Editing Inverse problem (section)

====Permeability matching in oil and gas reservoirs====
The goal is to recover the diffusion coefficient in the [[Diffusion equation|parabolic partial differential equation]] that models single phase fluid flows in porous media. This problem has been the object of many studies since a pioneering work carried out in the early seventies.<ref>{{cite journal |last1=Chavent |first1=Guy |last2=Lemonnier |first2=Patrick |last3=Dupuy |first3=Michel |title=History Matching by Use of Optimal Control Theory |journal=Society of Petroleum Engineers Journal |date=1975 |volume=15 |issue=2 |pages=74–86 |doi=10.2118/4627-PA}}</ref> Concerning two-phase flows an important problem is to estimate the relative permeabilities and the capillary pressures.<ref>{{cite journal |last1=Chavent |first1=Guy |last2=Cohen |first2=Gary |last3=Espy |first3=M. |title=Determination of relative permeabilities and capillary pressures by an automatic adjustment method |journal=Society of Petroleum Engineers |date=1980 |issue=January |doi=10.2118/9237-MS}}</ref>