Triple Porosity Research Articles

Unsteady inter-porosity flow modeling for a multiple media reservoir

The paper deals with unsteady inter-porosity flow modeling of underground fluid in a multiple media reservoir. Assuming spherical vugs, symmetrically distributed pressure, negligible inter-porosity flow between matrix and vug systems and centrifugal flow of the fluid from matrix blocks or vugs to fractures, and treating media directly connected with wellbore as the fracture system, we establish and solve a model of unsteady inter-porosity flow for dual and triple porosity media reservoirs. We provide simulated graphs of pressure and pressure derivative log-log type curves, and analyze the transient flow process and characteristics of type curves affected by different parameters. The new type curves of unsteady inter-porosity flow modeling are evidently different in shape and characteristics from those of pseudo-steady inter-porosity flow modeling. The location of dimensionless pressure of unsteady inter-porosity is lower than that of pseudo-steady inter-porosity, which indicates that unsteady inter-porosity flow accelerates an energy supplement during production. Qualitatively, the unsteady inter-porosity flow modeling reduces the classical V-shaped response. We also estimated parameters from well test data in real applications using this model.

History matching of enhanced coal bed methane laboratory core flood tests

Abstract Enhanced coalbed methane (ECBM) involves the injection of a gas, such as nitrogen or carbon dioxide, into the coal reservoir to displace the methane present. Potentially this strategy can offer greater recovery of the coal seam methane and higher rates of recovery due to pressure maintenance of the reservoir. While reservoir simulation forms an important part of the planning and assessment of ECBM, a key question is the accuracy of existing approaches to characterising and representing the gas migration process. Laboratory core flooding allows the gas displacement process to be investigated on intact coal core samples under conditions analogous to those in the reservoir. In this paper a series of enhanced drainage core floods are presented and history matched using an established coal seam gas reservoir simulator, SIMED II. The core floods were performed at two pore pressures, 2 MPa and 10 MPa, and involve either nitrogen or flue gas (90% nitrogen and 10% CO2) flooding of core samples initially saturated with methane. At the end of the nitrogen floods the core flood was reversed by flooding with methane to investigate the potential for hysteresis in the gas displacement process. Prior to the core flooding an independent characterisation programme was performed on the core sample where the adsorption isotherm, swelling with gas adsorption, cleat compressibility and geomechanical properties were measured. This information was used in the history matching of the core floods; the properties adjusted in the history matching were related to the affect of sorption strain on coal permeability and the transfer of gas between cleat and matrix. Excellent agreement was obtained between simulated and observed gas rates, breakthrough times and total mass balances for the nitrogen/methane floods. It was found that a triple porosity model improved the agreement with observed gas migration over the standard dual porosity Warren–Root model. The Connell, Lu and Pan hydrostatic permeability model was used in the simulations and improved history match results by representing the contrast between pore and bulk sorption strains for the 10 MPa cases but this effect was not apparent for the 2 MPa cases. There were significant differences between the simulations and observations for CO2 flow rates and mass balances for the flue gas core floods. A possible explanation for these results could be that there may be inaccuracy in the representation of mixed gas adsorption using the extended Langmuir adsorption model.

The Application of Boundary Element on Pressure Transient of Carbonat Reservoir

ABSTACT: The effect of the shape of reservoir boundaries on the well-bore pressure response is evident. The conventional analytical methods can only be used to calculate well-bore pressure response in regularly shaped reservoirs. A mathematical model for well test interpretation of arbitrary shaped triple porosity reservoir was established and transformed to modified Helmholtz equation in this paper. By using the boundary element method and Duhamel principle, well-bore pressure with effects of skins and well-bore storage is obtained. The type curves are plotted and analyzed considering effects of the dimension fracture storage parameter, the inter-porosity flow parameter, arbitrary shape and impermeable barries. At last, the boundary element method is verified against the analytical solution and is applicable to transient pressure analysis of arbitary shaped reservoir. KETWORDS: carbonate reservoir, triple porosity, boundary element method, transient pressure, type curve

Effect of Fracture Dip on Petrophysical Evaluation of Naturally Fractured Reservoirs

Abstract Recent models show the means of estimating the petrophysical porosity exponent (m) of a reservoir when it is composed of different combinations of matrix, fractures and vugs. For both dual and triple porosity reservoirs, the system is modelled as a parallel resistance network (for matrix and fractures), a series resistance network (for matrix and non-connected vugs) or a combination of parallel/series resistance networks (for matrix, fractures and non-connected vugs). In the case of matrix/fractures, it has been assumed that the flow of the current is parallel to the fractures. This paper shows the effect on m of current flow that is not parallel to the fractures. This type of anisotropy is co-relatable with fracture dip. Maxwell Garnett mixing formula for calculating effective permittivity of a system with aligned ellipsoids and depolarization factors of 0 and 1 leads to the parallel and series resistance networks used in the paper. It is concluded that the change in fracture dip can have a significant effect on the value of m. Not taking this into account can lead, in some cases, to significant errors. The effect of the change of fracture dip on water saturation calculations is illustrated using two examples. Introduction The petrophysical analysis of fractured and vuggy reservoirs has been an area of abundant interest in the oil and gas industry. For example, a key ingredient for successful completion of wells in naturally fractured tight gas formations is the ability to distinguish gas from water-bearing intervals. Proper estimates of petrophysical parameters, including the porosity or cementation exponent m, play an important role in correct estimations of watersaturation (Sw). Towle(1) gave consideration to some assumed pore geometries, as well as tortuosity, and noticed a variation in the porosity exponent m in Archie's(2) equation ranging from 2.67 to 7.3+ for vuggy reservoirs and values much smaller than 2 for fractured reservoirs. Matrix porosity in Towle's models was equal to zero. Aguilera(3) introduced a dual porosity model capable of handling matrix and fracture porosity. That research considered three different values of the porosity exponent: one for the matrix (mb), one for the fractures (mf = 1) and one for the composite system (m). It was found that as the amount of fracturing increased, the value of m became smaller. Rasmus(4) and Draxler and Edwards(5) presented dual porosity models that included potential changes in fracture tortuosity and the porosity exponent (mf) of the fractures. The models are useful, but must be used carefully as they calculate values of m > mb as the total porosity increases, even when the flow of current goes parallel to the fractures. Serra(6) developed a graph of the porosity exponent (m) versus total porosity for both fractured reservoirs and reservoirs with non-connected vugs. The graph is useful, but must be employed carefully as it can lead to errors for certain combinations of matrix and non-connected vug porosities(7). The main problem with the graph is that Serra's matrix porosity is attached to the bulk volume of the 'composite system.'

Application of the triple porosity model in well–log effectiveness estimation of the carbonate reservoir in Tarim oilfield

In carbonate reservoirs, effectiveness estimation using logging data has great challenges. According to the pore structure characteristics of the fractured and vuggy carbonate reservoir, Aguilera and Aguilera [Roberto F. Aguilera and Roberto Aguilera, 2004. A Triple Porosity Model for Petrophysical Analysis of Naturally Fractured Reservoir, Petrophysics, 45(2):157–166.] presented a triple porosity model, in which the secondary porosity was divided into connected fractured (and/or) vuggy porosity and non-connected vuggy porosity. In this paper, a new technology is presented to determine the values of the different porosity in the triple porosity model. Based on lateral logs responses, we derive analytical equations that contain connected fractured (and/or vuggy) porosity, non-connected vuggy porosity, matrix porosity and so on. Using these equations and the conventional log data, we can obtain the petrophysical parameters, such as connected fractured porosity, non-connected vuggy porosity and so on. Then the connected fractured (and/or vuggy) porosity and its percentage in the total porosity are used to indicate the effectiveness of the carbonate reservoir. This method has been applied for the well log interpretation of the 123 testing intervals from the 52 wells in Tarim oil field. Agreement ratio of the interpretation results is 91%, which verifies the validity of the presented method.

Pathogen and chemical transport in the karst limestone of the Biscayne aquifer: 3. Use of microspheres to estimate the transport potential of Cryptosporidium parvum oocysts

The vulnerability of a municipal well in the Northwest well field in southeastern Florida to potential contamination by Cryptosporidium parvum oocysts was assessed in a large‐scale, forced‐gradient (convergent) injection and recovery test. The field study involved a simultaneous pulse introduction of a nonreactive tracer (SF6, an inert gas) and oocyst‐sized (1.6, 2.9, and 4.9 μm diameter) carboxylated polystyrene microspheres into karst limestone of the Biscayne aquifer characterized by a complex triple (matrix, touching‐vug, and conduit) porosity. Fractional recoveries 97 m down gradient were inversely related to diameter and ranged from 2.9% for the 4.9 μm microspheres to 5.8% for 1.6 μm microspheres. Their centers of mass arrived at the pumping well approximately threefold earlier than that of the nonreactive tracer SF6 (gas), underscoring the need for use of colloid tracers and field‐scale tracer tests for these kinds of evaluations. In a modified triaxial cell using near in situ chemical conditions, 2.9 and 4.9 μm microspheres underestimated by fourfold to sixfold the attachment potential of the less electronegative 2.9–4.1 μm oocysts in the matrix porosity of limestone core samples. The field and laboratory results collectively suggested that it may take 200–300 m of transport to ensure even a 1‐log unit removal of oocysts, even though the limestone surfaces exhibited a substantive capability for their sorptive removal. The study further demonstrated the utility of microspheres as oocyst surrogates in field‐scale assessments of well vulnerability in limestone, provided that differences in attachment behaviors between oocysts and microspheres are taken into account.

OIL POLYMERISATION AND FLUID EXPULSION FROM LOW TEMPERATURE, LOW MATURITY, OVERPRESSURED SEDIMENTS

A mechanism for hydrocarbon expulsion from low temperature (T = <20 – 150° C), low maturity (Ro=<0.6), overpressured sediments (clays, shales and enclosed sands) with active hydrocarbon concentration and/or generation is outlined. Low temperature polymerisation of light hydrocarbons (e.g. biogenic methane) is considered to be a potential source for some oils found in association with hydrates (resulting from fluidisation discharges from overpressured zones), and some oils found in shales displaying suppression of vitrinite reflectance. It is observed that low temperature polymerisation will increase the potential pressure load retained within an overpressured zone and increase the overall volume of gas/fluids discharged on pressure release.Field observations, including measured recharge volumes and the fluid discharge volumes through a chimney from an overpressured zone, have been used to produce a triple porosity, poroelastic fluidisation expulsion model which links the discharge volume to pressure loading. The model predicts that expulsion from an active pressure mound will be cyclic and episodic.Published geochemical results from seismic chimneys in the Lower Congo Basin have been reinterpreted using the model to demonstrate that expulsion through a chimney is episodic, and to identify overpressured zones where the dominant fluid is oil and others where the overpressured zone contains both oil and gas. It is suggested that some of the oil in these overpressured zones, currently interpreted as thermogenic, may be derived from the polymerisation of biogenic gas.

Homogenization of a degenerate triple porosity model with thin fissures

We consider the problem of modelling the flow of a slightly compressible fluid in a periodic fractured medium assuming that the fissures are thin with respect to the block size. As a starting point we used a formulation applied to a system comprising a fractured porous medium made of blocks and fractures separated by a thin layer which is considered as an interface. The inter-relationship between these three characteristics comprise the triple porosity model. The microscopic model consists of the usual equation describing Darcy flow with the permeability being highly discontinuous. Over the matrix domain, the permeability is scaled by $(\varepsilon \delta)^2$ , where $\varepsilon$ is the size of a typical porous block, with $\delta$ representing the relative size of the fracture. We then consider a model with Robin type transmission conditions: a jump of the density across the interface block-fracture is taken into account and proportional to the flux by the mean of a function $(\varepsilon\delta)^{-\gamma}$ , where $\gamma$ is a parameter. Using two-scale convergence, we get homogenized models which govern the global behaviour of the flow as $\varepsilon$ and $\delta$ tend to zero. The resulting homogenized problem is a dual-porosity type model that contains a term representing memory effects for $\gamma\le 1$ , and it is a single porosity model with effective coefficients for $\gamma >1$ .

Karst groundwater: a challenge for new resources

Karst aquifers have complex and original characteristics which make them very different from other aquifers: high heterogeneity created and organised by groundwater flow; large voids, high flow velocities up to several hundreds of m/h, high flow rate springs up to some tens of m3/s. Different conceptual models, known from the literature, attempt to take into account all these particularities. The study methods used in classical hydrogeology—bore hole, pumping test and distributed models—are generally invalid and unsuccessful in karst aquifers, because the results cannot be extended to the whole aquifer nor to some parts, as is done in non-karst aquifers. Presently, karst hydrogeologists use a specific investigation methodology (described here), which is comparable to that used in surface hydrology. Important points remain unsolved. Some of them are related to fundamental aspects such as the void structure – only a conduit network, or a conduit network plus a porous matrix –, the functioning – threshold effects and non-linearities –, the modeling of the functioning – double or triple porosity, or viscous flow in conduits – and of karst genesis. Some other points deal with practical aspects, such as the assessment of aquifer storage capacity or vulnerability, or the prediction of the location of highly productive zones.

Matrix permeability of the confined Floridan Aquifer, Florida, USA

The Upper Floridan Aquifer of peninsular Florida retains most of its depositional porosity and, as a result, is a multi-porosity aquifer: double porosity (fractured porous aquifer) downdip where the aquifer is confined, and triple porosity (karstic, fractured porous aquifer) in the updip, unconfined region. Matrix permeability in the confined region varies in the range <10−14.4–10−11.1 m2, as determined by 12,000 minipermeameter measurements on 1,210 m of slabbed core. Limestones divide into 13 textural classes and dolomites into two. Depositional facies (textural class) strongly correlates with matrix permeability. As a result, the facies architecture of the Eocene and Oligocene carbonates that compose the confined portion of the aquifer controls the lateral and vertical distribution of its matrix transmissivity. The most-permeable facies are grainstones (median k, 10−12.4 m2) and sucrosic dolomites (median k, 10−12.0 m2). Together, they are responsible for ~73% of the matrix transmissivity of the logged cores, although they constitute only ~24% of the thickness. Examination of the flow equations of fractured porous aquifers suggests that the permeability of these two facies is large enough that matrix permeability cannot be discounted in modeling the hydraulics of the double-porosity system. This conclusion likely applies to most, if not all, Cenozoic double-porosity carbonate aquifers, as average matrix and fracture permeabilities in the Floridan Aquifer are similar to other Cenozoic carbonates from around the world.

Hydraulic Behavior and Contaminant Transport in Multiple Porosity Media

The hydraulic behavior and contaminant transport of aquifers containing distinct families of fractures are investigated by using the multiple porosity continuum model. We consider that the conditions are such that a horizontal 2D flow takes place. By writing the continuity of mass (including exchange terms between the various families of fractures) and Darcy's law for each family of fractures, macroscopic equations for both confined and unconfined flow are obtained. A classification procedure and geometrical idealization of the individual fractures for each family is proposed which enables the calculation of the exchange coefficients. Equations for the description of the contaminant transport in the field scale for both confined and unconfined aquifer are developed. It turns out that the adequate formulation of the macroscopic equations and their sink-source term depends on whether the aquifer investigated is confined or unconfined, and also on the value of an nondimensional parameter describing the transfer process at the microscopic scale (connection Peclet number). Numerical investigation of representative problems offers some insight into the behavior of double and triple porosity aquifers.

Exact solution of unsteady axisymmetrical two-dimensional flow through triple porous media

This paper seeks for the line source and cylindrical plane source solutions of unsteady axisymmetrical two-dimensional flow through infinite and finite reservoirs with triple porosity. They not only reveal the essential characteristics of fractured reservoirs but also generalize and develop the existing primal results of homogeneous and porous media.