Stimulation of carbonate formations by acid dissolution of the rock has been an efficient and successful method of bimproving production in oil and gas wells. Hydrochloric acid is the normal fluid of choice. However, in high temperature applications corrosion issues limit usage, especially in chrome completions. Acetic acid has been used with some success and with adequate corrosion protection. But due to its low reactivity at higher temperatures, the efficiency with which a gallon of acid dissolves the formation is perceived as low. This perception comes from reaction efficiency of acetic acid reported in the literature ranging in values from 90% at 25 °C to 40% at 121 °C for 2 to 15 wt%, respectively. Acetic acid reaction on calcium carbonate is controlled by its small dissociation constant, 1.754E-05 at 25 °C (77 °F) and therefore is labeled a weak acid.
The effects of permeability variable in formation on pressure derivative curve are studied in this paper. We view the general heterogeneous reservoir as a base homogeneous reservoir modified with multiple variable permeabilities at some locations. The sections where permeabilities are different from the base permeability are called as the variable permeability sections. A heterogeneous reservoir with only one variable permeability section can be well defined as long as the permeability, the size and the location of the section are specified. Its pressure derivative deviation from that of the base homogeneous reservoir has been thoroughly studied. Results show that the start time and the value and the occurred time of maximum magnitude of the pressure derivative deviation suggest the start position, the permeability and the end position of the variable permeability section, respectively.
In order to analyze a heterogeneous reservoir with multiple variable permeability sections, we proposed that its pressure derivative difference with respect to the base homogeneous reservoir is the summation of the pressure derivative differences, with respect to the base homogeneous reservoir, of the single-section multiple heterogeneous reservoirs, each of them possesses only one variable permeability section. This method has been proved and verified in the reservoirs with radial and areal permeability distribution using both analytical and numerical methods.
Applications show that this method provides a useful clue for heterogeneity reservoir well testing analysis. If the test noise can be ignored in pressure derivative curve, this method is very practicable for well testing analysis of variable permeability reservoirs. In the cases where pressure noise makes the pressure derivative zigzag, some de-noising methods, for example Schroeter's deconvolution method, wavelets and optimal model, can be used to de-noise pressure data in order to get smooth pressure derivative curve. Then, this de-noised test data can be diagnosed using the method proposed.
Traditional well testing analysis tends to determine an overall permeability, which cannot reflect the variation of permeability in formation. In our experiences on practical well testing interpretation, we often encounter the situations that we can match the shape and the trend of the pressure derivative curve perfectly, but we cannot match the slight waves in the pressure derivative curve. Generally there are two sources that produced these kinds of waves, pressure measurement noise and the response of heterogeneity of the reservoir. The waves generated from the pressure measurement noise are random and discontinuous, while those from the heterogeneity of the reservoir behave continuously and smoot