Part VI Formation Damage Models for Field Applications Fluids and Solids Invasion, Sand Production, and Scale Formation Chapter 18 Drilling Mud Filtrate and Solids Invasion and Mudcake Formation Summary Near wellbore mud filtrate and fines invasion during drilling operations and the resulting formation damage and filtercake formation are amongst the most important problems involving the petroleum reservoir exploita- tion. This chapter reviews the fundamental processes and their mathe- matical formulation necessary to develop models that can be used for assessment of the damaged zone, filtrate and fines concentrations, fluid saturations, and the filtercake thickness and permeability alteration during drilling. The effects of under and over balance drilling on near wellbore formation damage are discussed. The models for simulation of the single and two-phase flow situations in the formation with water or oil based drilling mud cases are described. External particle invasion prior to filtercake buildup and its effect on the formation damage by particle invasion and retention and filtercake formation are described. These models are demonstrated by various applications. The models presented here can be used for accurate estimation of the near wellbore fluid saturations and resistivity profiles, which are necessary for accurate well- log interpretation. Introduction As illustrated in Figure 18-1 by Yao and Holditch (1993), drilling of wells into subsurface reservoirs is usually accompanied with mud circula- tion in order to remove the frictional heat generated as the drill bit penetrates the rock, to provide a lubrication for reduction of the frictional 608 Drilling Mud Filtrate and Solids Invasion and Mudcake Formation 609 UnlnvicUd Zom Sandstone Shale Figure 18-1. Mud filtrate invasion in the near-wellbore formation (after Yao and Holditch, ©1993 SPE; reprinted by permission of the Society of Petroleum Engineers). effects, and to transport the cuttings of the rock produced during drilling. However, mud fines and filtrates can invade and damage the near wellbore formation as depicted in Figure 18-1. Typical drilling muds may be water- based, oil-based", or water-oil emulsion types. Usually, certain types of fine solid particles are added as weighting agents. Drilling muds are usually non-Newtonian fluids (Briscoe et al., 1994). As shown in Figure 18-2 using the data by Simpson (1974), the depth of filtrate invasion strongly depends on the type of muds. As can be seen, the depth of invasion is less with oil-based muds, more with water-based muds, and in between with emulsion muds applied to a water-wet formation. Drilling of wells may be accomplished by overbalanced or under- balanced drilling techniques. As explained by Bennion et al. (1995), both techniques have certain advantages and disadvantages. In the overbalanced drilling, the downhole pressure of the circulating mud is maintained above the reservoir fluid pressure to prevent the reservoir fluids entering into the wellbore. Bennion et al. (1995) state that overbalanced drilling is more common because the downhole pressures of the conventional muds are usually higher than typical reservoir fluid pressures. Consequently, the 610 Reservoir Formation Damage 35 Time 1 ", day' Figure 18-2. Depth of filtrate invasion data of Simpson (1974) plotted against the square root of time for different muds. overbalance pressure forces the mud filtrate and solids to invade and damage the near wellbore formation and eventually form a protective sealing filtercake over the formation face. This problem can be alleviated by underbalanced drilling. Bennion et al. (1995) state that underbalanced drilling can be accomplished naturally using unweighted drilling muds in geostatically overpressured reservoirs or using oil-based muds, which are lighter than the water-based muds or foamed muds. As a result, forced invasion of mud filtrate and fines into the near wellbore formation is prevented. Bennion et al. (1995) explains that underbalanced drilling is particularly advantageous for high permeability, naturally fractured, and heterogeneous formations and for clayey formations that are sensitive to chemicals. However, they explain that underbalanced drilling does not completely eliminate the formation damage, because underbalanced conditions cannot be maintained at all times during drilling, some drilling fluids can still enter the near wellbore formation by spontaneous imbibi- tion, and the formation face can be damaged due to insufficient lubrication and turbulence, and inefficient cooling. For these reasons, the protective sealing filtercake formed during overbalanced drilling is still beneficial. As shown in Figure 18-3 by Yao and Holditch (1993), the mud filtrate invading the near wellbore formation mixes with and/or displaces the reservoir fluids (Civan, 1994, 1996; Phelps, 1995, Bilardo et al., 1996). As a result, a damaged zone is created around the wellbore (Liu and Civan, 1993, 1994, 1996; Civan and Engler, 1994). Drilling Mud Filtrate and Solids Invasion and Mudcake Formation 611 Transition/ Cake tZone " Figure 18-3. Detailed schematic of the various zones and the mud filtrate invasion profiles at different times in the near-wellbore formation (after Yao and Holditch, ©1993 SPE; reprinted by permission of the Society of Petroleum Engineers). Prediction of the near wellbore conditions, such as mud filtrate and fines invasion and distribution, is important for accurate interpretation of the well-logs used for measurement and monitoring of the properties of the near wellbore formations and accurate estimation of the hydro- carbon content of the reservoirs (Civan and Engler, 1994; Phelps, 1995; Ramakrishnan and Wilkinson, 1997). Civan (1994) states: "This process is complicated by the formation of a mud filtercake and its effect on invasion by reducing the filtrate volume and the migration of fine particles into the porous formation. Simultaneously, the properties of the fluid phases in porous media, such as density and viscosity, vary as a result of mixing and interactions of reservoir fluids with the mud filtrate and fine particles." Therefore, for modeling purposes, the coupling of the external filtercake buildup and the near wellbore fluid invasion and formation damage is essential (see Figure 18-4). Donaldson and Chernoglazov (1987) developed a "leaky-piston" filtrate invasion and convection-dispersion filtrate transport model applicable to cases involving drilling muds that can mix with the formation fluid. This model considers the dispersion of the mud filtrate within the formation fluid in a single-phase fluid system to estimate the salinity variation in the near wellbore region, but neglects the affect of mud fines invasion. This model was formulated for linear flow and the filtercake affect is 612 Reservoir Formation Damage Mud A Well Reservoir formation Figure 18-4. Mud-cake buildup over the wellbore sandface and filtrate invasion in the near-wellbore formation (after Civan, ©1999 SPE; reprinted by permission of the Society of Petroleum Engineers). simulated by means of an empirically determined, decaying filter rate equation. Civan and Engler (1994) extended and improved this model for the radial filtrate invasion case applicable to actual openhole wells. Yao and Holditch (1993) and Bilardo et al. (1996) have developed radial filtration models for reservoirs containing some formation water. They assumed that the mud filtrate mixes with the formation water as a single phase. Because their interest is in the development of models to estimate the water phase saturation, they do not consider a convection-dispersion transport equation for estimation of the brine salinity variation due to the mixing of the mud filtrate with the formation brine. However, the salinity would be required for the resistivity measurements. Phelps (1995) presents a model to determine the fluid saturations in layered formations during mud filtrate invasion. Civan (1994, 1998, 1999) presented an improved formulation of the multi-species and two-phase fluid transport in deforming Drilling Mud Filtrate and Solids Invasion and Mudcake Formation 613 porous media; derivation of compressible and incompressible cake models with and without particle invasion; and an application for radial flow filtercake buildup and mud filtrate invasion. Olarewaju (1990) developed an analytical model for permeability alteration around wells due to drilling mud filtrate invasion and mudcake formation. Ramakrishnan and Wilkinson (1997) developed a radial model for water-based mud filtrate invasion. This model enables the determination of the saturations of the oil and water phases and the salt concentration in the water phase. They combine all the dissolved ions in brine into a single pseudo-component, called "salt." Chin (1995) presents numerical models for formation invasion for various applications including formation damage, measurement-while- drilling, and time lapse analysis. In the following, single- and two-phase mud filtrate invasion models are presented. Simplified Single Phase Mud Filtrate Invasion Model Similar to Donaldson and Chernoglazov (1987), Civan and Engler (1994) assumed that the mud filtrate mixes with the reservoir fluid and the salt concentration varies. This model implicitly assumes a piston type immiscible displacement of oil similar to the formulations by Collins (1961) and Olarewaju (1990). Thus, the fluid zone can be viewed in two parts: the water phase and oil phase zones behind and ahead of the displacement front, located at a distance, r e (t). In this case, the front moves with time. The formulation is also applicable when the mud filtrate can mix with the reservoir fluid (i.e., of the same wetting type). The filtrate mixture is considered as a pseudo-component. The filtrate mass balance is given by: dc u The initial condition is given by: c = 0, r w <r<r , r = 0 (18-1) (18-2) The boundary conditions at the wellbore and the moving front are given, respectively, by: ,9£ dr (18-3) 614 Reservoir Formation Damage (18-4) The volumetric flux is determined by: u- U — 2nrh (18-5) in which the filtrate invasion rate is assumed to follow an empiri- cally determined exponential decay law according to Donaldson and Chernoglazov (1987): q = ae~ bt (18-6) where a and b are empirical parameters. The dispersion coefficient is expressed as power-law function of the volume flux (Donaldson and Chernoglazov, 1987): D = fu* (18-7) where / and g are empirical parameters. Next, three dimensionless groups are defined for computational con- venience and scaling purposes. The dimensionless concentration is defined as: The dimensionless radial distance is given by: (18-8) (18-9) The dimensionless time can be defined based on the dispersion or convection time scales, respectively, as (Civan, 1994): t D =-^r (18-10) (18-11) Drilling Mud Filtrate and Solids Invasion and Mudcake Formation 615 Because the process is mainly convection dominated, we use Eq. 18-11. The porous media peclet number is expressed as: Pe = %&- (18-12) where « 0 and D 0 are some characteristic values that are the maximum values of u and D, determined as following. Note that the filtration rate varies in a range of where <7max = 4=0 = a according to Eq. 18-6. Thus, Eq. 18-5 yields: Thus, the volume flux varies in the range of or O<M D = — (18-13) (18-14) (18-15) (18-16) (18-17) where it can be shown by means of Eqs. 18-5, 6, and 11 that: (18-18) in which the convection time scale is given by: The dispersion coefficient varies in the range of: (18-19) (18-20) 616 Reservoir Formation Damage or 0<D D = where it can be shown by means of Eqs. 18-7 and 18 that D D =u s D (18-21) (18-22) Therefore, Eqs. 18-1 through 4 can be transformed into a set of dimension- less equations, respectively, as: i i a r D p e r D r D D ° 3r r (18-23) (18-24) — D ^ C ° D 3 P* or n — W^), TQ — 1, tQ > 0 (18-25) D_-Q r -Is. t >0 — u ' 'D ~ ' ' D •* U (18-26) Finally, substituting Eqs. 18-18 and 22 into Eqs. 18-23 through 26 and dropping the subscript "D" for dimensionless quantities, Eqs. 18-23 through 26, respectively, become: = Q,l<r<(r e /r w ),t = Q D 3c , uc (18-27) (18-28) (18-29) (18-30) [...]... Eng., Vol 1, No 1, 1987, pp 3- 13 Liu, X., & Civan, F., "A Multi-Phase Mud Fluid Infiltration and Filter Cake Formation Model," SPE 25215 paper, Proceedings, SPE 62 6 Reservoir Formation Damage International Symposium on Oilfield Chemistry, February 28-March 3, 19 93, New Orleans, Louisiana, pp 60 7 -62 1 Liu, X., & Civan, F., "Formation Damage and Skin Factors Due to Filter Cake Formation and Fines Migration... Canadian Petroleum Technology, Vol 34 , No 9, November 1995, pp 34 -41 62 4 Reservoir Formation Damage 1.0Sr • 0.25 Sc - 0.258 So r" 0 .3 (max) M 3 * • 0.2 r - 100 mm w 0.80 .6- — r 0.40.2- (a) _,_—,„., C 0.0- | i i i 200 30 0 Radius, mm j—L 1.0- 400 • 500 • i 0.8U 0 .6( b) 0.4- 0.0- 200 100 30 0 Radius, mm 400 500 1.U0.8- • ' i-— 0 .60 .40.20.01(M) S — Sr -0.25 Sc -0.775 AM-* 0 .3 (max) M *5 • «0.2 rw * 100 mm... fluid pressures at the wellbore, 63 0 Reservoir Formation Damage rw, and the external reservoir flooding radius, re, before and during damage, given respectively by: (19-4) (19-5) The flow resistance before damage is given by: 1 2nKh (19 -6) During damage, Sharma et al (1997) estimate the flow resistance of the external filter cake of thickness, hc, the damaged near wellbore formation extending from the... substituting Eq 18 -35 into Eq 18 - 36 yields: dt (18-41) r dr Next, the mass balance of the aqueous phase is given by: — at - —(rpwuw) = 0 r or (18^2) Substituting Eq 18 -34 into 42 and applying Eq 18-41 yields a volumetric water phase balance equation as: r dt r 3r [ ~\ r ~\ p^,Jr9r[ 3rJ (18- 43) The initial condition is given by: (18-44) The boundary conditions are given by: 62 0 Reservoir Formation Damage Sw=l-SNr,r=rw,t>0... Migration in the Near-Wellbore Region," SPE 2 7 36 4 paper, Proceedings of the 1994 SPE Formation Damage Control Symposium, Feb 9-10, 1994, Lafayette, Louisiana, pp 259-274 Liu, X., & Civan, F., "Formation Damage and Filter Cake Buildup in Laboratory Core Tests: Modeling and Model-Assisted Analysis," SPE Formation Evaluation J., Vol 11, No 1, March 19 96, pp 26 -30 Olarewaju, J S., "A Mathematical Model of... Paper 4779, 1974 Yao, C Y, & Holditch, S A., "Reservoir Permeability Estimation from Time-Lapse Log Data," SPE Paper 255 13, Proceedings of the Production Operations Sym Held in Oklahoma City, OK, March 21- 23, 19 93, pp 9 63 - 975 Yao, C Y, & Holditch, S A., "Reservoir Permeability Estimation from Time-Lapse Log Data," SPE Formation Evaluation, June 19 96, pp 69 -74 Chapter 19 Injectivity of the Waterflooding... from subsurface reservoirs for land-based reservoirs and the seawater for off-shore reservoirs The reservoir brines usually contain suspended particles When injected into a reservoir to drive the oil toward the production wells, the suspended particles are deposited within the near-wellbore formation by a deep-bed filtration process and formation of filter cakes over the injection well formation face,... Filter Cake Formation Model," SPE 28709 paper, Proceedings of the SPE International Petroleum Conference & Exhibition of Mexico, October 10- 13, 1994, Veracruz, Mexico, pp 39 9-412 Civan, F., "Interactions of the Horizontal Wellbore Hydraulics and Formation Damage, " SPE 35 2 13 paper, Proceedings of the SPE Permain Basin Oil & Gas Recovery Conf., March 27-29, 19 96, Midland, Texas, pp 561 - 569 Civan, F.,... bore formation and the performance of the injection wells To maintain economic operations, the injection wells should be treated frequently to stimulate the impaired formation and replenish the injectivity of these wells The injection water quality, injection conditions, the compatibility of the reservoir fluids and formation with the injected water, and the in-situ fluid 62 7 62 8 Reservoir Formation Damage. .. saturation can be defined as: _ (18- 63 ) Therefore, neglecting the capillary and gravity terms in Eq 18-52 and applying Eqs 18-51 through 57 into Eqs 18- 43 and 41, respectively, yields the following aqueous phase saturation and saturated solution concentration equations: 35 dF ac FW ac ar sw ax ~ = (18 -64 ) (18 -65 ) Drilling Mud Filtrate and Solids Invasion and Mudcake Formation 6 23 The initial conditions are: . Drilling and Formation Damage Is It a total solution?" J. Canadian Petroleum Technology, Vol. 34 , No. 9, November 1995, pp. 34 -41. 62 4 Reservoir Formation Damage U 1.0- 0.8- 0 .6- 0.4- 0.2- 0.0- _,_—,„., . pp. 3- 13. Liu, X., & Civan, F., "A Multi-Phase Mud Fluid Infiltration and Filter Cake Formation Model," SPE 25215 paper, Proceedings, SPE 62 6 Reservoir Formation Damage International . affect is 61 2 Reservoir Formation Damage Mud A Well Reservoir formation Figure 18-4. Mud-cake buildup over the wellbore sandface and filtrate invasion in the near-wellbore formation