Silica Dissolution and Its Inhibition with Quartz Sand: Static Model Approach

Author(s):  
Ashraf Basbar ◽  
Khaled Elraies
2017 ◽  
Vol 56 (1) ◽  
pp. 53-63
Author(s):  
Akvilė Mazanauskaitė

In this paper Nelson-Siegel model has been examined. The main purpose of this paper is to fit the best Nelson-Siegel model to the Euro Area yield curves and to compare with Lithuanian yields in order to draw conclusions about readiness of Lithuania to join the Euro Area. In order to succeed in achieving the goal, Euro Area zero coupon bonds have been examined and various static Nelson-Siegel models were developed. Also, the mean of absolute errorof the Lithuanian government treasury bills was calculated using the best-fitting Nelson-Siegel model of the Euro Areayields. The results have shown that if the static model is calculated for each year, the yield are described precisely in the model.


1985 ◽  
Vol 25 (06) ◽  
pp. 857-864 ◽  
Author(s):  
J.G. Southwick

Abstract The expected loss of useful alkalinity caused by, the slow dissolution of silica from pure quartz sand is shown for some typical alkaline flooding solutions (about 1 % NAOH or 1.25% sodium orthosilicate) to be only about 10 to 20%. This conclusion is based on the observation that alkaline solutions equilibrate with quartz and on the methodology proposed here for determining the useful alkalinity of a solution. Furthermore, the dissolution of quartz in alkaline flooding can be eliminated by the use of solutions saturated in silica with respect to quartz. Such formulations may be useful in controlling the erosion of the wellbore and gravel pack. Introduction Research results emphasize the importance of silica dissolution reactions, both in steamflooding and in alkaline flooding. Rapid dissolution of silica can quickly form a large cavity adjacent to the injection well. In unconsolidated reservoir sands, this cavity could collapse and produce lateral stresses that sever the well casing. Furthermore, for alkaline flooding it is uncertain whether alkaline pulses can propagate through reservoir sands before hydroxide concentrations drop to ineffective levels. Although many mechanisms that consume alkali exist in the reservoir, a recent paper by Bunge and Radke proposed that the slow silica dissolution reaction is of primary proposed that the slow silica dissolution reaction is of primary importance. When scaled to reservoir residence times, their calculations for the dissolution of silica by alkali predict dire conclusions: for many practical well predict dire conclusions: for many practical well spacings and flow rates, hydroxide concentrations drop to ineffective levels after - 15% of the interwell distance is traversed. Important assumptions inherent in their calculations are thatthe dissolution of silica by hydroxide can be treated as an irreversible reaction because the solubility of amorphous silica is not approached, which allows short-term dissolution rates to be extrapolated to reservoir times, andloss of hydroxide ion concentration (or pH,) with time is the critical parameter in estimating alkaline-pulse migration. In this paper, alkaline dissolution experiments are performed with a pure quartz sand. A methodology is performed with a pure quartz sand. A methodology is proposed for estimating the amount of useful alkalinity lost proposed for estimating the amount of useful alkalinity lost because of silica dissolution, and estimates for wellbore erosion are given. It is not the intent of this paper to determine the total alkaline consumption for reservoir sands. Consumption reactions important for reservoir sands such as precipitation of alkali by multivalent cations, and clay transformations-are not considered. However, discussions of the effect that clay minerals and cation precipitation might have on silica dissolution are presented. precipitation might have on silica dissolution are presented. Experimental Procedure Static bottle experiments in which quartz sand is contacted with alkaline solution are used to study silica dissolution. A basic argument in this paper is that the accumulation of silica in alkaline solution during storage with sand at elevated temperatures mimics silica accumulation in a given fluid element as the fluid propacates through the reservoir sand. Two assumptions are inherent in this statement: fluid flow at reservoir rates ft/D f - 0. 3 m/d]) has no effect on the chemical reaction of alkali with solid silica. and the surface area of sand in the static bottle tests does not drop significantly as dissolution proceeds. The first assumption is certainly reasonable, but the second deserves comment. Subsequent results show that the maximum silica dissolution observed in these experiments corresponds to only 0.5% of the quartz sand present in the bottles. Assuming spheres, such a dissolution reduces the surface area of sand grains by about 0.4%; thus the second assumption is also valid. This experimental approach is to determine the changes in soluble silica concentration and alkalinity with increasing time. For this pure quartz sand, soluble silica accumulations can be related directly to reaction rates. (In the absence of clays, aluminum is not present to cause the precipitation of silica in the form of aluminosilicate precipitation of silica in the form of aluminosilicate minerals.) Acid titrations of the alkaline solutions can be particularly useful because they reveal the effects that soluble particularly useful because they reveal the effects that soluble silica has on total alkalinity and buffering capacity. Methods Static Bottle Tests. For static bottle tests, 75 quartz sand (Clemtex No. 5, - 100 mesh) was stored with 33 g of alkaline solution in tightly sealed Teflon bottles at constant temperature. Special inserts were fabricated and placed in the necks of the bottles to [minimize vapor loss. placed in the necks of the bottles to [minimize vapor loss. The bottles were not agitated during storage because sufficient mixing is accomplished by Brownian diffusion and because agitation results in the abrasion or grinding of the sand grains, a phenomenon not encountered in reservoir flooding. Calculations show that Brownian diffusion completely distributes concentration changes caused by silica dissolution through the aqueous phase in 3 days. SPEJ P. 857


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