A procedure for predicting the stimulation ratio that will result from an acid fracturing treatment is presented. This procedure combines a theoretical model for acid reaction during flow along the fracture and experimentally determined rates of acid transfer to the fracture wall to predict the distance that reactive acid can move along the fracture. This distance, called the acid penetration distance, combined with the fracture conductivity allows the stimulation ratio to be predicted. Stimulation ratios predicted using this procedure are compared to results of acid fracturing treatments in limestone and dolomite formations. Included are treatments in Imperial's Boundary Lake and Quirk Creek fields. The predicted stimulation ratio is in general agreement with observed field results, thereby validating the procedure. Introduction ACID FRACTURING is a production stimulation technique that has been widely used by the oil industry. In an acid fracturing treatment, acid, or a fluid used in a pad prior to the acid, is injected down the well casing or tubing at rates greater than the fluid can flow into the reservoir matrix. This injection produces a buildup in wellbore pressure sufficient to overcome compressive earth stresses and the formation's tensile strength. Failure then occurs and a crack (fracture) is formed. Continued fluid injection increases the fracture's length and width. Acid injected into the fracture reacts with the formation to create a flow channel which remains open when the well is placed back on production. To achieve reservoir stimulation, an acid fracturing treatment must produce a conductive flow channel long enough to alter the flow pattern in the reservoir from a radial pattern to one which approaches linear flow. McGuire and Sikora(1) conducted an analog simulation of the productivity of a fractured well which serves as the basis for predicting the stimulation achievable with vertical fractures. Their study indicated that the variables which determine stimulation ratio are the ratio of fracture length to drainage radius, L/r and the ratio of fracture conductivity to formation permeability, wkr/k. To design an acid fracture treatment, therefore, it is necessary to predict the fracture geometry during the treatment, the fracture conductivity created by acid reaction and the conductive fracture length. A number of authors have studied various portions of the over-all problem of acid fracturing treatment design. Techniques for predicting fracture geometry were first proposed by Howard and Fast(2). Techniques which give improved results have been presented by Kiel(3) and Geertsma and deKlerk(4). Although the formulation of these last two calculation procedures is somewhat different, the resulting geometry predictions are in agreement. Either procedure can therefore be used to predict the dynamic fracture geometry in acid fracturing treatments. Broaddus and Knox(15,23) have carried out experiments to determine the conductivity resulting from acid reaction with different formations and have shown that conductivity is a function of formation type, acid concentration, and contact time between acid and rock. The conductivity which will result from an acid treatment, however, cannot be predicted with certainty.
The wall material thermal conductivity k is one of the surface characteristics that influences the pool boiling heat transfer coefficient (HTC). It is believed that growth rates of vapor bubbles and their frequency are mechanisms affected by the thermal conductivity. In order to investigate this effect, different surface materials (copper, aluminum, stainless steel) are tested in a horizontal surface geometry. From a physical point of view, the redistribution of local heat fluxes between the free surface (wet by the liquid) and the spot covered with nucleation centers is hindered in the case of low values of k. But the wall material k affects the nucleate boiling curve only in the case of a very limited number of nucleation sites. Previous experiments in fact concluded that for a rough surface that has a larger number of vapor generating centers, the wall thermal conductivity does not significantly affect the boiling HTC; therefore the tested surfaces are mechanically polished to avoid any roughness effect. In this paper, nucleate pool boiling curves of saturated nitrogen under ambient pressure are experimentally obtained on a horizontal flat surface and the effect of three different wall materials is evaluated. Hysteresis behaviour has been observed for the copper and aluminum surfaces, while the results for stainless steel are contradictory. The critical heat flux (CHF) is also compared and analyzed by taking into account the thermal effusivity of the different materials. Finally, experimental results are compared against the most common empirical correlations for nucleate pool boiling heat transfer.
During the start-up of the propulsion system of a satellite or spacecraft, the opening of the tank isolation valve will cause the propellant to flow into an evacuated feedline and slam against a closed thruster valve. This filling process, called priming, can cause severe pressure peaks that could lead to structural failure. In the case of monopropellants such as hydrazine, also, the risk of adiabatic compression detonation must be taken into account in the design of the feedline subsystem. The phenomenon of priming involves complex two-phase flow: the liquid entering the evacuated pipe undergoes flash evaporation creating a vapor cushion in front of the liquid that mixes with the residual inert gas in the line. Moreover, the dissolved pressurizing gas in the liquid will desorb making the priming process difficult to model. In order to study this phenomenon, a new test-bench has been built at DLR Lampoldshausen which allows fluid transient experiments in the same conditions as the operating space system. Tests are performed with water and ethanol at different conditions (tank pressure, vacuum level, pressurizing gas helium vs. nitrogen, etc.). The effect of the geometry is also investigated, comparing different test-elements such as straight, tees, and elbow pipes. The pressure profile is found to be dependent on the geometry and on the downstream conditions. The acoustic wave reflection caused by the pipe geometry and fluid dynamic effects such as the aforementioned desorption and flash evaporation induce a complex pressure profile of the first pressure peak. Finally, numerical simulations of the priming process are performed by means of EcosimPro software in conjunction with European Space Propulsion System Simulation (ESPSS) libraries and results are compared with experiments.
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