Class I Operational Constraints
Requiring Specialized Wellbore
Hydraulic Modeling
Tom Ortiz
TCEQ
A False Sense of Security?
• Surface measurements are straightforward, but can we
always use them to infer downhole well performance?
• We will discuss two UIC rules for which specialized
wellbore hydraulic modeling can shed light on gaps in
the information provided by surface measurements
– Positive annulus to tubing pressure differential
– Tubing pressure measurement under vacuum
Positive Pressure for Leak Prevention
• “[A]nnulus pressure shall be at least
100 psi greater than…tubing
pressure” (30 TAC §331.63(e))
• Pressure is measured at the
surface, but gravity and friction
affect pressure drop downhole
𝑓𝐷
∆𝑃 = 𝜌𝑔𝐷 −
𝜌𝑉 2
2𝑑𝑖
• Positive annulus pressure is
needed from surface to packer in
order to prevent waste leakage
Right is a schematic of an injection well that includes labels for the surface and bottomhole pressure differentials.
The schematic also includes the surface, intermediate, and long-string casing, the injection packer, and the
perforations
Pannulus – Ptubing
= 100 psi
Here is an illustration of a typical
wellbore. Surface pressure differential
can be measured and controlled at the
surface. However, below, down to the
packer, gravity and friction interact,
which can result in either a higher or
lower pressure differential.
Pannulus – Ptubing
=?
Base Case
Here is an illustration of the same
wellbore, with the base case inside
casing diameter, packer depth, and
inside tubing diameter all marked.
8.535 in ID
Casing
Tubing
Packer Depth
Injection Rate
Annulus Specific Gravity
Waste Specific Gravity
9⅝ in, 53.5 lb/ft, N-80
4 in, 9.5 lb/ft, N-80
6,000 ft. GL
200 gpm
1.0
1.1
Right is a schematic of an injection well that includes labels for the long string casing
and tubing ID, as well as the depth of the packer
•
Casing
•
Tubing
•
Packer Depth
•
Injection Rate
•
Annulus Specific Gravity
•
Waste Specific Gravity






9⅝ in, 53.5 lb/ft, N-80
4 in, 9.5 lb/ft, N-80
6,000 ft. GL
6,000 ft GL
200 gpm
1.0
1.1
3.548 in ID
Sensitivity Analysis – Injection Rate
•
•
•
Center is a graph with annulus pressure differential at 6000 ft (base case
packer depth) on the y-axis in psi
Injection rate is on the x-axis in gpm
Frictional pressure drop increases with the square of velocity (injection rate).
For example, decreasing injection rate from 200 to 150 gpm results in a 68
psi decrease in annulus pressure differential.
Sensitivity Analysis – Specific Gravity
•
•
•
Center is a graph with annulus pressure differential at 6000 ft (base
case packer depth) on the y-axis in psi
Waste specific gravity is on the x-axis
Hydrostatic pressure increases linearly with density. For example,
increasing waste specific gravity from 1.1 to 1.2 results in a 244 psi
decrease in annulus pressure differential
Sensitivity Analysis – Packer Depth
•
•
•
Center is a graph with annulus pressure differential at packer depth on the yaxis in psi
Packer depth is on the x-axis in ft
Both frictional pressure drop and hydrostatic pressure vary linearly with
depth. For example, setting the packer 1000 ft shallower results in a 16.5 psi
increase in annulus pressure differential
Sensitivity Analysis – Tubing Diameter
•
•
•
Center is a graph with annulus pressure differential at 6000 ft (base case packer depth) on the y-axis in psi
Tubing inner diameter is on the x-axis in in
The graph shows the limiting effects of tubing size on annulus pressure differential. Increasing tubing size beyond a threshold diameter will cause frictional pressure drop to become
negligible. On the other hand, continuing to decrease tubing size will cause the injection tubing to act as a throttling device. If you had enough pumping power available, in extreme
cases it could be possible to vaporize the waste stream, causing annulus pressure differential at the packer to approach the annulus fluid’s hydrostatic pressure. In this example, the
annulus fluid has a hydrostatic pressure of 2600 psig at 6000 ft.
Monitor Vacuum Well Pressure Downhole
Right is a schematic of an injection well that includes labels for the surface and bottomhole tubing pressures. The
schematic also includes the surface, intermediate, and long-string casing, the injection packer, and the
perforations. The tubing fluid column does not reach surface.
• “[I]njection pressure at the wellhead
shall…assure that…injection does
not initiate…or propagate fractures”
(30 TAC §331.63(c))
Ptubing = 0 psig
• Under vacuum, a wellhead gauge
will not provide usable tubing
pressure measurements: the fluid
column does not reach the surface
• Injection interval fracture risk is, in
that case, unknown unless tubing
pressure is measured downhole
Here again is an illustration of our
example well. It shows a standing
column of waste fluid in the tubing that
does not reach the surface. Therefore,
a wellhead tubing pressure gauge will
always read zero.
Ptubing = ?
Permanent Downhole Gauges
Right is a schematic of an injection well that includes labels for the surface and bottomhole tubing
pressures. The schematic also includes the surface, intermediate, and long-string casing, the injection
packer, and the perforations. The tubing fluid column does not reach surface. An expanded view of a
downhole pressure gauge run on tubing is also included at center.
• A downhole gauge mounted
near the well’s completion can
address the vacuum problem
• Flowing bottomhole pressure
must remain below injection
interval fracture stress
Electrical Cable
(to surface)
Downhole
Pressure Gauge
Injection Tubing
Here is another illustration of our
example well. This time, an offset
illustration of the lowermost section of
the injection tubing is also included to
show placement of a permanent
downhole pressure gauge and the
connected electrical cable, which
extends along the tubing to surface.
Limit Flowing Bottomhole Pressure
sh
This is an illustration of a section of the
reservoir immediately adjacent to the
wellbore. The wellbore pressure is
shown acting against the reservoir, and
the horizontal rock matrix stress and
reservoir pore pressure are shown as
opposing the force of the wellbore
pressure
Pr
Pw
Center is a diagram of the portion of the reservoir adjacent to the well’s completion. Labels for horizontal matrix stress, pore pressure, and flowing bottomhole pressure are shown.
Fracture stress = horizontal stress + formation pressure
𝑃𝑤 < 𝜎ℎ + 𝑃𝑟
Wellbore (flowing bottomhole) pressure must remain less than
the sum of the horizontal rock matrix stress and reservoir pore
pressure acting at that point in order to prevent fracturing
Estimate Fracture Stress
Right is a diagram of a portion of the reservoir with labels for overburden stress, pore pressure, and vertical stress, which together act to establish mechanical equilibrium
Left is a diagram of a cylindrical bar that shows its original, unstressed dimensions, as well as its deformed dimensions after being subjected to axial stress
Vertical stress = overburden stress – reservoir pressure
Reservoir rock is compressed by overburden
Pore pressure helps support overburden stress
NOTE – If one assumes that the ratio of vertical
to horizontal stress = 3, Poisson’s ratio = 0.25
𝜀ℎ
𝜇=−
𝜀𝑣
Here is an illustration
of a cylindrical bar
that has been
vertically. stressed
Vertical and
horizontal strains are
labeled
𝑃𝑓 = 𝜎ℎ + 𝑃𝑟
eh
𝑃𝑓 = 𝜎𝑣
ev
sv
sob
Pr
𝜇
+ 𝑃𝑟
1−𝜇
𝑃𝑓 = 𝜎𝑜𝑏 − 𝑃𝑟
Here is an illustration
of the overburden,
showing the
relationship among
overburden stress,
reservoir pressure,
and the magnitude of
vertical reservoir
stress below the
overburden.
𝜇
+ 𝑃𝑟
1−𝜇
sv
Final Thoughts
• Compliance with TCEQ UIC rules sometimes requires
gathering different data or constructing different models
• Considering these constraints early can assist with
optimizing performance over the life of the well
– Front end design, or workover? (Now or later?)
– Maximize flow rate? Minimize construction cost?
– Which is most economical? (Initial vs. total lifecycle?)
Thanks for Your Attention
Thomas Manuel Ortiz, Ph.D., P.E.
Project Manager
Texas Commission on Environmental Quality
Office of Waste
Radioactive Materials Division
Underground Injection Control Permits Section
+1-512-239-6406
[email protected]
Nomenclature
Roman
d
diameter (in)
D
depth (ft)
f
Darcy friction factor (-)
P
pressure (psig)
V
velocity (ft/s)
Greek
e
strain (in/in)
m
Poisson’s ratio (-)
r
density (lb/gal)
s
stress (psi)
Subscripts
f
fracture
h
horizontal
i
inner
ob
overburden
r
reservoir
v
vertical
w
wellbore