European Journal of Scientific Research ISSN 1450-216X Vol.39 No.4 (2010), pp.477-488 © EuroJournals Publishing, Inc. 2010 http://www.eurojournals.com/ejsr.htm

Analysis of Cone Formation and Water Movement in

Horizontal Wells

Ibelegbu, Charles Schlumberger Oilfield Services North Africa, Algiers, Algeria

E-mail: Cibelegbu@slb.com Tel: +213770934133, +2347055520233

Onyekonwu, Michael

University of Port Harcourt, Port Harcourt

Abstract

A knowledge of water cut and GOR trends in a reservoir is needed to ensure fair judgment of a depletion process in new and existing wells, and this judgment is the basic statistics that relates a well’s flow rate with its GOR and BS&W. Often critical rates are never economical to operators as they seek to produce above the established critical rates without any prior analysis of an economical stands-off rate at which continuous high GOR/ BS&W becomes uneconomical. Therefore, knowledge of the cone time, height and the water movement is critical toward remedial / adjustment decisions in wells.

This study calculates the cone time, cone height and present oil-water contact (water movement) of two field cases. The study principle adapted in the cone formation analysis is that of the tank balance which simply relates the cone height reached to displacement of oil by water and the total oil produced to pore volume of the oil column. Therefore an area depth computation of cone shape wells (volume enclosed in a cone) resulted to the volume of oil displaced, which when subtracted from the original oil in-place + oil produced (Np), gives us the present oil-water contact. A numerical model is used to validate these results. Keywords: Coning, critical rate, OWC- original oil water contact, POWC- present oil

water contact. Introduction Coning is a term used to describe the mechanism underlying the upward movement of water and/or the downward movement of gas into the perforations of a producing well. In most oil and gas field over the world, produced water due to coning is usually present in the reservoir even before production started, as in bottom water aquifer; and/ or in artificially improved recovery scheme, e.g., water injection.

In thin oil or gas pay sections, the presence of oil-water contact hinders production and often causes early abandonment of the afflicted well if a completion is even attempted. Even when relatively thick pay sections are found, the encroachment of water when a water drive is present will eventually pose serious water coning problem. In most field development plans the arrival of water at the production wells, the so called water breaking through, is put off as long as possible by an optimal well

Analysis of Cone Formation and Water Movement in Horizontal Wells 478

placement and by diligently manipulating fluid withdrawal and circulation rates. If three phase are present in the reservoir in a’ sandwich’- like situation, water and/or gas might be produced in a cone shape together with the oil.

An active aquifer is an aquifer which is large enough so as to maintain the reservoir pressure. Depending on the position of the active aquifer with respect to the well, we discern two extreme cases: the bottom water case where the oil bearing zone is fully underlain by water bearing layer, and the edge water case in which the water encroaches the oil. The edge –water case leads in the limit of negligible capillary pressure to the formation of Dietz water –tongue (Muskat and Wyckoff, 1935) as it is assumed that the reservoir is a dipping plane and that the water encroaches piston-like from below towards the well. Analytical formulations exist for the two-dimensional, aerial, shape of the water-oil interface. An active bottom-water aquifer is good for production as long as the water remains in the reservoir. Once the water breaks through in the production well, it means a loss of the natural drive energy. The production of water also means that the net production rate of oil or gas decreases, unless the production units are able to cope with extreme fluid withdrawal rates. Furthermore, the arrival of gas or water at a production well can cause lifting problems.

Now, if we imagine a zone of water fully underlying by oil. The movement of the water maintains the same streamlines. As the OWC is a material interface, it will move with a larger velocity when the streamlines are closer together. That means that the OWC forms a cone near the well, and eventually breaks through.

Produce water or cone water which is always present in the reservoir with the hydrocarbon tend to accompany or even by-pass the hydrocarbon when well is put on production. Thus this result to HGOR and HBS&W values which tend to reduce profitability of asset planned. Even when all the assumptions of the critical rate concept hold, technical and economic necessities may enforce production rate above the critical rate. It is therefore important to predict the evolution of the cone and the time to breakthrough so that the future completion and production scheme can be envisaged. Therefore the aim of this study is to analyze the develop of cone formation and the movement of water along from its original oil water contact. This will help in given us an estimated breakthrough time at the completions/ perforations. Horizontal Well Critical Rate, Breakthrough time Correlations In the early days of coning studies it was observed experimentally that there exists a rate below which water/ gas does not arrive at the production well. The maximal rate for which this is true was termed the critical rate

Many authors had come-up with critical rate and breakthrough time correlation; Meyer & Garder (1954) proposed the formula qc= ( )2 2

o w o oi p

eo

w

k g(p p ) h h

rlnr

π − −

⎛ ⎞μ ⎜ ⎟

⎝ ⎠

(1)

Chaperson (1986) provides a simple and practical estimate or the critical rate under steady-state or pseudosteady-state flowing conditions for an isotropic formation. Efros (1963) proposed a critical flow rate correlation that is based on the assumption that the critical rate is nearly independent of drainage radius. Joshi (1988) suggests the following relationships for determining the critical oil flow rate in horizontal wells. Sobocinski and Cornelius (1965) used a two-dimensional finite difference simulator to determine the behavior of a water cone under various conditions. Ozkan and Raghavan (1988) proposed a theoretical correlation for calculating time to breakthrough in a bottom-water-drive reservoir. Papatzacos et al. (1989) proposed a methodology that is based on semi-analytical solutions for time development of a gas or water cone and simultaneous gas and water cones in an anisotropic, infinite reservoir with a horizontal well placed in the oil column.

479 Ibelegbu, Charles and Onyekonwu, Michael

)(528.758.22

owv

DBToBT K

tht

ρρφμ−

= (2)

Where; tBT= time to water breakthrough as expressed in days ρo= oil density, lb/ft3 ρw= water density, lb/ft3

Coning Phenomenon in Horizontal Wells

For reservoirs with gas cap and bottom water, coning will never occur if piston-like displacement is maintained between the oil and gas, and/or oil and water interfaces. However, a non piston-like displacement can occur as production progresses. In such situation, there is cresting particularly when the viscous forces are much higher than the gravity forces. Thus gas and water will make their way to the wellbore. Coning tendencies are inversely proportional to density difference and are directly proportional to the viscosity –Joshi (1990). The density difference between gas and oil is normally larger than the density difference between water and oil. Hence gas has less tendency to cone than water. However gas viscosity is much lower than the water viscosity, and therefore, for the same pressure drawdown in the given reservoir, the gas flow rate will be higher than the water flow rate. Thus, density and viscosity difference between water and gas tend to balance each other. Therefore to minimize gas and/ or water coning, a preferred perforated or completion interval is at the centre of the oil pay zone. Practical, many wells are however completed closer to the OWC than to the GOC.

One of the major causes of coning is large pressure drawdown. Thus to achieve a given production rate, one has to impose a large pressure drawdown in a low permeability reservoir than in a high permeability reservoir. However in naturally fractured reservoirs, especially those with vertical fractures, one can have severe coning in spite of high reservoir permeability. This happens with the fact that bottom water and top gas travel through high-permeability (vertical) fractures. This is very true in fractured reservoirs with low matrix permeability and large matrix blocks where water imbibition in the matrix is very slow (Joshi, 1990). The analysis may be made with respect to either gas or water. Let the original condition of reservoir fluids exist as shown schematically in Figure 2, water underlying oil and gas overlying oil. For the purposes of discussion, assume that a well is partially penetrating the formation so that the production interval is halfway between the fluid contacts. Production from the well would create pressure gradients that tend to lower the gas-oil contact and elevate the water-oil contact in the immediate vicinity of the well. Counterbalancing these flow gradients is the tendency of the gas to remain above the oil zone because of its lower density and of the water to remain below the oil zone because of its higher density. These counterbalancing forces tend to deform the gas-oil and water-oil contacts into a bell shape as shown schematically in Figure 3.

Figure 1: Bottom-water drive (water conning)

Water

Oil zone

Cone

Analysis of Cone Formation and Water Movement in Horizontal Wells 480

Figure 2: Original reservoir static condition.

Figure 3: Gas and water coning

Water

Gas

Oil

Y

Figure 4: Oil rate and GOR for well SUF48

0

500

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-------------- 3/31/2001 11/30/2001 7/31/2002 3/31/2003 11/30/2003 7/31/2004 3/31/2005 11/30/2005Date

oilra

te (b

/d)

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GOR (cf/bbl)

Oil Rate bbl/dGOR cf/bbl

481 Ibelegbu, Charles and Onyekonwu, Michael

Figure 5: Water-cut plot for well SUF48

0

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12/6/1999 4/19/2001 9/1/2002 1/14/2004 5/28/2005 10/10/2006

DATE

Wat

er-c

ut

Cone Formation in Horizontal Well

Calculating Cone Formation (Cone height, cone time and water movement) A new reliable way of estimating the cone height and time reached with its present oil-water contact (water movement) is by first calculating the bulk volume and the pore volume of the thin oil column. This can be easily done by the volumetric method of estimating in place fluids. There after using the principle of tank balance to match volume of fluid withdrawn from the formation through production to the original in place pore volume of the formation. This is analysed as function of time (production time, start-time of cone and duration). Calculation of Fluid Volumes Consider a reservoir which is initially filled with liquid oil. The oil volume in the reservoir (oil in place) is

OIP= V ø (1- Swc) res vol. Where V = the net bulk volume of the reservoir rock

ø= the porosity, or volume fraction of the rock which is porous and Swc = the connate or irreducible water saturation and is expressed as a fraction of the pore

volume. The product Vø is called the pore volume (PV) and is the total volume in the reservoir which can be occupied by fluids. Similarly, the product Vø (1−Swc) is called the hydrocarbon pore volume (HCPV) and is the total reservoir volume which can be filled with hydrocarbons either oil, gas or both. Thus the newly proposed step is detailed below;

Step in computing cone height, cone time and water movement 1. An area- depth graph is made from the structural map 2. Compute the bulk volume (BV)of the height above original OWC 3. Compute the pore volume (PV) of this column (BV*ø) 4. Base on the PV computed; match your last cumulative production Np to the PV. The difference in

depth gives us the column displaced by the water (water movement). 5. The established depth difference is our present oil-water contact (POWC) 6. Make a table of cone height and match each Npi and Npi+1 with the PVi and PVi+1 as a function of

time (cone time). 7. Calculate delta t (Δt): Δti = ti – ti-1 8. Cone time = producing time – delta t (Δt).

Analysis of Cone Formation and Water Movement in Horizontal Wells 482

Example Calculation # 1 Well Review 1 (well SUF48)

Well came on stream in August, 2001 in D6.4 sand at a rate 2568 bopd on bean 44/64”, THP 300psi, GOR 300 scf/bbl BSW 0%.

In Sep. 2000: bean changed to 52/64”, rate: 3059 bopd. THP 275 psi, GOR 310 scf/bbl BSW 0. While in Aug. 2001: peak production 3714 bopd, bean 64” after that it declined. Again in Sep. 2001: an Acid job was carried out in this well but there was no improvement on production.

July 2003: Water breakthrough was observed and water-cut has steadily increased to about 50%. July 2006: Production rate was 874 bopd net, GOR = 424 scf/stb; FTHP = 368 psi BSW = 50% through bean 64/64”.Cum. Prod.3.75MMbbls. Cone Formation in Well SUF48

Using steps as detailed in earlier, the area-depth-bulk volume map (figure 6) was generated and pore volume (PV) calculated. The withdrawal (Np) was matched with corresponding PV and the water movement calculated from it original OWC. Below is the cone height, cone time and water movement calculated in table 1, figure 6 & 7.

Figure 6: CBV/area vs depth graph for well SUF48

483 Ibelegbu, Charles and Onyekonwu, Michael

Figure 7: Cone formation estimation (cone time, cone height) well SUF48

cone time adjusted

0

200

400

600

800

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1200

0 20 40 60 80 100 120

cone height (ft)

cone

tim

e (d

ays)

Table 1: Cone formation for well SUF48

Cone Height produce time Delta t cone time cone time adjusted 0 15 15 0 0 5 30 30 0 0

10 60 21 39 39 15 81 10 71 71 20 91 9 82 82 25 100 21 79 79 30 121 31 90 90 35 152 30 122 122 40 182 28 154 154 45 210 31 179 179 50 241 30 211 211 55 271 61 210 210 60 332 92 240 240 65 424 123 301 301 70 547 181 366 366 75 728 184 544 544 80 912 150 762 762 85 1062 215 847 847 90 1277 335 942 942 95 1612 334 1278 1025

100 1946 182 1764 1031 105 2128 1035 1035 1035

Example Calculation # 2 Well Review 2 (well SUF25)

Well started production from the E4.2 sand 1976 and stopped production in Jan. 1997: with an average production of 73 bopd, Cum. Oil 1266 Mbbl, Wcut 45%. Finally the interval was isolated by putting plug in nipple in 1999.

This well also produced from the E4.0 sand. This interval produced only 0.17 MMbbls before quitting on low FTHP and 52% BSW.

Below is the cone height, cone time and water movement calculated in table 2, figure 10 & 11.

Analysis of Cone Formation and Water Movement in Horizontal Wells 484

Figure 8: Oil rate and GOR for well SUF25

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4/30/1976 6/30/1980 8/31/1984 10/31/1988 12/31/1992

Date

oil r

ate

(b/d

)

0

500

1000

1500

2000

2500

3000

3500

GO

R (c

f/d)

oil rateGOR

Figure 9: Water-cut plot for well SUF25

w ater-cut

0

0.1

0.2

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1/0/1900 2/19/1900 4/9/1900 5/29/1900 7/18/1900 9/6/1900 10/26/1900

date

wat

er-c

ut

485 Ibelegbu, Charles and Onyekonwu, Michael

Figure 10: CBV/area vs. depth graph for well SUF25

Figure 11: Cone formation estimation (cone time, cone height) well SUF25

cone time

0

200

400

600

800

1000

1200

0 20 40 60 80 100 120 140 160

Cone height (ft)

Cone

tim

e (d

ays)

Analysis of Cone Formation and Water Movement in Horizontal Wells 486

Table 2: Cone Formation of SUF25

cone height produce time Delta t cone time cone time adjusted 0 0 0 0 0 5 0 7 -7 0

10 7 3 4 0 15 10 10 0 0 20 20 10 10 10 25 30 10 20 20 30 40 10 30 30 35 50 12 38 38 40 62 31 31 31 45 93 31 62 62 50 124 31 93 93 55 155 31 124 124 60 186 31 155 155 65 217 62 155 155 70 279 31 248 248 75 310 31 279 279 80 341 31 310 310 85 372 62 310 310 90 434 62 372 372 95 496 155 341 341

100 651 155 496 496 105 806 155 651 651 110 961 217 744 744 115 1178 279 899 899 120 1457 217 1240 1240 125 1674 403 1271 1271 130 2077 558 1519 1519 135 2635 806 1829 1829 140 3441 2356 1085 3441 145 5797 5797 0 1085

Discussion Knowledge of water cut and GOR trends in a reservoir is needed to ensure fair judgment of a depletion process in new and existing wells, and this judgment is the basic statistics that relates a well’s flow rate with its GOR and BS&W. Therefore, knowledge of the cone time, height the water movement with respect to the GOR and BS&W value attained in a well is critical toward remedial / adjustment well decisions.

The principle adapted in the cone formation analysis is that of the tank balance which simply relates the cone height reached to displacement of oil by water and the total oil produced to pore volume of the oil column. Therefore an area depth computation of cone shape (volume enclosed in a cone) would result to the volume of oil displaced, which when subtracted from the original oil in-place + oil produced (Np), gives you the present oil-water contact. For wells SUF48 and SUF25 with reservoir sand thick of 150ft & 220ft respectively, cone height reach is 105ft in 1035days and 145ft in 5797days. The Eclipse numerical model (figure 12) built also validated these results obtained. However it should be noted that cone height and time attained is dependant more on the production rate, the rock/ fluid properties plus the hysteresis of the system, rather than the reservoir thickness. Therefore correlation on the dependant variables is required to have detail process of the cone phenomenon. This study is limited to obtaining the cone time and height reached.

487 Ibelegbu, Charles and Onyekonwu, Michael

Figure 12: Varying Production rate: 0% water-cut (initial condition-2001)

Figure 13: Water coning: 50% water-cut (2006)

Conclusion The principle adapted in the cone formation analysis simply relates the cone height reached to displacement of oil by water and the total oil produced to pore volume of the oil column. This helps to trace the water movement in the reservoir and thus provides the present oil water contact at anytime. Recommendation The study principle adapted in the cone formation analysis which relates the cone height reached to displacement of oil by water and the total oil produced to pore volume of the oil column is recommended for use as it also generates the present oil water contact at any time.

Analysis of Cone Formation and Water Movement in Horizontal Wells 488

References [1] Chaperson, I., Oct. 5–8, (1986) “Theoretical Study of Coning Toward Horizontal and Vertical

Wells in Anisotrophic Formations: Subcritical and Critical Rates,” SPE Paper 15377, SPE 61st Annual Fall Meeting, New Orleans, LA.

[2] Efros, D. A., (1963), “Study of Multiphase Flows in Porous Media” (in Russian), Gastoptexizdat, Leningrad.

[3] Joshi, S. D., (June 1988) “Augmentation of Well Productivity Using Slant and Horizontal Wells,” J. of Petroleum Technology, pp. 729–739.

[4] Meyer, H. I., and Garder, A. O., (Nov. 1954) “Mechanics of Two Immiscible Fluids in Porous Media,” J. Applied Phys., No. 11, p. 25.

[5] Muskat, M. and Wyckoff, R.D. (1935): “An Approximate theory of Water-coning in Oil Production”, Trans. AIME, pp 144-163.

[6] Ozkan, E., and Raghavan, R., (Nov. 2–4, 1988) “Performance of Horizontal Wells Subject to Bottom Water Drive,” SPE Paper 18545, presented at the SPE Eastern

[7] Papatzacos, P., Herring, T. U., Martinsen, R., and Skjaeveland, S. M., (Oct. [8] 8–11, 1989) “Cone Breakthrough Time for Horizontal Wells,” SPE Paper 19822, presented at

the 64th SPE Annual Conference and Exhibition, San Antonio, TX, [9] Sobocinski, D. P., and Cornelius, A. J., (May 1965) “A Correlation for Predicting Water

Coning Time,” JPT, pp. 594–600.