Horizontal Well IPR Estimations.Krishna Kumar, Heriot Watt University

AbstractThis paper aims to review some of the most widely used conventional and other contemporary IPR models that exist for Horizontal wells, and comment on their limitations by drawing on the experiences of other author’s critiques on these IPR models.

IntroductionA large number of Horizontal Wells exist today, and field operators are continuing to drill an even larger numbers of horizontal wells throughout the world, in all kinds of reservoirs, as these wells offer much higher productivities, and are effective in a much wider range of reservoir conditions than their vertical counterparts are. The appeal of horizontal well technology is further boosted by the continued developments in drilling and completion technologies, which is enabling horizontal wells to be placed with much greater accuracy in increasingly complex reservoirs, and also have the ability to produce selectively, within those sections, giving rise to increased efficiencies and an overall increased economic potential.

Horizontal wells can potentially be several times more productive than vertical wells, even when they are draining the same reservoir volumes, but because drilling a

horizontal well is still a lot more expensive, proper care must be taken to ensure that the economic practicality of drilling and completing a horizontal well vis-à-vis its expected productivity is given due consideration.

The advantages of horizontal wells mainly result from:

i. Increased productivities and/or Injectivities.

ii. Improved Volumetric Sweep Efficiencies.

iii. Increased Drainage Areas.

iv. Reduced Viscous Fingering and/or Coning, can be considered as a part of improved sweep efficiencies (ii), leading to increased productivities (i).

The productivity of a horizontal well can be greater than a vertical well for several number of reasons, some of which include:

a. They can access a much greater area of the reservoir section they are draining,

b. Possess much greater flexibility in terms of being selective to a preferred orientation in order to

better target a certain reservoir section, such as naturally occurring fractures within the reservoir, or higher permeability streaks within a larger heterogeneous reservoir section.

c. Provides the ability to induce multiple hydraulic fractures within the chosen reservoir section.

This increased productivity in horizontal wells also allows for reduced drawdowns, for the same withdrawal rates, allowing for lower water/gas production in the field, which is especially useful if the surface facilities are insufficient in terms of their water and/or gas handling capacities,

This is especially beneficial for condensate reservoirs, where this increased productivity can result in reduced instances of failures due to liquid dropouts in near wellbore region.

As such, Horizontal wells can significantly outperform vertical/conventional wells in fields with

a. Numerous thin reservoir sections.

b. Reservoirs that have significant natural fractures.

c. Reservoir that are experiencing, or have the potential for water/gas coning problems.

d. Reservoirs with comparatively high vertical permeabilities.

e. Heavy Oil or Bitumen Sand Reservoirs.

The advantages of using Horizontal Wells in fields carry over well into the later stages of the life of the field, where the focus shifts

from increasing productivities to increasing recoveries.

While the use of horizontal wells in itself is not an end-all solution to the maladies, which are normally associated with vertical wells, they still have the potential to alleviate the barriers to proper drainage by enabling the injected stream to better sweep and displace the oil.

These barriers may exist due to a number of reasons such as:

a.Low Injectivity and/or Productivity,

b. Coning / Cusping,

c.Viscous Fingering,

d. Heterogeneities,

e.Fractures,

f. Poorly connected or compartmentalized reservoir blocks,

g. High Gravity Overrides.

Removal of these barriers, with a properly designed and executed development plan has the ability to reduce not only the potential unit production/injection costs, but also the capital costs, in the later field life, as fewer new wells may be needed during the future EOR/IOR phases.

This is especially important for the future development of numerous marginal fields, and also for sweeping small oil pools, within older/depleted reservoirs, which are otherwise considered uneconomical to produce.

Literature ReviewThe most simplistic model to represent the pressure behavior in a horizontal well drainage scenario is done by assuming that

the pressure drop inside the horizontal well is non-existent. Since, there is virtually no pressure drop inside of the well during fluid flow, the pressure along the well-bore face will be uniform, giving the well an infinite conductivity.

However, the infinite conductivity model is not feasible for the evaluation of well-bore pressure, necessitating the use of approximations, with the use of an equivalent pressure point, or by pressure-averaging techniques. Even then, Finite well-bore conductivity, non-uniform skin effects, selective completion, and multiple laterals are some of the new concepts that need to be integrated into the contemporary horizontal well productivity models.

A number of attempts have been made to describe and estimate the productivity/Injectivity indices of horizontal wells, and their corresponding sweep efficiencies using numerous models [1, 2, 3, 4, 5,

6] that have been proposed. These models are similar to the vertical well productivity models, in that they use analogous well and reservoir geometries, such as the parallel-piped model, where the top and bottom surfaces are either at no-flow/constant-boundary conditions, and the sides affected by no-flow/infinite-acting boundaries.

One of the earliest models describing horizontal wells was by J.P. Borisov [7], wherein, he assumed a constant pressure drainage inside an ellipse, with the dimensions depending on the length of the well section.

F.M. Giger, in “Reservoir Engineering Aspects of Horizontal Drilling” made further refinements to Borisov’s equation by the use of a constant coefficient FR, known as replacement ratio, used to describe the

equivalent number of vertical wells that would be needed to replace the production from a single horizontal well, assuming equal drawdowns for both. Later additions to this equation were made to accommodate the effect of fractures, and reduced water coning in horizontal wells.

In 1987, another equation was proposed by L.H. Reiss [12], followed by S.D. Joshi’s Equation in 1988[13] refinements to Joshi’s Equation were made in 1989, by D.K. Babu who reduced the complex three dimensional equations proposed by Joshi into an easy-to-use formula, with the assumption that the drainage area, was box shaped, with sealed boundaries[14, 15]. Economides, Brand, and Frick [16] made later additions in 1996 with equations that are more generally accepted, and are applicable to multilateral wells.

Butler[17,18], in his review of the horizontal well technology in 1988 summarized the main advantages offered by horizontal wells over conventional wells, focusing on the aspects leading to higher productivities from the use of Horizontal Wells. He derived equations for the flow of oil under the effects of gravity drainage, and predicted that under favorable conditions the critical rates for very long horizontal wells could be up to 100 times higher than conventional wells.

Horizontal Well Productivity Estimations.

Babu-Odeh [14, 15] Productivity Model.This particular productivity model is derived from the solution of the standard diffusivity equation for a well that is located inside a bounded box-shaped reservoir as is visible in the figure below, and is dependent on a number of assumptions, which are:

a) Uniform flux and uniform formation damage along the well-bore

b) The sides of the bounded box are parallel to the directions of the three principal permeabilities i.e. Kx, Ky

and Kz.

c) The well-bore is assumed as being parallel to the sides of the box-shaped reservoir.

d) All the boundaries in the reservoir are under the conditions of “no-flow” and the reservoir itself is in the pseudo-steady state.

Economides et al. [16] Productivity Model.The model proposed by Economides et al. is a more general solution for the estimation of the productivity index, with the added benefit of being valid for multilateral wells in a single plane, and dependency on the orientations of the principal permeabilities. This model can also be used for infinite conductivity Hz. Wells, but is dependent on

interpolation between limited sets of drainage area data.

Where Σs is the sum of all skin resulting from formation damage, turbulence, and all other pseudo-skin factors.

Jing Lu [19] Productivity Model.Jing Lu, in 2001 proposed new productivity formulae for horizontal wells, which are based on the average potential and point convergence pressure, derived from the three dimensional solution of the Laplace equation, with separate formulae for wells with either a gas cap, or bottom water.The main assumptions made were:

a) Horizontal, Homogeneous, and anisotropic reservoir with constant permeabilities Kx, Ky and Kz in all three directions, a fixed thickness H, and constant porosity ϕ.

b) The reservoir is infinite in its lateral extent, i.e. the external boundaries cannot be felt.

c) The Reservoir pressure is initially constant, is equal to the pressure at the initial value at the boundary, and is confined on the top and bottom by a constant pressure boundary.

d) Single-phase fluid of small and constant compressibility Cf, constant viscosity µ and formation volume factor B, with the well located at a distance Zw from the bottom.

Figure 1: The horizontal well and the accompanying reservoir geometry, as used in the

Babu-Odeh Model

…1

…2

…3

…6

…5

…4

Is to be used if the pressure drop is measured at the endpoint. of the well.

Also, Is to be used if the pressure drop is measured at the midpoint. of the well.

Incorporating Near Wellbore Effects in Horizontal Well Productivity Models.Thomas et al. [20] in 1996 modified the conventional well productivity equations to include near well-bore skin and Non-Darcy flow coefficients, based on how the wells are drilled and completed, a typical example of such well is shown in Appendix 2.

Mechanical Skin FactorThe laminar skin for a horizontal well can be expressed as the sum of the individual components from perforation geometry, damaged zone and the crushed zone.

Perforation Skin (Sp) is usually very small and is calculated from well diameter, well

length, shot phasing and shot frequency per foot.

Skin resulting from formation damage (Sd) can be calculated from the formula,

Skin resulting from flow restrictions through the crushed and compacted zone are calculated from the following equation.

Non-Darcy Flow.Non-Darcy flow primarily occurs inside of the near well-bore regions where the fluid velocities are higher, and the coefficient consists of three components, for each of the flow regions in the near wellbore, similar to components in the total skin formula.

Modified Horizontal Well Productivity Equations.

a.) Babu and Odeh.[20]

b.) Economides et al.[20]

…10

…11

…12

…13

…14

Figure 2: Typical Geometry of the drainage volume used for comparing the different IPR models for Horizontal Wells, Thomas et al. 1996

…7

…8

…9

These modified equations were then compared with a reservoir model with both coarse and fine scale gridding, with the authors concluding that the results from these equations were sufficient enough, as the results were “Essentially Identical”, with the caveat that the fine grid simulations

were calculated without any pressure drop inside the wells.

Results & Discussion.Ozkan [21] in 2001, made a comparison between the conventional and contemporary horizontal well models, wherein he highlighted the major limitations of the conventional productivity models including the Babu-Odeh and Economides et al. models.

a.) Most conventional models assume the well to be parallel to one of the principal permeability directions (Babu-Odeh), but in a large number of real world cases these are very ambiguous , which corrections to the length (Economides et al.) are no longer useful. Moreover, these models also indicate that it is not possible to infer the parallel nature of

the well, based on the transient response.

b.) Most of these models also implicitly assume a uniform skin/damaged region surrounding the wellbore, which is observed to not be true, and usually varies along the length of the wellbore increasing towards the heel of the well; this problem is compounded by the presence of variable permeability along the wellbore.

c.) A large majority of the horizontal wells are selectively completed, and can also affected by large local variations in permeability and high-skin effects , resulting in wells that are not entirely open to flow. This can affect the pressure response inside the well, and can affect productivity estimations esp. if the location and length of the open intervals are unknown.

d.) Some models also assume negligible pressure drops inside of the wellbore, and/or a uniform flux along the length of the well, which is highly unlikely to occur in real world scenarios.

Still, the use of contemporary horizontal well models is unfortunately not easily applicable for predicting well productivities, as their utility is highly dependent on the availability of high quality well and reservoir data, limiting their use to quantifying uncertainty and history matching observed data.

ConclusionSemi-Analytical Equations are mainly useful for making initial screening calculations, but for more complex reservoir and multiphase flow problems reservoir simulation should be used, as these equations fail to take into the account the unconventional features in the horizontal well.

Figure 3: Comparison with fine grid simulation. [Thomas et al. 1996]

Abbreviations Used.A = drainage area, m2

aH = total width of reservoir perpendicular to the well-bore, ft

aH′ = modified total width of reservoir perpendicular to the well-bore, ft

bH = length in direction parallel to well-bore, ft

bH′ = modified length in direction parallel to well-bore, ft

B = formation volume factor, res volume/surface volume

= anisotropic permeability factor, fraction.

Cf = fluid compressibility, MPa-1

dx = shortest distance between horizontal well and x boundary, ft

dy = shortest distance between tip of horizontal well and y boundary, ft

dz = shortest distance between horizontal well and z boundary, ft

FR = Replacement Ratio used for F.M. Giger’s Equation.

h = net formation thickness, ft

H = reservoir effective thickness, metres

J = productivity index, STB/D, psi

k = absolute permeability, µm2, md

= average permeability, md

kx = permeability in x-direction, md

ky = permeability in y-direction, md

kz = permeability in z-direction, md

L = well length, meters

Lw = completed length of horizontal well, ft

= volumetric average or static drainage-area pressure, psi

pw = BHP in well-bore, psi

pwf = flowing BHP, psi

pxy = parameter in horizontal well analysis equations

pxyz = parameter in horizontal well analysis equations

py = parameter in horizontal well analysis equations

pD = 0.00708 kh(pi – p)/qBμ, dimensionless pressure as defined for constant-rate production

rsp = radius of source or inner boundary of spherical flow pattern, ft

rw = well-bore radius, ft

Re = drainage radius, metres

sc = convergence skin, dimensionless

sd = skin caused by formation damage, dimensionless

se = skin caused by eccentric effects, dimensionless

sp = skin resulting from an incompletely perforated interval, dimensionless

α = exponent in deliverability equation

α = parameter characteristic of system geometry in dual-porosity system

β = turbulence factor

β′ = transition parameter

γm = matrix density

μ = viscosity, cp

μw = water viscosity, cp

= viscosity evaluated at  , cp

V = drainage volume, m3

ϕ = porosity, dimensionless

Notations UsedA = average

d = damaged zone

D = dimensionless

dp = compacted zone

E = endpoint

g = gas

o = oil

p = perforation

s = skin

M = midpoint

e = external

h = horizontal

i = initial

v = vertical

w = well

x,y,z = coordinate indicators

References1. CLARIDGE, E.L., Sweep Efficiency

Comparisons of Horizontal and Vertical Wells; Journal of Canadian Petroleum Technology, Vol. 30(4), pp. 52-57, August 1991.

2. DIETRICH, J.K., Predicting Horizontal Well Productivity; Journal of Canadian Petroleum Technology, Vol. 35(6), pp. 42-48, June1996.

3. GILMAN, J.R., Evaluating Horizontal vs. Vertical Well Performance; World Oil, 213(4), pp. 67-72, April 1992.

4. GILMAN, J.R., Evaluating Horizontal vs. Vertical Well Performance; World Oil 213(6), pp. 55-60, June 1992.

5. LICHTENBERGER, G.J., Data Acquisition and Interpretation of Horizontal Well Pressure Transient Tests, Journal of Petroleum Technology, Vol.46 (2), pp. 129-132, February 1994.

6. MUKHERJEE, H.A., A Parametric Comparison of Horizontal and Vertical Well Performance; SPE Formation Evaluation, Vol. 6(2), pp. 209-246, June 1991.

7. BORISOV, J.P., Oil Production Using Horizontal and Multiple Deviation Wells; the R&D Translation Company, Bartlesville, OK, 1984.

8. GIGER, R.M., Reservoir Engineering Aspects of Horizontal Drilling; paper SPE 13024, SPE Annual Technical Conference and Exhibition, Houston, TX, September 1984.

9. GIGER, R.M., Horizontal Wells Production Technique in Heterogeneous Reservoirs; paper SPE 13710, SPE Middle East Oil Technical Conference and Exhibition, Bahrain, March 1985.

10. GIGER, R.M., Some Practical Formulas to Predict Horizontal Well Behavior; paper SPE 15430, SPE Annual Technical Conference and Exhibition, New Orleans, October 1986.

11. GIGER, R.M., Analytic Two-Dimensional Models of Water Cresting Before Breakthrough for Horizontal Wells; SPE Reservoir Engineering, Vol.4 (4), pp. 409-416, November 1989.

12. REISS, L.H., Production from Horizontal Wells after Five Years;

Journal of Petroleum Technology, Vol.39 (11), pp. 1411-1416, November 1987.

13. JOSHI, S.D., Augmentation of Well Productivity with Slant and Horizontal Wells; Journal of Petroleum Technology, Vol.40 (6), pp. 729-739, June 1988.

14. BABU, D.K., Flow Capabilities of Horizontal Wells; Journal of Petroleum Technology, Vol.41 (9), pp. 914-915, September 1989.

15. BABU, D.K., Productivity of a Horizontal Well; SPE Reservoir Engineering, Vol.4 (4), pp. 417-421, November 1989.

16. Economides, M. J., Brand, C. W., & Frick, T. P. Well Configurations in Anisotropic Reservoirs. Society of Petroleum Engineers. (1996, December 1).

17. Butler, R. M. The Potential for Horizontal Wells for Petroleum Production. Petroleum Society of Canada. (1989, May 1).

18. Butler, R. M. Gravity drainage to Horizontal Wells. Petroleum Society of Canada. (1992).

19. J. Lu, “New productivity formulae of horizontal wells,” Journal of Canadian Petroleum Technology, vol. 40, no. 10, pp. 55–67, 2001.

20. Thomas, L. K., Todd, B. J., Evans, C. E., & Pierson, R. G. (1998, October 1). Horizontal Well IPR Calculations. Society of Petroleum Engineers.

21. Ozkan, E. (1999, January 1). Analysis of Horizontal-Well Responses: Contemporary vs. Conventional. Society of Petroleum Engineers.

22. Estimating Horizontal Well Productivity. (n.d.). In Petrowiki. Retrieved August 19, 2014, from

http://petrowiki.org/Estimating_horizontal_well_productivity