Part 3
Wellbore Storage Effect
Dr. Sayed Gomaa
Wellbore Storage
Types of wellbore storage
▪ A wellbore storage effect caused by fluid
expansion
▪ A wellbore storage effect caused by changing
fluid level in the casing–tubing annulus
Wellbore Storage
▪ Wellbore storage effect caused by fluid
expansion:-
▪ During the drawdown (Unloading)
▪ As the bottom-hole pressure drops, the
wellbore fluid expands and, thus,
▪ the initial surface flow rate is not from the
formation, but basically from the fluid that had
been stored in the wellbore.
Unloading
Rate Surface Rate
Bottomhole
Rate
0 Time
Wellbore Storage
▪ Wellbore storage effect caused by fluid
compression:-
▪ During the buildup (Afterflow)
▪ As the well is shut in at the surface, bottom-
hole flow continues.
▪ The pressure increase due to the compression
of fluid in the wellbore.
Afterflow
Bottomhole flow
Rate
Surface Rate continues after
shut-in
Bottomhole
Rate
Time
Wellbore Storage
▪ Wellbore storage effect caused by fluid
expansion:-
∆𝑉
𝑐=
𝑉∆𝑃
𝑞𝐵𝑜 ∆𝑡
𝑐=
24𝑉∆𝑃
𝑞𝐵𝑜 ∆𝑡
∆𝑃 =
24𝑐𝑉
𝑞𝐵𝑜
log ∆𝑃 = log + log ∆𝑡
24𝑐𝑉
Wellbore storage effect caused by fluid expansion:
∆𝑉
𝐶𝐹𝐸 = 𝐶 = 𝑐𝑉 = 𝑉𝑤𝑏 𝑐𝑤𝑏 = ∆𝑃
Wellbore Storage
Unit-slope
line
(wellbore storage)
Early-time Middle- Late-time
region time region
region
Elapsed time (Dt ), hrs
Wellbore Storage
▪ Wellbore storage effect caused by fluid
expansion:-
𝑞𝐵𝑜 ∆𝑡
𝑐=
24𝑉∆𝑃
∆𝑃 𝑞𝐵𝑜
=
∆𝑡 24𝑐𝑉
∆𝑃 𝑞𝐵𝑜
𝑡 = .𝑡
∆𝑡 24𝑐𝑉
∆𝑃 𝑞𝐵𝑜
log 𝑡 = log + log 𝑡
∆𝑡 24𝑐𝑉
Wellbore Storage
▪ Wellbore storage effect caused by changing fluid
level in the casing–tubing annulus:-
▪ Falling level during a drawdown test
▪ Rising fluid level during a pressure buildup test
Wellbore Storage
▪ Wellbore storage effect caused by changing fluid
level in the casing–tubing annulus:-
144𝐴𝑎
𝐶𝐹𝐿 =
5.615𝜌
𝜋 𝐼𝐷𝐶 2 − 𝑂𝐷𝑇 2
𝐴𝑎 =
4 × 144
Unit Slope
▪ Early unit slope (EUS)
✓In case of wellbore storage
▪ Late unit slope (LUS)
✓In case of closed reservoir to determine the
reservoir extension (using boundary test)
𝑞𝐵𝑜 ∆𝑡
𝐴ℎ𝜙 =
24𝑐∆𝑃
𝑞𝐵𝑜
log ∆𝑃 = log + log ∆𝑡
24𝑐𝑉
Δ𝑝 & Derivative Function
• For drawdown:
Δ𝑝 = 𝑝𝑖 − 𝑝𝑤𝑓
𝑑(Δ𝑝)
𝑑𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 = −𝑡
𝑑(𝑡)
• For buildup:
Δ𝑝 = 𝑝𝑤𝑠 − 𝑝𝑤𝑓 𝑎𝑡 Δ𝑡=0
𝑝𝑖+1 − 𝑝𝑖−1
∆𝑝′ =
𝑥𝑖+1 − 𝑥𝑖−1
𝑡𝑝 + ∆𝑡
∆𝑡𝑒 = ∆𝑡
𝑡𝑝
𝑑𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 = ∆𝑡𝑒 ∆𝑝′
The Diagnostic Plot
Pressure change (Dp)
Pressure derivative (Dp )
Elapsed time (Dt ), hrs
The Diagnostic Plot
Early-time Middle- Late-time
region time region
region
Elapsed time (Dt ), hrs
Multiple-well Tests
The two main types of multiple-well testing are:
▪ Interference Test
▪ Pulse Test
Multiple-well Tests
The main objectives of multiple-well tests:
• The presence or lack of communication between the test well and
surrounding wells
• Estimation of formation permeability
• Estimation of porosity-compressibility product
Interference Test
The procedure of interference test
• All the test wells are shut-in until their wellbore pressures
stabilize.
• The active well is then allowed to produce or inject at constant
rate and the pressure response in the observation well (s) is
observed.
• When the active well starts to produce, the pressure in the
shut-in observation well begins to respond after some "time
lag" that depends on the reservoir rock and fluid properties.
Interference Test
q
. . . measure
pressure response
at another well
produce one well
at constant rate
Interference Test
Interference Test
Vertical Interference Test
• This test is conducted to:
• Determine vertical permeability
• Determine cross flow between two layers separated by a low-
permeability layer
Pulse Test
Test Procedure:
▪ The active well produces and then, is shut in, returned to
production and shut in again
▪ Repeated but with production or shut-in periods rarely
exceeding more than a few hours
▪ Produces a pressure response in the observation wells
which usually can be interpreted unambiguously (even
when other wells in the field continue to produce)
▪ The pulse length used in a pulse test is short, ranging
from a few hours to a few days, so boundaries seldom
affect the test data.
Pulse Test
q
. . . measure
pressure response
at offset well(s)
Alternately
produce and shut
in one well . . .
Pulse Test
Drill Stem Test
The information that may obtained from a drill stem test:
• Initial reservoir pressure
• Flow rate
• Fluid sample
• Effective permeability
• Transmissibility
• Skin factor
• Radius of investigation
• Well productivity
• Wellbore storage effect
Drill Stem Test
Test Duration
Drill Stem Test
• First flow period (Cleanup period)
• to remove any excess pressure, which may have
resulted from setting the packers.
• the wellbore fluids, and, later, the drilling fluid (mud) that
has invaded the formation in the vicinity of the wellbore
flow to surface.
• First shut in period
• To determine the initial reservoir pressure
Drill Stem Test
• Main flow period
• to evaluate the formation for some distance from the
well.
• Final shut in period.
• to calculate the transmissibility and other
characteristics of the reservoir.
Drill Stem Test
Test Duration
Period Duration, min
Initial Flow Period 5 - 10
Initial shut in Period 30 - 60
Final Flow Period 60 - 80
Final shut in Period 1.5 – 2 × second flow period
Example on RFT
A series of formation tests were obtained for three adjacent wells in a sand
that was indicated from open hole logs to be oil-bearing in Well 1 and
water-bearing in Wells 2 and 3. Geological mapping suggests that they are
in a continuous reservoir and that there should be an oil – water contact
Wells 2 and 3 below the bottom of Well 1.
Unfortunately, no fluid samples were obtained with any of the formation
tests.
Use the following data to answer the following questions:
• Which wells are in hydraulic communication?
• What contacts are present in any of the wells?
• What is the insitu density of the oil, and of the water?
Example
Solution
OWC = 6179 ft
Solution
Thank YOU
