INTRODUCTION
This paper reviews previous work done on mathematical modeling of the chemical reactions between sandstone and mud acid, which is a mixture of HF and HC1 acids. These models are lumped-parameter model, two-parameter model, four-parameter model, and detailed chemistry models. The models are compared with the experimental data at different flow rates. The lumped-parameter model simplifies the chemistry of the dissolution of sandstone minerals with mud acid. The two-parameter model predicts lab experiments at high flow rates only. Predictions based on the four-parameter model agreed with the experimental data over a wide range of flow rates. Detailed chemistry models have no advantage in predicting experimental data over the four-parameter model. In addition, detailed chemistry models fail to predict coreflood experiments at low acid injection flow rates.
Oil and gas reservoirs are classified as carbonate or sandstone reservoirs. The main minerals of carbonate reservoirs are calcite (CaCO3) and dolomite (CaMg(CO3)2). The main minerals of sandstone reservoirs are quartz, feldspars, clays and other minerals (Table 1). Drilling, workover and/or longtime operation cause deposition of various minerals around the wellbore, and loss in the productivity or injectivity of the well. The second type of formation damage occurs deep in the formation. However, most of the formation damage occurs near the wellbore. 1'2 Injecting acid, which will react with the damaging minerals can treat damaged wells. Matrix acidization is also done to increase the permeability of tight zones.
Mathematical modeling of matrix acidization goes back to 1960, and many models have been developed since then. This paper reviews these models and highlights advantages and limitations of each model.
CHEMICAL REACTIONS
Both homogeneous and heterogeneous reactions occur during acid stimulation of sandstone reservoirs. Homogeneous reactions occur in the aqueous phase, whereas heterogeneous reactions occur between the aqueous phase and the mineral surface. In heterogeneous reactions, the acid diffuses to the mineral surface, and then reacts with the minerals. When the mass diffusion is infinite, the chemical reaction rate determines the rate of mineral dissolution. However, for infinite reaction rate, mass transfer to the surface determines the mineral dissolution. During acid treatments, both mass diffusion and the rate of reaction determine the heterogeneous reactions. This, however, depends on reservoir temperature and the mineralogy of sandstone.
Lund et al. 3 studied solid-liquid reactions for mud acids using a rotating disk apparatus. They showed that the dissolution of feldspars (albite and microcline) with HCI/HF acid is reaction rate limited at T _<100 "C. Most previous studies done on the modeling of sandstone acidization assumed that mineral dissolution is determined only by the surface reaction. This assumption is valid only at low temperatures where the rate of mass transfer is higher than that of the chemical reactions. Deep in the well, the temperature can be higher than 100 °C.4 Therefore, dispersion cannot be neglected. For surface reaction controlled systems, the consumption rate of acid, Rj, can be calculated using Eq. 1.3
EQUATION (1)
Where rtj is the rate of reaction of a species j with a mineral l, v,j is the stoichiometric coefficient of the acid in this reaction, and Nk is the total number of reactions involved with the species j.
Mud acid is commonly used in sandstone acidization. The reaction between HC1 and quartz and silicates is very slow relative to that between HF and sandstone minerals. Therefore, for sandstone reservoirs w
