predicted and actual productions of horizontal wells in heavy-oil fields

Predicted and actual productions of horizontalwells in heavy-oil ®elds

Peter Catania*

Chairman, International Energy Foundation, Faculty of Engineering, University of Regina,

Regina, Saskatchewan, Canada 545 0A2

Abstract

This paper discusses the comparison of predicted and actual cumulative and daily oil pro-

duction. The predicted results were obtained from the use of Joshi's equation, wherein, thee�ects of anisotropy and eccentricity were included. The cumulative production obtainedfrom the use of equations developed by Borisov, Giger, Renard and Dupuy resulted in errors

in excess of 100%, thus, they were not considered applicable for predicting cumulative anddaily ¯ows of heavy oils in horizontal wells. The wells considered in this analysis varied from537 to 1201 metres with corresponding well bores of 0.089 to. 0.110 m. Using Joshi's equa-tion, the predicted cumulative oil-production was within a 20% di�erence for up to 12 months

of production for long wells and up to 24 months for short wells. Short wells were de®ned asthose being under 1000 m. # 1999 Elsevier Science Ltd. All rights reserved.

1. Introduction

Horizontal wells have helped in advancing the oil industry since they were intro-duced in 1980 [1].As useful as horizontal wells have become, the need for careful preparation became

even more imperative before drilling can begin. As a result, the oil industry wants tobe sure that a horizontal well is the right choice and will be economical. This reas-surance is obtained through the use of ®eld simulators which simulate a well's opera-tion and production. These computer simulations require careful preparation andaccurate input data with the results being within accepted tolerances.Engineers and oil companies also require a quick and easy method (plug and

solve) of calculating production rates with `ballpark' results. Thus, the questionarises, what variables should be used and what models should be used? The answer

Applied Energy 65 (2000) 29±43

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is to simply use horizontal ¯ow-rate equations based on a few reservoir and ¯uidproperties and reservoir and well dimensions. This paper will examine the results ofa number of calculations using four horizontal ¯ow-rate equations (Borisov [2],Giger [3], Renard and Dupuy [4], and Joshi [5,6] and compare the predicted resultswith actual daily averaged oil ¯ow-rates and cumulative oil production ®gures.

2. Horizontal well history

Horizontal drilling and production started in Saskatchewan in the 1950s. These earlyoil wells consisted of only vertical wells. This conventional method of oil-recovery

Nomenclature

a half the major axis of the drainage ellipse (m)A cross-sectional area of ¯ow (cm2)Bo formation volume factor (dimensionless)h reservoir height (m)I current (A)k formation permeability (md)kh horizontal permeability (md)ks skin zone permeability (md)kv vertical permeability (md)L well length (m)q oil-¯ow rate (m3/day)qh horizontal well oil-¯ow rate (m3/day)R resistance ()reh horizontal drainage radius (m)rs skin-zone radius (m)rw wellbore radius (m)s skin factor (dimensionless)So initial reservoir oil saturation (fraction)SW initial reservoir water saturation (fraction)V voltage (V)X ellipsoidal drainage area (m2)� anisotropy index=

��kh=kvp

� horizontal well eccentricity (m)�p pressure drop from the drainage radius to the skin zone (kPa)�x distance (cm)� ¯uid viscosity (cp)�o oil viscosity (cp)�w water viscosity (cp)

30 P. Catania /Applied Energy 65 (2000) 29±43

initially met the production needs and oil-recovery percentages of the time. Underfavorable conditions (no formation damage, high initial reservoir pressure, no gas orwater coning, etc.) vertical wells could recover no more than 60% of the original oilin place (OOIP) [1].As oil needs increased and existing oil reservoirs were being abandoned before the

reservoirs were depleted because no further oil could be recovered using conven-tional vertical wells or enhanced oil recovery (EOR) methods, other oil-recoverymethods were required. The latest method is the use of horizontal wells.The use of horizontal wells in Saskatchewan began in 1987 and has greatly in¯u-

enced the province's oil-production. As of December 1994, there were 1385 producinghorizontal wells and 14138 producing vertical wells in Saskatchewan [7]. Althoughhorizontal wells accounted for only 8.9% of the total number of wells, horizontalwells accounted for 33.8% of the total oil production. More speci®cally, the annualproduction of heavy oil increased to almost 6 million m3 of oil per year. The quar-terly provincial oil production for horizontal wells steadily increased to where it isapproximately a third of the total oil production. Fig. 1 shows the provincial monthlyoil production from horizontal wells with the total oil production broken down intoheavy oil and light/medium oil production with a noticeable substantive increase inwell production occurring in the middle of 1992.Fig. 2 shows the number of horizontal wells drilled per year in Saskatchewan and

the type of oil being produced since 1987. The number of horizontal wells broke the500 barrier in 1993. Fig. 2 also shows the total cumulative number of horizontalwells in Saskatchewan and the number of wells drilled for heavy and light/medium

Fig. 1. Horizontal well monthly production of oil for Saskatchewan (data provided by SEM).

P. Catania /Applied Energy 65 (2000) 29±43 31

oil. This ®gure clearly demonstrates that there was a consistent increase of hor-izontal wells in Saskatchewan over the ®ve year period, 1989±1994.

3. Horizontal wells

There are three types of horizontal wells used today. The type of well is based onthe curvature rate, that is, the rate at which the vertical section becomes horizontal,and are described as follows [8]:

1. Short radius: curvature rate of 1.5±3 per ft with up to 125 ft ofhorizontal section.

2. Medium radius: curvature rate of 8±20 per 100 ft with up to 2000 ft ofhorizontal section.

3. Long radius: curvature rate of 2±6 per 100 ft with up to 4000 ft ofhorizontal section.

Horizontal wells have applications in all types of reservoirs. Reservoir simulationsand ®eld experience show that horizontal wells can increase production in all typesof reservoirs such as tight and highly permeable formations, homogeneous andnaturally-fractured reservoirs, horizontal and inclined reservoirs, light and heavy oilreservoirs, and thin and thick reservoirs. Horizontal wells are especially useful withtwo common cases. The special cases are natural vertical fractures and coning. Avertical well can only penetrate natural vertical fractures which happen to be in thedownward path of the well while a horizontal well can drill `sideways' throughmultiple fractures.

Fig. 2. Horizontal wells per annum (data provided by SEM).


In addition, a small number of horizontal wells are required to recover oil from anoil ®eld compared with the number of vertical wells. For example, four horizontalwells with multiple extensions can be used to drain a reservoir where it would take20 or more vertical wells [9]. In addition to primary and secondary recovery meth-ods, tertiary recovery methods or enhanced oil recovery (EOR) methods can beconducted employing horizontal wells.Horizontal wells can recover up to 80% of the original-oil-in-place (OOIP) under

normal circumstances. The increased recovery factor can result in a signi®cantincrease in pro®ts. The obvious and main disadvantage of horizontal wells is thatwell-for-well, a horizontal well is more expensive (reported to be 1.3±2 times morethan a vertical well) [10] and is more di�cult to drill than a conventional verticalwell. Horizontal wells are not applicable for:

. shallow reservoirs (1000±3000 ft) where vertical wells are inexpensive and easyto drill;

. thick, low-permeability reservoirs where hydraulically-fractured wells mayproduce more than fractured horizontal wells, and

. highly-permeable reservoirs that can be drained quickly with vertical wells.

4. Flow rates

Four di�erent steady-state horizontal ¯ow-rate equations were initially used tocalculate the horizontal ¯ow rates. The equations were developed by Borisov [2],Giger [3], Renard and Dupuy [4], and Joshi [5,6] with Joshi's Model 1 given below.

Joshi (Model 1):

qh � 0:007078khh�p=��Bo�

lna�

��a2 ÿ �L=2�2

qL=2

24 35� �h=L� ln h=�2rw�� 1�

where

a � �L=2� 0:5��0:25� 2reh=L� �4

q� �0:5�2�

Since the reservoir ¯uid viscosity is two-phase ¯ow (oil and water), the ¯uid visc-osity was calculated, using the oil and water viscosity (�o and �w), and the initialreservoir oil and water saturation (So and Sw), by the use of Eq. 3.

� � ��oSo� � ��wSw� �3�

All of the above mentioned ¯ow-rate situations are for isotropic reservoirs, that is,where the horizontal and vertical permeability are identical, (kh � kv). Anisotropy is


the di�ering of horizontal and vertical permeabilities. Joshi's model can be modi®edsuch that anisotropy is taken into account. The result is a modi®ed equation wherethe term (h=L) is replaced by (�2h=L) and is referred to as the Joshi-Model 2, Eq. (4).

qh � 0:007078khh�p=��Bo�

lna�

��a2 ÿ �L=2�2

qL=2

24 35� ��2h=L� ln h=�2rw�� 4�

where � � ��kh=kvp

In Fig. 3, � represents well eccentricity or the distance that the horizontal well isfrom the centre of the reservoir in the vertical plane. The in¯uence of eccentricity ona horizontal well's production can be calculated by modifying Eq. (4), so resulting inEq. (5), Joshi's Model 3.

qh � 0:007078khh�p=��o�

lna�

��a2 ÿ �L=2�2

qL=2

24 35� ��h=L� ln ��h=2�2 � �2�2��hrw=2��

forL > �h; � < h=2 andL < 1:8reh

�5�

where �=horizontal well eccentricity, m.

5. Calculations

Using Eqs. (1), (4) and (5), the predicted ¯ow rates were compared with actual¯ow rates for an oil ®eld owned and operated by Wascana Energy Inc. located in thenorthwest corner of Saskatchewan. The speci®c location of the wells remains con-®dential. Seven wells from the same ®eld were chosen: the wells vary in length andwellbore radius.

Fig. 3. A schematic view of an o�-centred horizontal well [11].


Borisov's equation gave negative results because the well length must be less thanfour times the horizontal drainage radius. Therefore Borisov's equation was notapplicable to the wells in this report since the well lengths are greater than four timesthe horizontal drainage radius. Giger's horizontal ¯ow rate equation also could notbe applied as well because the well length (L) must be less than double the horizontaldrainage radius (reh). Finally, Renard and Dupuy's equation produced positiveresults but consistently produced much lower results than actual average oil-¯owrates. Thus, Joshi's Models 1, 2 and 3 were used in this evaluation.Several assumptions were made in order to calculate the horizontal ¯ow rates. The

assumptions used within this research were as follows:

1. no formation damage;2. no sand production;3. skin factor (s) was assumed to be zero;4. steady-state ¯ow was assumed;5. ¯uid properties are independent of pressure;6. gravity e�ects are neglected;7. the reservoir is fully fractured;8. oil viscosity was live oil viscosity;9. the reservoir temperature was 27.8�C.

6. Reservoir properties and dimensions

The oil viscosity was measured from a PVT (pressure, volume and temperature)study and was taken at the bubble point.The reservoir height, penneabilities and pressure drop were average values. The

reservoir properties and dimensions used in this analysis were:

Permeability: horizontal (kh) =6000 mdvertical (kv) =5400 md

Reservoir height (h) =11 mPressure drop (�p) =19 kPaFormation volume factor =1.043Oil viscosity (�o) =3100 cpWater viscosity (�w) =1.2 cpInitial oil saturation (So) =0.91Initial water saturation (Sw) =0.09Fluid viscosity (�) =2821.1 cp

The common well dimensions were:

Horizontal drainage radius (reh) =84.6 mWell eccentricity (�) =4 m

The well eccentricity was averaged and the horizontal drainage radius was basedon a 2250 m2 or 5.6 acre well spacing and was calculated using


reh � �A=��0:5 �6�

whereA � drainage area; m2

The well lengths, assumed to be the e�ective horizontal well length, and wellboreradius vary from well to well and are given in Table 1. The depth and completiontechnique for each well cannot be revealed since the data are con®dential.

7. Results and analysis

The results for each well are depicted in three di�erent graphs:

1. daily oil production;2. cumulative oil production;3. percentage di�erences.

A typical result for the daily oil-production analysis is depicted in Fig. (3). Over-all, Joshi's models 1, 2 and 3 predicted daily oil-production results that were con-sistently higher (by +3 m3/day to +30 m3/day) than the actual average daily oil-production. The short wells (<l000 m) predicted average daily oil-production valueswhich were closer to the actual average daily oil production (+3 m3/day to +12 m3/day), whereas for the long wells (>l000 m) the predicted actual average daily oil-production was consistently higher (by +14 m3/day to +30 m3/day). Based on theanalysis of the seven wells in the study, the results indicate that the Joshi-Model 3was consistently the `best' model in predicting average daily oil-production.Typical results for the predictive and actual cumulative oil-production are shown

in Figs. 4 and 5 for short and long wells respectively. The closest predicted value tothe actual value for all wells was based on the Joshi-Model 3. Fig. 4 (for a short well)indicates that the predicted and actual cumulative oil produced are, within a 20%deviation, identical up to approximately 24 months of production. Beyond this, theactual and predicted values diverge signi®cantly because the predicted values assumea constant pressure-di�erence while in reality the pressure di�erence will decrease asthe reservoir is depleted. The predicted values still follow the trend of actual values,but are higher in value. Fig. (5) (for a long well) indicates that the predicted and

Table 1

Well length and wellbore radius

Well Well length (L) (m) Wellbore radius (rw) (m)

1 537 0.089

2 567 0.122

3 755 0.122

4 765 0.122

5 1201 0.110

6 1202 0.110

7 1198 0.110


actual cumulative oil-productions are, within reason (less than 20% di�erence),identical up to approximately 15 months of production.Typical percentage di�erences between the actual and predicted average daily and

cumulative oil-productions are shown in Figs. 6 and 7. The limit of `reasonable accu-racy' is assumed to be 20%. For short wells, the percentage di�erences for the averagedaily oil-production are reasonably accurate (Fig. 6). With respect to the cumulative

Fig. 4. Well number 1 Ð actual and predicted daily oil productions.


oil-production, the percentage di�erence steadily declines to approach zero withinthe ®rst year of production. The percentage di�erence stays below 20% untilapproximately 25 months of production. Beyond this, the percentage di�erencesteadily increased to values exceeding the 20% level. The initial high percentage

Fig. 5. Well number 1 Ð actual and predicted cumulative oil-productions.


Fig. 6. Well number 5 Ð actual and predicted oil-productions.


Fig. 7. Well number 1 Ð average daily and cumulative oil-production percentage di�erences.


Fig. 8. Well number 5 Ð average daily and cumulative oil-production percentage di�erences.


di�erence is assumed to be due to the horizontal well production start-up, whereinsteady-state ¯ow does not exist. Thus, there will be a higher percentage di�erence atthe beginning of a well's production-life.Fig. 7 (for long wells) shows, as with the short wells, that the percentage di�erence

for the average daily oil-production exceeds the reasonable accurate limit of 20%.The cumulative oil-production percentage di�erence in the ®rst few months of pro-duction was signi®cantly greater than the reasonable level of 20%. The ®rst monthof cumulative oil-production had a di�erence of 590%. The remaining two longwells, which were part of this study, had initial di�erences of 65 and 179%. Theseextremely high percentage di�erences are assumed to be due to the absence of stea-dystate ¯ow, which is compounded by the longer well length. The percentage dif-ference diminishes to an acceptable level (<20%) after approximately 6 months ofproduction. The exception was for Well 6, wherein the percentage di�erence was32%. Overall, the long horizontal wells reviewed in this study resulted in percentagedi�erences of 20% or less, except for the initial 6 months, for up to the ®rst 12months of production. (Fig. 8).

8. Conclusions

The results of the analysis presented in this paper have shown that Joshi's hor-izontal ¯ow-rate equation, model 3, accounting for anisotropy and eccentricity is themost accurate of the prediction models: -Borisov, Giger, Renard and Dupuy, Joshi-Model 1, Joshi-Model 2 and Joshi-Model 3.The percentage di�erence for the daily oil-production and cumulative oil-produc-

tion was shown to increase from 20 to 40% and 70 to 130% respectively as the welllength was increased.The predicted cumulative oil-production can be calculated within a reasonable

percentage di�erence (assumed to be <20%) for up to approximately 12 months ofproduction for long wells (>1000 m) and up to approximately 25 months for shortwells (<1000 m).Finally, during the ®rst month of production the percentage di�erence for cumu-

lative oil production is above the reasonable percentage di�erence (20%) due to theabsence of a steady-state ¯ow and is compounded as the well length increases. Areasonable percentage di�erence is achieved, usually in the second month of pro-duction, for a short well (<1000 m) and in the sixth month of production for a longwell (>1000 m).

9. Recommendation

Further calculations and analyses should be undertaken with additional wells ofvarying lengths, and accurate reservoir and well data. These analyses would yieldincreasing accuracy and allow a more accurate generalization of the results for di�erentwell-lengths, di�erent reservoir-characteristics, and di�erent well-characteristics.


References

[1] Gilbertson G. Collective approach helping horizontals. Oilweek, January 28, 1991.

[2] Borisov JP. Oil production using horizontal and multiple deviation wells. Moscow: Nedra, 1964.

[3] Giger F. Reduction du nombre de puis par l'uitilisation de forage horizontaux. Revue de I'Institut

Francais du Petrole 1983; 58 (3).

[4] Renard GI, Dupuy JM. In¯uence of formation damage on the ¯ow e�ciency of horizontal wells,

SPE paper 19414. 1990.

[5] Joshi SD, A review of horizontal well and drainhole technology. SPE paper 16868, May 1988.

[6] Joshi SD, Augmentation of well productivity using slant and horizontal wells: SPE paper 15375,

1986.

[7] Second International Williston Horizontal Well Workshop, 24±26 April, Minot, USA. 1994.

[8] CIM, Practical aspects of horizontal well applications, Calgary Section. CIM-34, October, 1991.

[9] Mahong BL, Horizontal drilling use on the rise: why and how. World Oil October, 1985.

[10] Mukherjee H, Economides MJ. A parametric comparison of horizontal and vertical well perfor-

mance. SPE paper 18303, 1988.

[11] Joshi SD. Horizontal well technology. Tulsa, OK: Pennwell Books, 1991.


predicted and actual productions of horizontal wells in heavy-oil fields

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