Definition

WFP – Well Performance Analysis is a specialized analysis of correlation between surface flowrate and wellbore pressure as function of formation pressure and associated production optimization procedures.

Application

Setting up the optimal production targets
Create WFP – Well Flow Performance as input for 3D simulations

Technology

WFP is performed on stabilised flow and does not cover transient behavior which is normally covered in Well Testing domain.

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

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

The stabilised 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 flow may not represent a stabilised 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	$\begin{array}{l}J(t) = \frac{q}{\Delta p}\end{array}$	constant	constant
Flow rate	$\begin{array}{l}q(t)\end{array}$	constant	constant
Drawdown	$\begin{array}{l}\Delta p(t) = p_e(t) - p_{wf}(t)\end{array}$	constant	constant
Botom-hole pressure	$\begin{array}{l}p_{wf}(t)\end{array}$	constant	varying
Formation pressure	$\begin{array}{l}p_e(t)\end{array}$	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 not 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-lot with two physical models:

IPR – Inflow Performance Relation

and

Vertical Lift Performance also called Outflow Performance Relation or Tubing Performance Relation

IPR – Inflow Performance Relationship

IPR – Inflow Performance Relation represnts the relation between the bottom-hole pressure $\begin{array}{l}p_{wf}\end{array}$ and surface flow rate $\begin{array}{l}q\end{array}$ during the stabilised flow:

(1)	$\begin{array}{l}\displaystyle p_{wf} = p_{wf}(q)\end{array}$

which will be non-linear in generic case.

The IPR analysis is closely related to well PI – Productivity Index $\begin{array}{l}J_s(q)\end{array}$ which is defined as below:

(2)	$\begin{array}{l}\displaystyle J_s(q_{\rm liq}) = \frac{q_{\rm liq}}{p_R-p_{wf}}\end{array}$

for oil producer with surface liquid production $\begin{array}{l}q_{liq} = q_o + q_w\end{array}$ (water and oil)

(3)	$\begin{array}{l}\displaystyle J_s(q_g) = \frac{q_g}{p_R-p_{wf}}\end{array}$

for gas producer

(4)	$\begin{array}{l}\displaystyle J_s(q_g) = \frac{q_g}{p_{wf}-p_R}\end{array}$

for gas injector

(5)	$\begin{array}{l}\displaystyle J_s(q_w) = \frac{q_w}{p_R-p_{wf}}\end{array}$

for water injector

where

$\begin{array}{l}q_w, \, q_o, \, q_g\end{array}$	water, oil, gas flow rates at separator
$\begin{array}{l}p_R\end{array}$	field-average formation pressure withing the drainage area of a given well

Based on these notions the general WFP – Well Flow Performance can be wirtten in univseral form:

(6)	$\begin{array}{l}\displaystyle p_{wf} = p_R - \frac{q}{J_s(q)}\end{array}$

providing that $\begin{array}{l}q\end{array}$ has a specific meaning and sign as per the table below:

$\begin{array}{l}-\end{array}$	for producer
$\begin{array}{l}+\end{array}$	for injector
$\begin{array}{l}q=q_{\rm liq}=q_o+q_w\end{array}$	for oil producer
$\begin{array}{l}q=q_g\end{array}$	for gas producer or injector
$\begin{array}{l}q=q_w\end{array}$	for water injector or water-supply producer

Despite of terminological similarity there is a big difference in the way WFP and Well Testing deal with formation pressure and flowrates which results in a big difference in productivity index definition and corresponding analysis.

This difference is summarized in the table below:

	WFP	Well Testing
Formation pressure	$\begin{array}{l}p_R\end{array}$ – field-average pressure within the drainage area $\begin{array}{l}A_e\end{array}$	$\begin{array}{l}p_e\end{array}$ – pressure value at boudary of the drainage area $\begin{array}{l}A_e\end{array}$
Flow rate	$\begin{array}{l}q_{\rm liq}=q_o+q_w\end{array}$ – surface liquid rate	$\begin{array}{l}q_t = B_w \, q_W + \frac{B_o - R_s B_g}{1 - R_v R_s} \, q_O + \frac{B_g - R_v B_o}{1 - R_v R_s} \, q_G\end{array}$ – total flowrate at sandface

For single-layer formation with low-compressibility fluid the PI does not depend on flowrate $\begin{array}{l}J_s = \rm const\end{array}$ 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.

For gas wells, condensate producers, light-oil producers, and oil producers below bubble point $\begin{array}{l}P_{wf} < P_b\end{array}$ the fluoid compressibility is high and formation flow in well vicinity becomes non-linear (deviating from Darcy) inbflicting 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 growth.

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

VLP – Vertical Lift Performance

КВЛ активно используется для анализа оптимального режима работы скважины.

Fig 3. VLP for low-compressible fluid

Fig 4. VLP 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

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