1. INSTRUCTOR © 2017, John R. Fanchi
All rights reserved. No part of this manual may be reproduced in any form without the express written permission of the author.
© 2004 John R. Fanchi All rights reserved. Do not copy or distribute.

2. To the Instructor
The set of files here are designed to help you prepare lectures for your own course using the text Introduction to Petroleum Engineering, J.R. Fanchi and R.L. Christiansen (Wiley, 2017)
File format is kept simple so that you can customize the files with relative ease using your own style. You will need to supplement the files to complete the presentation topics.

3. PRODUCTION EVALUATION TECHNIQUES
© 2017, John R. Fanchi
All rights reserved. No part of this manual may be reproduced in any form without the express written permission of the author.
© 2004 John R. Fanchi All rights reserved. Do not copy or distribute.

4. Outline Field Performance Data Decline Curve Analysis Material Balance
Oil Reservoir Material Balance
Gas Reservoir Material Balance
Drive Mechanisms
Inflow Performance Relationships
Homework: IPE Ch. 13

5. FIELD PERFORMANCE DATA

6. Well Surveillance – Oil Wells
Rapid decline in total fluid production due to
Artificial lift problem
Formation damage
Offset well effects (interference)
Rapid decline in oil and increase in water due to
Casing leak
Watered out
Forecast production with Decline Curve Analysis

7. DECLINE CURVE ANALYSIS
© 2004 John R. Fanchi All rights reserved. Do not copy or distribute.

8. Decline Curve with Solutions
Harmonic Decline
(n = 1)
Hyperbolic Decline
(0 < n < 1)
Exponential Decline
(n = 0)

9. Exponential Decline Curve Analysis
Exponential (often used)
Decline rate (% per year)
Straight Line on Semi-log plot
Economic limit required
Assumes no water drive (water influx)
Must know reservoir conditions and area
Decline Factor
Cumulative Production

10. Probabilistic DCA Workflow
Specify
constraints
Gather rate-time data
Specify input parameter distributions
Uniform
Triangle
Constraint Options
Objective Function
Gas Rate
Cum Gas
Apply Constraints (Select Subset)
Generate Range of Decline Curves
Generate EUR distribution for subset
Determine P10, P50, P90

11. MATERIAL BALANCE
© 2004 John R. Fanchi All rights reserved. Do not copy or distribute.

12. Material Balance Concept
Apply conservation of mass to reservoirs and aquifers.
Assumptions:
Reservoir space voided by production is immediately filled
Remaining fluids and rock expand to completely fill space
Reservoir fluids in phase equilibrium
Instantaneous equilibrium
Single, weighted average pressure
Pressure gradients not considered
Fluid saturations uniform
Saturation gradients not considered
Conventional PVT relationships applicable

13. Uses of Material Balance
Determine OGIP and OOIP
Determine drive mechanisms
Quantify importance of each
Predict future reservoir behavior
Required Data
Average reservoir pressures
Cumulative fluid production at the same times
PVT data and formation compressibility

14. OIL RESERVOIR MATERIAL BALANCE

15. Oil Material Balance Equation
Determine OOIP
Determine drive mechanisms
Quantify importance of each
Predict future reservoir behavior
Required Data
Average reservoir pressures
Cumulative fluid production at the same times
PVT data and formation compressibility

16. Schilthuis Material Balance Equation [1961]
Determine OOIP (N)
Production Term
Physical Significance Np
Cumulative oil produced Gp
Cumulative gas produced Wp
Cumulative water produced

17. Express Schilthuis MBE Using Volume Changes
Term
Define Volume Changes
NDo
Change in volume of initial oil and associated gas
NDgo
Change in volume of free gas
N(Dw + Dgw)
Change in volume of initial connate water
NDr
Change in formation pore volume

18. Express Schilthuis MBE Using Drive Indices
Define DHC (RHS of Schilthuis MBE)
Divide by DHC to obtain sum of drive indices = 1
Relative magnitude of index indicates importance of drive mechanisms
Term
Drive Index
Solution Gas
Isg = NDo / DHC
Gas Cap
Igc = NDgo / DHC
Water
Iw = [(We - Wp)Bw] / DHC
Injected Fluids
Ii = [WiBw + GiBg] / DHC
Connate Water and Rock Expansion
Ie = [N(Dw + Dgw) + NDr] / DHC

19. GAS RESERVOIR MATERIAL BALANCE

20. Gas Compressibility Factor
Real gas law 𝒑𝑽=𝒁𝒏𝑹𝑻 where Z is gas compressibility factor.
Estimate Z:
EoS
Standing and Katz chart: Z is a function of pseudoreduced temperature and pseudoreduced pressure

21. Gas Formation Volume Factor
Real gas law 𝒑𝑽=𝒁𝒏𝑹𝑻
Let r denote reservoir conditions and s denote standard conditions. Gas FVF is
𝑩 𝒈 = 𝑽 𝒓 𝑽 𝒔 = 𝒑 𝒔 𝒑 𝒓 𝑻 𝒓 𝑻 𝒔 𝒁 𝒓 𝒁 𝒔
Define {ps = 14.7 psia, Ts = 60°F = 520°R, Zs = 1}
Calculate
𝑩 𝒈 = 𝑽 𝒓 𝑽 𝒔 =𝟎.𝟎𝟐𝟖𝟐𝟕 𝑻 𝒓 𝒁 𝒓 𝒑 𝒓

22. Gas Reservoir Recovery Efficiency
Ultimate Recovery Efficiency:
Substitute volumetric terms and simplify:
𝑬 𝑹 = 𝒑 𝒁 𝒊 − 𝒑 𝒁 𝒂 𝒑 𝒁 𝒊

23. Gas Reservoir Material Balance
Gas reservoir with water influx:
where
We = cumulative water influx
Wp = cumulative water production
We-Wp = net influx
Bw = water FVF
Bg = gas FVF
Bgi = gas FVF at initial pressure
G = OGIP
Gp = cumulative gas production

24. Depletion Drive Gas Reservoirs
High recovery efficiencies (80 to 90%)
Gas has very low viscosity and high mobility
Gas is very compressible and expandable
Gas wells are drilled on larger spacing than oil wells
Water and formation compressibilities are usually neglected in gas material balance calculations
Water and formation compressibility << gas compressibility

25. Gas Reservoir Material Balance (p/Z) Equation
Cumulative gas production:
Substitute Z – factors and set G = OGIP:
𝑮 𝒑 =𝑮 𝟏− 𝒑 𝒁 𝒑 𝒁 𝒊
Rearrange:
𝒑 𝒁 = 𝒑 𝒁 𝒊 − 𝒑 𝒁 𝒊 𝑮 𝒑 𝑮
Note linear relationship between p/Z and GP.

26. Water - Drive Aquifers flatten p/Z curve
A. Depletion Drive (straight line)
B. Partial Water Drive
C. Strong Water Drive; Full Pressure Maintenance C
p/Z B A
Cum. Gas Production

27. Practical Considerations
In practice, several factors may cause p/Z vs Cum. Prod. plot to be nonlinear
Average reservoir pressure may not be well known
Water drive present
If formation compressibility significant, extrapolation will give optimistically high OGIP

28. Depletion Drive Gas Reservoir
No water influx – depletes like “tank”
High recoveries – up to 95% for non-water drives

29. DEPLETION DRIVE MECHANISMS AND RECOVERY EFFICIENCIES
© 2004 John R. Fanchi All rights reserved. Do not copy or distribute.

30. Primary Production Drive Mechanisms

31. Solution Gas Drive Also called Depletion Drive or Dissolved Gas Drive
Gas comes out of solution in the oil – “pushes” oil toward producing wells
Rapid decline of oil and rapid increase of GOR
Pressure in reservoir depletes quickly
15% typical oil recovery factor
Sometimes make good waterflooding candidates

32. Start undersaturated; then drop below bubble point pressure
Solution Gas Drive
GOR
Reservoir Pressure
Oil Rate
Time
Start undersaturated; then drop below bubble point pressure

33. Gas Cap Drive
Gas cap helps maintain reservoir pressure and assists in “pushing” oil toward wells
Must not produce gas cap to maximize oil recovery
Gas-Oil contact eventually reaches wells and GOR goes up rapidly.
Typically oil recovery is around 25%

34. Gas Cap Mechanism
Oil is saturated (full of gas) and leftover gas rises to make gas cap layer
2 Stage Depletion Management:
Produce only oil portion at first to let gas drive oil to the wells (maintains pressure)
Blowdown gas cap when oil is depleted later in reservoir life
GOR stays lower until gas-oil contact reaches wells then rapidly rises

35. Start with free gas; first produce oil; then produce oil and free gas
Gas Cap Drive
GOR
Reservoir Pressure
Oil Rate
Time
Start with free gas; first produce oil; then produce oil and free gas

36. Water Drive Reservoir contains bottom water
Water moves when oil is produced
Reservoir pressure and GOR do not decline much throughout field life

37. Water Drive (cont.) “Nature’s waterflood”
Do not produce oil too quickly
Minimize trapping oil with water encroachment
Oil well rapidly changes from mostly oil to mostly water (weeks to months) when oil-water contact reaches perfs
Must handle produced water
Typically recover 50% of oil

38. Start undersaturated; first produce oil; then produce oil and water
Water Drive
Reservoir Pressure
Water Cut
GOR
Oil Rate
Time
Start undersaturated; first produce oil; then produce oil and water

39. Managing Water Drives Oil-Water Drives Gas-Water Drives
Want to produce slowly to avoid pulling in water ahead of oil (like in East Texas Field)
Water (the driving fluid) is thinner than oil
Gas-Water Drives
Want to produce gas quickly to out run water
Gas is much thinner than water (driving fluid)

40. Compare Drives Solution Gas Drive Gas Cap Drive Water Drive GOR
Time
Oil Rate
Pressure
GOR
Solution Gas Drive
Gas Cap Drive
Water Cut
Water Drive

41. Depletion Drive Mechanisms
Recovery Efficiencies for Different Depletion Drive Mechanisms [Data from Ahmed, 2000]
Depletion Drive Mechanisms
Recovery Efficiency
(% OOIP)
Water drive
35 – 75
Gas cap drive
20 – 40
Solution gas drive
5 – 30
Note: Percentages indicated are for comparison only since recovery factors vary widely among reservoirs

42. INFLOW PERFORMANCE RELATIONSHIPS
© 2004 John R. Fanchi All rights reserved. Do not copy or distribute.

43. Nodal Analysis and PI
qfluid
Tubing
Casing
pres
pwf
Reservoir

44. Typical TPC* Curve for Production Wells
pwf
qfluid
TPC
(outflow)
Unstable
Flow
Stable
*TPC = Tubing Performance Curve

45. IPR vs TPC pwf IPR (inflow) pres TPC (outflow) pwf,op qfluid,op qfluid
(pwf at qfluid = 0)
qfluid
TPC
(outflow)
pwf,op
qfluid,op
IPR = Inflow Performance Relationship
Note: In IPR curve, qfluid = 0 at pwf = pres
TPC = Tubing Performance Curve
Operating qfluid,op and pwf,op at intersection of IPR and TPC curves

46. Multiphase Flow In Tubing
Factors effecting multiphase flow in tubing
Flow rate
Critical velocity
Flow rate high enough to lift liquid
Erosional velocity
Flow rate low enough to minimize tubing damage
Flow pattern
End-of-tubing

47. QUESTIONS?
© 2004 John R. Fanchi All rights reserved. Do not copy or distribute.

48. SUPPLEMENT
© 2004 John R. Fanchi All rights reserved. Do not copy or distribute.