Analysis of Cone Formation and Water Movement in Horizontal Wells
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: [email protected] 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 inplace + 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
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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 2 2 (1) qc= π k o g (p w − p o ) ( h oi − h p ) ⎛r ⎞ μ o ln ⎜ e ⎟ ⎝ rw ⎠ 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.
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Ibelegbu, Charles and Onyekonwu, Michael
t BT =
22.758.528hφμo t DBT K v (ρ w − ρo )
(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)
Oil zone Cone
Water
Analysis of Cone Formation and Water Movement in Horizontal Wells
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Figure 2: Original reservoir static condition.
Figure 3: Gas and water coning
Y Gas
Oil
Water
Figure 4: Oil rate and GOR for well SUF48 Oil Rate bbl/d
oilrate (b/d)
GOR cf/bbl 4000
1600
3500
1400
3000
1200
2500
1000
2000
800
1500
600
1000
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0 --------------
0 3/31/2001
11/30/2001
7/31/2002
3/31/2003 11/30/2003 Date
7/31/2004
3/31/2005
11/30/2005
GOR (cf/bbl)
481
Ibelegbu, Charles and Onyekonwu, Michael Figure 5: Water-cut plot for well SUF48 0.5 0.45 0.4 0.35
Water-cut
0.3 0.25 0.2 0.15 0.1 0.05 0 12/6/1999
4/19/2001
9/1/2002
1/14/2004
5/28/2005
10/10/2006
DATE
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
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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
1200
1000
conetime(days)
800
600
400
200
0 0
20
40
60
80
100
120
cone he ight (ft)
Table 1:
Cone formation for well SUF48
Cone Height 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105
produce time 15 30 60 81 91 100 121 152 182 210 241 271 332 424 547 728 912 1062 1277 1612 1946 2128
Delta t 15 30 21 10 9 21 31 30 28 31 30 61 92 123 181 184 150 215 335 334 182 1035
cone time 0 0 39 71 82 79 90 122 154 179 211 210 240 301 366 544 762 847 942 1278 1764 1035
cone time adjusted 0 0 39 71 82 79 90 122 154 179 211 210 240 301 366 544 762 847 942 1025 1031 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.
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Figure 8: Oil rate and GOR for well SUF25 1000
3500 oil rate
900
GOR
3000
800
oil rate (b/d)
600
2000
500 1500
400 300
GOR (cf/d)
2500
700
1000
200 500 100 0 4/30/1976
0 6/30/1980
8/31/1984
10/31/1988
12/31/1992
Date
Figure 9: Water-cut plot for well SUF25 w ater-cut
1 0.9 0.8 0.7
water-cut
0.6 0.5 0.4 0.3 0.2 0.1 0 1/0/1900
2/19/1900
4/9/1900
5/29/1900 date
7/18/1900
9/6/1900
10/26/1900
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 1200
Cone time (days)
1000
800
600
400
200
0 0
20
40
60
80 Cone height (ft)
100
120
140
160
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Table 2: Cone Formation of SUF25 cone height 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145
produce time 0 0 7 10 20 30 40 50 62 93 124 155 186 217 279 310 341 372 434 496 651 806 961 1178 1457 1674 2077 2635 3441 5797
Delta t 0 7 3 10 10 10 10 12 31 31 31 31 31 62 31 31 31 62 62 155 155 155 217 279 217 403 558 806 2356 5797
cone time 0 -7 4 0 10 20 30 38 31 62 93 124 155 155 248 279 310 310 372 341 496 651 744 899 1240 1271 1519 1829 1085 0
cone time adjusted 0 0 0 0 10 20 30 38 31 62 93 124 155 155 248 279 310 310 372 341 496 651 744 899 1240 1271 1519 1829 3441 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
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References [1] [2] [3] [4] [5] [6] [7] [8] [9]
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. Efros, D. A., (1963), “Study of Multiphase Flows in Porous Media” (in Russian), Gastoptexizdat, Leningrad. Joshi, S. D., (June 1988) “Augmentation of Well Productivity Using Slant and Horizontal Wells,” J. of Petroleum Technology, pp. 729–739. Meyer, H. I., and Garder, A. O., (Nov. 1954) “Mechanics of Two Immiscible Fluids in Porous Media,” J. Applied Phys., No. 11, p. 25. Muskat, M. and Wyckoff, R.D. (1935): “An Approximate theory of Water-coning in Oil Production”, Trans. AIME, pp 144-163. 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 Papatzacos, P., Herring, T. U., Martinsen, R., and Skjaeveland, S. M., (Oct. 8–11, 1989) “Cone Breakthrough Time for Horizontal Wells,” SPE Paper 19822, presented at the 64th SPE Annual Conference and Exhibition, San Antonio, TX, Sobocinski, D. P., and Cornelius, A. J., (May 1965) “A Correlation for Predicting Water Coning Time,” JPT, pp. 594–600.
Analysis of Cone Formation and Water Movement in Horizontal Wells Ibelegbu, Charles Schlumberger Oilfield Services North Africa, Algiers, Algeria E-mail: [email protected] 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 inplace + 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 2 2 (1) qc= π k o g (p w − p o ) ( h oi − h p ) ⎛r ⎞ μ o ln ⎜ e ⎟ ⎝ rw ⎠ 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
t BT =
22.758.528hφμo t DBT K v (ρ w − ρo )
(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)
Oil zone Cone
Water
Analysis of Cone Formation and Water Movement in Horizontal Wells
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Figure 2: Original reservoir static condition.
Figure 3: Gas and water coning
Y Gas
Oil
Water
Figure 4: Oil rate and GOR for well SUF48 Oil Rate bbl/d
oilrate (b/d)
GOR cf/bbl 4000
1600
3500
1400
3000
1200
2500
1000
2000
800
1500
600
1000
400
500
200
0 --------------
0 3/31/2001
11/30/2001
7/31/2002
3/31/2003 11/30/2003 Date
7/31/2004
3/31/2005
11/30/2005
GOR (cf/bbl)
481
Ibelegbu, Charles and Onyekonwu, Michael Figure 5: Water-cut plot for well SUF48 0.5 0.45 0.4 0.35
Water-cut
0.3 0.25 0.2 0.15 0.1 0.05 0 12/6/1999
4/19/2001
9/1/2002
1/14/2004
5/28/2005
10/10/2006
DATE
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).
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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
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Ibelegbu, Charles and Onyekonwu, Michael Figure 7: Cone formation estimation (cone time, cone height) well SUF48 cone time adjusted
1200
1000
conetime(days)
800
600
400
200
0 0
20
40
60
80
100
120
cone he ight (ft)
Table 1:
Cone formation for well SUF48
Cone Height 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105
produce time 15 30 60 81 91 100 121 152 182 210 241 271 332 424 547 728 912 1062 1277 1612 1946 2128
Delta t 15 30 21 10 9 21 31 30 28 31 30 61 92 123 181 184 150 215 335 334 182 1035
cone time 0 0 39 71 82 79 90 122 154 179 211 210 240 301 366 544 762 847 942 1278 1764 1035
cone time adjusted 0 0 39 71 82 79 90 122 154 179 211 210 240 301 366 544 762 847 942 1025 1031 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.
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Figure 8: Oil rate and GOR for well SUF25 1000
3500 oil rate
900
GOR
3000
800
oil rate (b/d)
600
2000
500 1500
400 300
GOR (cf/d)
2500
700
1000
200 500 100 0 4/30/1976
0 6/30/1980
8/31/1984
10/31/1988
12/31/1992
Date
Figure 9: Water-cut plot for well SUF25 w ater-cut
1 0.9 0.8 0.7
water-cut
0.6 0.5 0.4 0.3 0.2 0.1 0 1/0/1900
2/19/1900
4/9/1900
5/29/1900 date
7/18/1900
9/6/1900
10/26/1900
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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 1200
Cone time (days)
1000
800
600
400
200
0 0
20
40
60
80 Cone height (ft)
100
120
140
160
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Table 2: Cone Formation of SUF25 cone height 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145
produce time 0 0 7 10 20 30 40 50 62 93 124 155 186 217 279 310 341 372 434 496 651 806 961 1178 1457 1674 2077 2635 3441 5797
Delta t 0 7 3 10 10 10 10 12 31 31 31 31 31 62 31 31 31 62 62 155 155 155 217 279 217 403 558 806 2356 5797
cone time 0 -7 4 0 10 20 30 38 31 62 93 124 155 155 248 279 310 310 372 341 496 651 744 899 1240 1271 1519 1829 1085 0
cone time adjusted 0 0 0 0 10 20 30 38 31 62 93 124 155 155 248 279 310 310 372 341 496 651 744 899 1240 1271 1519 1829 3441 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.
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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.
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References [1] [2] [3] [4] [5] [6] [7] [8] [9]
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. Efros, D. A., (1963), “Study of Multiphase Flows in Porous Media” (in Russian), Gastoptexizdat, Leningrad. Joshi, S. D., (June 1988) “Augmentation of Well Productivity Using Slant and Horizontal Wells,” J. of Petroleum Technology, pp. 729–739. Meyer, H. I., and Garder, A. O., (Nov. 1954) “Mechanics of Two Immiscible Fluids in Porous Media,” J. Applied Phys., No. 11, p. 25. Muskat, M. and Wyckoff, R.D. (1935): “An Approximate theory of Water-coning in Oil Production”, Trans. AIME, pp 144-163. 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 Papatzacos, P., Herring, T. U., Martinsen, R., and Skjaeveland, S. M., (Oct. 8–11, 1989) “Cone Breakthrough Time for Horizontal Wells,” SPE Paper 19822, presented at the 64th SPE Annual Conference and Exhibition, San Antonio, TX, Sobocinski, D. P., and Cornelius, A. J., (May 1965) “A Correlation for Predicting Water Coning Time,” JPT, pp. 594–600.
