The problem of formation damage (i.e., permeability reduction due to injection of particulates), is a matter of interest in several engineering fields. In the previous attempts to model the external cake formation, cake thickness has been considered to be only dependent on time; even though in practical applications, the dependency of the cake profile on space can be important. In this article, a novel model has been developed to describe the steady state external filter cake thickness profile along the wellbore. A set of equations is derived from the force balance for a deposited particle on the cake surface and the volume conservation of the fluid in the wellbore. These equations are combined with Darcy's law in radial geometry and the equation of flow in the wellbore, and solved numerically to obtain the cake thickness and fluid velocity profiles along the wellbore.
fax 01-972-952-9435. AbstractWe present a new 2D analysis based on the recently developed stochastic bubble population foam model, focusing on the effect of the core heterogeneity. In the frame of the model presented in a parent paper in the conference, we assume that the bubble generation kinetics is dependent on layer permeability. We present experiments consisting of coinjection of N 2 gas and surfactant solution in layered cores, with layering parallel and to the flow directions. The cores are obtained by combining two porous media chosen from Benteimer and Berea sandstone and sintered glass, with large permeability contrast. X-ray computed tomography (CT) scans are used to visualize and quantify local fluid distributions and differentiate foam propagation in the different layers. From both the model and the experiments we conclude that foam is primarily generated in the high-permeability layers, where it propagates at a much higher speed than in the low permeability layer. The propagation of foam in the low permeability layer requires that the pressure gradient is higher than the capillary entry pressure for the layer. The new stochastic population balance foam model reproduces rather well the main features of foam motion in heterogeneous cores containing a surfactant. Core floods combined with CT scan imaging provide valuable specific information about the effect of heterogeneity for better design of acid diversion operations.
The problem of formation damage, i.e., permeability reduction due to injection of particulates, is a matter of interest in several engineering fields. In the previous attempts to model the external cake formation, cake thickness has been considered to be only dependent on time; even though, in practical applications the dependency of the cake profile on space can be important. In this paper a novel model has been developed to describe the steady state external filter cake thickness profile along the well-bore. A set of equations are derived from the force balance for a deposited particle on the cake surface and the volume conservation of the fluid in the well-bore. These equations are combined with the Darcy's law in radial geometry and the equation of flow in the well-bore, and solved numerically to obtain the cake thickness and fluid velocity profiles along the well-bore. 1. Introduction Many oil and gas reservoirs are connected to water source connected to their hydrocarbon reserves. Therefore, the produced fluids are not exclusively hydrocarbons but contain water, often in very large amounts of water Worldwide 75% of the production is water [1] and in some regions this fraction may reach to 98% [2]. Produced water (PW), depending on the geological formation and lifetime of the reservoir, contains organic and inorganic materials including solid particles and oil droplets. Disposal of the PW is a challenge for petroleum industry due to the high costs of the transportation and filtration facilities and the increasingly stricter environmental regulation. One economically and environmentally friendly method is to re-inject the produced water into the formation. By re-injecting the produced water reservoir pressure can be maintained simultaneously. Nevertheless a rapid injectivity decline is usually observed in the PW injection processes due to the presence of impurities, usually solid particles and oil droplets. The injectivity decline is caused by the deposition of the particles inside porous media (internal filtration) [3] or accumulation of the particles on the surface (external filtration) [4]. In the latter case, particles form a cake (porous medium), which is orders of magnitude less permeable than the reservoir. Filtration of the particles in the borehole can occur under either static (dead-end) or dynamic (crossflow) flow conditions. Crossflow filtration refers to a pressure driven separation process in which the permeate flow is perpendicular to the feed flow. In the crossflow filtration, the thickness of the fiklter-cake is limited by the shear forces due to the flow of the produced water containg particles parallel to the borehole surface. A similar phenomenon happens when drilling mud flows across the borehole surface [5]. The drag force caused by the flux of permeate pushes the suspended particles towards the cake. Many authors have investigated the problem of crossflow filtration [6–17]. It has been suggested in the literature that temperature, pressure, shear rate (i.e., flow rate) and the permeability of the formation influences the filtration process. However, the effect of individual parameters has remained unclear [5]. In petroleum engineering transport of fluid containing particles in the subsurface is similar to crossflow filtration. For example, in the fractures, the transport of the particles in the injected fluid results in formation of the cake on the rock surface. Al-Abduwani et al. [18] developed a model to obtain the filter cake profiles in an experimental set-up. Their model can be applied for the formation of cake in the fractures (linear cases). Another example is the build-up of mud cake during the water injection or drilling of the well around the borehole. In this paper we adapt the model described in ref. [18] to obtain the filter cake and velocity profiles in a radial geometry.
Summary Recent developments in the deployment of distributed-pressure-measurement devices in horizontal wells promise to lead to a new, low-cost, and reliable method of monitoring production and reservoir performance. Practical applicability of distributed-pressure sensing for quantitative-inflow detection will strongly depend on the specifications of the sensors, details of which were not publicly available at the time of publication. Therefore, we theoretically examined the possibility of identifying reservoir inflow from distributed-pressure measurements in the well. The wellbore and nearwellbore region were described by semianalytical steady-state models, and a gradient-based inversion method was applied to estimate the specific productivity index (SPI) as a function of along-well position. We employed the adjoint method to obtain the gradients, which resulted in a computationally efficient inversion scheme. With the aid of two numerical experiments (one of which was based on a real well and reservoir), we investigated the effects of well and reservoir parameters, sensor spacing, sensor resolution, and measurement noise on the quality of the inversion results. In both experiments, we generated synthetic measurements with the aid of a high-resolution reservoir-simulation model and used these to test the semianalytical inversion algorithm. In the first experiment, we considered a 2000-m horizontal well passing through two 300-m high-permeability streaks in a background with a permeability that was 10 times lower. The location of the streaks and the SPIs along the well were detected with fair accuracy using 20 unknown parameters (SPI values) and 20 pressure measurements. Decreasing the number of measurements resulted in a poorer detection of the streaks and their SPIs. The detection performance also decreased for increasing noise levels and deteriorated sensor resolution, though the negative effect of random measurement noise was cancelled out primarily by stacking multiple measurements. The detrimental effects of measurement noise and low sensor resolution were strongest in areas where the inflow was lowest (usually close to the toe). The second experiment concerned a high-rate near-horizontal well with slightly varying inclination that intersected a dipping package of formations with strongly variable permeabilities. Additionally, a satisfactory detection of SPIs was obtained even though the heterogeneities were no longer perpendicular to the well as in the first experiment. As a result of using the simple semianalytical forward model and the adjoint method, the inversions typically required less than 90 seconds on a standard laptop. This offered the opportunity to extend the algorithm to multiphase flow and dynamic applications (pressure-transient testing), while still maintaining sufficient computational speed to perform the inversion in real time.
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