Fig. 1)

Given a tubing head pressure 

Workflow

...

1. Check the current production rate against the production target from FDP
   
   
2. If the diffference is big enough to justify the cost of production optimization (see point 8 below) then proceed to the step 3 below
   
   
3. Assess formation pressure based on well tests
   
   
4. Simulate IPR /OPR based  LC based on the current WOR/GOR
   
   
5. Calculate the stabilized flow bottom-hole pressure
   
   
6. Gather the current bottom-hole pressure

   LaTeX Math Inline
   body p_{wf}

   
   
   
7. Check up the calculation aganst the actual 

   LaTeX Math Inline
   body p_{wf}

   
   
   
8. Recommend the production optimisation activities to adjust bottom-hole pressure 

   LaTeX Math Inline
   body p_{wf}

   :
   
   
   • 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  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 

p_{wf} = p_{wf}(q)

  which may be non-linear. 

...

The IPR analysis is closely related to well PI – Productivity Index  

...

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

for oil producer with liquid flowrate

See Also

...

Petroleum Industry / Upstream / Production / Subsurface Production / Well & Reservoir Management

Subsurface E&P Disciplines / Production Technology 

[ WFP – Water Injector ]

[ Inflow Performance Relation (IPR) ] [ Lift Curves (LC) ]

Anchor
WFP WFP

...

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

for gas producer with gas flowrate

...

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

for gas injector with gas flowrate

...

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

for water injector with water flowrate

where

...

...

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  

...

...

...

...

...

...

The  Productivity Index can be constant or dependent on bottom-hole pressure 

In general case of multiphase flow the PI 

Some analytical correlations can be used to approximate the numerical solutions and some of them are brought below. 

These correlations are usually expressed in terms of 

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.

Water and Dead Oil IPR

For a single layer formation with low-compressibility fluid (water or dead oil) the PI does not depend on drawdown (or flowrate) 

...

...

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 

The alternative form of the conatsnt PI WFP – Well Flow Performance is:

\frac{q}{q_{max}} = 1 -\frac{p_{wf}}{p_R}

Dry Gas IPR

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 

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 

It needs two well tests at two different rates to assess

But obviously more tests will make assessment more accruate.

Saturated Oil IPR

For Saturated Oil reservoir with bottom-hole pressure below bubble point 

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

But when field-average formation pressure is above bubble-point 

Multiphase IPR

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

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} = p_{wf}(q)

  which may be non-linear. 

...

...

...

Sample Case 1 –  Oil Producer Analysis

...

...

...

Sample Case 2 – Water Injector Analysis

...

References

...

Joe Dunn Clegg, Petroleum Engineering Handbook, Vol. IV – Production Operations Engineering, SPE, 2007

...