The impact of a chemical reaction,
$A+B \rightarrow C$
, on the stability of a miscible radial displacement in a porous medium is established. Our study involves a comprehensive analysis employing both linear stability analysis and nonlinear simulations. Through linear stability analysis, the onset of instability for monotonic as well as non-monotonic viscosity profiles corresponding to the same end-point viscosity are discussed and compared. We establish a
$(R_b,R_c)$
phase plane for a wide range of Damköhler number (
$Da$
) and Péclet number (
$Pe$
) into stable and unstable regions. Here,
$R_b=\ln (\mu _B/ \mu _A)$
and
$R_c=\ln (\mu _C/ \mu _A)$
and
$\mu _{i}$
is the viscosity of fluid
$i$
$\in \{A$
,
$B$
,
$C$
}. The stable zone in the
$(R_b, R_c)$
phase plane contracts with increased
$Da$
and
$Pe$
but never vanishes. It exists even for
$Da \rightarrow \infty$
. Interestingly, we obtain a
$Da$
independent stable region in the neighbourhood of
$R_c=R_b$
where no transition occurs in stability despite changes in reaction rate. The study allows us to acquire knowledge about the transition of the stability for varying
$Da, Pe$
and different reactions classified using
$R_b, R_c$
.