1. Class I Operational Constraints Requiring Specialized Wellbore Hydraulic Modeling
Tom Ortiz
TCEQ

2. 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
TCEQ rules require a 100 psi annulus-to-tubing pressure differential “to prevent leaks…and detect well malfunctions.” This pressure differential is measured at the surface: it is not constant, a fact that can limit its effectiveness.
The rules also stipulates that “injection pressure at the wellhead shall…assure that…injection does not initiate…or propagate…fractures”. Maximum Allowable Surface Injection Pressure (MASIP) is intended to provide that assurance. However, wellhead gauges do not display usable surface pressures for wells operating under vacuum.

3. 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
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
Pannulus – Ptubing = ?
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.
∆𝑃=𝜌𝑔𝐷− 𝑓𝐷 2 𝑑 𝑖 𝜌 𝑉 2
High specific gravity waste streams will gain hydrostatic pressure faster than annulus fluid.
Low injection rates or large tubing diameters will cause less frictional pressure drop in tubing.

4. Base Case 6,000 ft GL 3.548 in ID 8.535 in ID Casing
Here is an illustration of the same wellbore, with the base case inside casing diameter, packer depth, and inside tubing diameter all marked.
Casing
9⅝ in, 53.5 lb/ft, N-80
Tubing
4 in, 9.5 lb/ft, N-80
Packer Depth
6,000 ft. GL
Injection Rate
200 gpm
Annulus Specific Gravity
1.0
Waste Specific Gravity
1.1
Here, we offer a contrived base case example—based on realistic well parameters—that will be used to quantify the sensitivity of annulus pressure differential to important design and operational variables.
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
9⅝ in, 53.5 lb/ft, N-80
Tubing
4 in, 9.5 lb/ft, N-80
Packer Depth
6,000 ft. GL
Injection Rate
200 gpm
Annulus Specific Gravity
1.0
Waste Specific Gravity
1.1

5. 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.

6. 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

7. Sensitivity Analysis – Packer Depth
Center is a graph with annulus pressure differential at packer depth on the y-axis 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

8. 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.

9. 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))
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
Ptubing = 0 psig
Ptubing = ?
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.

10. 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
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.
Downhole Pressure Gauge
Electrical Cable (to surface)
Injection Tubing

11. Limit Flowing Bottomhole PressurePw sh Pr
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
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
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
𝑃 𝑤 < 𝜎 ℎ + 𝑃 𝑟

12. 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
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.
sob Pr sv ev eh sv
𝑃 𝑓 = 𝜎 ℎ + 𝑃 𝑟
𝜇=− 𝜀 ℎ 𝜀 𝑣
Hubbert and Willis (1972) assumed that the ratio of vertical to horizontal stress was equal to 3, or, equivalently, that the ratio of horizontal to vertical stress was 1/3. Under that assumption, Poisson’s ratio for the reservoir rock takes on a value of This modeling assumption is often used where local data is unavailable.
𝑃 𝑓 = 𝜎 𝑣 𝜇 1−𝜇 + 𝑃 𝑟
Here is an illustration of a cylindrical bar that has been vertically. stressed Vertical and horizontal strains are labeled
𝑃 𝑓 = 𝜎 𝑜𝑏 − 𝑃 𝑟 𝜇 1−𝜇 + 𝑃 𝑟

13. 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?)

14. 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

15. 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
This presentation assumes that a consistent set of units is always used, and does not specify any particular unit system. The units listed here for each variable are typical of those used domestically in the United States. However, unit conversion constants have not been added to any of the equations in which they appear, in order to simplify the presentation.