Part 16 Horizontal Well Testing

Chapter 16

Horizontal Well Testing

M stafa On r

1

Mustafa Onur

Useful References

• Kuchuk, F., Goode, P.A., Brice, B.W., Shrerrard, D.W., Thambynayagam, “Pressure-Transient Analysis for Horizontal Wells,” JPT, Aug 1990, 1022-1030 (paper SPE 18300).

• Odeh, A.S., and Babu, D.K.: “Transient Flow Behavior of Horizontal Wells: Pressure Drawdown, and Buildup Analysis,” SPEFE March 1990, 7-15. • Odeh, A.S., and Babu, D.K.: “Productivity of a Horizontal Well,” SPERE Nov.

1989, 417-421.

• Abbaszadeh M and Hegeman P S : “Pressure-Transient Analysis for a Slanted

2 Abbaszadeh, M. and Hegeman, P.S.: Pressure Transient Analysis for a Slanted Well in a Reservoir With Vertical Pressure Support,” SPEFE (September 1990) 277.

• Kuchuk, F., Goode, P.A., Wilkinson, Thambynayagam, R.K.M.: “Pressure-Transient Behavior of Horizontal Wells With and Without Gas Cap or Aquifer,” SPEFE, March 1991, 86-94 (paper SPE 17413).

• Kuchuk, F., and Habashy, T.: “Pressure Behavior of Horizontal Wells in Multilayer Reservoirs With Crossflow,” SPEFE, March 1996, 55-66.

• Thompson, L.G., and Temeng, K.O., “Automatic Type-Curve Matching for Horizontal Wells,” paper SPE 25507, March 1993.

Useful References

• Onur, M., Hegeman, P.S., and Kuchuk, F.J.: “Pressure-Transient Analysis of Dual Packer-Probe Wireline Formation Testers in Slanted Wells,” paper SPE 90250 presented at the SPE Annual Technical Conference and Exhibition held in Houston, Texas, U.S.A., 26–29 September 2004.

• Ozkan, E.: “Analysis of Horizontal-Well Responses: Contemporary vs. Conventional”, SPEREE, Aug 2001, 260-269.

• Sada, D.J.: Horizontal Well Technology, PennWell Publishing Co. Tulsa, OK.,

3

gy g

1991.

• Bourdet, D.: Well Test Analysis: The Use of Advanced Interpretation Models, Elsevier Science B.V., Amsterdam, The Nethelands, 2002.

• Horne, R.: Modern Well Test Analysis-A Computer-Aided Approach, Second Edition, Petroway, Inc., Palo Alto (1995).

Introduction

ƒ Since 1980’s, horizontal wells have been extremely popular. The major purpose is to enhance reservoir contact and hence well productivity. ƒ In general, a horizontal well is drilled parallel to the reservoir bedding plane

(see below figure θw= 90o), while a vertical well is drilled perpendicular to

the bedding plane (θw= 0o). The wells intersecting the bedding plane with

an angle θwdifferent from 0 to 90oare called slanted (or deviated) wells.

4 θ y z zw θw z h (x,y,z) rw x

Introduction (Cont’d)

ƒ The increase in the applications of horizontal (and also slanted) wells has brought an impetus development of the procedures to evaluate the performances and productivity of horizontal wells. ƒ Here, we will focus only on the interpretation of pressure transient

measurements from horizontal wells to be able to determine formation parameters that control performance and productivity of

5 horizontal wells.

ƒ However, I should note that interpretation of pressure transients is much more difficult than interpretation of those from vertical wells:

— 3D nature of the flow geometry (so many parameters affecting the pressure behavior of the horizontal well; This makes the application of classical conventioal analysis methods very difficult. Non linear regression seems to be the most useful)

Introduction (Cont’d)

— Considerable wellbore storage effects (this mask critical reservoir flow regimes, e.g., early-radial flow governed by the vertical permeability of the reservoir. Deconvolution can be useful to eliminate wellbore storage effects, but requires accurate measurements of “sandface” rates, although there are “wellbore storage” deconvolution methods not requiring “sandface rate” measurements which assume that a constant wellbore storage model is adequate to represent the wellbore storage effect)

6 effect).

— Wellbore haydraulic (conductivity of the wellbore is in general finite). — Non uniform skin effect along the wellbore.

— Selective completions along the horizontal well.

Pressure Transient Behavior of a

Horizontal Well

7

Horizontal Well

Basic Flow Regimes—Infinite System in

the x-y Plane

z x y kx kz ky 8 yz w k k L μ y t w kφc L h μ

Early (or Vertical) radial flow due to convergence of flow only in the vertical (y-z) plane

normal to the well axis.

Slope of p vs. lnt controlled by Intermediate-time linear flow regime (occurs if Lw>> h)

Slope of p vs. sqrt(t) controlled by

Late (or Horizontal) radial flow (some people referred to as

pseudo-radial flow). Slope of p vs. lnt controlled by xy k k h μ

On Anisotropic Permeability

• If we define principal directions of permeability as kx, ky( in x-y

plane) and kz(z is the vertical direction), then

– (3D anistotropic reservoir).

– (isotropic in the x-y plane, but

z y x k k k ≠ ≠ ) ( , z v h v h y x k k k k k k k = = = ≠ 9 anisotropic in the z-direction)

• For vertical wells, the radial flow is governed by the horizontal permeability,

• For horizontal wells, early radial flow is governed by the geometric mean of khand kv, while late-radial flow is governed by horizontal

permeability, only. y

( )

h x y

On Anisotropic Skin Factor

• If we have anisotropy in permeability in the horizontal and/or vertical plane, this causes our well to be an ellipse in the equivalent isotropic system, and this appear as skin effect on pressure. well Horizontal/Vertical plane ⎤ ⎡ k /k k /k 10 kmin kmax ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + = ′ 2 / / 4 4 min max max min w w k k k k r r 0 2 / / ln 4 4 < ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + −

= min max max min

ani

k k k k

s k_kmax/kmin= 1 ise, sani= 0

max/kmin= 10 ise, sani= -0.2 kmax/kmin= 500 ise, sani = -0.9

On Mechanical Skin

• I believe it is more appropriate to define a mechanical skin factor based on the producing well length (L_w) than based on the formation thickness because skin pressure drop has noting to do with formation thickness and, particularly if we do not observe the effects of top and bottom boundaries.

11 141.2 141.2 h v w h w v skin w skin w sc sc h k k L k L k s p or s p s s q Bμ q Bμ k = Δ = Δ ⇒ = 141.2 h h skin sc k h s p q Bμ = Δ

Pressure Behavior of Horizontal Wells

10 100 p /d ln t, ps i h x y k or k k h k or k 12 0.0001 0.001 0.01 0.1 1 10 100 1000 Time (h) 0.1 1 Δp and d Δp h v yz k k or k k

Early radial (0-slope)

h y

k or k

Early Radial Flow Pressure Equation

• Radial flow in the vertical direction (p

_wf

vs. lnt plot):

L zw h kv kh 13 Lw w ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ μ φ + μ = − tre w t v h w v h sc wf i s r c k k t L k k B q p p 162.6 log log 2 3.23 0.87 v tre ani h k s s s k = + kh ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ + − = 2 / / ln 4 4 v h h v ani k k k k s

Intermediate Linear Flow Pressure

Equation

• Linear flow analysis (p

_wf

vs. t

1/2

_plot):

8.128sc 141.2sc v w v i wf z q B q B k L k p p t s s hL k k h k μ μ μ φ ⎛ ⎞ − = + ⎜_⎜ + ⎟_⎟ 14 i wf z w th hv w h h p p hL φc k k k L ⎜⎜_⎝ k h k ⎟⎟_⎠ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ₊ π − = h z k k h r L h k k s w h v w w v h z ln 1 sin

Late Radial Flow Pressure Equation

•

Late-time radial flow (p

_wf

vs. lnt plot):

2 162.6 log log 1.93 0.87 sc h i wf trg h t w q B k p p t s k h c L μ φ μ ⎡ ⎛ ⎞ ⎤ − = ⎢ + ⎜ ⎟− + ⎥ ⎢ ⎝ ⎠ ⎥ ⎣ ⎦ 15 ⎣ ⎦ trg p w h s s s L = + 2 2 2 2 2 1 ln 1 sin 3 h w v w h w w p v w h v w k h r k z k h z z s k L h k h k L h h π π ⎡ ⎛ ⎞ ⎛ ⎞⎤ ⎛ ⎞ = − ⎢ ⎜ + ⎟ ⎜_⎝ ⎟_⎠⎥− ⎜ − − ⎟ ⎢ ⎝ ⎠ ⎥ ⎝ ⎠ ⎣ ⎦

Geometric Skin for Horizontal Wells

• In practice, the efficiency of a horizontal well is described by the total skin STHdefined with reference to a fully penetrating vertical

well of radius rw: 2 162.6 log log 3.23 0.87 sc h i f TH q B k p−p = μ⎡⎢ t+ ⎛⎜ ⎞⎟− + s ⎤⎥ 16 TH G w h s s s L = + 0.81 ln 2 w G p L s = − ⎛_⎜ ⎞_⎟+s ⎝ ⎠

The equation of Spis given in the previous slide. 2 log log 3.23 0.87 i wf TH h t w p p t s k h ⎢⎢⎣ + ⎜⎝φ μc r ⎟⎠ + ⎥⎥⎦

Geometric Skin for Horizontal Wells

(Cont’d)

_{Ref: Bourdet’s book}

Short horizontal well lengths

17

and/or low kv can give positive

geometric skin.

Investigating the

Effect of Some Parameters on

18

Horizontal Well Pressure Behavior

Conventional Analysis

• If the data exhibit all of these flow regimes, then we determine kh, kv, (Or even kx, kyand kz) and s mechanical skin factor by the

specialized plots of bottom-hole pressure vs time as explained before.

• However, data exhibiting all three flow regimes are rare.

• If the early-radial is masked by the wellbore storage effects, we will

t h h t ti t ti l bilit f it

19

not have a chance to estimate vertical permeability from its conventional analysis.

• Because of the large wellbore volumes, wellbore storage effects usually mask the early-time radial and part of intermediate-time linear flow characteristics.

• Only recourse seems to attempt to use nonlinear regression or try to use deconvolution to eliminate wellbore storage effects.

Conventional Analysis

• Also, the existence of a well-defined intermediate-time linear flow period usually requires extremely long horizontal wells. • On the other hand, the beginning of the late-radial flow is further

delayed as the horizontal well becomes longer.

T b bl t b th li d l t di l fl th d t

20

• To be able to see both linear and late radial flows on the data, we may need to run tests with duration of several months, which may not be practical.

• For most of the horizontal well tests that I have seen, the intermediate linear and/or late-radial flow periods do not exist.

Effect of Wellbore Storage, C

10 100 d ln t, ps i C = 0 bbl/psi C = 5 bbl/psi Δp dΔp/dlnt 21 0.01 0.1 1 10 100 1000 10000 100000 Time (h) 0.01 0.1 1 Δp and d Δp /d C 5 bbl/psi Lw= 2626 ft, kh= 196 md, kv/kh= 0.06, zw/h = 0.5

Effect of Horizontal Well Length, L

_w

10 100 ln t, ps i Δp Lw = 200 ft 22 0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000 Time (h) 0.1 1 Δp and d Δp /d Lw = 3000 ft Lw = 1500 ft dΔp/dlnt Lw = 500 ft kh= 196 md, kv/kh= 0.06, zw/h = 0.5, h = 84 ft

Effect of L

_w

and k

_v

10 100 p /d ln t, ps i Δp dΔp/dlnt Lw = 1000 ft k /k 0 54

kv and Lw in such a way that sqrt(khkv)Lw is fixed

23 0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000 Time (h) 0.1 1 Δp an d d Δp Lw = 3000 ft kv/kh = 0.06 Lw = 1500 ft kv/kh = 0.24 kv/kh = 0.54 kh= 196 md, zw/h = 0.5, h = 84 ft

Effect of Vertical Offset (z

_w

)

10 100 p /d ln t, ps i Δp dΔp/dlnt kh= 196 md, kv/kh= 0.1, h = 84 ft 24 0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000 Time (h) 0.1 1 Δp an d d Δp zw/h= 0.5 zw /h= 0.25 p zw/h = 0.06

Investigation of Various Factors

Complicating Horizontal Well Test

25

p

g

Interpretation

Effect of Nonuniform Skin along the Wellbore

Aritmetic mean value of skin is 0.367 for Cases 2 through 4.

26

“Conical” skin distribution, skin is linearly decreasing from the heel to toe. From SPE 52199, Ozkan

Effect of Nonuniform Skin (Cont’d)

27

“Conical” skin distribution, skin is linearly decreasing from the heel to toe. From SPE 72494, Ozkan

Effect of Nonuniform Discontinous Skin

28

“Discontinous skin distribution, SPE 72494, Ozkan

Selective Completed or Partially Open

Horizontal Wells

• It is a common practice to selectively complete horizontal wells. • In some other cases, some segments of the well may not be open to flow

from the reservoir because of high-skin or low permeability streaks. • All such cases can be called selective completion and may be treated as

29 a nonuniform skin distribution case where some segments have extremely large formation damage.

• Goode and Wilkonson (SPE 19341, 1991), Kamal et al. (SPE 26444, 1993, and Yildiz and Ozkan (SPE 28388, 1994) have studied the effect of selective completion on productivity and pressure-transient behavior of horizontal wells.

• Production logging could be useful to identify productive intervals in identifying the productive and low productive segments.

Selective Completed or Partially Open

Horizontal Wells

30

Effect of Selective Completion on PT Behavior

31

Effect of Selective Completion on PT Behavior

• The slope of early-time radial will be proportional to the open well

length, but its duration depends on the length of individual open segments.

• We observe a intermediate-time radial with a slope equal to ml/m;

32

We observe a intermediate time radial, with a slope equal to mlr/m;

where mlris the slope of the late-radial semilog str. line, and m is

equal to the total number of open segments, each segment acts as a horizontal well.How about if the open segments are not equal? Still we see intermediate radial, but slope equation is not available. • The slope of the late-time semilog str. line is not affected by the

length or the distribution of open segments.

Effect of Wellbore Hydraulics

• The conventional horizontal well models assume infinite conductivity horizontal wells, i.e., no pressure drop along and inside the wellbore. • In the literature, there is evidence horizontal wells can, in fact, display

finite-conductivity characteristics.

• This problem has been investigated by Dikken (JPT Nov. 1990); Ozkan et al (SPE Advanced Technology Series Vol 3 March 1995; and Suzuki

33 al. (SPE Advanced Technology Series, Vol. 3, March 1995; and Suzuki (SPEFE, Sept. 1997).

• These studies indicate that finite-conductivity horizontal wells do not lend themselves to simple well-test analysis techniques.

• Finite conductivity destroys the characteristics of early radial and intermediate linear flow unless if the effects of finite conductivity is low or moderate.

• Ignoring wellbore hyraulics can lead to a significant underestimation of sqrt(khkv)Lw( a factor of 3 or more).

Effect of Wellbore Hydraulics on PT Behavior

4 13 7.395 10 w hD w r C khL = × 2 Re 6.157 10 2 t w w v D q N r L k L h k ρ μ − = × = 34 ( ) ( ) ( ) 1/ 4 1/ 4 0.65 1.5 6 2 / / 2 6 10 , h w wD h v v h Rett corr wD hD corr h k r r k k k k h N f T r C if T wellbore hyraulics are negligible

− ⎡ ⎤ = _⎣ + _⎦ = < × ∞

Slanted Wells

35

Slanted Wells

Slanted and Horizontal Wells

(r, θ, z) θw h w w h L θ = cos 36 θ r z zw z h

θwis the well’s inclination angle measured from vertical to well axis.

If θw = 0o, a vertical well If θw = 90o, a horizontal well

Possible Flow Regimes

•

Early-time radial flow

-

(but, usually

masked by storage).

h w

k k

37

•

Spherical (and/or hemispherical) flow

-•

Latetime radial flow

-( )

₂ 1/3 v h s

k

k

k

=

h

k

w v w h w k k k = 2θ + 2θ sin cos If it is limited entry

Slanted Well Flow Regimes

• Early time radial flow:

38

Lw

h

Flow Regimes For Slanted Wells

•

Early time radial flow equation:

162.6 l l h q Bμ⎡ ⎛ k ⎞ ⎛ k ⎞⎤ ⎢ ⎜ ⎟ ⎜ ⎟⎥ 39 2 162.6 log log 3.23 0.87 sc h w i w f ani t w h h w w q B k k p p t s s c r k k k L μ φ μ ⎛ ⎞ − = ⎢ + ⎜ ⎟− + ⎜_⎜ + ⎟_⎟⎥ ⎢ ⎝ ⎠ ⎝ ⎠⎥ ⎣ ⎦ w v w h w k k k = 2θ + 2θ sin cos

(

)

[

]

⎭ ⎬ ⎫ ⎩ ⎨ ⎧ + θ + θ − = 2 sin / cos / 1 1 ln 2 2 w h v w ani k k s

Sani, changes between -0.4 ile 0 arasındadır, it depends on kv/khand θw.

Flow Regimes For Slanted Wells

•

From early-time radial flow analysis, we can estimate:

162.6 sc h w 162.6 sc re h k k q B q B m m L k k L μ μ μ = ⇒ = 40 re w h w w m L k k L μ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ + ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ μ φ − Δ =1.151 log 3.23 2 1 w t h re hre tre _{c r} k m p s ani h w tre s s k k s = + w v w h w k k k = 2θ + 2θ sin cos

Flow Regimes For Slanted Wells

• Late time radial flow:

41

Flow Regimes For Slanted Wells

•

Late-time radial flow equation:

162.6 l l h q Bμ⎡ ⎛ k ⎞ ⎤ ⎢ ⎜ ⎟ ⎥ 42 2 162.6 log log 3.23 0.87 sc h i wf trg h t w q B k p p t s k h c r μ φ μ ⎛ ⎞ − = ⎢ + ⎜ ⎟− + ⎥ ⎢ ⎝ ⎠ ⎥ ⎣ ⎦

(

)

ani p w w h v w w trg _L s s s h k k s _⎟⎟+ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ₊ θ + θ θ = 2 2 _{/ sin} cos cos

Flow Regimes For Slanted Wells

•

Besson’s equation for pseudo skin:

(

)

(

)

⎥⎥ ⎤ ⎢ ⎢ ⎡ θ θ θ + θ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ = D D wD D w v h w p k k k k h h h h h h h s 2 2 2 2 i / sin / cos ln 4 ln 2 4 ln 43

(

)

_⎥⎦ ⎢⎣ + θ + θ ⎠ ⎝ ⎟ ⎠ ⎜ ⎝ wD wD wD w v h w p k k h h h _{2 4 1 cos}2 _{/ sin}2

(

h v

)

w w w w wD k k r L h = _{/ cos}2θ +_sin2θ v h w D k k r h h =

It is valid for inclination angles, but assumes fully penetrating slanted well, 0<θw<90, sptypically changes between 0 ile -5.

Flow Regimes For Slanted Wells

•

From the late-time radial flow analysis, we can determine:

162.6 sc h 162.6 sc rg h rg q B k q B m k h m h μ μ μ = ⇒ = 44 h μ rg ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ μ φ − Δ =1.151 1 log ₂ 3.23 w t h rg hrg trg r c k m p s

(

)

ani p w w h v w w trg _L s s s h k k s _⎟⎟+ ⎠ ⎞ ⎜⎜ ⎝ ⎛ + θ + θ θ = 2 2 _{/ sin} cos cos

Pressure and Derivative

45

Behaviors of Slanted Wells

PT Behavior of Slanted Wells

100 1000 s i θw = 0o θw = 30o θw = 65o

(No wellbore storage effect, kh= kv= 1 mD, fully penetrating slanted well)

46 0.01 0.1 1 10 100 1000 10000 Time (h) 0.1 1 10 d Δp /d ln t, p s θw = 85o θw = 89o

Effect of Storage on PT Behavior of

Slanted Wells

100 1000 d ln t, ps i 47 0.001 0.01 0.1 1 10 100 1000 10000 Time (h) 1 10 Δ p and d Δ p /d

C = 0 bbl/psi (Slanted well Theta_w = 70)

C = 0.03 bbl/psi (Slanted well Theta_w = 70) C = 0.3 bbl/psi (Slanted well Theta_w = 70)