GNGTS 2014 - Atti del 33° Convegno Nazionale

where F is the ratio between electrical conductivity of fluid and electrical conductivity of porous media, ε 0 is the vacuum dielectric permittivity (8.854x10 -12 F/m), ε r is the fluid dieletric permittivity , �� �� ��� ����� ������� ��������� ������� �� �� ��� ��������� ���������������� ���� η� �� ��� ����� ������� �� �� ��� ��������� is the fluid dynamic viscosity [Pa.s], ζ� is the so-called “zeta-potential” [V]. Moreover, due to the Ohm’s law, the l 11 coefficient could be assumed as equal to the electrical conductivity of porous media [S/m] and, due to the Darcy’s law, the l 22 coefficient could be assumed as equal to its permeability [m 2 ]. With this kind of assumption, Eqs. (1) and (2) could be rewrite as : (4) (5) Eq. (4) is the generalized Ohm’s law. Its first term coincides with conduction electrical current (Ohm’s law) while the second one corresponds to convection electrical current induced by a displacement of electrical charges existents in the double layer. Eq. (5) is the generalized Darcy’s law. Its first term describes the fluid flow induced from an electrical potential difference while the second term embodies a flux of fluid originated by a pressure gradient. Considering Eq. (4) and combine it with conservation of total current density in the absence of external sources it follows: (6) In this diffusive equation the right term represents electrical sources generated by electrokinetism. Eq. (6) can be developed as: (7) Being the electrokinetic coupling coefficient constant (Darnet et al., 2003), only the last source of the right term of the Eq. (7) has to be considered. Also the conductivity of the underground has to be taken into account, in the case of self-potential generated in heterogeneous media. In this paper, a heterogeneous conductive model has been adopted for the underground that consider the resulting of a magnetotelluric survey realized in the area (Geierman et al., 2010). l, as stated above, represents the electrokinetic coupling coefficient of the injected fluid. In most cases, instead of l, the streaming potential coupling coefficient C is considered, that results equal to l divided by the rock electrical conductivity σ r , that is only temperature- and salinity- dependent . Following Revil et al. (1999b), (8) Where f is the fluid dynamic viscosity [Pa.s], ε f is the fluid dielectric permittivity [F/m], σ f is the fluid electrical conductivity [S/m] and is the “zeta-potential” [V] at the fluid/matrix interface generated by the chemical interaction of the rock and the fluid. The fluid viscosity and dielectric constant are only temperature-dependent , while the fluid electrical conductivity is temperature- and salinity-dependent. The zeta potential is also temperature- and salinity- dependent and we used the results of Revil et al. (1999a) for quartz-water systems. To estimate streaming potential coupling coefficient, Darnét et al. (2003) used the downhole temperature and salinity of injected fluid during and after pumping stimulation. At the start of the stimulation experiment, when brine is injected, C is weak (less than 2 mV/bar) but as soon as fresh water is injected, it increases and reaches the value of 200 mV/bar, remaining constant until shut-in. After shut-in, even if no more fluid is injected, C increases further caused by thermal effect. The average value of C, around 200 mV/bar, can be considered a good approximation for 226 GNGTS 2014 S essione 1.3