PETROLEUM ENGINEERING AND FLUID MECHANICS IN POROUS MEDIA
G. Brighenti, G. Gottardi, P. Macini, E. Mesini
The Petroleum Engineering and Fluid Mechanics in Porous Media group performs research in several areas of
petroleum engineering, including flow in porous media, reservoir simulation, reservoir characterisation, drilling,
pollutant transport, sustainable development of oil and gas reservoirs and waste disposal. The research
includes the investigation of complex, non-linear phenomena in highly disordered geological media, and draws
on techniques borrowed from many different engineering and scientific disciplines. On all length scales, from
micron-sized pores up to the kilometre extent of most hydrocarbon reservoirs, the rock is heterogeneous, with
different geological structures of all sizes and with transport properties (such as permeability) that may vary by
orders of magnitude over short distances. The following research themes have been developed and will be
presented in short below:
• Two phase flow in non-aqueous phase
• Transport of pollutants in coastal aquifers
• Hydrocarbon and water reservoir simulation
• Effects on hydraulic conductivity of grain size distribution and porosity of soils
• Sustainable development of oil and gas reservoirs
• CO2 injection
• Soil subsidence studies
• Radioactive marker monitoring technique
• Rock compressibility at great depth
• Studies on rock-bit and drill-bit performances
• Performance evaluation of gravel pack completions
• Non Darcy’s flow
Two phase flow in non-aqueous phase
Many reservoirs are fractured, and fluid flow is mostly controlled by the properties and geometry of the fracture
network rather than the rock matrix. Fractures are very poorly understood and there is a significant research
effort on determining the transport properties of individual fractures and their consequences for large-scale
recovery from fractured reservoirs. The research concerned the study of multi-phase flow of NAPL/DNAPL
(Non-Aqueous-Phase-Liquids, Dense-Non-Aqueous-Phase-Liquids) in porous media and in fractured
reservoirs, by means of fluid flow modelling of liquid pollutants in aquifers (liquid hydrocarbons and their
derivates, chlorinated solvents, etc.). The main goal of this research is the determination of flow models and
the identification of the most suitable laws (empiric in nature) governing the phenomena in the different cases.
In a further approach, some cases have been examined in which the classic extension of the Darcy’s Law to
the two-phase flow is not valid – in particular the case of non-simultaneous flow of two phases where the
inertial forces are not negligible. Here, it has been showed that the fluid flow laws largely depend on the
interplay between viscous, gravitation, inertia and capillary forces.
Transport of pollutants in coastal aquifers
Pollutant migration in costal aquifer was numerically simulated by improving the reservoir simulator TOUGH2-
T2VOC to model three-phase flow conditions generated by spill of organic contaminants in the unsaturated
zone of costal aquifers affected by sea water intrusion. A new version of the thermodynamic module T2VOC,
used in conjunction with reservoir numerical simulator TOUGH2, was prepared. An application of the code has
been presented that shows the containment, by means of an impervious wall, of a NAPL lens in the
unsaturated zone of a phreatic aquifer affected by seawater intrusion.
Hydrocarbon and water reservoir simulation
Reservoir simulation models the flow by solving the partial differential equations of motion on a grid that
describes the transport properties of the reservoir on length scales of the order of several metres. One major
aspect of the research is history matching, where the reservoir description is altered to match the production
data. Here, Finite-Difference (FD) and Finite-Element (FE) numerical methods have been experimented in the
construction of hydrocarbon and water reservoir simulator codes to compare the performances of the different
formulations on the basis of global mass-balance errors. Recently, a FE code for predicting flow of pollutant in
confined and unconfined aquifers and a code for modelling water flow in saturated and unsaturated soils have
been developed and published. Moreover, numerical modelling has also been applied to study shock
phenomena in open-channel flow by using second order central schemes. In this research, the numerical
integration of the non-linear set of hyperbolic Saint-Venant equations by using the second-order central
schemes of Nessyan and Tadmor (NT), Kurganov and Tadmor (KT), extended to the non-homogeneous case,
and the first-order central scheme of Lax-Fredrichs (LF) have been compared for predicting dam-break and
hydraulic jumps in rectangular open channel flow. The solutions obtained for two test cases of two-dimensional
flow have been compared, showing a good agreement with experimental results.
Effects on hydraulic conductivity of grain size distribution and porosity of soils
The importance of developing relationships between some petrophysical properties of porous media has been
recognized since a long time. Parameter estimation techniques, incorporating mathematical expressions
assumed to describe the flow properties, are commonly used. In particular, many applicative solutions have
been developed to correlate geometrical or statistical properties to dynamical properties. To this purpose,
grain size distribution curves have been determined on the same samples and hydraulic conductivity was
determined from d10, modified Carman-Kozeny relationships and literature models. The research shows that
for samples where the fine fraction (<38 µm) is not significant, the proposed relationships fit well the
Sustainable development of oil and gas reservoir
The increase of world population is making it more and more difficult to use large parts of territory for mining
operations or dedicated to energy production operations. Thus, there is a growing need for techniques that
allow sequential and/or multiple use of the territory, while keeping a high standard of life and safeguarding the
environment against degradation and pollution – a priority for preserving the welfare of the population.
Concerning this matter, one must distinguish between global environmental damages due to energy
production, which might have an effect on the entire ecosystem, and localized damages, which have a marked
effect only on the site of production, more sensible in areas of strong urban concentration. The main danger
from the global damages seems to come from the greenhouse gases. As for localized environmental issues,
one must distinguish between the damage due to usage of hydrocarbons and damage produced directly by
the operations of the upstream/downstream hydrocarbon industry. This research topic is aimed to show that in
the upstream oil industry operations produce limited environmental damages, with a moderate impact on the
This research topic concerns the application of the experiences of petroleum engineering and fluid mechanics
in porous media of this group to the analysis of reservoirs behaviour under CO2 injection, which could help
meeting the future objectives of the Kyoto protocol. Mathematical modelling seems the most accurate tool to
predict reservoir performance during the injection and to control the chemical reactions that happen inside the
reservoir. Recent studies evaluated that the installation of the best CO2 underground confinement technology
could cost about 40 €/ton. Apparently, the technology is quite expensive, but it could be shared between
producers and consumers, as in the future it will not be possible to discharge CO2 at no cost.
Soil subsidence studies
During the last decades, in Northern Italy underground fluid withdrawals have induced severe cases of land
subsidence, with severe damages and impairments to the environment. These phenomena have occurred
since the early ‘50s in the Po Delta, due to the exploitation of shallow aquifers containing dissolved gas. In the
late ‘70s, subsidence was detected in Venice, Ravenna, with its artistic heritage from the late Roman Empire
and Byzantine period, Bologna and other areas of the Po Plain. Most of the above cases are largely due to
groundwater withdrawal. The study discusses the subsidence problems occurred in the Po plain area and in
the Adriatic offshore, emphasizing both the different geological and hydrogeological characteristics of the
subsoil and the different altimetrical positions.
Radioactive marker monitoring technique
This research topic is oriented to examine the fundamentals of a recent technique for the direct measurement
of both the in situ formation compaction and the uniaxial compressibility coefficient. The latter is of paramount
importance for the correct estimate of surface land subsidence performed by mathematical modelling. This
technique has been developed for the in situ compaction monitoring of producing formations caused by pore
pressure decline. It is based on the placement of low-emission radioactive markers along the wellbore, in the
interval in front of the formations under depletion. The critical stage of the marker technique can be split into
two major points: a) detection of markers position, and b) measurement of relative distances between each
pair of adjacent markers. It is worthwhile considering that, even in the ideal case of measurements not affected
by errors, this technique doesn’t always assure that the surveyed deformations reflect the actual deformation
of the undisturbed rocks. In fact, a rigid casing is likely to perturb the deformation of layers under depletion,
particularly in the close vicinity of the well.
Rock compressibility at great depth
The correct estimation of the oil in place is fundamental to evaluate the economic performance of any
reservoir. In the case of oil reservoirs without water drive, the only drive forces available for oil production are
rock and reservoir fluids compressibility. In this research, experimental studies have been carried out on
different reservoir rocks, cored inside the oil-bearing zone of sandstone and carbonatic reservoirs. Two
different methodologies have been applied: 1) acoustic measurements (dynamic test), to acquire P and S
wave transit times for the indirect evaluation of dynamic undrained compressibility, accordingly to the theory of
poroelasticity; 2) deformation measurements (static test), to acquire stress and deformation of drained
samples for the direct calculation of bulk and pore compressibility. Results show that compressibility is not
constant, but it is a function of reservoir pressure.
Studies on rock-bit and drill-bit performances
The objective of this research topic is the analysis of a new drilling model for bit performance evaluation known
as Bit Index (BI) and the investigation of the possibility of BI to establish guidelines for the development of a
mathematical tool able to help during well planning, well drilling and post-well analysis. The BI distinguishes
between bit independent and dependent operational parameters and establishes the cost per foot as an
indirect evaluation tool. The model was tested by mining data from the “Formation Drillability Catalog” (FDC)
prepared at E&P Division of Eni Group. The proposed model, although in its early stage, proved to be
economic and reliable. The quality of bit performance analysis obtained with this model seems also more
effective than the traditional “quick look” analysis, performed on bit records, or on the pure evaluation of the
Experimental investigations on glycol enhanced water-base drilling fluids
The research investigates the inhibitive effects of water-based drilling fluids prepared with polymers, glycol and
inorganic electrolytes formulated to reduce the instability of shaly formations. The instability of clay and shaly
formations is mainly due to interactions with the mud filtrate. The research investigated the inhibitive effects of
some water-based muds prepared with polymers (such as Partially Hydrolysed PolyAcrylamide, PHPA, and
others), glycol and an inorganic electrolyte (KCl) to aid in performance. While polymers provide the rheological
properties and filtration control of the system, glycol and KCl stabilize water-sensitive formations. Results show
that the addition of small amounts of glycol to inhibitive systems, such as KCl + PHPA water based drilling
fluids, allows to get the inhibition values typical of oil-based muds, a class of fluids which is subject to stricter
and stricter environmental regulations. Glycol enhanced water-based drilling fluids are environmentally
acceptable and potentially non-toxic.
Performance evaluation of gravel pack completions
This research topic is aimed to develop a method for the evaluation of productivity of gas wells drilled in the
Adriatic Offshore. Here, almost the totality of the wells is completed in gravel pack (both open-hole gravel-
pack/inside-casing gravel pack), with partial fracturing of the productive formations (Frac-Pack). The study
started with data collection (permeability, net-pay thickness, bottom hole flowing pressure, static bottom-hole
pressure, gas flow rate, etc.) and their integration into a structured database, in which the recorded
parameters are eventually listed in function of time. Data analysis proved its usefulness in calculating several
indexes, which can be utilized for characterizing the well (Pseudo Productivity Index, Flow Efficiency, Skin
factor) during the production phase. However, critical is the evaluation of the non-Darcy’s flow.
Non Darcy’s flow
Darcy’s law cannot describe fluid flow accurately when the flow rate is high. In porous media the Darcy’s law
governs the underground fluid flow and fluid production. But when the flow rate is very high, for instance, in
proximity of the wellbore, the Darcy’s law is inadequate to describe fluid flow. In this study, theoretical and
empirical correlations of the non-Darcy coefficient in one-phase and multi-phase cases in the literature have
G. Gottardi, M. Venutelli, “POLF: two-dimensional finite-element model for predicting the areal flow of pollutant
in confined and unconfined aquifers”. Computers & Geosciences, 24, n. 6, pp. 509-522 (1998).
P. Macini, E. Mesini, “Static and dynamic reservoir rock compressibility at high pressure”, Proc. 8th Adipec
(Abu Dhabi Petroleum Conference), (Abu Dhabi, Oct. 11-14), Paper SPE 49549, pp. 813-820, 1998.
P. Macini, E. Mesini, “Preliminary investigations on glycol-enhanced water-base drilling fluids”, Mineral
Processing & Extractive Metallurgy Review, 20, pp. 301-309 (1999).
N. Bevilacqua, G. Cassiani, P. Macini, E. Mesini, “Compaction monitoring in Adriatic gas fields”, Proc. 10th
International Scientific and Technical Conference ‘New Methods and Technologies in Petroleum
Geology, Drilling, Reservoir and Gas Engineering’, (Krakow, June 24-25), pp. 103-112, 1999.
G. Brighenti, P. Macini, E. Mesini, “Reservoir compaction: a parametric study on in-situ measurements”, Proc.
of the Sixth Int. Symp. on Land Subsidence, (Ravenna, 24-29 Sept.), Vol. II, pp. 17-29, 2000.
G. Brighenti, “Hydrocarbon pollution of subsoil and groundwater: mobile oil recovery by means of gravity
drainage, air or water-flood”, Proc. Int. Symp. on Sanitary and Environmental Engineering, (Trento, 18-
23 Sept.), pp. 421-428, 2000.
P. Macini, E. Mesini, “Compaction monitoring from radioactive marker technique”, Sixth Int. Symp. on Land
Subsidence, (Ravenna, Sept. 24-29), Vol. II, pp. 43-55, 2000.
G. Gottardi, M. Venutelli, “UPF: two-dimensional finite-element groundwater flow model for saturated-
unsaturated soils”, Computers & Geosciences, Vol. 27, pp.179-189 (2001).
G. Brighenti, P. Macini, E. Mesini, “Subsidence induced by offshore gas production in the Northern Adriatic
Sea”, SPE/EPA/DOE Exploration and Production Conference, (S. Antonio, TX, Feb. 26-28), Paper SPE
66571, pp. 1-11, 2001.
G. Gottardi, M. Venutelli, “UPF: two-dimensional finite-element groundwater flow model for saturated –
unsaturated soils”. Computer & Geosciences, 27, pp. 179-189 (2001).
P. Macini, E. Mesini, “Measuring Reservoir Compaction Through Radioactive Marker Technique”, Journal of
Energy Res. Tech., Vol. 124, December 2002, pp. 269-275.
P. Macini, E. Mesini, “Radioactive marker technique applications to evaluate compaction in environmentally
sensitive areas”, SPE International Petroleum Conference and Exhibition, (Villahermosa, Mexico), Feb.
10-12), Paper SPE 74411, pp. 101-112, 2002.
P. Macini, E. Mesini, “Probing the effects on Hydraulic conductivity of grain size distribution and porosity of
soils”, Proc. 9th Congress of the International Association of Engineering Geology, (Durban, Sept. 16-
20), pp. 1566-1575, 2002.
G. Brighenti, P. Macini, E. Mesini, “Rock compressibility measurements help the EIA of gas production in the
Adriatic Sea”, Proc. 9th Congress of the International Association of EngineeringGeology, (Durban,
Sept. 16-20), pp. 895-905, 2002.
G. Brighenti, “NAPL Migration in fractured rocks), Proc. 9th Congress of the International Association of
Engineering Geology, (Durban, Sept. 16-20), pp.1503-1511, 2002.
G. Brighenti, P. Macini, E. Mesini, “Environment and sustainable management of oil and gas reservoirs in
Italy”, SPE/EPA/DOE Exploration and Production Conference, (S. Antonio, TX, Mar. 10-12), Paper SPE
G. Brighenti, “Non-Darcian Two Phase Flow In Fractured Rocks”, Int. Conf. on Groundwater in Fractured
Rocks, (Prague, 15-19 September; Krasny, J., Hrkal, Z., Bruthans, J., Eds.), pp. 101-105, 2003.
L. Sanese, A. Battistelli, G. Gottardi, “Simulazione numerica della migrazione di contaminanti organici in
acquiferi costieri con T2VOC-BRINE”. Ingegneria e Geologia degli Acquiferi, 18, pp. 2003.
G. Gottardi, M. Venutelli, “Central schemes for open-channel flow”. Int. J. Numer. Meth. Fluids, 41, pp. 841-
G. Gottardi, M. Venutelli, “Central scheme for two-dimensional dam-break flow simulation”, Advances in Water
Resources, 27, pp. 259-268 (2004).