Well Testing Analysis
5.1 introduction
Pressure Build Up Test is performed by shutting down the wells and allowing the
pressure to build up. In a producing well, pressure can be build up by performing pressure Build
Up tests. In order to perform such tests, the production rate needs to be stabilized for several
days in the oil and gas wells that need to be tested for pressure Build Up. Once the stabilization
is reached, a pressure measuring device is placed near the perforations for several hours before
shut-in of the well is done. This method helps in building up the pressure in the reservoir, and
formation properties can be estimated by understanding the rate of pressure Build Up in the time
for which well was shut in. In this case study a buildup test was run for Ras Ghareb oil field in
Egypt determines formation characteristics such as, Formation Permeability, Initial Pressure,
Skin, and other information.
5.2 Horner’s solution for pressure test analysis
Assumption for the Horner’s solution:
Homogeneous reservoir permeability
The fluid compressibility is small or neglected
Single phase flow
The well diameter is approach to zero
Infinite acting reservoir
From the given data of time and the pressure, this plotting has been done to get the (tp) and the
pressure at the time of shut in (pwf)
12000
10000
8000
PWS,psi
6000
4000
pw
f
2000
0
0 20 40 60 80 100 120 140 160 180 200
∆t, hrs
Figure 5.1 recorded data of the buildup test
Fig 5.1 shows the value of tp and Pwf at ∆t =0
Tp=30 hrs.
Pwf = 3500 psi
The following data in table 5.1 was gathered from PVT report, logging and geology
Table 5.1 PVT report, well logging & geological data
Tp(hrs) Q(stb/ Rw Ф% Βo(bbl/stb) H(ft) Co(1/psi) μ(cp)
d) (ft)
30 3388.3 0.30 0.16 1.8081 28 14.90(10^-6 0.139
We will use the Horner plot model to find the requirements.
Horner plot
4600
4500
4400
4300
4200
Pws (psi)
4100
4000
3900
3800
3700
100000.00 10000.00 1000.00 100.00 10.00 1.00
tp+∆t/∆t (hrs)
Figure 5.2 Horner plot
Fig 5.2, commonly referred tp as the Horner plot.
We can note that on the Horner plot, the scale of time ratio (tp+ ∆t/∆t) increases from right to
left. Graphically this means that the initial reservoir pressure pi, can be obtained by extrapolating
the Horner plot straight line to (tp+∆t/∆t) =1
We need to read the pressure after 1 hour of Shut-in. Since we are using Horner time, hour 1 in
real time represents:
( tp+dtdt ) … … … … … …
1+ tp 1+30
= =31 hrs
1 1
pr
Horner plot
P1hr
4600
∆t,MTR
4500
4400
4300
4200
4100
4000
3900
3800
3700
100000.00 10000.00 1000.00 100.00 10.00 1.00
Figure 5.3 Horner plot shows P 1hrs in green line, and pr in black
From fig 5.3 we read the pressure at Horner time of 31hrs. on the steady-state line, as
4440 psi, the initial reservoir pressure at (tp+∆t/∆t) =1 is 4520 psi. and we found the slope of the
steady state line per cycle.
4410−4465
m=
log 100−log10
m= - 55 psi/cycle
5.3 Permeability
We have calculated the slope of the steady state line per cycle as 55. So we will use it in
order to find the permeability from the equation below
162.6 quB
K= ………………
hm
Where
q: oil production rate.
B: oil formation factor.
u: oil viscosity.
h: bed thickness.
162.6∗3388.3∗0.139∗1.8081
K= =90 md
28∗|55|
5.4 Skin pressure drop due to skin
Skin pressure drop is one of the most important parameter used in production
engineering. Higher pressure drop around the well bore due to mud filtrate, reduced
permeability, improve permeability, change of flow streamlines. The skin factor affects the shape
of the pressure buildup data. And any early time deviation from the straight line can be caused by
skin factor as well as by wellbore storage, as illustrated in fig 5.4. The deviation can be
significant for the large negative skins that occur in hydraulically fractured wells. The skin factor
value may be estimated from the buildup test data plus the flowing pressure immediately before
the buildup test.
5.4.1 Skin indicators
1. ∆Pskin>0, indicates an additional pressure drop due to wellbore damage.
2. ∆Pskin<0, indicates less pressure drop due to wellbore improvement
3. ∆Pskin =0, indicates no changes in the wellbore condition
Horner plot
4600
4500
4400
4300
Deviation due Deviation
to wellbore 4200
due to
Pws (psi)
storage and 4100
boundary
well damage effects
4000
3900
3800
3700
100000.00 10000.00 1000.00 100.00 10.00 1.00
tp+∆t/∆t (hrs)
Figure 5.4 Horner plot shows the deviation points
After finding the parameters we need to calculate skin factor, we start getting the skin effect
parameters (skin factor and pressure loss due to skin factor) by using the equations below:
S=1.151
( Pws , 1hr −Pwf
m
−log
k
(
∅∗μ∗Ct∗r w
2 ) )
+3.23 … … … … …
ct: Total compressibility.
rw: Well radius.
k: Permeability.
m: Slope of steady state line.
∅ : Formation porosity.
u: Oil viscosity.
Pws, 1 hr.: Shut in pressure after 1 hour of shut-in.
S=1.151
( 4440−3500
|55|
−log ( 90
0.16∗0.139∗14.90∗10−6∗0.32 )
+3.23
)
S = 6.9
In this case since the skin is (+) indicates an additional pressure drop due to wellbore damage
5.5 Pressure Drop
With an additional pressure drop across the altered zone of:
Δ P skin =0.87 |m| s
S= skin factor
|m| = absolute value of the slope in the Horner plot (psi /cycle).
ΔP skin = 0.87|55| * 6.9
∆Pskin =330.165 psi
5.6 Flow efficiency
pr −p wf −∆ p
FE= s
pr −p wf
4520−3500−330.165
FE=
4520−3500
FE= 0.67 = 67%
Flow efficiency means how efficient is the oil flowing through the formation. In our case
the FE is estimated to be 67% which means that the formation is producing 67% from its actual
production rate.
5.7 Area of wellbore:
2
π I.D
A wb= ×
4 144
2
π 3.5
A wb= ×
4 144
Awb = 0.066ft˄2
5.8 Wellbore effect storage:
we can find the wellbore effect by using the wellbore area that we found from the equation
before and plugging it in the equations below:
144 × A wb
c=
5.615 × ρo
144 ×0.066
c=
5.615 ×37.37
C= 0.045bbl/psi
5.9 Δ T for MTR region
So we need to find the point that the MTR region begins and we can get that by using the
equation below:
170000 × μ ×c ×e (0.14 × S )
ΔT=
K×h
170000 ×0.139 ×0.045 × e(0.14 ×0 )
ΔT=
160× 28
Δ T =0.23 hr
tp + Δt 30+0.23
ΔT =
Δt
¿
0.23
=131.4 hrs.
Δ T for MTR region=4345 hrs
5.10 Summary result
Pwf K(md) S ∆Pskin(psi) FE% Awb(ft˄2) C(bbl/psi) Pi(psi) Δ T , MTR (hr )
(psi)
3500 90 6.9 330.165 67 0.066 0.045 4520 4345
5.11 Conclusion
Buildup tests are performed by shutting down wells and allowing the pressure to build
up, by using Horner time, permeability, skin factor and reservoir pressure, and some other
information where determine. However, based on the well testing results this skin is positive
which means that we have a damage around the wellbore. To improve the well’s productivity or
injectivity we can use an acidizing. This way we know how our well is performing and well
perform in the next years.
