44711 - Petroleum Engineering (Graduate Course)

Learning outcomes

The learning outcome of this course is to give the students the fundamental knowledges of the study of hyrocarbon oil and gas reservoirs, to design their development and rational exploitation. For completion of the matter of this course the students are suggested to attend the course of Hydrocarbon Production and Transport.

Course contents

Hydrocarbon reservoirs: conditions for the existence of an oil or gas reservoirs, sedimentology, generation of hydrocarbons and their migrations,
hydrocarbon traps, temperature and pressure in the reservoir. Reservoir fluids: composition, phase behavior of hydrocarbons systems under reservoir conditions, thermodynamic properties of reservoir fluids, volumetric behavior of gases and condensates, volumetric behavior and viscosity of oil, viscosity of oil with dissolved gas, correlations for estimating the solubility of gas into oil, the formation volume factor, the compressibility of oil, property of reservoir water.Reservoir rocks: core logs, porosity, compressibility, wettability, basic concepts of capillary, drenage and imbibition, capillary pressure curves, conversion of laboratory capillary pressure curves to reservoir conditions, calculation of the average capillary pressure curve for a reservoir –Leverett J-Function, porosity, absolute permeability. Dynamic properties of rocks: porosity, permeability, relative permeability curves (gas-oil, and oil- water), effective permeability, calculation of the average relative permeability curve in a sedimentary unit, the use of statistical analysis in reservoir zonation.Evaluation of oil and gas reserves: definitions, classification of reserves according to production status, basic data for the volumetric calculations of reserves, reservoir area, net pay thickness, porosity and average porosity, water saturation and average water saturation, oil volume factor, gas volume factor, recovery factor. Classification of Fields in terms of hydrocarbon volume.Radial flow through porous media for slightly compressible fluids: equation of single flow radial flow, linearisation of the diffusivity equation, horizontal radial flow, dimensionless form of the radial diffusivity equation of fluid of constant compressibility, solution of the diffusivity equation for transient, pseudo steady-state and steady state flow, treatment of real well, skin effect. The principle of superimposition applied to the solution of the diffusivity equation.Interpretation of production tests in oil wells: calculation of the non dimensional pressure, time and radius, constant rate drawdown tests, multi-rate pressure drawdown tests, use of type curves, skin effect due to well geometry, interference testing between wells. Interpretation of production tests in gas wells: the real gas pseudo pressure, linearisation of the diffusivity equation for real gas , dimensionless form of the diffusivity equation for gas, non-Darcy flow, the radial horizontal flow of gas toward the well, transient flow, pseudo-steady flow, steady flow. General solution for the diffusivity equation for gas, gas well deliverability testing, the empirical back pressure test, isochronal test, multi-rate drawdown test, pressure buildup test.The influx of water into the reservoir by the following methods: Schilthuis, Huntus , global equation, Van Everdingen and Hurst, and Fetkovich .Material balance equation and prediction of the gas production as function of time for : dry gas reservoirs in contact with an aquifer and for condensate reservoirs. Pressure maintenance by water injection or gas recycling in gas condensate reservoirs. Calculation of the volumetric and phase behavior of a condensate reservoir using EOS. General material balance equation for oil reservoirs, drive indices , material balance for undersaturated oil and saturated oil reservoirs without gas cap.Immiscible displacement in homogeneous porous media: the fractional flow equation, the Bukley-Leverett displacement equation, fraction flow curves concave downward, upward, and S-shaped.Calculation of the average saturation behind the displacing front by Welge's equation. Calculation of oil recovery as function of time. The effect of oil viscosity and flow rate on displacement process.
Factor influencing oil recovery by water injection: microscopic displacement efficiency, volumetric efficiency, vertical invasion efficiency. Water and gas coning , calculation of the critical flow rate for water and gas coning. Simulation of reservoir behavior using numerical modeling: philosophy and methodology behind numerical modeling, classification of models based on geometry and classification and number of mobile phases, the continuity equation, flow equation of single phase flow of slightly compressible fluid, flow equation for gas fluid, equation for a two and three phases models without mass exchange among phases, black oil model for heavy oil reservoirs, volatile oil model, compositional flow model.Basic principle of Finite Difference (FD) method for the numerical integration of the partial differential equations regulating the behavior of the reservoir models: finite difference analogs for the spatial derivatives of the first and second order, truncation errors and stability condition for a FD scheme. Matrix form of a FD scheme. Different grade of implicitness in the simulation of multiphase models: IMPES (implicit Pressure Explicit saturations), SEQ (Sequential method), SIMULTANEOUS (full implicit method).Solution of the sparse linear algebraic equations by: direct methods (Gauss elimination method, factorization method, Thomas algorithm for tridiagonal systems), iterative methods (Jacobi, Gauss Siedel, PSOR , LSOR) methods.

Readings/Bibliography

- GIAN LUIGI CHIERICI, PRINCIPI DI INGEGNERIA DEI GIACIMENTI PETROLIFERI, VOL. 1-2, AGIP, 1991 - L.P. DAKE, FUNDAMENTAL OF RESERVOIR ENGINEERING, ELSEVIER, NEW-YORK, 1978

Teaching methods

The lessons will be of traditional type by demonstrations on the blackboard and numerical exercises on the arguments of the lessons. Numerical FD and FE codes for the simulation of problems of flow and transport of pollutants will be  explained and given to the students, with the purpose to accustom the students to the use of codes of calculus which are,  at present,  largely used in the projection of engineering works.

Assessment methods

The assessment of the profit will be oral and will be done by questions regarding the theoretical knowledge of the subject, and the numerical solutions of simple practical problems.

Teaching tools

Blackboard, overhead projector

Office hours

See the website of Guido Gottardi