A dual‐porosity fractal model is derived that considers transient flow from block to fissure, skin between the fissure and the block, and storage capacity and skin effect on the pumping well. Type curves for different flow dimensions are provided. They concern the pumping well and observation wells located either in the fissure system or in a matrix block. The interpretation of a field case using this model shows good agreement between the theoretical drawdown and the observed data, with consistent results from the pumping well and the observation well. A flow dimension of 1.45 is obtained.
A semianalytic solution is given for steady state flow around a well bore or a drift with a complex skin. The hydraulic conductivity of the skin may vary continuously as a function of the radial distance from the well (or drift) and may also be radially anisotropic. Such configurations can be found around damaged or acidized well bores or around a drift near which the stress redistribution induces changes in hydraulic conductivity. Purely radial flow, regional flow around an open or cemented hole without pumping or injection, and combined regional and radial flow are considered. Variations of hydraulic potential and Darcy velocity in various radial directions are studied for several cases and are found to be strongly affected by a complex skin. It is shown that the convergence of the streamlines toward the borehole, which is used in applications involving the point dilution method of measuring regional flow velocity, is significantly enhanced by a complex negative skin. Negative skin values may also reduce the size of the capture zone of a withdrawal well. Head distribution and tracer transport in combined radial and regional flow around a drift have also been modeled. It is demonstrated that tracer breakthrough curves from an experiment of tracer transport from an injection zone in the rock to the drift can be significantly affected by the fluid flow pattern around the drift, so the commonly used radial pattern may lead to erroneous results for tracer dispersivity.
Modelling the discontinuity network of fractured reservoirs may be addressed (1) by purely stochastic means, (2) with a fractal approach, or (3) using mechanical parameters describing the spatial organisation of fracture systems. Our paper presents an approach where the geometrical properties of the fracture networks are incorporated in the form of both statistical and mechanical rules. This type of approach is particularly suitable to model stratified fractured rock masses comprising two orthogonal families of joints and a family of sedimentary discontinuities. Their geometrical arrangement is governed by two kinds of rules based on (1) statistical parameters such as the mean, standard deviation of joint length and of bed thickness, both determined by field observations, and (2) geometrical parameters that result from genetic processes inferred from field observations and analogue experiments on the nucleation and propagation mechanisms of joints. Using these parameters, we generate realistic networks in terms of the relative position of joints that control the overall network connectivity: the model enables all combinations of joint spacing and vertical persistence for orthogonal patterns ranging from ladder type to grid type patterns. It also integrates the concept of mechanical "saturation" of a bed, thereby permitting the generation of both "saturated" and "unsaturated" networks.
A model that incorporates a pseudo-random process controlled by mechanical rules of fracturing is used to generate 3D orthogonal joint networks in tabular stratified aquifers. The results presented here assume that two sets of fractures, each with different conductivities, coexist. This is the case in many aquifers or petroleum reservoirs that contain sets of fractures with distinct hydraulic properties related to each direction of fracturing. Constant rate pump-tests from partially penetrating wells are simulated in synthetic networks. The transient head response is analyzed using the type curve approach and plots, as a function of time, of pressure propagation in the synthetic network are shown. The hydrodynamic response can result in a pressure transient that is similar to a dual-porosity behavior, even though such an assumption was not made a priori. We show in this paper that this dual porosity like flow behavior is, in fact, related to the major role of the network connectivity, especially around the well, and to the aperture contrast between the different families of fractures that especially affects the earlier hydrodynamic response. Flow characteristics that may be interpreted as a dual porosity flow behavior are thus related to a lateral heterogeneity (large fracture or small fault). Accordingly, when a dual porosity model matches well test data, the resulting reservoir parameters can be erroneous because of the model assumptions basis that are not necessarily verified. Finally, it is shown both on simulated data and well test data that such confusion in the interpretation of the flow behavior can easily occur. Well test data from a single well must therefore be used cautiously to assess the flow properties of fractured reservoirs with lateral heterogeneities such as large fractures or small faults.
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