Abstract
A mathematical model representing the changes in pore structure attending the invasion of a porous material by a reactive fluid tending to dissolve the solid bas previously been tested and found to be valid. This mathematical model is solved by a simulation procedure using Monte Carlo techniques. The results so obtained are indicative of the acidization of sandstone using a last-reacting acid (diffusion limited).
A correlation relating the permeability improvement to the change in porosity is presented and found to be applicable to a wide class of initial pore-size distributions. This means that the designer need not have explicit knowledge of the initial pore structure to utilize the correlation. The generality of the correlation stems from the fact that after exposure to fast-acting acids (diffusion-controlled reactions) wormholing tends to occur in all porous matrices, and the acid allows preferentially through these channels. Thus, the process is independent of the fine pore structure since the fine pores receive no acid Wormholing bas been observed in almost all experimental studies of acidization, thus further confirming the validity of the model.
Introduction
Matrix acidization as practiced in the petroleum industry is a simple operation. Acids treated so as to prevent their corrosive attack on metal parts contacted are pumped down the wellbore and forced into the pore spaces of an oil-bearing rock. The rate of penetration is normally maintained small enough to prevent fracturing of the reservoir The aim of matrix acidization is to enhance the permeability of the region around the wellbore by permeability of the region around the wellbore by dissolving either a portion of the rock or of the foreign impurities that may have been introduced during the drilling operations. The success of this technique of oilwell stimulation is attested to by the fact that a significant fraction of the acids used for stimulation are injected at matrix rates. There were, moreover, in excess of 87 million gal of hydrochloric acid used last year in carbonate formations with many other special purpose acids such as acetic and formic having also been used for stimulation purposes.
Despite the fact that acids have long been routinely used as a means of stimulating oil wells to greater production, there is, as yet, no reliable design procedure incorporating all of the essential features into a prediction of the new production that will result from a given acid treatment of a particular well. This lack of a design procedure particular well. This lack of a design procedure has been responsible for the rather minimal efforts expended in obtaining meaningful reaction rate data, for there is very little enthusiasm for obtaining data which cannot be put to practical application.
This paper is an extension of some recently reported work on predicting the permeability change resulting from acid treatment of an oil-bearing rock. It has been proposed that the changes in the microstructure owing to acidization in a porous rock can be simulated by considering the effect of acidization of a collection of small, randomly distributed capillaries that are interconnected to the extent that a fluid will be conducted from point to point under the influence of an external pressure gradient. This model, the capillaric model, has been used with varying success in understanding the behavior of porous media. The use of the capillaric model in determining only the results of the evolution of a pore-size distribution, rather than as a vehicle for predicting a number of mare or less independent phenomena, such as capillary pressure curves and dispersion, is, as has been pressure curves and dispersion, is, as has been noted by Schechter and Gidley, a more limited and perhaps attainable goal. Taking the capillaric model to be correct, Guin et al. have shown that an equation relating the porosity change and the permeability change caused by an ideally retarded permeability change caused by an ideally retarded acid can be derived without any assumptions.
SPEJ
P. 390
Mathematical Model to Simulate the Transfer of Heavy Metals from Soil to Plant