Keelan and Koepf (1977) describes the testing schemes and equations necessary for determining the damage and evaluation of remedial chemical treatment of water block. Keelan and Koepf (1977) facilitate surface tension reducing chemicals to remove the water forming the water-block.

Critical Interstitial Fluid Velocity and pH for Hydrodynamic Detachment of Fines in Porous Media

The drag force acting upon a fine particle attached to the pore surface is proportional to the interstitial velocity and viscosity of the fluid and the surface area of the particle. As the fluid velocity is increased gradually, a critical velocity necessary for detachment of fine particles from the pore surface can be reached. Amaefule et al. (1987) state that "The critical velocity is dependent on the ionic strength and pH of the carrier fluid, interfacial tension, pore geometry

and morphology, and the wettability of the rock and fine particles." Then, the particles are hydrodynamically removed from the pore surface and entrained by the fluid flowing through porous media. Fine particles migrating downstream with the fluid may encounter and plug narrow pore throats by a jamming process. This causes the pressure difference across the core to increase and the permeability to decrease. Therefore, from a practical point of view, the critical interstitial velocity is characterized as the interstitial velocity at which permeability reduction and pressure differential increase begin as the fluid velocity is increased gradually from a sufficiently low value (Gruesbeck and Collins, 1982; Gabriel and Inamdar, 1983; Egbogah, 1984; Amaefule et al, 1987, 1988; Miranda and Underdown, 1993).

The theory of the critical velocity determination is based on Forchheimer's (1914) equation, given below, which describes flow through porous media for conditions ranging from laminar to inertial flow:

Considering horizontal flow, and constant fluid and core properties averaged over the core length, Eq. 15-2 can be integrated over the core length for applications to laboratory core tests. In view of Eq. 15-3, the resultant expression can be given in terms of the interstitial fluid velocity as

At sufficiently low fluid velocities, the fine particles remain attached to the pore surface and, therefore, there is no formation damage by fines migration and Δp/v remains constant as depicted schematically in this article by

Amaefule et al. (1988). However, when the fluid velocity is gradually increased, first a critical velocity at which particle detachment by hydrodynamic forces begins, is reached, and then the value of Δp/v or Ap/q continuously increases and permeability continuously decreases by fines migration and deposition in porous media. As emphasized by Amaefule et al. (1987, 1988), the increase in Δp/v or Δp/q at high flow rates may be due to both fines migration and inertial flow effects. For decoupling these two effects, Amaefule et al. (1987) propose a subsequent velocity reducing test. When the flow rate is reduced gradually, the Δp/q value should reach its original value measured during the velocity increasing test, if the critical velocity has not been reached during the previous velocity increasing test.

However, if the critical velocity has been exceeded during the velocity increasing tests, a permeability impairment by fines mobilization and deposition would have occurred. Therefore, a subsequent velocity decreasing test will yield a value of Δp/q different than the previous value measured during the velocity increasing test. Amaefule et al. (1987) presents a schematic illustration of their approach to decoupling the fines migration and inertial effects using KC1 saturated brine (55 kppm KC1) and kerosene oil at different saturation levels:

1 100% water,

2 saturated with oil in the presence of irreducible water, and

3 100% oil.

They determined that the critical velocity is zero for oil flowing through cores at irreducible water saturation. Amaefule et al. (1987) verified their proposed approach by a series of tests: they injected a SOP (standard operating brine containing 50 kppm NaCl and 5 kppm CaCl2) brine into a field core sample (2.54 cm diameter and 12.2% porosity) and measured &p/q. During the increasing flow cycle, they determined the critical velocity to be 0.0674 cm/s based on their plot of data shown in this article. They also measured the effluent brine pH during the flow tests, as it may provide some evidence of the physico-chemical interactions of the aqueous solution with the formation (Amaefule et al., 1987; Millan-Arcia and Civan, 1992).

Therefore, Keelan and Amaefule (1993) recommend monitoring injection and produced water pH as an integral part of critical interstitial velocity determination. Amaefule et al. (1987) explain the change of pH to attain a minimum at the critical velocity due to the increase of the K* ion in the aqueous phase by exchange of the K* cations of the formation minerals with the Na+ and Ca2+ cations of the aqueous phase. Following the velocity increasing cycle, Amaefule et al. (1987) conducted a velocity reducing cycle until a velocity of 0.027 cm/s was reached. As can be seen in Figure 15-24b, the permeability first reduced to 66% of its initial value and then to 55% after an additional one pore

volume of the SOP brine injection at the same rate of 0.027 cm/s, indicating the dependency of the permeability reduction to the brine throughput as a result of simultaneous entrainment, migration, and redeposition of fine particles in porous media. When Amaefule et al. (1987) reversed the flow, they observed a rebound of permeability to 90% of the initial permeability because of dislodging of clogged pores, but the permeability decreased to 87% of initial after a one pore volume brine injection. Amaefule et al. (1987) explain this affect due to the fines entrainment and then migration and redeposition phenomena. They observed a similar affect on the effluent brine pH variation.

Scaling from Laboratory to Bottom Hole

Miranda and Underdown (1993) developed a method for scaling laboratory data to the bottom hole dimensions based on the schematic given in this article. For this purpose, the interstitial fluid velocities expressed in terms of the parameters of the core plug and perforated wellbore are equated as:

The cross-sectional area of the core plug is known. They expressed the total inflow area of the perforated wellbore interval by:

where Es denotes the shot efficiency in percent, Ns is the perforation density expressed as the number of shots per foot, L. is the interval length in ft, d is the diameter of perforations in ft, and h and h' denote the lengths of the cylindrical and conical portions of the perforation tunnel, respectively. The factors 0.7 and 0.3 represent the fractions of flow entering the cylindrical and conical sections of the perforation tunnel, determined as inferred by the studies of Deo et al. (1987).


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