Chemical Engineering Science 57 (2002) 323–337 www.elsevier.com/locate/ces Simulating oil ow in porous media under asphaltene deposition Jorge E. P. Monteagudo a , Krishnaswamy Rajagopal b , Paulo L. C. Lage a ; * a Programa de Engenharia Qu mica-COPPE, Universidade Federal do Rio de Janeiro, C.P. 68501, Rio de Janeiro, RJ, 21945-970, Brazil b Escola de Qu mica, Universidade Federal do Rio de Janeiro, C.P. 68542, Rio de Janeiro, RJ, 21949-900, Brazil Received 19 March 2001; received in revised form 24 August 2001; accepted 27 August 2001 Abstract A simulator for one-phase ow in porous media near a wellbore is coupled with a thermodynamic model and a network model in order to predict the change in petroleum ow under asphaltene deposition. The thermodynamic model is capable of predicting the quantity of precipitated asphaltene. The network model is used to predict formation damage due to in situ asphaltene deposition. The model is qualitatively evaluated using data from literature. Results are in concordance with expected physical behavior. ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: Porous media; Multiphase ow; Simulation; Asphaltene precipitation; Network model; Percolation theory 1. Introduction In situ asphaltene deposition in oil reservoirs causes seri- ous impairment to the oil ow towards the wellbore. It is of interest to develop a reservoir simulator capable of predict- ing changes in oil ow pattern due to asphaltene deposition. Nowadays, the most common way to simulate oil ow in reservoirs is to solve the set of partial dierential equa- tions established by continuum theory using some numerical method, i.e. nite dierences, nite elements, or nite vol- ume methods. Alternatively, some recent discrete methods can be used, such as the LGA (Hardy, Pomeau, & Pazzis, 1973; Hardy, Pazzis, & Pomeau, 1976; Frisch, Hasslacher, & Pomeau, 1986) and LBA (McNamara & Zanetti, 1988; Higuera & Jim enez, 1989; Quian, D’Humi eres, & Lalle- mand,1992)models.ItcanbestatedfromtheworkofBerns- dorf, Durst, and Sch afer (1999) that ow through porous media is simulated faster by LBA model than by solving Navier–Stokes equations at porous level. However, these discrete methods cannot compete yet in speed with simula- tors based upon continuum theory. The continuum theory admits that porous-level hetero- geneities can be homogenized at some representative ele- mentary volume (REV). This REV must be large enough to homogenize porous-level heterogeneities but small enough ∗ Corresponding author. Tel.: +55-21-2562-8346; fax: +55-21- 2562-8300. E-mail address: paulo@peq.coppe.ufrj.br (P. L. C. Lage). to take into account heterogeneities at larger scales. Has- sanizadeh and Gray (1979, 1980) showed, using their averaging method, that Darcy law can be recovered at macroscopic level from Navier–Stokes equations at pore- level with the sole condition of negligible inertial forces, i.e., small velocities. Darcy law is commonly employed by most of the reservoir simulators currently available, avoid- ing the necessity of establishing a set of partial dierential equations at the microscopic level, which cannot be numer- ically solved using current available computer technology. Conventional models for reservoir simulators usually admit that rock permeability is constant or, if some het- erogeneity has to be taken into account, they attribute a time-independent permeability distribution in the whole reservoir. However, when the rock morphology is aected by the uid ow, such as in the case of solid deposition, permeability varies in time. Most of the early works on solid deposition damage (Barkman & Davidson, 1972; Abrams, 1977) were based upon completely empirical rules. Later works (Eleri, Ursin, & Rogaland, 1992; Khatib, 1994; Oort, 1993) focused on obtaining empirical or semi-empirical correlations between permeability damage and solid concentration, but without taking into account changes in porous medium morphol- ogy. In a dierent approach, Gruesbeck and Collins (1982) developed a model in which the morphology of the medium was taken into account in a very simplied way. In that work, the porous medium was represented as a set of par- allel pathways, some of them pluggable and the others not. 0009-2509/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved. PII:S0009-2509(01)00407-9