Permeability is one of the most important characteristics of hydrocarbon bearing formations. Formation permeability is often measured in the laboratory from reservoir core samples or evaluated from well test data. However, core analysis and well test data are usually only available from a few wells in a field. On the other hand, almost all wells are logged. This paper presents a non-parametric model to predict reservoir permeability from conventional well log data using an artificial neural network (ANN). The ANN technique is demonstrated by applying it to one of Saudi Arabia's oil fields. The field is the largest offshore oil field in the world and was deposited in a fluvial dominated deltaic environment. The use of conventional regression methods to predict permeability in this case was not successful. The ANN permeability prediction model was developed using some of the core permeability and well log data from three early development wells. The ANN model was built and trained from the well log data and their corresponding core measurements by using a back propagation neural network (BPNN). The resulting model was blind tested using data which was taken from the modelling process. The results of this study show that the ANN model permeability predictions are consistent with actual core data. It could be concluded that the ANN model is a powerful tool for permeability prediction from well log data. Introduction Many oil reservoirs have heterogeneity in rock properties. Understanding the form and spatial distribution of these heterogeneities is fundamental to the successful exploitation of these reservoirs. Permeability is one of the fundamental rock properties, which reflects the rock's ability to transmit fluids when subjected to pressure gradients. While this property is very important in reservoir engineering, there is no specific geophysical well log for permeability, and its determination from conventional log analysis is often unsatisfactory(1). In general, porosity and permeability are independent properties of a reservoir. However, permeability is low if porosity is disconnected, whereas permeability is high when porosity is interconnected and effective. Despite this observation, theoretical relationships between permeability and porosity have been formulated, such as the Kozeny-Carmen theory. The Kozeny-Carmen theory relates permeability to porosity and specific surface area of a porous rock which is treated as an idealized bundle of capillary tubes. This theory, however, ignores the influence of conical flow in the constrictions and expansions of the flow channels and treats the highly complex porous medium in a very simple manner. Empirical relationships based on the Kozeny-Carmen theory have also been developed that relate permeability to other logs and/or log-derived parameters such as resistivity and irreducible water saturation(2). These relationships are applied only to the region above the transition zone or to the transition zone itself. Since core permeability data are available for most exploration and development wells, statistical methods have become a more versatile alternative in solving the problem of determining reservoir permeability. Regression is widely used as a statistical method to search for relationships between core permeability and well log parameters(3, 4).

Résumé -Estimation de la saturation en eau au laboratoire par régression 3D -La détermination précise des réserves initiales d'un réservoir est très importante pour obtenir une bonne estimation de la capacité de production d'un gisement d'hydrocarbures. La formule modifiée d'Archie (S w = (a R w /φ m R t ) 1/n ) constitue l'équation de base au calcul de la saturation en eau dans le sable ou l'utilisation d'un modèle de saturation pour le sable argileux. Une bonne évaluation de la saturation en eau dépend de la détermination la plus précise possible des paramètres d'Archie a, m, n. Cet article presente une nouvelle technique destinée à déterminer les paramètres a, m, n d'Archie. Cette technique est basée sur le principe de régression en 3D. Elle surmonte le problème de l'incertitude des valeurs de saturation en eau. Deux exemples de terrain sont présentés afin de bien tester les résultats de la technique de régression 3D et les comparer à trois autres techniques -méthode CAPE (Core Archie-Parameters Estimation) méthode conventionnelle et valeurs par défaut -concernant les valeurs des paramètres a, m and n de la formule d'Archie et de la saturation en eau. Oil & Gas Science and Technology -Rev. IFP, Vol. 57 (2002), No. 6 NOMENCLATURE a = tortuosity factor m = cementation factor n = saturation exponent S w = water saturation, fraction V sh = shale volume, Ω⋅m R sh = shale resistivity GR = gamma ray reading, API R t = resistivity of rock, Ω⋅m R w = resistivity of brine, Ω⋅m R o = resistivity of rock with S w = 1.0, Ω⋅m I r = resistivity index F = formation resistivity factor φ = formation porosity, fraction σ Sw = standard deviation in water saturation. Abstract

Résumé -Estimation de la saturation en eau au laboratoire par régression 3D -La détermination précise des réserves initiales d'un réservoir est très importante pour obtenir une bonne estimation de la capacité de production d'un gisement d'hydrocarbures. La formule modifiée d'Archie (S w = (a R w /φ m R t ) 1/n ) constitue l'équation de base au calcul de la saturation en eau dans le sable ou l'utilisation d'un modèle de saturation pour le sable argileux. Une bonne évaluation de la saturation en eau dépend de la détermination la plus précise possible des paramètres d'Archie a, m, n. Cet article presente une nouvelle technique destinée à déterminer les paramètres a, m, n d'Archie. Cette technique est basée sur le principe de régression en 3D. Elle surmonte le problème de l'incertitude des valeurs de saturation en eau. Deux exemples de terrain sont présentés afin de bien tester les résultats de la technique de régression 3D et les comparer à trois autres techniques -méthode CAPE (Core Archie-Parameters Estimation) méthode conventionnelle et valeurs par défaut -concernant les valeurs des paramètres a, m and n de la formule d'Archie et de la saturation en eau. Oil & Gas Science and Technology -Rev. IFP, Vol. 57 (2002), No. 6 NOMENCLATURE a = tortuosity factor m = cementation factor n = saturation exponent S w = water saturation, fraction V sh = shale volume, Ω⋅m R sh = shale resistivity GR = gamma ray reading, API R t = resistivity of rock, Ω⋅m R w = resistivity of brine, Ω⋅m R o = resistivity of rock with S w = 1.0, Ω⋅m I r = resistivity index F = formation resistivity factor φ = formation porosity, fraction σ Sw = standard deviation in water saturation. Abstract

The technology of extended reach and horizontal wells has recently progressed significantly. These wells have very few cost effective choices like slotted liners and openhole completion methods. Hole instability and sand production are the main problems of these completion techniques. To predict sand production an elastic plastic spherical cavity or cylindrical symmetry is assumed. Also, Mohr-Coulomb criterion is proposed for bore hole failure solution.These methods have limited applications and need actual cores to measure shear failure properties of rocks. This paper introduces developed equations to predict sand production from extended reach and horizontal wells. A combination of Mohr Coulomb criterion and Von Mises criterion for cylindrical symmetry is developed and proposed to determine the hole instability and sand production. These equations allow calculating the sand free production rate for extended reach and horizontal wells depending on the uniaxial compressive strength of the rock. They also allow evaluating the effect of inclination angle, azimuth angle, well length and values and directions of in-situ stresses. Also, the equations can be applied easily in any area. Introduction The benefits that come from drilling horizontal and extended reach wells such as achieving high flow rates and reducing gas and water coning in thin reservoirs have been well documented. Horizontal and extended reach wells have been applied through the oil and gas industry to enhance project economics and develop reservoirs that would otherwise not be commercial. These wells have also been applied in high productivity reservoirs for the purpose of reducing gas and/or water coning, thereby improving drainage efficiency and ultimate recovery [1]. The completion technology for horizontal and extended reach wells presents numerous design possibilities. The simplest and least expensive method is completing the well as open hole or using slotted liner. The majority of the wells are being completed using these design methods. However these techniques are usually facing sand production when excessive drawdown is applied [1].