Injectivity of the Waterflooding Wells
As stated by Civan (1998), "Waterflooding is one of the economically viable techniques for recovery of additional oil following the primary recovery." Among other factors, the efficiency of Waterflooding depends on the performance of the water injection wells. Typical sources of water used for Waterflooding are the brine produced 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, and reduce the permeability of the near-well 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 conditions are among the most important factors in determining the rate, extend and extent of damage, and the frequency of the stimulation treatments necessary for the water injection wells. Although the filtration of solids from the brine prior to injection can somewhat alleviate the well impairment, filtration of large quantities of brine is an economic detriment, as is the stimulation of the wells. Also, the foreign brines, such as sea water, are usually incompatible with the reservoir brine and cause inorganic precipitation in the near wellbore formation. The experimental studies using laboratory core tests, including those by Barkman and Davidson (1972), Donaldson et al. (1977), Davidson (1979), Todd et al. (1979), Todd et al. (1984), Vetter et al. (1987), and Pang and Sharma (1994), have provided some insight into the mechanisms of the governing damage processes and yielded qualitative measures and rules-of-thumbs to predict the conditions leading to well impairment.
However, application of such results in the field have often been unsatisfactory. For this reason, mathematical models are used to determine the performance and the economic life of the injection wells, injectivity decline, and the optimum conditions leading to extended economic operating life and optimum intervals required for well treatment. Mathematical models provide scientific guidance for accurate interpretation of the well performance and for developing optimal operating strategies. As explained by Pang and Sharma (1994), Liu and Civan (1994, 1995, 1996), and Civan (1994), proper modeling of the well injectivity loss requires the coupling of the external cake buildup over the formation face and the particle retention in the near wellbore formation. Pang and Sharma (1994) point out that the models treating the internal and external filter cakes separately are, therefore, over simplified.
Pang and Sharma (1994, 1995) have derived the equations for evaluation of the performance of water injection into laboratory core plugs, and open-hole, perforated, and fractured wells, separately for the internal and external filtration phases. Their models apply for single-phase fluid because they assume that the near wellbore fluid system is water after a short period of the initial waterflooding. Liu and Civan (1994, 1995, 1996) developed a numerical model coupling the internal and external filtration processes. Liu and Civan models apply for both single- and twophase fluids. Their model is especially suitable for interpretation of the laboratory core flow tests, for which the flow system is mostly two-phase.
we present a formulation according to Sharma et al. (1997) with slight modifications of the nomenclature. The injectivity ratio, α(t), is defined
as the ratio of the instantaneous to the initial injectivity indices, // and //„, as:
In Eqs. 19-2 and 3, q is the constant water injection flow rate and Δpo and Δp represent the difference of the fluid pressures at the wellbore, rw, and the external reservoir flooding radius, re, before and during damage, given respectively by:
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 wellbore radius of rw to a radial distance of the damaged region, rf , and the nondamaged formation beyond the radius, rf , of the damage region extending to the reservoir radius, re, respectively, by:
Ḱ is the average permeability of the damaged near wellbore region. Laboratory damage tests are commonly conducted with core plugs. Therefore, the equations corresponding to Eqs. 19-6 through 9 for the linear case as given below according to Figure 19-2 are required:
Half-Life of an Injector
Inferred by Fogler (1986), the half-life of an injector, tl/2, can be defined as the time required for the injectivity to decline to half of its initial value. Hofsaess and Kleinitz (1998) expressed that:
The half-life is defined as the injection time (or volume) at which the rate declines to l/2 of its original value (for constant-pressureinjection) or the flowing pressure reaches twice its initial value (for constant-rate-inj ection). Although many researchers, including Barkman and Davidson (1972), Pang and Sharma (1995), Sharma et al. (1997), have used "the half-life" extensively, Fogler (1986) states: "There is nothing special about using the time required for" the half-life. In fact, Fogler suggests that: "One could just as well use the time required to fall to 1/n of the initial value," that is to the t1/n-life. Hence, there is no significance of the use of the injector well half-life.
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