SPE 152545 Water Coning in Naturally Fractured Carbonate Heavy Oil Reservoir – A Simulation Study E. Pérez-Martínez, F. Rodríguez-de la Garza, PEMEX E&P; F. Samaniego-Verduzco, UNAM Copyright 2012, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Latin American and Caribbean Petroleum Engineering Conference held in Mexico City, Mexico, 16–18 April 2012. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright. Abstract During production in a naturally fractured reservoir with natural water influx, under certain flow conditions an imbalance can be generated between gravity and viscous forces within the fracture system. This phenomenon is characterized by the gradual growth of a cone of water in the vertical and radial directions. When the radial growth of the cone base at the oil-water contact reaches the drainage radius, the cone of water reaches its maximum height. After this, the oil-water interface advances without suffering deformation in the pseudo stationary regime. However, when this interface is a short distance from the bottom of the completion interval, the movement of the oil-water interface accelerates and water flows into the well. This phenomenon may shorten the well’s life due to the complexity of oil-water separation offshore and resulting increases in operating costs. In many of the Cretaceous formations of the offshore Mexico Bay of Campeche, oil recovery is limited at the top by the presence of a gas-oil contact and at the bottom by an oil-water contact. To recover the remaining hydrocarbon reservoirs it is necessary to: (1) define the optimal operating range which should be established for each well to delay water and gas breakthrough and (2) to schedule the necessary infrastructure to handle high production rates of water and gas as the field matures. The objectives of this work are to: Model in detail the water coning in the porous fracture system using a fine radial grid, with one meter thick layers concentric around the well, and 2 inches thick layers in the annulus, with and without cement. Obtain an equation to determine the maximum height of water coning, the time it takes to form the cone, and the well shut-in time necessary to undo or “heal” the water cone. Introduction In oil fields with bottom water, water cuts typically increase as time passes and the fields mature. When these fields don’t have adequate facilities to separate, treat and manage formation water production, mechanical and/or chemicals treatments are applied to reduce the water content in the produced oil and avoid penalties for its sale. Therefore, if the phenomenon of water coning is not understood, this can translate into huge economic losses, by having to oversize the infrastructure for water management or in the worst case scenario, when water management infrastructure is undersized or non-existent, prematurely abandon wells with the consequent loss of significant amounts of remaining oil and economic value. The main producing formations of the fields in the Bay of Campeche are Cretaceous and Kimmeridgian Upper Jurassic (KUJ), characterized by considerable formation thickness and/or structural relief. The Breccia Tertiary Paleocene Upper Cretaceous (referred to as the BTPKS from the nomenclature in Spanish), consists of densely fractured carbonate rocks of very high permeability. This causes severe problems during cementing of the last casing string, since, when circulating cement to bond the formation and casing, almost all the cement is lost in the formation, resulting in an empty space in the annulus space between the producing formation and the casing. This empty space results in a channel where the fluids can flow without any restrictions, exacerbating water coning phenomena. 2 SPE 152545 The coning and channeling behavior of fluids in naturally fractured reservoirs depends upon petrophysical and fluid properties, the geometry and mechanical condition of the wells and the production conditions under which they operate. The diversity of the types of oil found in the Bay of Campeche’s reservoirs imposes an additional challenge, because, as the quality of oil decreases, oil viscosity increases and the oil density also increases, to approximately the water density, creating conditions more conducive for water coning. The objectives of this work are to: - Model in detail the water coning in the porous fracture system using a fine coning radial grid, with one meter thick layers concentric around the well, and 2 inches thick layers in the annulus, with and without cement. - Develop an equation to determine the maximum height of water coning, the time it takes to form the cone, and the well shut-in time necessary to undo or “heal” the water cone. Water coning “Water coning”6 is the term given to the water influx mechanism underlying oil producing wells. Coning of water is usually associated with high oil production rates and develops only under certain flow conditions. In a broader sense the phenomenon of water coning is one of the most complex problems in reservoir engineering. Under typical static reservoir conditions, the water zone consists of a layer below the oil zone, because oil is less dense than water; then the start of production produces a pressure gradient which results in an imbalance between gravity and viscous forces1. This phenomenon is characterized by the gradual growth of a cone of water in the vertical and radial directions. When the radial growth of the cone base (oil-water contact) reaches the drainage radius, the cone of water reaches its maximum height, then the oil-water interface envelope advances without suffering deformation in the pseudo stationary regime2 given maintaining a constant oil production rate and constant pressure throughout the aquifer. When this interface is a short distance from the producing interval, movement accelerates and water breaks through into the wellbore and is produced at the platform. Most of the offshore oil fields of Mexico lack adequate facilities to separate, treat, and manage produced water; therefore, when the water cut increases to approximately 5%, wells that produce the highest percentage of water must be shut-in to reduce water content and avoid penalties for its sale. Because of this, it is important to model water coning and optimize production from the wells, producing the maximum amount permissible while avoiding water breakthrough into the well. Development There are several parameters that influence water coning, some can be controlled and others cannot. This paper analyzes the sensitivity of the parameters that have the greatest impact upon the behavior of the production wells, such as oil production rate, qo, fracture permeability, kf , oil viscosity, µo , gravity drainage, oil formation volume factor, Bo , drainage radius, re, matrix-fracture porosity partitioning and distance between the completion interval and the oil-water contact (OWC). An additional parameter that adds another level of complexity to the phenomenon of water coning in the Gulf of Mexico offshore fields is that the largest producer of oil is the Upper Cretaceous (UC) formation. This formation is composed of densely fractured carbonate rocks of very high permeability, which results in severe problems during cementing the last casing. Often most of the cement is lost to the producing formation, causing an empty space in the annulus between the producing formation and the casing. This allows fluids to flow upwards from the OWC toward the completion interval without any restriction, increasing the water coning problems. To analyze the effect of these parameters upon water coning, we constructed a coning radial model of an individual well drainage3 volume using the numerical simulator Eclipse-100, with the following characteristics: - - Radial model with 30 cells in direction r and 207 layers in Z (Fig. 1). Drainage radius of 400 m. The first 200 layers of the model are 1 m thick, representing the oil band. The 7 underlying layers are saturated with water and the total thickness of this zone is 300 m. Layers 201, 202, 203, 204, 205, 206 and 207 are assigned the following thicknesses: 1.5, 3.0, 6.1, 12.2, 24.4, 61.0 and 191.8 m. o Porosity of the matrix-fracture system: The fracture porosity in the simulator represents the geological fractures and vuggy interconnected pores. The matrix in the simulator represents the primary porosity and includes microfractures. The total porosity of the rock is 8.55%. Partitioning of the matrix – fracture porosity: 0% -100%, 50% - 50% and 85% - 15%. Properties of the matrix-fracture system: SPE 152545 - 3 o Matrix block height = 8 ft. o Sigma = 0.17. o kHm = 10 md. o kVm = 1 md. o kHf = 0.5 - 10 Darcys. o kv = 0.5 - 10 Darcys. o cm = 4 x 10-6 psi-1. -6 o cf = 40 x 10 psi-1. Top of the producing formation = 2835 vmss. Original oil-water contact (OOWC) = 3035 vmss. Thickness of the perforated interval = 15 m (2951-2965 vmss). Casing diameter OD = = 7 5/8 inches. Annular space between producing formation and casing = 2 inches. o Annular space with or without cement, figs. 2 and 3. PVT properties of fluids from the Ku field. Petrophysical properties from the Ku field. Oil production rate The phenomenon of water coning involves several parameters4 and the oil production rate parameter has the most control over this phenomenon. In homogeneous reservoirs, producing at rates below the critical production rate can prevent water coning5. However, in naturally fractured reservoirs with high permeability and massive oil bearing thickness, this may not be economic in practice due to low critical production rates. If oil wells are completed away from the OWC, then they can produce high flow rates, by constantly monitoring the progress of the OWC. When the OWC rises to a certain distance from the producing interval, water breakthrough can be forestalled by doing one the following: (1) decrease the choke size (thereby reducing oil production) to reduce the imbalance of gravitational and viscous forces or (2) if the remaining oil band thickness is significant above the top of the perforated interval, seal the lower interval and re-perforate in a higher interval. As pressure drops in the aquifer due to the production of oil, a cone of water forms beneath the well, gradually growing outwards to the drainage radius. At this time the water cone growth stops and all the points that define the three-dimensional surface formed by the oil-water interface will move up vertically at the same speed in a pseudo stationary regime. When the oil-water interface is close to the perforated interval, movement accelerates and immediately the water breaks through. The height of the cone of water (hwc) is measured at the time of water breakthrough, taking as reference the depth of the base of the perforated interval and the depth of the oil-water interface in the drainage radius, as illustrated in Figure 4. Figure 5 graphs the oil production rate at reservoir conditions (qoBo) in the abscissa axis and hwc in the ordinate axis on a log-log plot and exhibits a linear behavior of hwc, where higher oil production rates result in a larger water cone height. Fracture permeability Fracture permeability is the most important uncontrolled parameter in the phenomenon of water coning to analyze the effect upon coning, different oil production rates were simulated, and hwc versus qoBo was evaluated for the following values of kf : 10, 5, 2, 1, 0.7 and 0.5 Darcys. All other parameter of the rock and fluid were kept constant in the simulations. In these simulations the water and oil viscosities are 0.242 and 2 cp, respectively, and the water and oil density at reservoir conditions are 1.00 and 0.7996 g/cm3, respectively. Table 1 shows the results obtained with the radial model, highlighting the values of hwc achieved at different oil production rates. From the analysis obtained for each value of kf (Table 1), a family of curves was developed, characterized by higher values of kf resulting in lower values of hwc and vice versa, as illustrated in Fig. 5. For a higher kf, the horizontal distribution of water is higher due to gravity force and consequently the height of the cone is smaller, resulting in a more stable oil-water interface. Figure 5 shows that the curves of kf = 10, 5 and 2 Darcys have a log linear behavior, while, for lower permeability curves (kf = 1, 0.7 and 0.5 Darcys) high production rates tend to be horizontal converging to a value approximately hwc = 100 m. This value is not a coincidence, since it is the distance between the OOWC and the top of producing interval. Reducing kf increases the pressure drawdown, causing further growth of the water cone until the water cone reaches the producing interval and water breakthrough occurs. 4 SPE 152545 In other words, if the producing interval is located farther from the OOWC, the water cone continue to grow vertically and horizontally until the base of it reaches the drainage radius (outer boundary); then the whole water-oil interface will move upward at the same rate in a pseudo steady state regimen. The above is modeled by modifying the depth of the producing interval, 60 additional meters away (from 2935-2950 vmss to 2875-2890 vmss) OOWC, Fig. 6; and repeating the simulations for cases shaded in Table 1. Table 1. Results of the simulation model, shaded scenarios are discarded because the water cone is not fully developed. kf (Darcys) 10 10 10 10 10 5 5 5 5 5 2 2 2 2 2 1 1 1 1 1 0.7 0.7 0.7 0.7 0.7 0.5 0.5 0.5 0.5 0.5 μo (cp) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 k f μo (Darcy/cp) 5 5 5 5 5 2.5 2.5 2.5 2.5 2.5 1 1 1 1 1 1 0.5 0.5 0.5 0.5 0.35 0.35 0.35 0.35 0.35 0.25 0.25 0.25 0.25 0.25 qo (MSTB/D) 20 10 5 2 1 20 10 5 2 1 20 10 5 2 1 20 10 5 2 1 20 10 5 2 1 20 10 5 2 1 Bo (RB/STB) 1.200 1.204 1.206 1.209 1.212 1.194 1.200 1.204 1.206 1.209 1.176 1.190 1.198 1.204 1.204 1.256 1.176 1.187 1.193 1.201 1.256 1.162 1.172 1.194 1.201 1.256 1.146 1.174 1.192 1.200 qo Bo (MRB/D) 23.999 12.039 6.031 2.418 1.212 23.871 12.001 6.019 2.412 1.209 23.511 11.904 5.991 2.408 1.204 25.123 11.756 5.934 2.386 1.201 25.123 11.617 5.859 2.389 1.201 25.123 11.458 5.870 2.384 1.200 h wc (m) 41.5 29.9 21.1 13.9 10.0 57.8 41.6 29.8 19.0 13.9 88.1 62.3 46.3 29.9 21.4 99.9 88.1 62.2 41.7 29.9 99.9 97.0 72.0 49.4 35.6 99.9 97.6 88.2 57.8 41.7 Table 2 shows the results for the furthest interval from the OWC, and Fig. 7 shows a comparison of hwc in both intervals. Increasing the distance from the producing interval with respect the OWC, increases the height hwc, allowing for a fuller water cone, so its curve exhibits linear behavior for the hwc versus oil production relationship. Table 2. Model results of the second perforated interval. kf (Darcys) 1 1 1 1 1 0.7 0.7 0.7 0.7 0.7 0.5 0.5 0.5 0.5 μo (cp) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 k f μo (Darcy/cp) 0.5 0.5 0.5 0.5 0.5 0.35 0.35 0.35 0.35 0.35 0.25 0.25 0.25 0.25 qo (MSTB/D) 20 10 5 2 1 20 10 5 2 1 10 5 2 1 Bo (RB/STB) 1.131 1.176 1.187 1.193 1.201 1.123 1.162 1.172 1.194 1.201 1.146 1.174 1.192 1.200 qo Bo (MRB/D) 22.622 11.756 5.934 2.386 1.201 22.459 11.617 5.859 2.389 1.201 11.457 5.870 2.384 1.200 h wc (m) 132.6 88.1 62.2 41.7 29.9 145.4 97.0 70.9 49.4 35.6 133.5 88.2 57.8 41.7 SPE 152545 5 Partition matrix-fracture porosity To analyze the effect of the ratio of the pore volume associated with the matrix with respect to the pore volume associated with the system of fractures, three numerical models were built with matrix-fracture porosity (primary-secondary) relationships as follows: 1. 2. 3. φf = φtotal, φf = 0.50φtotal and φm = 0.50φtotal, φf = 0.15φtotal and φm = 0.85φtotal. Previous models analyzed the following cases: kf = 1 Darcy and µ0 = 2 cp kf = 5 Darcy and µ0 = 2 and 20 cp kf = 10 Darcy and µ0 = 2 and 20 cp This shows that there is little variation in results obtained by the three models, retaining the linear behavior of the maximum height of water coning versus the production rate in a log-log plot. The curves with the highest value of ratio kf /µo have large differences and the differences decrease as the kf /µo ratios decrease, as shown in Fig.8. Table 3 Results of the double porosity model, φf = 0.15φtotal and φm = 0.85φtotal. kf (Darcys) 1 1 1 1 1 5 5 5 5 5 10 10 10 10 10 5 5 5 10 10 10 10 μo (cp) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 20 20 20 20 20 20 20 k f μo (Darcy/cp) 0.5 0.5 0.5 0.5 0.5 2.5 2.5 2.5 2.5 2.5 5 5 5 5 5 2.5 2.5 2.5 5 5 5 5 qo (MSTB/D) 20 10 5 2 1 20 10 5 2 1 20 10 5 2 1 5 2 1 10 5 2 1 Bo (RB/STB) 1.156 1.186 1.201 1.213 1.218 1.205 1.213 1.217 1.220 1.221 1.211 1.214 1.217 1.219 1.220 1.147 1.187 1.194 1.169 1.184 1.193 1.199 qo Bo (MRB/D) 23.122 11.860 6.004 2.427 1.218 24.101 12.134 6.086 2.440 1.221 24.218 12.139 6.086 2.439 1.220 5.737 2.373 1.194 11.689 5.918 2.386 1.199 h wc (m) 103 74 54 34 24 48 34 24 16 11 34 24 17 11 8 106 69 46 107 77 48 30 Oil Viscosity To analyze the effect of oil viscosity upon water coning phenomena, simulations were performed at different oil production rates, varying the oil viscosity at 5, 10, 20 and 40 cp. Figs. 9, 10, 11 and 12 presents the results obtained, showing the same linear behavior (logarithmic scales) hwc versus kf , and it is observed that the higher oil viscosity, the higher water cone. Oil Density To analyze the effect of oil density simulations were performed varying the oil density and oil viscosity considering a fractured porous media with a value of kf = 10 Darcys. The oil density at reservoir conditions was varied from 0.63 to 0.9 g/cm3, so that each curve in Fig. 13 represents the behavior of the water coning for constant values of oil viscosity and oil density, where the blue curves represent an oil viscosity 2 cp, observing that the higher oil density results in greater water coning. This effect is shown in the red and green curves where the oil viscosities are 10 and 20 cp, respectively. 6 SPE 152545 Drainage Radius To investigate the effect of the drainage radius over a range 120 to 4,000 m, simulations were conducted for a fractured porous media with kf = 10 Darcys, oil viscosity = 2 cp and oil density = 0.7996 g/cm3 at reservoir conditions and an oil production rate, qo = 10,000 STB/D. The behavior of the height of the water cone versus radial distance to the no-flow outer boundary is shown in Fig. 14. There is a greater increase in the water coning at distances close to the well. As the drainage radius increases, the vertical height between the cone oil-water interface and the OOWC decrease, because the depression caused by disturbance of the well production is also attenuated according with the increment of the drained volume. Annular Space (between the producing formation and casing) with poor cement To evaluate the phenomenon of water coning in poorly cemented wells, where the annular space between the casing and the producing formation is without cement and behaves as a channel without flow restrictions, which magnifies the water coning, Fig. 2. This feature is modeled in the simulation study with cells of 2 inches thick adjacent to the well, with a porosity of 100% and kf = 100 Darcys. The analysis of parameters affecting water coning with a poorly cemented well were conducted in a similar fashion to that carried out with the flow model with a good cemented well, discussed previously. The results of the hwc from a poorly cemented well compared to that for a good cemented well, are very similar, exhibiting the same linear log-log plot behavior, hwc versus qoBo. In the poorly cemented well model the hwc was slightly higher than that obtained from a good cemented well model, as illustrated in Figs. 15, 16, 17 and 18; the hwc difference is more evident for low kf / µo and high production rates. Because the behavior of the height of the water cone is linear with respect to oil production rate for a given kf / µo, when is plotted on logarithmic scales, then hwc be adjusted very precisely to a power equation as follows: hwc = a ( qo Bo ) b , ............................................................................................................................................(1) Obtaining correlations to determine the maximum water cone height, hwc Adjusting to a power equation the coefficient “a” in the ratio kf / µo, all the curves obtained with the good cemented well model yields the following relationship: a = 19.211 ( μ o k f ) 0.5 , ….........................................................................................................................................(2) While “b” tends to a value of 0.5, by substituting Eq. 2 and “b” in Eq. 1, 0.5 ⎛q B μ ⎞ hwc = 19.211⎜ o o o ⎟ ⎜ kf ⎟ ⎝ ⎠ , .......................................................................................................................................(3) Considering only the gravitational potential term of two immiscible liquids in contact, we have: Δγ wo = g ( ρ w − ρo ) ≈ ( ρ w − ρo ) 9.81 , ....................................................................................................................(4) Considering the term Ln(re / rw) and Eqs. 3 and 4 through a dimensional analysis, Eq. 3can be written: 0.5 ⎛ q B μ Ln ( re rw ) ⎞ hwc = 2.963 ⎜ o o o ⎟⎟ ⎜ k f Δγ wo ⎝ ⎠ , .......................................................................................................................(5) where Eq. 5 accurately reproduces the results obtained with the flow model of a well with good cement, and it is also dimensionally homogeneous, thus hwc has units of length. Performing a similar analysis to the results obtained with the poorly cemented well model yields the following equation: 0.5 ⎛ q B μ Ln ( re rw ) ⎞ hwc = 3.180 ⎜ o o o ⎟⎟ ⎜ k f Δγ wo ⎝ ⎠ , .......................................................................................................................(6) SPE 152545 7 By comparing Eqs. 5 and 6, which reproduce the results for poorly and completely cemented well models, a dimensionless factor for poor cementation, Fbc, can be obtained: 0.5 ⎛ q B μ Ln ( re rw ) ⎞ hwc = ( 2.963 + Fbc ) ⎜ o o o ⎟⎟ ⎜ k f Δγ wo ⎝ ⎠ , ...........................................................................................................(7) where: Fbc = 0.217 Fbc = 0 hwc kf re rw qoBo μo Δγwo ≈ ρw-ρo for poor cement or cementless in the annular space. for good quality of cement in the annular space. meter. Darcy. meter. meter. MRB/D. cp. Represents the potential of two no-miscible liquids in contact, gr/cm³. Thus the Eq. 7 takes the form of Eq. (5) when Fbc = 0, which determines the height of the cone in a good cemented well, and, for the poorly cemented well, Fbc = 0.217, and Eq. 7 takes the form of Eq. 6. In field units Eq. 7 is transformed to: 0.5 ⎛ q B μ Ln ( re rw ) ⎞ hwc = ( 9.721 + Fbc ) ⎜ o o o ⎟⎟ , ...........................................................................................................(8) ⎜ k Δ γ f wo ⎝ ⎠ Where: Fbc = 0.712 Fbc = 0 hwc kf re rw qoBo μo Δγwo ≈ ρw-ρo for poor cement or cementless in the annular space. for a good cemented well. ft. md. ft. ft. RB/D. cp. gr/cm³. Time for the formation of a water cone The time for formation of the cone, thwc, is determined by taking into account the time of production of each well, until the base of the cone reaches the drainage radius, resulting in curves similar to those obtained in determining the maximum height of the coning water, when plotting thwc versus qoBo, as shown in Figure 19. The curves obtained from thwc versus qoBo were fitted to power equations of the form of Eq. 1. From these equations coefficients “a” and “b”, can be estimated which correlated with the kf / µo, yielding the following correlation: ⎛ kf ⎞ thwc = 182.9 ⎜ ⎟ ⎝ μo ⎠ where, kf qoBo −0.26 ( qO BO ) −0.72 , ...............................................................................................................................(9) = = Fractured permeability, Oil production rate at reservoir conditions, Darcys. MRB/D. thwc = Time of formation of the water cone, days. µo = Oil viscosity, cp. 8 SPE 152545 Well’s shut-in time to reverse the water cone In the case of shutting in a well with high water production, it is required to have a tool to indicate the shut-in time for the well to “heal” or reverse the water cone. For this purpose, the curves were built by plotting the well’s shut-in time versus water cone height as a function of fractured permeability and oil viscosity. Figure 20 shows that, the higher the permeability, the shorter the wells shut-in time required to reverse the cone; as the fracture permeability decreases, the well’s shut-in time increases. In Figs. 20, 21, 22 and 23, as the oil viscosity increases, the well’s shut-in time increases. These results are consistent with the flow dynamics in porous media, since as kf / µo decreases, the porous media requires more time to equilibrate fluids based on the gravity force. Conclusions The main aim of this work has been the modeling of water coning in a naturally fractured porous medium with a fine radial grid around the well, with layers of 1 m thick in the reservoir, whereas the annulus, between the producing formation and casing, is modeled with layers of 2 inches thick. It was found that water coning occurs in fractured porous media with permeabilities up to 10 Darcys and that water coning occurs in both good and poorly cemented wells. A “poor cementing factor” was discussed, which is associated with an additional height of the water cone due to an uncemented the annulus between the producing formation and casing, where the annulus serves as a highly conductive channel which accelerates the flow of fluids from the aquifer to the wellbore. The second objective of this work was to obtain correlations to determine the maximum height of water coning considering good and poor cement (no cement in the annulus), The time for the development of the water cone and the well shut-in time to reverse the water cone. With the correlations obtained, the minimum safe distance between the oil-water contact and the producing interval for a specified free of water oil production rate can be easily determined. Or, for the reverse case, the critical oil production rate can be determined in order for the wells to produce free of water for a reasonable time period, for a specified distance between the oil-water contact and the producing interval. In a fractured porous medium, the water coning phenomenon is dominated by viscous and gravitational forces. Based on an analysis of the results of three dual-porosity models, it appears that the matrix-fracture partition ratio has little influence in determining the maximum height of water coning. Nomenclature Symbols Bo cf cm Fbc g hwc kf kHf kHm kVf kVm Np pi Sor Sw Swi qo re = = = = = = = = = = = = = = = = = = Formation (Oil) volume factor, Fracture compressibility, Matrix compressibility, Poor (bad) cementation factor, Acceleration of gravity, Maximum height of the water coning, Fractured permeability, Horizontal permeability of fracture, Horizontal permeability of matrix, Vertical permeability of fracture, Vertical permeability of matrix, Cumulative oil production, Starting pressure, Residual oil saturation, Water saturation, Initial water saturation, Oil flow rate, External radius, RB/STB. psi-1. psi-1. dimensionless. meter/seg2, ft/seg2. meter, ft. Darcy, md. Darcy, md. Darcy, md. Darcy, md. Darcy, md. million of STB/D. psi. fraction. fraction. fraction. MSTB/D, STB/D. meter, ft. SPE 152545 rw GOC OWC OOWC ρo ρw Δγwo μo 9 = = = = = = = = Wellbore radius, Gas-Oil contact, Oil-Water contact, Original Oil-Water contact, Oil density, Water density, Water-Oil density difference (=ρw-ρo) Viscosity, meter, ft. meter, ft. meter, ft. meter, ft. grm/cm3. grm/cm3. grm/cm3. cp. References 1 2 3 4 5 6 Al-Afaleg N.I. and Ershaghi I., 1993, (Coning Phenomena in Naturally Fractured Reservoirs), SPE 26083. Alikhan A. A., 1985, (State-of-the-art of Water Coning Modelling and Operation), SPE 13744. Hua-zhang C., 1983, (Numerical Simulation of Coning Behavior of a Single Well in a Naturally Fracture Reservoir), SPE 10566. Hφyland, L. A. and Papatzacos, P. 1989, (Critical Rate for Water Coning: Correlation and Analytical Solution), SPE Reservoir Engineering. Kuo M.C.T. and DesBrisay C.L., 1983, (A Simplified Method for Water Coning Predictions), SPE 12067. Muskat, M., 1981, pages 226-240, (Physical Principles of Oil Production), Springer. Figures. Figure 1. Radial simulation model of a well. Figure 2. Annulus without cement. Figure 3. Annulus with cement. 10 SPE 152545 Figure 4. Representation of the maximum height of the water coning, hwc. 100 hwc , m kf=10 kf=5 kf=2 kf=1 kf=07 kf=05 10 1 10 qoBo, MRB/D 100 Figure 5. hwc curves as a function of kf. Cima = =2835 Topde of la theformación formation 2835MVbnm vmss 0 0 0*00000 0*00000 0*00000 0*00000 0*00000 0*00000 0*00000 0*00000 0*00000 0*00000 0*00000 0*00000 0*00000 0*00000 000 0 0 0 000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Second perforated interval Segundo intervalo disparado 2875 – 2890 vmss 2875 – 2890 mVbnm 60 m Primer intervalo disparado First perforated interval 2935 – 2935- 2950 mVbnm. 2950 vmss CwoOOWC inicial = 3035 3035 mVbnm. vmss Figure 6. Depth of the two intervals analyzed 0 0 SPE 152545 11 hwc , m 1000 kf=0.5 Int. 1 kf=0.5 Int. 2 kf=0.7 Int. 1 kf=0.7 Int. 2 kf=1 Int. 1 kf=1 Int. 2 100 10 1 10 qoBo, MRB/D 100 Figure 7. hwc comparison of two perforated intervals at different depths. The average level of the first interval is located at 92.5 vm from the OWC (solid curves) and the second is located at 152.5 vm from the OWC (dashed curves). 1000 kf=1_VISo=2_ Fit kf=1_VISo=2_2P=100% kf=1_VISo=2_2P=50% kf=1_VISo=2_2P=15% kf=5_VISo=2_Fit kf=5_VISo=2_2P=100% kf=5_VISo=2_2P=50% kf=5_VISo=2_2P=15% kf=5_VISo=20_Fit kf=5_VISo=20_2P=100% kf=5_VISo=20_2P=50% kf=5_VISo=20_2P=15% kf=10_VISo=2_Fit kf=10_VISo=2_2P=100% kf=10_VISo=2_2P=50% kf=10_VISo=20_2P=15% kf=10_VISo=20_Fit kf=10_VISo=20_2P=100% kf=10_VISo=20_2P=50% kf=10_VISo=20_2Por=15% hwc , m 100 10 1 1 10 qoBo, MRB/D 100 Figure 8. hwc comparison of three models with different porosity ratio of matrix-fracture, φf = φtotal, φf = 0.5φtotal, and φf = 0.15 φtotal. 100 y2 y3 y4 hwc , m y1 y5 y1 (k f =0.5) = 60.762 x 0.51 y2 (kf=1) = 44.163 x 0.49 y3 (k f =2) = 31.586 x 0.49 y4 (k f =5) = 20.081 x 0.50 y5 (k f =10) = 14.529 x 0.49 10 1 10 qoBo, MRB/D Figure 9. hwc curves as a function of kf for µo = 5 cp. 100 12 SPE 152545 100 y3 y2 y4 hwc , m y1 y1 (kf =1) = 59.930 x 0.52 y2 (kf =2) = 43.087 x 0.50 y3 (kf =5) = 28.518 x 0.48 y4 (kf =10) = 19.919 x 0.49 10 1 10 100 qoBo, MRB/D Figure 10. hwc curves as a function of kf for µo = 10 cp 100 y2 hwc , m y1 y3 y1 (kf =2) = 64.078 x 0.51 y2 (kf =5) = 38.651 x 0.50 y3 (kf =10) = 26.066 x 0.51 10 1 10 qoBo, MRB/D 100 Figure 11. hwc curves as a function of kf for µo = 20 cp. 100 hwc , m y1 y2 y1 (kf =5) = 53.961 x 0.51 y2 (kf =10) = 37.463 x 0.51 10 1 qoBo, MRB/D Figure 12. hwc curves as a function of kf for µo = 40 cp. 10 SPE 152545 13 hwc , m 100 10 VIS= 2-Den=0.626 VIS= 2-Den=0.792 VIS=10-Den=0.792 VIS=10-Den=0.845 VIS=20-Den=0.792 VIS=20-Den=0.860 VIS=40-Den=0.892 1 1 10 100 qoBo, MRB/D Figure 13. hwc curves as a function of oil density and oil viscosity. 100 hwc , m kf=10-VISo=2 10 100 1,000 10,000 re , m Figure 14. hwc curves as a function of re. kf =10 AS W-C kf =5 AS W-C kf =2 AS W-C kf =1 AS W-C kf =0.7 AS W-C kf =0.5 AS W-C kf =10 AS N-C kf =5 AS N-C kf =2 AS N-C kf =1 AS N-C kf =0.7 AS N-C kf =0.5 AS N-C hwc , m 100 10 1 10 qoBo, MRB/D Figure 15. hwc comparison between wells with good and poor cement quality of the annular for µo = 2 cp. 14 SPE 152545 100 hwc , m kf =10 AS W-C kf =5 AS W-C kf =2 kf =1 kf =1 kf =2 AS AS AS AS W-C W-C N-C N-C kf =5 AS N-C kf =10 AS N-C 10 1 10 qoBo, MRB/D 100 Figure 16. hwc comparison between wells with good and poor cement quality of the annular for µo = 5 cp. hwc , m 1000 kf =10 AS W-C kf =2 AS W-C 100 kf =5 AS W-C kf =10 AS N-C kf =5 AS N-C kf =2 AS N-C 10 1 10 100 qoBo, MRB/D Figure 17. hwc comparison between wells with good and poor cement quality of the annular for µo = 20 cp. hwc , m 1000 100 kf =10 AS W-C kf =5 AS W-C kf =5 AS N-C kf =10 AS N-C 10 1 10 qoBo, MRB/D Figure 18. hwc comparison between wells with good and poor cement quality of the annular for µo = 40 cp. SPE 152545 15 1000 y1 = y2 = y3 = y4 = Time, days y1 280.67x -0.75, R² = 1.0 229.13x -0.72, R² = 1.0 178.41x -0.71, R² = 1.0 156.25x -0.72, R² = 1.0 100 y2 y3 y4 10 1 k10_Viso=5 10 qoBo, MRB/D k5_Viso=5 100 k2_Viso=5 k1_Viso=5 Figure 19. Water cone formation time as a function of qoBo. Reverse water cone, % 100% kf=10 kf= 5 kf= 2 kf= 1 50% -Viso= -Viso= -Viso= -Viso= 2 2 2 2 0% 1 10 100 1,000 Well's shut-in time, days Figures 20. Comparison of the water cone reversal as a function of the well’s shut in time for µo = 2 cp. Reverse water cone, % 100% 50% kf=10 -Viso= 5 kf= 2 -Viso= 5 kf= 5 -Viso= 5 0% 1 10 100 1,000 Well's shut-in time, days Figures 21. Comparison of the water cone reversal as a function of the well’s shut in time for µo = 5 cp. 16 SPE 152545 Reverse water cone, % 100% 50% kf=10 -Viso=10 kf= 2 -Viso=10 kf= 5 -Viso=10 0% 1 10 100 1,000 Well's shut-in time, days Figures 22. Comparison of the water cone reversal as a function of the well’s shut in time for µo = 10 cp. Reverse water cone, % 100% 50% kf=10 kf= 5 kf= 2 kf=10 kf= 5 -Viso=40 -Viso=40 -Viso=40 -Viso=20 -Viso=20 0% 1 10 100 1,000 Well's shut-in time, days Figures 23. Comparison of the water cone reversal as a function of the well’s shut in time for µo = 20 and 40 cp.