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 

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.

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 

• 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 )

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JP JP

The intersection of WFP – Well Flow Performance and OPR curves represent the stabilized 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 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 

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   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 – Well Flow Performance analysis is often very tentative and production technologists spend some time experimenting with well regimes on well-by-well basis. 

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IPR IPR

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}}

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

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

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

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 

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 

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).

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 the free gas flow inflict the downward trend of WFP – Well Flow Performance plot  similar to dry gas (Fig. 3).

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}

Undersaturated Oil IPR

For undersaturated oil reservoir

When it is higher than bubble point

When bottom-hole pressure goes below bubble point 

It can be interpreted as deterioration of near-reservoir zone permeability when the fluid velocity is high and approximated by rate-dependant skin-factor.

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}

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).

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VLP VLP

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. 

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WFP WFP

Sample Case 1 –  Oil Producer Analysis

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