Considerations of the Model

Here, the formulation of Civan's (1995) model is presented. The reservoir fluid system can be single phase or multiphase depending on

the prevailing reservoir conditions. Above the bubble-point pressure conditions, the oil is undersaturated and single phase. Below the bubblepoint pressure conditions, the oil is saturated and can be two-phase. Civan (1995) developed a model that is applicable for both conditions. His model also considered the possibility of simultaneous deposition of asphaltenes and paraffins. As stated by Civan (1995), "Although they are a mixture of different molecular weight components, the paraffins and asphaltenes are lumped into two groups as the paraffin, p, and the asphaltene, a, pseudo-components. The other components of the oil are grouped as the oil pseudo-component, o, which acts as a solvent. The mixture of the various gases are grouped as the gas pseudo-component, g" Thus, Civan's (1995) model considers four pseudo-components:

(a) paraffin, par,

(b) asphaltene, asp,

(c) oil, o, and

(d) gas, g.

The system of the fluids and the porous formation is considered in three phases as the vapor, V, liquid, L, and solid, S, following Ring et al. (1994). The solid phase is considered in two parts:

(1) porous matrix (unchanged), and

(2) organic deposits (varying).

Civan (1995) considers that the paraffin and asphaltene transport may occur both in dissolved and precipitate forms depending on the state of saturation of the oil phase. This assumption is supported by Mansoori (1997) who points out that: ". . . asphaltenes are partly dissolved and partly in colloidal state (in suspension) in oil peptized (or stabilized) primarily by resin molecules that are adsorbed on asphaltene surface." The permeability impairment may occur by

(a) gradual pore size reduction, and

(b) pore throat plugging and sealing.

The ratio of the plugging and nonplugging paths vary by organic deposition. Single- or two-phase fluid conditions may exist depending on whether the condition is above or below the bubble-point pressure. The various phases are assumed at thermal equilibrium within the bulk volume. Non-Newtonian fluid behavior is considered for high concentrations of organic precipitates and solutes. Non-Darcy flow behavior is assumed for flow through passages narrowing due to precipitation.

Porosity and Permeability Relationships

The porosity and permeability alterations are predicted based on a modified version of the plugging and nonplugging pathways concept of Gruesbeck and Collins (1982). Relatively smooth and large diameter flowpaths are assumed to mainly undergo a surface deposition and are called nonplugging. Highly tortuous and variable diameter flowpaths are called plugging. The retainment of organic deposits in the plugging pathways occurs by jamming and pore throat blocking. Consider that ɸpo and ɸnpo denote the pore volume fractions and ep and enp are the fractions of the bulk volume occupied by organic deposits of the plugging and nonplugging pathways of the porous media. Thus, the instantaneous porosities in the plugging and nonplugging flow paths are given, respectively, by:

Although, Gruesbeck and Collins (1982) assume characteristic constant values, it is reasonable to consider that the fractions of the bulk volume containing the plugging and nonplugging pathways vary during deposition and are estimated by, because of the lack of a better theory:

The instantaneous and initial porosities of the porous medium are given, respectively, by:

Here, tp is the time of initiation of the particle bridges and jamming. This is the time at which the pore throat-to-particle diameter ratio drops to below its critical value determined by the following empirical correlation (Civan, 1990, 1996):

The rate of deposition in the nonplugging tubes can be expressed by (Civan, 1994, 1995, 1996):

For simplification purposes, Civan (1995) assumed that organic deposits are sticky and, therefore, once deposited they cannot be removed. Consequently, the second term in Eq. 14-76 can be dropped. Mansoori (1997) tends to support this argument. Although Leontaritis (1998) considered the possibility of erosion of deposits, it is not apparent if he actually implemented this possibility in his calculational steps. kd and ke are the surface deposition and mobilization rate constants. re is the fraction of the uncovered deposits estimated by:

The permeabilities of the plugging and nonplugging pathways are given by the following empirical relationships (Civan, 1994):

Considering the simultaneous deposition of paraffins and asphaltenes, ep and enp in Eqs. 14-62 through 69 denote the sum of the paraffins and asphaltenes, that is,


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