Double porosity

Actual responses of tuo carbonate petroleum reservoirs to matrix injection of hydrochloric acid are compared with a recently proposed experimental model for wormholing. This model is shown to be applicable in undamaged primary porosity reservoirs, and should be useable in damaged double porosity ones. Formations of no primary porosity are shown to respond very differently. 

The dissolution channels (wormholes), obtained under certain conditions of attack of carbonate rocks by hydrochloric acid, have been recently proven to have a fractal geometry. An equation was proposed, relating the increase of the equivalent wellbore radius (i.e. the decrease of the skin) to the amount of acid injected, in wellbore geometry and in undamaged primary porosity rocks. This equation is herein extended to damaged double porosity formations through minor modifications. 

In damaged double porosity reservoirs, the influence of the fractal dimension df is masked by the severity ratio kpp/kpp (Equation 12). ... 

The actual response of Well A to the injection of acid cannot fit with any kind of theoretical equation for undamaged primary porosity or damaged double porosity reservoir. Therefore, the acid attack in secondary porosity formations proceeds very differently, as expected. 

Figure 1 Permeability profile in a damaged double porosity reservoir during acidizing. rw wellbore radius, re wormholes penetration, damage radius, kptp undamaged reservoir permeability (total contribution of both primary and secondary porosities), kPP damaged permeability (primary porosity contribution only).

Confined, homogeneous, Double porosity block Curve fitting 1 Fractured rock or karst Boulton and Streitsova... 

The oil industry has developed and used a double porosity model to describe flow in certain fracture systems (7). Little data on application to actual field problems are available in the literature suggesting that this model has had only limited success and has been used only after the fact, not in a predictive mode. 

Goode DJ (1999) Age,double porosity,and simple reaction modifications for the MOC3D ground-water transport model. Water-Resources Investigation Rep 99-4041. United States Geological Survey, Washington, DC... 

Convection, diffusion, and dispersion can only describe part of the processes occurring during transport. Only the transport of species that do not react at all with the solid, liquid or gaseous phase (ideal tracers) can be described adequately by the simplified transport equation (Eq. 94). Tritium as well as chloride and bromide can be called ideal tracers in that sense. Their transport can be modeled by the general transport equation as long as no double-porosity aquifers are modeled. Almost all other species in water somehow react with other species or a solid phase. These reactions can be subdivided into the following groups, some of which have already been considered in the previous part of the book. 

Aquifers with double porosity (e.g. sandstones with fractures and pore volume) require special considerations with regard to transport modeling even if no reactive mass transport in its proper sense is taken into account. This problem is demonstrated with the following example of an aquifer regeneration in an uranium mine. The ore was leached in this mine by in-situ leaching (ISL) using sulfuric acid. The hydrochemical composition of the water that is in the aquifer after this in-situ leaching process is shown as ISL in Table 40 ... 

Fig. 45 Scheme for the model approach of a double porosity aquifer... 

In this chapter we use a three-dimensional version of the ILG model to simulate liquid infiltration in double porosity porous media. Our objective is to compare this approach with the kinematic wave analytical solution. Lattice gas methodology provide information that we are not able to obtain with available experimental methods. 

Di Pietro, L., and F. Lafolie. 1991. Water flow characterization and test of a kinematic wave model for macropore flow in a highly contrasted and irregular double porosity medium. J. Soil Sci. 42 551-563. 

The impurities stick to the periphery of particle pores making the gas flow into the catalyst difficult or impossible. This in turn leads to a considerable increase in the diffusion resistances during the catalytic process. One way of fighting this phenomenon is to use double-porosity alumina. Micropores of about 20 nm are always useful to develop the specific surface area necessary for a good dispersion and stability of the catalytic phase. Macropores over 100 nm in diameter help to diffuse the reagents within the particles. However, the proportion of macropores must not be too great, as that would diminish the mechanical properties of the support correspondingly. For this reason, Rhone Poulenc has, since 1974, developed and marketed various exhaust, gas catalyst supports with specific surface areas of 2... 

Double porosity model. The double porosity model (Wang 1993 Skelton et al. 

Examples of double porosity models applied to stable isotope transport in regional and contact metamorphism are given by Bowman et al. (1994) (see discussion of Alta contact aureole below), though this is not explicitly stated. Curves calculated for onedimensional transport using a first order rate law were fitted to observed profiles with a... 

Rebour et al. (1997) review the literature describing gas diffusion in a porous medium as a double porosity process. In this model, gas diffusion is affected by the increase in water viscosity when in the close vicinity of clay minerals. This produces an environment in which the gas diffusion rate is expected to be variable in the porous network depending on the local tortuosity and grain-size distribution. In modeling this type of system, diffusion is considered to occur along a direct pathway. These fast routes interconnect slow regions, into and out of which gas also diffuses. Experimental work by the same authors (Rebour et al. 1997) determines Rf = 200 for a clayey marl from Paris basin Callovo-Oxfordian sediments that have a porosity and permeability of 23% and 10 m, respectively. 

H- He dating has also been applied in fractured rock aquifers (Cook et al. 1996 Aeschbach-Hertig et al. 1998). Typical problems encountered in fractured systems are their extreme heterogeneity, double porosity causing differences between hydrodynamic and H- He age, and geochemical complications due to the presence of other He sources. 

Wu Y and Zhang Z. 1996. An application of generalized double porosity media model for coupled stress and groundwater flow analysis in fractured rock mass. J. of Engineering Geology, 1(3), pp. 40-46. 

The specific nature of the host rock (fractured tuff) makes it necessary to recognize that a double porosity and double permeability play a role in the hydrological problem. Properties that correspond to the tuff in the vicinity of the drift (tptpmn) are sutiunarized in Table 1. Properties for tptpul and tptpll are in the same range and can be found elsewhere. 

A DOUBLE-POROSITY POROELASTIC MODEL TO RELATE P-WAVE ATTENUATION TO FLUID FLOW IN VUGGY CARBONATE ROCK... 

The bulk modulus Ki of the rock matrix in terms of the grain density, Pj, the P- and S-wave velocities of the dry skeleton (v, vj, and the porosity allow us to constrain the double porosity model by use of the well log data and the equation. 

Where K, is the modulus of the solid grain, is porosity, and c is a consolidation parameter that represents the sediments and fluid inside the vugs (unconsolidated material). We use c = 200. The effective compressional modulus (harmonic average of the Ki and /fj drained moduli) and the shear bulk modulus, G, of the double porosity medium can be obtained, respectively, from... 

Where 0 is the effective porosity of the double porosity medium given by... 

Pride, S., and Berryman, J., 2003. Linear dynamics of double-porosity and dual-permeability materials, submitted to Geophysical Letters. 

ON THE CONSTITUTIVE MODELLING OF THERMO-HYDRO-MECHANICAL COUPLING IN ELASTIC MEDIA WITH DOUBLE POROSITY... 

In this paper, the governing equations for THM processes in an elastic medium with double porosity are derived using a systematic... 

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