Determination of oil reservoir permeability and porosity from resistivity measurement using an analytical model Tudor Boaca a, * , Ion Malureanu b a Department of Computer Science, Information Technology, Mathematics and Physics, Petroleum-Gas University of Ploies¸ti, 39 Bucharest Bvd Street, 100680, Ploies¸ti, Romania b Department of Petroleum Geology and Reservoir Engineering, Petroleum-Gas University of Ploies¸ti, 39 Bucharest Bvd Street, 100680, Ploies¸ti, Romania ARTICLE INFO Keywords: Porosity Permeability Resistivity Mud filtrate invasion Inverse problem ABSTRACT In this paper we propose two new algorithms in order to determine the oil reservoir permeability and porosity starting from the experimental values of the radial resistivity variation. Starting from the experimental values of the resisitvity measured in the invaded zone we determine the water saturation values (and as a result the mud filtrate concentration values) in the invaded zone. For the analytical determination of the mud filtrate concen- tration in the invaded zone we use a mathematical model that describes two coupled phenomena that occur during the invasion: the mud cake formation and the mud filtrate diffusion process through the porous media. In this context we determine the reservoir porosity and permeability by minimizing a functional which establishes the difference between the measured values and the analytical values of the mod filtrate concentration in the invaded zone. In order to determine the minimum of this functional we use Rosen's algorithm, the bisection al- gorithm and a fixed point procedure. We check the algorithm's efficiency by testing it on four data sets corre- sponding to four wells. The numerical results obtained with our algorithms are in good agreement with the experimental values. 1. Introduction Porosity and permeability are two of the most important physical properties of an oil reservoir. The values of these parameters influence the storage capacity of the reservoir and the oil flow through the porous media. There are three main methods for the determination of the oil reservoir permeability and porosity: (Mohaghegh et al., 1996; Moha- ghegh, 1997; Makar and Kamel, 2011): a) laboratory measurements (core analysis); b) well test interpretation; c) well logging interpretation. In the oil reservoir modeling the permeability-porosity correlations are used (Civan, 1994, 2001, 2007). At the same time the empirical correlations permeability-porosity-irreducible water saturation obtained from well log data processing are used: Kozeny relation, Tixier relation, Willy and Rose relation, Timur relation, Coates-Dumanoir relation, Coates and Denoo relation (Balan et al., 1995). Some empirical correlations for computing the reservoir porosity are obtained from sonic transit time: Wyllie et al. relation (clean for- mations), Tixier et al. (unconsolidated sand), Raymer et al. relation, Raiga-Clemenceau et al. relation, Kamel et al. relation, Kamel and Mohamed relation (clay formations) (Makar and Kamel, 2011). Makar and Kamel (2011) introduced the second order acoustic porosity model. This model can be used both for the clean reservoirs and for the clay reservoirs. The methods that use well logging interpretation are based on the phenomenon of mud filtrate invasion. This phenomenon leads to the occurrence of the contaminated area where the physical properties of the oil reservoir are deteriorated (permeability, porosity, resistivity, water saturation, etc.). The processes that produce the deterioration of the porosity in the invaded zone contain (Chang and Civan, 1992; Civan and Knapp, 1987): a) clay particle deposition; b) particle retention; c) mineral dissolution; d) formation swelling. Civan and Knapp (1987) study the variation of the porosity due to the * Corresponding author. E-mail addresses: tboaca@upg-ploiesti.ro, tboaca@yahoo.com (T. Boaca), imalureanu@upg-ploiesti.ro (I. Malureanu). Contents lists available at ScienceDirect Journal of Petroleum Science and Engineering journal homepage: www.elsevier.com/locate/petrol http://dx.doi.org/10.1016/j.petrol.2017.07.077 Received 10 April 2017; Received in revised form 19 July 2017; Accepted 31 July 2017 Available online 2 August 2017 0920-4105/© 2017 Elsevier B.V. All rights reserved. Journal of Petroleum Science and Engineering 157 (2017) 884–893