Injection tests can give such information as the effective mobilities
of fluids, wellbore damage, and saturation change during displacement,
which often require use of rate and pressure data. Although exact sol
utions for injection and falloff pressure response of a well in an inf
inite reservoir may be obtained for a constant injection rate, they ar
e not readily extended for the general case of varying flow rates and
bounded reservoirs. We present a perturbation theory for multiphase te
sting that leads to a weakly nonlinear convolution and give a techniqu
e to calculate pressure response rapidly for arbitrary flow rates for
this form of convolution. The technique is specifically suited for sol
ving inverse problems with nonlinear estimation. We present modificati
ons to the solutions for positive and negative skin factors and demons
trate that the effect of wellbore storage is not easily accounted for
in an injection test, unlike single-phase well testing. We give a proc
edure to correct the system response to storage and propose a variable
-rate injection test to improve system parameter estimation. The main
idea of the test is to excite the reservoir sequentially and continuou
sly to keep it under strong transient conditions. We present interpret
ation results for such a sequential testing.