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The polymerization of dissolved silica in aqueous solutions up to 100 degrees C and containing up to 1 M NaCl has been studied experimentally, and theoretically. In this paper, the results of this work are presented in a form suitable for practical use in interpreting and predicting the chemistry of silica in geothermal brines. Empirical equations for calculating the rate of molecular deposition of silica on surfaces as a function of silica concentration. temperature, pH. and salinity are presented. Theoretically calculated type curves that depict the decrease of dissolved silica concentration by homogeneous nucleation and particle growth are presented, along with the procedures for using them to predict the course of this process under different conditions. Introduction Usually, silica precipitates from geothermal brines as colloidal amorphous silica (AS). The process of AS precipitation consists of the following steps.Random growth of silica polymers past critical nucleus size. Above this size, the polymers become colloidal AS particles that are large enough to grow spontaneously and without interruption. This process is called homogeneous nucleation.Growth of the supercritical AS particles by further chemical deposition of silicic acid on their surfaces.Coagulation or flocculation of the colloidal particles to give a floc-like precipitate or gel.Cementation of the coagulated particles by chemical bonding and further deposition of silica between them to form silica scale and other solid deposits. The preceding sequence of processes occurs when the concentration of dissolved silica is high enough for homogeneous nucleation to occur at a significant rate. Very roughly, this requires supersaturation by a factor of 2.5 or more. If this condition is met, rapid polymerization occurs, and massive precipitation or scale deposition may follow. This is the case with the brine at Niland (CA). Cerro Prieto (Mexico), and Wairakei (New Zealand). after it has been flashed down to atmospheric pressure. The voluminous floc-like silica deposits encountered in these areas consist of colloidal AS that has been flocculated by the salts in the brine. The crumbly gray and white scales associated with this material are cemented aggregates of colloidal silica. If the concentration of dissolved silica is too low for rapid homogeneous nucleation to occur, relatively slow heterogeneous nucleation and the deposition of dissolved silica directly on solid surfaces become the dominant polymerization processes. The product of the latter process (essentially Step 2 of the preceding sequence alone) is a dense vitreous silica. At higher temperatures, this process may produce scale at a significant rate. This paper has two purposes: to summarize succinctly and quantitatively what we have learned in our kinetic studies of silica polymerization and to demonstrate by example how our results may be applied to studying practical problems in geothermal energy utilization. Because it is a summary, actual experimental data and most details of derivation have been omitted, they may be found else where. Because some of the material in this paper is condensed from an earlier paper, it is partly of a review nature. It is an updated version of an earlier article. Studies of the actual formation of silica scale and the removal of colloidal silica from geothermal brines have been reported elsewhere. Molecular Deposition on Solid Surfaces By molecular deposition we mean the formation of compact, nonporous AS deposits by chemical bonding of dissolved silica directly onto solid surfaces. This is also the mechanism by which colloidal silica particles grow once nucleated. SPEJ P. 9^

When producing from an unconsolidated sand, sand arches may form behind the perforation opening. On the basis of a theoretical model, we have analyzed the stresses in the sand. The effect of flowing fluids has been studied, and criteria describing the stability and failure of the sand are given.The arching phenomenon was studied in the laboratory. The experiments qualitatively reproduced the theoretical results. To the extent that comparison was possible, the quantitative agreement between theory and experiments was fairly good. Introduction Literature Survey The principle of arching, where a self-supporting structure is spanning an opening, has been known and used in manmade constructions for centuries. The first analysis of this mechanism, related to the earth sciences, was done by Terzaghi in his trapdoor experiment. He used a box filled with sand where a section of the bottom (trap door) could be removed. He observed that the sand was able to transfer the loads exerted on the trap door to its surroundings as the trap door was removed. The work was done to get a better understanding of the stress distribution around tunnels, and he concluded that arching is a real and stable phenomenon that is insensitive to flow.Paslay and Cheatham studied the stresses induced by a flowing fluid into a wellbore. Geertsma recently studied this and other rock mechanical problems related to sand-free petroleum production. These studies were based on the work Blot did on three-dimensional consolidation. Medlin and Masse recently presented a paper concerning laboratory investigation of fracturing pressures, also based on Blot's work.Hall and Harrisberger called attention to the trap-door experiment again when they studied the stability of sand arches and its relation to maximum sand-free production rate. They found that arching may be rate sensitive at low confining stress levels, while it is independent of flow rate at high confining stress levels. They did not quantify the rates at which an arch failed when it is in the rate-sensitive region.Stein and coworkers assumed that the maximum flow rate an arch can withstand is proportional to the shear modulus G for the sand, which is obtained from density and acoustic logging data. Bradley has worked out a semiempirical approach to the wellbore stability problem, discussing specially inclined boreholes. This approach is useful to predict when the limit of elastic behavior is reached; however, it gives no information on the behavior in the plastic state.At the Colorado School of Mines a program has begun laboratory studies of the arching phenomenon and its relation to flow rate and confining stress level. As this work is still in progress, no final conclusions have been drawn. However, preliminary results seem to be very similar to the observations made in our experiments. Qualitative Description of the Experiments The laboratory model used to study the arching phenomenon consisted of a steel cylinder with a central hole in the bottom to simulate a perforation. This cylinder was filled with unconsolidated sand and compressed vertically by a piston to simulate overburden. Fluid was introduced at the top beneath the piston, spread over the total area by a multiwrapped wire screen, and forced through the sandpack. SPEJ P. 236^

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