The productivity index of a horizontal well in an anisotropic medium i
s calculated during a process of partial acidization in which damage r
emoval occurs only over a fraction of the length of the well. Two nume
rical simulators are used in this work: an acidizing simulator which c
alculates the permeability distribution around the wellbore and a rese
rvoir simulator which calculates the productivity index of the well. B
y applying mathematical transformations, it was possible to reduce the
acidizing model from a two-dimensional (2D) problem to a one-dimensio
nal (1D) one. By comparing treatment results, it is possible to select
the optimal volume of acid, injection rate, and fraction of the lengt
h to be acidized for each particular well. The same procedure may also
be applied for vertical wells both with and without anisotropy. Simul
ations results indicate that the application of a partial acidizing st
rategy reduces the total amount of acid required for a significant imp
rovement in well productivity. This may substantially reduce the finan
cial, operational, and environmental risks involved in the treatment o
f a horizontal well. In most cases, the optimal injection rate for san
dstone acidizing is the maximum rate which does not fracture the forma
tion.