1. Chapter 2: Directional & Horizontal Drilling
Evaluation of Horizontal Wells

2. Introduction
Horizontal wells are nothing new. Engineers in the old Soviet Union drilled a number of them in the 1950s, although they ultimately abandoned the practice as uneconomical.
The general concept of horizontal drilling dates back even earlier (Ranney, ).
It wasn't until the early 1980s, however, that two western petroleum companies (Elf and AGIP) established horizontal wells as viable substitutes for vertical wells in certain types of reservoirs.

3. Introduction
Since then, the industry has drilled thousands of horizontal wells worldwide, in a large array of reservoirs.
Horizontal sections of more than 3500 ft. are commonplace.
On 28 January 2011 the world’s longest borehole was drilled at the Odoptu field, Sakhalin-I (Island, Russia) with a measured total depth of 12,345 m (40,502 ft) and a horizontal displacement of 11,475 m (37,648 ft).
Maersk Oil Qatar had the previous world record in a well with a measured depth of 12,290 m (40,320 ft) including a horizontal reach of 10,900 m (35,770 ft) in the Al Shaheen Field offshore Qatar.

4. Introduction
We can divide horizontal wells into three general categories, based on their curvature from vertical to horizontal:
Short radius: with the radius R = ft (DLS = 180 – 30 deg/100ft)
Medium radius: with the radius R = ft (DLS = 30 – 6 deg/100ft)
Long radius: with the radius R = ft (DLS = 5 – 3 deg/100ft)
These categories are starting points for designing the well completion.

5. Introduction
Short radius wells have curvature radii of less than 50 ft, and as low as 30 ft. Their buildup angles are consequently very large — as much as 180 degrees per 100 ft [0.115 rad/m]. With current technology, it is not possible to run casing or measurement-while-drilling (MWD) tools in these sections. Hole diameters are limited to a maximum of about 6 1/4 inches.
Medium radius wells have curvature radii ranging from 200 to 1000 ft, and buildup angles of between 6 and 30 degrees/100 ft. These wells can be logged and cased. Hole diameters are limited to approximately 12 3/4 inches.
Long radius wells use standard drilling equipment to attain build angles of 3 to 5 degrees per ft. This configuration is becoming commonplace, with lengths of 3,500 ft now considered routine, and sections approaching 20,00ft being reported as of 1996.

6. Introduction
Stimulation and completion needs, more often than not, point towards long- radius wells.
Of the three configurations, we should therefore consider long radius first (keeping in mind that we might want to limit the length to better manage the well).
We should consider short radius second, for multiple horizontal completions and, in enhanced recovery applications, for injection/production configurations. Medium radius wells represent an intermediate option, and are relatively less common.

7. Introduction

8. Horizontal Well Evaluation Horizontal Well Deliverability

9. Horizontal Well Evaluation Horizontal Well Deliverability
Under the right conditions, a horizontal well exhibits a much-improved productivity index over that of a comparable vertical well.
This can result either in a substantial production rate increase at constant pressure drawdown, or a greatly reduced pressure drawdown at constant production rates.
Reduced pressure drawdown is particularly beneficial in reservoirs subject to gas or water coning and, more recently, in reservoirs with sand control problems.
Joshi (1988) has introduced, and Economides et al. (1991) have augmented, the following expression for horizontal well deliverability:

10. Horizontal Well Evaluation Horizontal Well Deliverability
Vertical well deliverability
Note: Where q is expressed in m3/d (with k in md, pe and pwf in kPa, B in m3/m3, µ in cp and h, L and rw in m), becomes 1867.
(1.1)

11. Horizontal Well Evaluation Horizontal Well Deliverability
This equation contains two other important variables: the index of horizontal-to- vertical permeability anisotropy (Iani), defined as
where kv = vertical permeability (md) and the large half-axis (a) of the drainage ellipse formed by a horizontal well, which equals
reH = rdH: horizontal drainage radius
(1.2)
(1.3)

12. Horizontal Well Evaluation Horizontal Well Deliverability
q = flow rate (STB/D)
kH = horizontal permeability (md)
h = reservoir thickness (ft)
pe = reservoir pressure at outer flow boundary (psi)
pwf = flowing bottomhole pressure (psi)
B = formation volume factor (Bbl/STB)
µ = viscosity (cp)
L = length of well's horizontal section (ft)
rw = wellbore radius (ft)

13. Horizontal Well Evaluation Horizontal Well Deliverability
Suppose that a reservoir has a horizontal permeability (kH) of 5 md and a thickness (h) of 75 ft. Using the following data, plot production rate vs well length for Iani values of 5, 3 and 1. Compare the performance with a vertical well in the same reservoir.
pe = 5000 psi
pwf = 3000 psi
A = 640 acres = 27,878,400 ft2
B = 1.1 Bbl/STB
µ = 0.7 cp
rw = ft.

14. Horizontal Well Evaluation Horizontal Well Deliverability
Solution:
For the three values of Iani, the vertical permeabilities, kv are 0.2, 0.56 and 5 md, respectively. The drainage radius (reH) for A = 640 acres is 2980 ft.
If, for example, L = 2000 ft, then
a = 3065 ft

15. Then, the production rate for Iani = 5 q = 2490 STB/D [396 m3/D]
Horizontal Well Evaluation
Horizontal Well Deliverability
Then, the production rate for Iani = 5
q = 2490 STB/D [396 m3/D]

16. Horizontal Well Evaluation Horizontal Well Deliverability
By comparison, a vertical well, whose state-steady production is given by the well-known equation:
q = 757 STB/D [120 m3/D]

17. Horizontal Well Evaluation Permeability Anisotropy Effects
The second bottom term in eq. 1.1 is the only term affected by the vertical-to- horizontal permeability anisotropy.
Referring back to the example, the first logarithmic term is equal to 1.79 in each case. In contrast, for differing Iani values of 5, 3 and 1, the second term values become 0.984, and 0.178, respectively. Thus, a well in a reservoir of Iani = 1 would produce 1.4 times the rate attainable from the reservoir where Iani = 5.
1.79
0.178

18. Horizontal Well Evaluation Permeability Anisotropy Effects

19. Horizontal Well Evaluation Reduced Pressure Drawdown
As we noted earlier, a horizontal well affords reduced pressure drawdown over a comparable vertical well.
Referring again to Example 1.1, we see that the vertical well production rate of STB/D corresponds to a pressure drawdown of 2000 psi.
For horizontal well with L = 2,000 ft then the flow rate q = 2490 bpd.
If we want to produce with a rate of 757 bpd for this horizontal well (L = 2,000 ft), then the pressure drawdown would be

20. Horizontal Well Evaluation Reduced Pressure Drawdown
The flowing bottomhole pressure would be:
instead of Pwf = 3000 psi for the vertical well.
In reservoirs with coning or sand production problems, the ability to reduce drawdown while maintaining constant production can be a distinct advantage.

21. Horizontal Well Evaluation Effect of Reservoir Thickness

22. Horizontal Well Evaluation Effect of Reservoir Thickness
The figure describes productivity index ratios (horizontal well/vertical well) as a function of lateral section length
We can see from the Figure that:
While permeability anisotropy is crucial for thick reservoirs (as shown by the distance between the curves of the different Iani values), it is less important for thin reservoirs: Comparing 1A and 5A (thin reservoir) and 1C and 5C (thick res.)
For each Iani value, the thinner reservoirs exhibit the largest productivity index ratios.

23. Horizontal Well Evaluation Effect of Damage (Skin Factor)
Up until now, our calculations have assumed an undamaged horizontal well producing from its entire length. This assumption does not accurately describe real well behavior.
For now, it is useful to study the effect of near-wellbore damage on horizontal well performance. We characterize this damage, as we do in vertical wells, by means of a skin effect (seq).

24. Horizontal Well Evaluation Effect of Damage (Skin Factor)
This skin effect may easily have a value as high as 10 or even 20.
Although we multiply it by the scaled aspect ratio (Ianih/L), it nevertheless can drastically reduce a horizontal well's production rate.
For instance, returning once again to Example 1.1, remember that the calculated horizontal well production rate was 2490 STB/D.
For an seq value of 10 (where Iani = 5, h = 75 ft and L = 2,000 ft) the rate falls to STB/D, representing a 40% production loss.

25. Horizontal Well Evaluation Effect of Damage (Skin Factor)

26. Horizontal Well Evaluation
Horizontal Wells vs. Hydraulically Fractured Vertical Wells
In mature petroleum environments such as North and South America, an estimated 80% or more of all wells are hydraulically fractured (Willard, 1989).
Hydraulic fracturing is a long-established means of completing and stimulating wells in moderate-to low-permeability reservoirs.
Recently, there has been a tendency to fracture higher permeability formations as well, either to bypass near-wellbore damage or to control sand production by reducing pressure drawdown.

27. Horizontal Well Evaluation
Horizontal Wells vs. Hydraulically Fractured Vertical Wells
Reduced pressure drawdown, of course, also represents one of the main benefits of horizontal wells.
This raises the possibility of using horizontal wells in place of fractured vertical wells.
To evaluate this possibility, we must compare each alternative based on expected well performance.

28. Horizontal Well Evaluation
Horizontal Wells vs. Hydraulically Fractured Vertical Wells
In low permeability reservoirs where vertical wells are almost always hydraulically fractured, the engineering feasibility of unfractured horizontal wells should always be based on comparison with equivalent vertical wells with hydraulic fractures.
An easy way to do such a comparison is to use the concept of equivalent or effective wellbore radius.
Equivalent wellbore radius is the extended wellbore radius that results in an equivalent PI of a well with a fixed fracture half-length and conductivity.

29. Horizontal Well Evaluation
Horizontal Wells vs. Hydraulically Fractured Vertical Wells
Mukherjee and Economides (1991) developed the following comparison for equal well performance: =
xf is the fracture half-length in the vertical well, and r'wD is the dimensionless effective wellbore radius, which is a function of the relative fracture capacity a  (Prats, 1962):
Fracture conductivity
= rwa
(1.4)

30. a (or Cfd) is related to the dimensionless effective well radius:
Horizontal Well Evaluation
Horizontal Wells vs. Hydraulically Fractured Vertical Wells
a (or Cfd) is related to the dimensionless effective well radius:

31. Horizontal Well Evaluation
Horizontal Wells vs. Hydraulically Fractured Vertical Wells
Using this relationship and Equation 1.4, we can determine the required section length for a horizontal well to perform at the same level as a hydraulically fractured vertical well having a fracture half-length xf and a dimensionless effective wellbore radius r'wD.

32. Horizontal Well Evaluation
Horizontal Wells vs. Hydraulically Fractured Vertical Wells
r‘wD = rwa/xf : dimensionless effective wellbore radius
rwa – effective or equivalent wellbore radius resulting from a fracture half length xf
xf – half length fracture, ft
re – reservoir radius, ft
k – formation permeability, md
kf – fracture permeability
kH, kV – horizontal and vertical permeability
w – fracture width, ft

33. Horizontal Well Evaluation
Horizontal Wells vs. Hydraulically Fractured Vertical Wells

34. Horizontal Well Evaluation
Horizontal Wells vs. Hydraulically Fractured Vertical Wells
It also shows the optimum fracture lengths, based on a Net Present Value (NPV) calculation.
For example, for a reservoir permeability of 1 md, the optimum fracture half- length is 1,800 ft; for a horizontal well to produce at the same level, its section length would have to be 2,800 ft.
The decision regarding a horizontal versus a fractured vertical well thus becomes an issue of cost, and of whether we can attain the optimum fracture length.

35. Horizontal Well Evaluation
Horizontal Wells vs. Hydraulically Fractured Vertical Wells
On the other hand, Equation above assume no formation damage in the horizontal well.
A damage skin effect would require a longer section length.
In general, we may conclude that unfractured horizontal wells are not attractive in reservoirs where hydraulically fractured vertical wells have traditionally been successful.
This implies that in such environments, horizontal wells themselves need to be fractured.

36. Horizontal Well Evaluation
Horizontal Wells vs. Hydraulically Fractured Vertical Wells
If the value “a” is approximately equal to reH (almost always true) and if reH = reV, then Equation 1.4 has a much simpler approximation:
= rwa
(1.5)

37. Horizontal Well Evaluation
Horizontal Wells vs. Hydraulically Fractured Vertical Wells
Example:
Suppose that a reservoir has a permeability of 1 md, a thickness of 75 ft, and an Iani value of 3. Optimized hydraulic fracture design suggests that xf should be ft and fracture conductivity of FCD = 1.8.
If reH = 2980 ft and rw = ft, calculate the minimum horizontal well length required for equal well performance.

38. Horizontal Well Evaluation
Horizontal Wells vs. Hydraulically Fractured Vertical Wells
; With FCD = 1.8 then The relative fracture capacity () is:
a = From the plot gives: r'wD = 0.25.
Therefore, from Equation 1.5 and appropriate substitutions,
and by trial and error, L = 2400 ft [732 m].

39. Horizontal Well Evaluation
Horizontal Wells vs. Hydraulically Fractured Vertical Wells
0.25