Pseudo-Damage Versus Formation Damage
Amaefule et al. (1988) plainly stated that "Formation damage is an expensive headache to the oil and gas industry." A number of factors cause formation damage in a complicated manner. Amaefule et al. (1988) grouped these factors in two categories:
1. Alteration of formation properties by various processes, including permeability reduction, wettability alteration, lithology change, release of mineral particles, precipitation of reaction-by products, and organic and inorganic scales formation
2. Alteration of fluid properties by various processes, including viscosity alteration by emulsion block and effective mobility change
The impact of formation damage can be observed in a variety of ways, including
1 abnormal decline in well productivity or injectivity,
2 misdiagnosis of potential pay zones as nonproductive, and
3 delay of payout on investment (Amaefule et al., 1988).
Hayatdavoudi (1999) points out that the analysis of production data is complicated because of:
1. Mechanical problems related to the tubing, safety valves, lift equipment, and wax, paraffin, and scale build-up in the tubing
2. Formation damage due to fines migration, development of skin, completion damage, and many other factors
3. Changes in reservoir conditions, like appearance of water-cut, changes in productivity index, and other related factors
Among other factors, the productivity or injectivity of wells depend on the pressure losses that occur along the flow path of produced or injected fluids. As schematically depicted in Figure 22-4, pressure losses may occur at various locations along the well and in the reservoir formation. Therefore, Piot and Lietard (1987) expressed the total skin of a well as a sum of the pseudoskin of flow lines from the formation face to the pipeline and the true skin due to formation damage. Here, the focus is on the near-wellbore formation damage problem. Figure 22-5 schematically depicts the damaged region around a well.
Measures of Formation Damage
Formation damage can be quantified by various terms, including
1 damage ratio,
2 skin factor,
3 permeability reduction index,
4 flow efficiency, and
5 depth of damage.
The skin factor is a dimensionless parameter relating the apparent (or effective) and actual wellbore radii according to the parameters of the damaged region:
where s is the skin factor. The skin factor is a lumped parameter incorporating the integral affect of the extend and extent of damage in the near wellbore region. Frequently, in reservoir analysis and well test interpretation, the skin factor concept is preferred for convenience and simplicity, and for practical reasons. Therefore, many efforts have been made to express the skin factor based on the analytical solutions of simplified models relating well flow rate to formation and fluid conditions. In this respect, incompressible one-dimensional flow in a homogeneous porous media formulation approach has been popular. Other cases, such as anisotropic elliptic and isotropic radial flow problems can be readily transformed into one-dimensional flow problems, using respectively
where Kx, Ky, and Kz are the permeabilities in the x, y, and z-principal directions in an anisotropic porous media; a, b and c denote the coordinates of the well; and r and I denote the radial and linear distances in the flow direction. The formation anisotropy ratio of permeability, β, is defined following Muskat (1937):
Although this transformation distorts the wellbore shape from the cylindrical shape (Mukherjee and Economides, 1991), it can still be used for all practical purposes with sufficient accuracy.
Permeability Variation Index (PVI)
The permeability variation index expresses the change of formation permeability by near-wellbore damage as a fraction, given by
where K and Kd denote the formation permeabilities before and after damage, respectively.
Viscosity Variation Index (VVI)
The viscosity variation index expresses the change of fluid viscosity by various processes, such as emulsification, defined by:
where u and ud denote the fluid viscosities before and after fluid damage, respectively.
Damage Ration (DR)
The damage ratio expresses the change of well flow rate by nearwellbore damage as a fraction, given by (Amaefule et al., 1988):
where q and qd denote the undamaged and damaged standard flow rates, respectively. The production loss by alteration of formation properties can be formulated as following. The theoretical undamaged and damaged flow rates for a steadystate incompressible radial flow in a homogeneous and isotropic porous media are given, respectively, by (Muskat, 1949; Amaefule et al., 1988):
Therefore, substituting Eqs. 22-6 and 7, Eq. 22-8 yields the following expression for the damage ratio:
where u, and B are the fluid viscosity and formation volume factors. K and Kd are the undamaged and damaged effective permeabilities, h is the thickness of the effective pay zone, pw and pe are the wellbore and reservoir drainage boundary fluid pressures, rw and re are the wellbore and reservoir drainage radii, and rd is the radius of the damaged region. The effective skin factor, s, is defined by (Craft and Hawkins, 1959):
Thus, substituting Eq. 22-10 into Eq. 22-9 yields the relationship between the damage ratio and the skin factor as:
The economic impact of formation damage on reservoir productivity can be estimated in terms of the annual revenue loss by formation damage per well (FD$L) at a given price of oil, p, according to Amaefule et al. (1988):
Figure 22-6 by Amaefule et al. (1988) shows the typical curves of the damage ratio and annual revenue loss per well as a function of the damage radius and degree determined by Eqs. 22-8 and 12, respectively. Because the degree of damage varies in the near-wellbore region, it is more appropriate to express the total skin as a sum of the individual skins over consecutive segments of the formation as (Li et al., 1988; Lee and Kasap, 1998):
where N represents the number of segments considered (see Figure 22-7). The production loss by alteration of fluid properties can be formulated as following. Rapid flow of oil and water in the near-wellbore region promote mixing and emulsification. This causes a reduction in the hydrocarbon effective mobility, k(K = Ke/u = Kkr/u) (Leontaritis, 1998), because emulsion viscosity is several fold greater than oil and water viscosities. High viscosity emulsion forms a stationary block which resists flow. It is called emulsion block. If (U, and [id represent the viscosities of oil and emulsion, respectively, and a steady-state and incompressible radial flow is considered, the theoretical undamaged and damaged flow rates are given, respectively, by:
Thus, substituting Eqs. 22-14 and 15 into Eq. 22-6 Leads to the following expression for the damage ratio:
Figure 22-8 by Amaefule et al. (1988) shows the effect of emulsion block on oil production rate according to Eq. 22-16. The viscous skin effect can be expressed similar to Zhu et al. (1999) as:
Flow efficiency is the ratio of the damaged to undamaged formation flow (production or injection) indices:
where p and pwf denote the average reservoir fluid and flowing well bottom hole pressures, respectively, and Δps is the additional pressure loss by the skin effect. The flow efficiency of vertical wells for radial
and incompressible fluid flow at a steady-state condition is given by (Mukherjee and Economides, 1991):
For practical purposes, flow efficiency of damaged wells has been correlated by means of the inflow performance relationship (IPR). For example, Dias-Couto and Golan (1982) developed the following inflow performance relationship for wells producing oil with average reservoir fluid pressures at or below the bubble point pressure:
Lekia and Evans (1990) extended this equation for wells producing oil with average reservoir fluid pressures above the bubble point pressure as:
where qd is the oil flowrate of the damaged well, qdb is the oil flow rate at the bubble point from a damaged well, qmax is the maximum oil flow rate at Pwf = 0 from a non-damaged well, and qc is the maximum oil flow rate of the Vogel (1968) part of the generalized IPR. Lekia and Evans (1990) express these by the following equations:
Depth of Damage
The depth of damage represents the distance of formation damage region measured from the wellbore. Yan et al. (1997) correlated the depth of invasion of drilling and completion fluids by regression analysis of experimental data obtained by means of the slice cutting of damaged core plugs. Their empirical correlation is given by
where d is the invasion depth in cm, p is the pressure in MPa, Vf is the cumulative filtrate loss in cm3, ɸ is porosity in percentage, and K is permeability in um2(~ Darcy). Figure 18-5 given in this article by Evan depicts the variation of the depth of damage during mud invasion as a function of the pore volume of filtrate invasion.
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