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One of the Productivity Diagnostics methods based on relation between the bottom-hole pressure
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and surface flow rate
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p_{wf} = p_{wf}(q) |
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which may be linear or non-linear.
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One of the two key concepts of Well Flow Performance analysis along with Vertical Lift Performance (VLP).
The word "Inflow" is misnomer as IPR analysis is applicable for both producers and injectors.
The most general proxy-model is given by LIT (Laminar Inertial Turbulent) IPR model:
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a \, q + b \, q^2 = \Psi(p_r) - \Psi(p_{wf}) |
where
| static wellbore pressure | ||||
| laminar flow coefficient | ||||
| turbulent flow coefficient | ||||
| pseudo-pressure function specific to fluid type |
It needs well tests at least three different rates to assess
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The IPR
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analysis is closely related to well
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| for water injector with injection rate
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where
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Based on above defintions the aribitrary IPR
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can be wirtten in a general form:
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p_{wf} = p_r - \frac{q}{J_s} |
providing that
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gas producer |
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water injector or |
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water producer or water production from |
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oil producer |
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See more on the variations of PI definition between Dynamic Modelling, Well Flow Performance
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and Well Testing.
The Productivity Index can be constant
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(showing a straight line on IPR like on Fig. 2) or dependent on bottomhole pressure
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In general case of multiphase flow the PI
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For undersaturated reservoir the numerically-simulated IPR
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s have been approximated by analytical models and some of them are brought below.
These correlations are usually expressed in terms of
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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
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customised IPR
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model for a given formation.
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Water and Dead
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Oil IPR
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For a single layer formation with low-compressibility fluid (water or dead oil) the PI does not depend on drawdown (or flowrate)
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plot is
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represented by a straight line (Fig.
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2)
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2.IPR |
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plot for constant productivity (water and dead oil) |
This is a typical IPR
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plot for water supply wells, water injectors and dead oil producers.
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For the oil/water production the PI can be estimated using the
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J_s = \frac{2 \pi \sigma}{ \ln \frac{r_e}{r_w} + \epsilon+ S} |
where
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transmissibility above bubble point
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The alternative form of the constant Productivity Index IPR
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is given by:
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\frac{q}{q_{max}} = 1 -\frac{p_{wf}}{p_ |
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r} |
where
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atmospheric pressure and also called
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Dry Gas IPR
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For gas producers, the fluid compressibility is high and formation flow is essentially non-linear, inflicting the downward trend on the whole IPR
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plot (Fig.
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3).
Fig. |
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3.IPR |
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for dry gas producer or gas injector into a gas formation |
The popular dry gas IPR
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correlation is Rawlins and Shellhardt:
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\frac{q}{q_{max}} = \Bigg[ \, 1- \Bigg( \frac{p_{wf}}{p_ |
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r} \Bigg)^2 \, \Bigg]^n |
where
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The more accurate approximation is given by LIT (Laminar Inertial Turbulent) IPR model:
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a \, q + b \, q^2 = \Psi(p_R) - \Psi(p_{wf}) |
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flow
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It needs two well tests at two different rates to assess
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Saturated
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Oil IPR
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For saturated oil reservoir the free gas flow inflict the downward trend of IPR
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plot similar to dry gas (Fig.
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4).
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4.IPR |
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for 2-phase oil+gas production below and above bubble point |
The analytical correlation for
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saturated oil reservoir flow is given by Vogel IPR @ model:
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\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} |
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Undersaturated Oil
IPR
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For undersaturated oil reservoir
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model will vary on whether the bottom-hole pressure is above or below bubble point.
When it is higher than bubble point
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When bottom-hole pressure goes below bubble point
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plot (Fig.
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It can be interpreted as deterioration of near-reservoir zone permeability when the fluid velocity is high and approximated by rate-dependant skin-factor.
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5.IPR |
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for 2-phase oil+gas production below and above bubble point |
The analytical correlation for undersaturated oil flow is given by modified Vogel model:
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r - p_{wf}}{p_ |
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r - p_b} \quad , \quad p_ |
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r > p_{wf} > p_b |
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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_ |
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r > p_b > p_{wf} |
with AOF
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q_{max} = q_b \, \Big[1 + \frac{1}{1.8} \frac{p_b}{(p_r - p_b)} \Big] |
Saturated
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Multiphase IPR
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For saturated 3-phase water-oil-gas reservoir the IPR
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analysis is represented by oil and water components separately (see Fig.
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6.1 and Fig.
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6.2).
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6.1. Oil IPR |
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for saturated 3-phase (water + oil + gas) formation flow | Fig. |
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6.2. Water IPR |
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for saturated 3-phase (water + oil + gas) formation flow |
The analytical correlation for saturated 3-phase oil flow is given by Wiggins model:
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\frac{q_o}{q_{o, \, max}} = 1 - 0.52 \, \frac{p_{wf}}{p_ |
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r} - 0.48 \Bigg(\frac{p_{wf}}{p_ |
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\frac{q_w}{q_{w, \, max}} = 1 - 0.72 \, \frac{p_{wf}}{p_ |
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Undersaturated
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Multiphase IPR
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For undersaturated 3-phase water-oil-gas reservoir the IPR
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analysis is represented by oil and water components separately (see Fig.
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7.1 and Fig.
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7.2).
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7.1. Oil IPR |
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for udersaturated 3-phase (water + oil + gas) formation flow | Fig. |
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7.2. Water IPR |
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for undersaturated 3-phase (water + oil + gas) formation flow |
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The analytical correlation for saturated 3-phase oil flow is given by Wiggins model:
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See Also
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Petroleum Industry / Upstream / Production / Subsurface Production / Subsurface E&P Disciplines / Field Study & Modelling / Production Analysis / Productivity Diagnostics
[ Production Technology / Well Flow Performance ]
[ Vogel IPR @model ] [ Richardson and Shaw IPR @ model ] [ Wiggins IPR @ model ][ LIT IPR @ model ][ PADE IPR @ model ]
[ Dual-layer IPR][ Multi-layer IPR ] [ Dual-layer IPR with dynamic fracture ]
Reference
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