Iraqi Journal of Chemical and Petroleum Engineering 

 Vol.15 No.2 (June 2014) 61- 73  

ISSN: 1997-4884 

 
 
 
 

Formulation of New Equation to Estimate Productivity Index of 

Horizontal Wells  

 
Ghanim M. Farman and Maha Raouf Abdulamir 

College of Engineering - University of Baghdad 

 
Abstract 

   Significant advances in horizontal well drilling technology have been made in 

recent years. The conventional productivity equations for single phase flowing at 

steady state conditions have been used and solved using Microsoft Excel for various 

reservoir properties and different horizontal well lengths. 

   The deviation between the actual field data, and that obtained by the software based 

on conventional equations have been adjusted to introduce some parameters inserted 

in the conventional equation. 

   The new formula for calculating flow efficiency was derived and applied with the 

best proposed values of coefficients ψ=0.7 and ω= 1.4. The simulated results fitted the 

field data. 

   Various reservoir and field parameters including lateral horizontal length of the 

horizontal well (L), Skin factor (S), ratio of the vertical to horizontal permeability of 

the formation (KV/KH), and the vertical thickness of the productive zone (h) were 

studied and verified to generalize the suggested equation to estimate the horizontal 

well productivity indices for various reservoir kinds. This led to creating a new 

formula of flow efficiency equation that could be applied in AHDEB field. 
 

Keywords: Productivity index, AHDAB oil field, Horizontal well, Horizontal well 

length 
 

Introduction 

   Throughout the last decade, 

horizontal well technology ruled the oil 

and gas industry with growing success 

worldwide. It has now been a widely 

accepted approach for hydrocarbon 

recovery optimization. The post 

implementation recovery, in most 

cases, has been exceptional with the 

achievement of the following general 

goals [1]: 

a) Reduction of exploitation time by 
increasing the production rate and 

thereby improving the cash flow 

and rate of return on investment. 

b) Improving recovery by reaching the 
by-passed area in an effective way 

and increasing the drainage area. 

   The actual productivity of a 

horizontal well depends on many 

reservoir and well parameters such as 

Kv/KH, reservoir thickness, drainage 

area, fracture patterns and intensity, 

horizontal well length, etc. [3]. 

   Numerous models are available in 

the literature to predict the productivity 

of horizontal wells.  These models are 

applicable directly only to single phase 

systems and in reservoirs under "steady 

state" and "pseudo steady state". 

Iraqi Journal of Chemical and 
Petroleum Engineering 

 

University of Baghdad 
College of Engineering 



Formulation New Equation to Estimate Productivity Index of Horizontal Wells  

62                                        IJCPE Vol.15 No.2 (June 2014)               -Available online at: www.iasj.net 
 

   The performance of a horizontal well 

can be strongly influenced by the 

anisotropy of horizontal to vertical 

permeability. Thus, modeling of a 

horizontal well is much more complex 

than modeling a vertical well. There 

are basically two categories of methods 

for calculation of horizontal well 

productivity: analytical and semi-

analytical models. 

   Borisov [4] developed one of the 

earliest analytical models for 

calculating steady state oil production 

from a horizontal well. The horizontal 

flow was assumed from an equivalent 

circular drainage area toward a vertical 

fracture with drainage radius much 

larger than the vertical fracture length; 

he presented the equation below: 

 

     
       

     (
  e 
 

) (
 

 
)   (

 

    
) 

      …(1)  

                                                         

Where reH is the drainage radius of the 

horizontal well. 

   Giger [5] proposed a model similar 

to Borisov’s, but assumed an 

ellipsoidal drainage area, 

 

     
       

   
 

 
  (

  √         ⁄
 

 
)   (

 

    
) 

    ...(2) 

                                                       

   Karcher, Giger, and Combe [6] 

summarized the existing productivity-

prediction models, and addressed the 

limiting assumptions and applicability 

of each model. 

   Joshi [7] developed a model with 

elliptical flow in the horizontal plane 

and radial flow in the vertical plane. 

The model was modified to take into 

account the influence of the horizontal 

well eccentricity from the vertical 

center of reservoir and the anisotropy 

of horizontal to vertical permeability, 
 

     
       

     [
  √      ⁄   

   ⁄  
]  

  

 
  [

  

     
] 

      ...(3)  

                                                      

where a is the semi-major axis of the 

drainage ellipse, 
 

  (
 

 
)      √     (

   

  ⁄
)

 

             

For  
 

 
                                     …(4) 

 

and β is the permeability anisotropic 

factor 

 

  √
  

  
                                         ...(5) 

 

   Economides et al. [8] augmented the 

Joshi’s equation  ith Peaceman’s 

equivalent wellbore radius in an 

anisotropic formation: 

 

       
    y ⁄

 
    y   ⁄  

 
 

 
               ...(6)   

 

Which,  ith the β variable, becomes 

 

       
   

 √ 
                                …(7)  

 

Also, according to Peaceman’s 

transformation, the equivalent vertical 

height must be: 

 

 eq   √                                     …(8) 
 

   All these expressions are based on 

Muskat’s [9] original work on 

permeability anisotropy. Thus, the 

second logarithmic expression in the 

denominator of Joshi’s equation must 

be: 

 
 eq

    
 

 

       
                                   ...(9) 

 

and therefore, more appropriate 

expression for horizontal well inflow 

is: 

 
   

  
       

     [
  √      ⁄   

   ⁄  
]  

  

 
  [

  

       
] 

          …(10) 

 



Ghanim M. Farman and Maha Raouf Abdulamir 

 

-Available online at: www.iasj.net                      IJCPE Vol.15 No.2 (June 2014)                                 63 
 

Which for β=1 reverts e actly the 

Joshi’s equation. 

   Renard and Dupuy [10] modified the 

steady state equation to include the 

effective wellbore radius: 
 

   
       

             (
  

 
)   (

 

     
) 
    ...(11)  

 

Where X=2a/L, a is the same as state 

in Eq. 4; cosh
-1

(X) is the invers 

hyperbolic cosine function, and 

effective wellbore radius is: 
 

    (
   

  
)                               …(12)  

 

   Later, a number of models, both 

analytical and semi-analytical, were 

developed using the source function 

method. The well drainage area was 

assumed to be a parallelepiped or 

infinite with no-flow or constant 

pressure boundaries at top, bottom and 

the sides. In general, the analytical 

models are asymptotic solutions under 

some appropriate simplifications and 

specific conditions, while the semi-

analytical models are rigorous 

solutions of the original boundary 

value problem but have to be solved 

numerically. 
 

Formulation of the Proposed 

Equations 

Estimation of productivity index in 

horizontal well is directly affected by 

two key parameters which determine 

flow direction toward the horizontal 

well. Joshi [7] developed a widely 

accepted equation to estimate steady 

state productivity from a horizontal 

well. He introduced horizontal and 

vertical resistances in the  arcy’s flo  

equation and gave the following 

relationship: 

 

   
     

       
                               ...(13) 

 

Where α=Kh/µB and RHP and RVP are 

horizontal and vertical resistance’s to 

flow. 

To simplify the mathematical analysis 

of the three-dimensional (3D) problem,  

Joshi [7] subdivided it into two two-

dimensional (2D) problems; see 

Figure1. 

 

 
Fig. 1: Division of 3D Horizontal-Well Problem into 2D Problems [7] 

 
   The total flow into the horizontal 

well is having the following 

components: 

1.) Flow into a horizontal well in a 
horizontal plane.  

   The pressure at the drainage 

boundary Pe is: 

 

     [
  √      

  
 ]                   …(14) 



Formulation New Equation to Estimate Productivity Index of Horizontal Wells  

64                                        IJCPE Vol.15 No.2 (June 2014)               -Available online at: www.iasj.net 
 

   The pressure drop between the 

drainage boundary and  ell ΔP is the 

same as Pe defined in Eq. 14 because 

wellbore pressure is assumed to be 

zero. Substituting this into Darcy's 

porous-medium equation, we can show 

it to be: 

 

   
          ⁄

  [
  √      

  
]

                        …(15) 

 

 here Δr is the  ell half-length (L/2). 

 

   
          ⁄

  [
  √      ⁄   

   ⁄  
]

                     …(16) 

 

Eq. 16 represents flow to a horizontal 

well from a horizontal plane. 

   To calculate horizontal-well drainage 

radius, reH, areas of a circle and ellipse 

(in a horizontal plane, Fig. 2) are 

equated. This reduces to: 

 

    √                                    …(17) 
 

where a and b are major and minor 

axes of a drainage ellipse. Moreover, 

+L/2 and –L/2 represent foci of a 

drainage ellipse. Hence, using 

properties of an ellipse, we can show 

that: 

 

  √      ⁄                        …(18) 
 

   Using an electrical analog concept, 

flow resistance in a horizontal 

direction is given as: 

 

    
  

  
 

   

    
  [

  √      ⁄   

  ⁄
]      …(19)    

 

 
Fig. 2: Schematic Potential Flow to a Horizontal Well: Horizontal Plane and Vertical Plane [3] 

 

2.) Flow into a horizontal well in a 
vertical plane.  

   Darcy's equation for flow through a 

porous medium to a vertical well is: 

 

   
        

     
  
  

 
                               ...(20) 

 

   In this equation, the term in the 

denominator refers to horizontal flow. 

Flow in a horizontal well is the same 

as flow in a vertical well rotated ninety 

degree. We can state that re for vertical 

well is equivalent to h/2 for a 

horizontal well. After replacing re by 

h/2 into Eq. 20, it yields: 

 

   
        

     
  ⁄

  
 
                               ...(21) 

 

   The influence of vertical flow in 

horizontal wells is closely linked to 

relation between reservoir thickness 

and wellbore length, h/L, which means, 

the lower h/L is, the lower the 

influence of this type of flow is. 

Applying this concept to Eq. 21, we 

obtain: 



Ghanim M. Farman and Maha Raouf Abdulamir 

 

-Available online at: www.iasj.net                      IJCPE Vol.15 No.2 (June 2014)                                 65 
 

   
        

      ⁄    
 

   
 
                      …(22) 

 

   The vertical-resistance term 

represents resistance in a vertical plane 

in a circular area of radius h/2 around 

the wellbore which is: 

 

    
  

  
 

   

    
  [

 

   
]            …(23) 

 

   Part of this resistance is already 

accounted for in the horizontal 

resistance term    . 
   Different methods of combining 

   and     were considered to 
calculate effective flow resistance. 

Horizontal and vertical resistances 

were added to calculate horizontal-well 

oil production: 

 

          (
 

  
 

 

  
)  

  

  
     …(24) 

 

And 

 

   
        

  {  [
  √      ⁄   

   ⁄  
]  

 

 
  [

 

   
]}

    

For L>h and L/2˂ 0.9 reH            …(25) 
 

Where a, half the major axis of a 

drainage ellipse in a horizontal plane in 

which the well is located Fig. 2, is 

obtained as shown below: 

 

  (
 

 
) [    √     (

   

  ⁄
)

 

 ]

   

      …(26) 

 

   The above relationships were 

developed for isotropic reservoirs 

(     ). In many reservoirs, the 
vertical permeability is less than the 

horizontal permeability. In really 

anisotropic reservoirs, it is possible to 

have a higher vertical permeability 

than the effective horizontal 

permeability. For a horizontal well, a 

decrease in vertical permeability 

results in an increase in vertical-flow 

resistance and a decrease in oil 

production rates. As Muskat [9] 

showed, the reservoir anisotropy could 

be accounted for by modifying the 

vertical axis as    √    ⁄  and the 
average reservoir permeability as 

√    . The modification of the z axis 
makes the wellbore elliptic. If the 

elliptic wellbore effects are assumed to 

be negligible, Eq. 25 is modified to 

account for the reservoir anisotropy: 

 

    
         

  {  [
  √      ⁄   

   ⁄  
]  

  

 
  [

  

   
]}

       

for L>βh and L/2˂ 0.9 reH           …(27)  
 

Where   √    ⁄   
   In Eq. 27, the variable β,  hich is the 

measure of reservoir permeability 

anisotropy [i.e., (KH/Kv)
1/2

] is 

particularly important. Obviously, the 

smaller β is, the larger the inflow 

performance of a horizontal well is. 

   Economides et al. [8] augmented the 

Joshi’s [7] equation, with Peaceman's 

equivalent wellbore radius in an 

anisotropic formation:
 

 

       
    y ⁄

 
    y   ⁄  

 
 

 
            …(28) 

 

This,  ith the β variable, becomes: 

 

       
   

 √ 
                               ...(29) 

    

Also, according to Peaceman’s 

transformation, the equivalent vertical 

height must be: 

 

 eq   √                                   …(30) 
 

   All these expressions are based on 

Muskat’s [9] original  ork on 

permeability anisotropy. Thus, the 

second logarithmic expression in the 

denominator of Joshi’s equation,      

Eq. 27, must be: 

 



Formulation New Equation to Estimate Productivity Index of Horizontal Wells  

66                                        IJCPE Vol.15 No.2 (June 2014)               -Available online at: www.iasj.net 
 

 eq

    
 

 

       
                                …(31) 

  

And therefore, more appropriate 

expression for horizontal well inflow 

developed by Economides et al. [8] is: 

 

   
       

  {  [
  √      ⁄   

   ⁄  
]  

  

 
  [

  

       
]}

   …(32) 

 

Which for β=1 reverts e actly the 

Joshi’s equation, Eq. 27. 

   There are two terms in the 

denominator of Eq. 32. The first one 

(left-hand side) responds for flow in 

the horizontal direction and the second 

one is responsible for flow in the 

vertical direction that can be seen in 

any of the productivity index 

correlations (Eqs. (Borisov) [4], (giger) 

[5], (joshi) [7] and (renared and 

Dupuy) [10]). 

   The flow towards horizontal well has 

been verified for different dependent 

parameters; the results were compared 

with the actual well productivity for 

AHDEB field. We found that the 

horizontal flow factor proposed by 

Economides et al. is the same as the 

one in Josh’s correlation. Therefore, 

we took the correlation factor proposed 

by Economides et al. to represent this 

type of flow. It can be concluded a new 

adjustment for the weighting 

coefficient that should be done to fit 

the result of Economides et al. with 

actual data. Thus: 

 

     
       

  {  ( [
  √      ⁄   

   ⁄  
])   

  

 
  [

  

       
]}

 

  ...                                                  .(33) 
 

Where ψ and ω are constants 

(weighting coefficients), which will be 

determined by using a trial and error 

procedure. 

Where FD is the unit conversion factor. 

In field units, FD=0.001127; in metric 

units, FD=86.4. 
 

Impact of Skin Effect on Horizontal 

Well Performance 

   The horizontal well skin effect is 

added to the denominator of Eq. 33, 

 ith multiplied it by ωβh/L, and the 

anisotropic scaled aspect ratio is called 

in the following manner: 

 
   

  
       

  {  ( [
  √      ⁄   

   ⁄  
])   

  

 
[  [

  

       
]  ]}

    …(34) 

                                 

   The skin effect, denoted as S, is the 

characteristic of the shape of damage 

in horizontal wells, taking into account 

the permeability anisotropy and the 

likelihood of larger damage penetration 

near the vertical section. 

   The productivity index, JH, for the 

horizontal well can be estimated by 

dividing qH by ΔP as follo s: 

 
   

  
     

  {  ( [
  √      ⁄   

   ⁄  
])   

  

 
[  [

  

       
]  ]}

         

…(35)  

  

   Different to other correlations, this 

correlation includes t o constants, ψ 

and ω, to allo  an optimum match 

with respect to the simulated results. 

   Using a trial and error procedure 

[11], the values of constants ψ and ω in 

Eq. 35 were determined at the lowest 

deviation error with the simulated 

results attained. These values were 

found to be ψ=0.7 and ω= 1.4; Eq. 35 

has been arranged to involve (ψ=0.7), 

(ω= 1.4) and (FD=0.001127) to fit the 

field results and yield the following 

equation: 

 

   
          

  {  (   [
  √      ⁄   

   ⁄  
])     

  

 
[  [

  

       
]  ]}

 

                                                  …(36) 
  

   The simple Excel Spreadsheet 

program was developed to calculate 

the productivity values of horizontal 

wells using three major available 

productivity equations. These 



Ghanim M. Farman and Maha Raouf Abdulamir 

 

-Available online at: www.iasj.net                      IJCPE Vol.15 No.2 (June 2014)                                 67 
 

equations include: Joshi [7] Equation 

3, Economides et al. [8] Equation 10 

and Renard and Dupuy [10] Equation 

11. 

Also, the developed spreadsheet 

program was used to compute the 

productivity index employing the 

improved equation, Eq. 34. The 

stimulated results obtained using 

FAST WELLTEST software is also 

presented. 

   It can be noticed that the productivity 

index of horizontal well is mainly the 

function of six parameters of the 

reservoir: horizontal length (L), 

anisotropy factor (β), formation 

thickness (h), drainage radius (re), well 

radius (rw) and skin factor (s). 

   To develop a general equation for 

estimation horizontal well productivity 

index, various parameter reservoir 

properties have been made to assist to 

generate Eq. 36 which can be used to 

estimate horizontal well productivity 

index for AHDEB or any other field. 
 

Effect of Horizontal Well Length (L) 

   The improved equation and the 

stimulated results are used to study the 

effect of horizontal well length on 

productivity index of horizontal well 

for a wide range of horizontal well 

length in the range of 250 to 6000 ft, as 

shown in Figures 3 to 11. 

   Figures 3 to 11 show that the 

modified equation gives extremely 

exact results with that obtained from 

AHDEB field. While original equation 

and other selected equations give 

biggest deviation from the field data. 

This conclusion has been proved for all 

parameters affecting horizontal well 

productivity index as shown in Figures 

3 to 11. The results of all equations 

show that horizontal well productivity 

increases as well length increases. 

 

 

 
Fig. 3: Effect of Well Length on PI of HW for (s=0) and (KV/KH=2) 

 

 

 

 



Formulation New Equation to Estimate Productivity Index of Horizontal Wells  

68                                        IJCPE Vol.15 No.2 (June 2014)               -Available online at: www.iasj.net 
 

 

 

 

 
Fig. 4: Effect of Well Length on PI of HW for (s=+3) and (KV/KH=2) 

 

 

 

 
Fig. 5: Effect of Well Length on PI of HW for (s=-3) and (KV/KH=2) 

 

 



Ghanim M. Farman and Maha Raouf Abdulamir 

 

-Available online at: www.iasj.net                      IJCPE Vol.15 No.2 (June 2014)                                 69 
 

 

 

 

 

 

 
Fig. 6: Effect of Well Length on PI of HW for (s=0) and (KV/KH=1) 

 

 

 

 
Fig. 7: Effect of Well Length on PI of HW for (S=3) and (KV/KH=1) 

 



Formulation New Equation to Estimate Productivity Index of Horizontal Wells  

70                                        IJCPE Vol.15 No.2 (June 2014)               -Available online at: www.iasj.net 
 

 

 

 

 

 

 
Fig. 8: Effect of Well Length on PI of HW for (S=-3) and (KV/KH=1) 

 

 

 

 
Fig. 9: Effect of Well Length on PI of HW for (S=0) and (KV/KH=0.5) 

 



Ghanim M. Farman and Maha Raouf Abdulamir 

 

-Available online at: www.iasj.net                      IJCPE Vol.15 No.2 (June 2014)                                 71 
 

 
Fig. 10: Effect of Well Length on PI of HW for (S=3) and (KV/KH=0.5) 

 

 
Fig. 11: Effect of Well Length on PI of HW for (S=-3) and (Kv/KH =0.5) 

 

Brief Description of the Field 

AHDEB oil field is located between 

Nomina town and Kut town of Wasit 

Province, 180km southeast away from 

Baghdad.  

The AHDEB oil field is an anticline 

elongated trending NWW-SEE.  There 

are three heights which are AD-1, AD-

2, and AD-4 within the anticline. 

Based on testing data, the main oil-

bearing formations in the AHDEB 



Formulation New Equation to Estimate Productivity Index of Horizontal Wells  

72                                        IJCPE Vol.15 No.2 (June 2014)               -Available online at: www.iasj.net 
 

field are Khasib formation of upper 

Cretaceous, Mishrif, Rumaila and 

Mauddud formations of middle 

Cretaceous. The cover depth of the oil 

reservoirs is from 2600m to 3300m. 

Horizontally, the oil-bearing 

formations of Khasib is distributed all 

over the field, the oil-bearing 

formations of Mishrif, Rumaila and 

Mauddud mainly are distributed in the 

eastern part. 

The average core porosity is 17.3%; 

the average permeability is 25 mD. 

The AHDEB reservoirs have moderate 

porosity with lower permeability. 

Pressure coefficient is 1.135 averagely. 

Reservoir temperature is 71-85 ℃. 
 

Conclusions 
1. A new formula for calculating flow 

efficiency is derived and applied in 

AHDEB field. This equation takes 

into consideration the proposed 

values of   ψ=0.7 and ω= 1.4.  

2. The factors (well length, 
permeability ratio, reservoir 

thickness, skin factor, drainage 

radius, and well radius) affect the 

pressure drop between the wellbore 

and the reservoir affect productivity 

index in horizontal wells. 

3. The productivity index of horizontal 
well results obtained for well 

AD10-H show very close agreement 

with other results obtained for other 

wells drilled by Chinese Company. 

4. The simulation of AHDEB field 
indicates that the reservoir is 

affected by the existence of a partial 

edge water drive. This conclusion 

agreed also with that of the Chinese 

Company. 

5. The horizontal well productivity 
index is highly affected by the 

lateral horizontal well section and 

the net pay thickness of the 

reservoir. Since studying the net, 

production thickness for each well 

is very important to estimate the 

horizontal well productivity index. 

Recommendations 

1. Prediction of the reservoir 
performance when the reservoir 

pressure declines below the bubble 

point pressure and multiphase flow 

of fluid is an important future case 

of study. 

2. A study of water and gas injection 
to increase the productivity of 

horizontal wells can be taken into 

consideration. 

3. A study of forecast for the 
horizontal well productivity index 

of previous drilled wells in AHDEB 

oil field is important to maximize 

the production of the field. 

4. For reservoirs with small vertical 
permeability value, KV can be 

increased by fracturing the 

reservoirs to reduce the anisotropy 

value and as a result increasing 

horizontal well productivity idex. 

 

Nomenclature 

A = Drainage area, acres 

a = Semi-major axis of the drainage 

ellipse, (ft), (m) 

Bo  = Oil formation volume factor 

(BBL/STB) 

FD = unit conversion factor. In field 

units (0.001127); and in metric units 

(86.4). 

h = Formation thickness (ft),
 
(m) 

J = productivity index (STB/d/psi) 

JH = Oil productivity index for 

horizontal well (STB/d/psi) 

K = Permeability (millidarcy) 

KH = Horizontal Permeability 

(millidarcy) 

Kv= Vertical permeability (millidarcy) 

L = Horizontal lateral length, ft 

q = Flow rate, (STB/d) 

qH = flow rate for horizontal well, 

(STB/d) 

qV = flow rate for vertical well, 

(STB/d) 

P = Pressure, (psi) 

   = Bubble point pressure, (psi) 
   = Bounded pressure (psi) 
   = Reservoir pressure (psi) 



Ghanim M. Farman and Maha Raouf Abdulamir 

 

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    = Bottom hole flowing pressure 

(psi) 

re = Drainage radius (ft), (m) 

reH = Drainage radius for horizontal 

well (ft), (m) 

reV = Drainage radius for vertical well 

(ft), (m) 

rw = Wellbore radius (ft), (m) 

S = Skin Factor (dimensionless) 

STB =Stock tank barrel 

β = Anisotropy ratio (√    ⁄ ) 

o = Oil viscosity, (cp) 

Ø = porosity (percentage) 

 

References 

1- Joshi, S.D.: "Horizontal Well 
Technology ", Penn. Well 

Publishing Company, Tulsa, OK, 

U.S.A., 1991. 

2- FDP Study of AHDEB Oilfield, 
Iraq- Reservoir Engineering- CNPC 

Science and Technology Research 

Institute. June, 2011. 

3- Joshi, S.D.: "Horizontal Well 
Productivity", 2009. 

4- Borisov, J., P., (1964):  “Oil 
Production Using Horizontal and 

Multiple- eviation Wells”, 

Moskva, Nedra, 1964. 

5- Giger, F., M. (1986):  “The 
Reservoir Engineering Aspects of 

 orizontal  rilling”, SPE paper 

13024. 

6- Kuchuk, F., J., Goode, P.A, Brice, 
B. W., and Sherrard, D., W., 

(1988B):  “Pressure Transient 

analysis and Inflow Performance for 

 orizontal Wells”,  SPE Paper  

18300, Presented at the 63rd Annual 

SPE Conference, Houston, Texas 

Oct. 2-5. 

7-  Joshi, S. D. (1988): "Augmentation 
of Well Productivity Using Slant 

and Horizontal Wells", Journal of 

Petroleum Technology, p 729. 

8-  Economides, M. J., 
“Comprehensive Simulation of 

 orizontal Well Performance” SPE 

20717, 1990. 

9- Muskat, M.: The Flow of 
Homogeneous Fluids Through 

Porous Media, McGraw-Hill Book 

Co. Inc., New York City (1937). 

10- G. Renard and J.M. Dupuy, 
(1991): “Formation Damage Effects 

on Horizontal Well Flow 

Efficiency” paper spe 19414. 

11- Ghanim M. Farman “Study of 
the Flow Efficiency of Horizontal 

Wells in A  EB Oil field” 

Dissertation submitted to the 

college of engineering university of 
Baghdad in partial fulfillment of the 

requirements for the degree of 

doctor of philosophy in petroleum 

engineering.