1. PRO-2003 Natural Gas Processing Natural Gas Deliverability
Adjunct Professor Jon Steinar Gudmundsson
Department of Engineering and Safety
University of Tromsø
January 2014

2. Outline Production profiles (field life cycle, field development)
Reservoir properties and near-wellbore properties
Concept of deliverability (pressures and flowrates)
Reservoir, inflow and outflow performances
Flow equation (PSS) and skin
Transient (well) testing and multi-rate testing (for properties)

3. Deliverability Reservoir performance (whole reservoir)
Inflow performance (near-wellbore flow)
Outflow performance (production tubing)
Methodology to calculate the flowrate and pressure of production wells in field development. Other words/concepts used in the literature, for example nodal analysis

4. Source: Jahn et al. 1998, Hydrocarbon Exploration and Production, Elsevier.

5. Production Profiles
Three different fields: a, b and c. New process technology d. Improved recovery e.

6. Distribution of Gas, Oil and Water in Reservoir
Reservoir properties k, φ, h, c and well property s. Well testing gives kh (permeability thickness) for flow capacity and φch (porosity-compressibility thickness) for storage capacity (of oil and/or gas)
GOC = Gas Oil Contact
WOC = Water Oil Contact

7. Deliverability and Performances
Pressure Profile from Reservoir to Wellhead
Reservoir performance gives reservoir pressure against cumulative production (or average reservoir pressure with time). For example, p/z method for simple gas reservoirs.
Inflow performance gives downhole flowing pressure against well production rate. Practically equal to reservoir pressure when no production (well shut-in).
Tubing performance gives the pressure drop from downhole to wellhead. Assuming a wellhead pressure, the downhole pressure can be calculated (compressible flow in pipes) for different well production rates. One curve for each wellhead pressure. Also called outflow performance.
Deliverability is the overall effect of the reservoir, inflow and tubing performances.

8. Deliverability and Performances
Analyse and Synthesis
Pressure profile from reservoir to wellhead is analysed in terms of several performances.
Reservoir performance gives reservoir pressure with time, which is used in inflow performance curve.
Shape of inflow performance curve remains the same with time, unless near-wellbore damage occurs during production.
Tubing performance curve plotted together with inflow performance, gives the well production rate where the two curves cross each other.

9. Inflow and Outflow pwf = 247 – q – 1,1q2

10. States and Pressure Profile in Reservoir
Steady-state (stasjonært tilstand), SS
Pseudosteady-state (pseudostasjonært tilstand), PSS
Transient state (ikke-stasjonært tilstand)
Pressure profile from rw to re, from well radius to reservoir outer (external) boundary

11. Pressure States in Reservoirs
Transient state (pressure transient testing)
Steady-state (injection replaces produced volume)
Pseudosteady-state (most usual)

12. Drainage Area Pseudosteady-state when pressure profiles meet

13. Skin Represent Deviation from Ideal Well
Damaged near-wellbore, s >0
Stimulated near-wellbore, s<1
Geometric skin also important

14. Wellbore skin

15. Geometric Skin Two wells in homogeneous reservoir Same RP, Same OP, Different IP

16. Material Balance for Natural Gas Fields Reservoir Performance by Volumetric Balance Gas volumes taken at standard conditions (s.c.) Constant volume reservoir without water influx Gi = Gas initially in place (resource, not reserve) G = Gas already produced (Gp in many texts) FVF (symbol B) for natural gas (Gi – G)Bg = GiBgi (p/z) = (pi/zi) [1 - G/Gi]

17. Reservoir Performance Material Balance for Natural Gas Fields p/z Method
pi/zi
p/z Gi G
Gabandonment

18. Huldra, Kvitebjørn and Kristin are HPHT fields
Source: Saksvik, 2004, TPG4014 Naturgass, NTNU

19. Natural Gas Reservoir Performance
[GSm3] pR
[bara]
pR/z
5.7
11.3
22.6
45.3
275
254
236
199
126
296
277
260
222
140

20. Flow Equations for Natural Gas in Reservoir Symbols in Flow Equations
p = Pressure, Pa (pwf = well flowing pressure)
r = Radial Distance, m
rw = Wellbore Radius, m
re = Distance to Drainage (Outer) Boundary, m
µ = Fluid Viscosity, Pa.s
k = Permeability, m2
h = Height of Producing Formation (Reservoir), m
q = Volumetric Flowrate, m3/s
z = Compressibility Factor (z-Factor)
T = Temperature, K
s = Skin factor (-)

21. Flow Equations for Natural Gas in Reservoir Darcy’s Law for Radial Flow in Circular Reservoir

22. Flow Equation for Natural Gas in Reservoir Low Pressure Pseduosteady-State Flow Equation
Use pressure transient testing (well testing) to find kh

23. Flow Equations for Natural Gas in Reservoir
Near-Wellbore Skin
The near-wellbore region (radial distance of 1-10 m) can be damaged during drilling, completion and/or workover operations, leading to extra pressure drop.
The extra pressure drop is called skin, expressed in the flow equations as a positive number in the logarithmic term (shown below for pseudosteady-state).
But, instead of being damaged, the near-wellbore region can be stimulated (hydraulic fracture, acid treatment), resulting in negative skin.
[ ln(re/rw) – 3/4 + s ]

24. Flow Equation for Natural Gas in Reservoir Forchheimer Equation (High Velocity Flow)

25. Flow Testing of Natural Gas Wells High-Velocity Flow Equation (pR2 - pw2) = a1 qs.c + a2qs.c2 (pR2 - pw2)/qs.c = a1 + a2qs.c
Multi-rate testing at stabilized flow, PSS, to obtain empirical constants.

26. Two-phase and high-velocity inflow have 2nd order effects
Flow Testing of Wells
Two-phase and high-velocity inflow have 2nd order effects
Δ p2/qs.c. a2 a1
qs.c

27. Step-Rate Testing Practically stable flow and pressure

28. Deliverability and Performances
Inflow Performance
pwf q
Properties from pressure transient testing or from multi-rate testing used to draw inflow performance curve.

29. Deliverability and Performances
Tubing (Outflow) Performance
pwf q
Wellbore flow simulator (pressure drop calculation) used to determine outflow performance curve. One curve for each wellhead pressure.

30. Outflow Performance

31. Reference: Wennberg, 2005, TPG4014 Naturgass, NTNU

32. Inflow decreases with time, outflow increases with lower wellhead pressure
Leveringsevne til en brønn vist som bunnhullstrykk mot produksjonsrate. Kurver <a> og <b> viser nærbrønnformasjonens innstrømningsevne henholdsvis tidlig og senere i et felts levetid. Kurver <c> og <d> viser brønnens utstrømningsevne ved henholdsvis høyt og lavt brønnhodetrykk.

33. Flow Equations for Natural Gas in Reservoir
Effect of Pressure
The equations shown above are for low-pressure gas, where pressure-squared is used, p2R-p2w.
When the pressure is intermediate, the so called pseudopressure m(p) needs to be used (from numerical integration)
At high-pressure, the gas behaves similar to liquid and the pressure drop is expressed by simple difference, pR-pw, which is the same as for oil.
What is low-pressure, intermediate pressure and high-pressure depends on the gas composition through the pressure function F(p)={p/(μz)}

34. Natural Gas Inflow Performance

35. Pressure Function and Specific Gravity

36. Characterization of Reservoir Rocks
Types of Rocks
Sandstone and carbonate main reservoir rocks, porous and permeable. Sandstone made of sand grains, carbonate either limestone or dolomite.
Sandstone porosity typically 10-40% while carbonate porosity 5-20%. Permeability of sandstone correspondingly higher (Kozeny-Carman Equation).
Shale (clay, mud, silt) also found in reservoirs. Shale beds have low porosity and are practically impermeable.

37. Characterization of Reservoir Rocks
Porosity, Permeability and Saturation
Darcy’s Law

38. Characterization of Reservoir Rocks Symbols and Permeability Values Φ = Porosity VP = Pore Volume, m3 VT = Total Volume, m3 u = Filtration Velocity, m/s (lower than actual velocity) k = Permeability, m2 µ = Fluid Viscosity, Pa.s p = Pressure, Pa x = Distance, m (r = radius) 50 mD < k < 200 mD 1 D = m2

39. Characterization of Reservoir Rocks Symbols and β-coefficient Equation p = Pressure, Pa x = Distance, m (r = radius) µ = Fluid Viscosity, Pa.s k = Permeability, m2 u = Filtration Velocity, m/s (“superficial velocity”) β = High Velocity Coefficient, 1/m ρ = Fluid Density, kg/m3 β = Φ(-3/2) k(-1/2)

40. Pressure Transient Testing Drawdown and buildup to determine properties

41. Pressure Transient (Well) Testing Diffusivity equation gives kh, φch and s

42. Superposition “The workhorse of reservoir engineering”

43. Summary
Production rate and pressure can be represented by overall deliverability consisting of reservoir, inflow and outflow performances.
Reservoir pressure decreases with time. Inflow calculated/obtained from transient testing or PSS multi-rate testing. Outflow obtained from calculation of pressure drop in production tubing (flow in wells).