Theory of simulationAssumptions for ideal SWCT test modelingMathematical modeling of the ideal SWCT test assumes that: The carrier fluid flow is incompressible, pseudosteady state, single-phase, and radial only That the formation is a homogeneous layer of thickness (h) and porosity () extending from the wellbore radius (rw) to an external boundary radius (re), where reservoir pressure is constantWith these assumptions, the interstitial fluid velocity (vfi) is given by....................(1)wherer= radial position;q= fluid flow rate in the single well (q> 0 is injection andq< 0 is production);h= height of test zone;= porosity; andSf= flowing fluid saturation, constant.The additional assumptions regarding the tracers are: ThatKAfor tracer A is constant and that A is in local equilibrium between flowing fluid (saturationSf) and residual fluid (saturationSr). For Case 1,Sr=SorandSf= 1.0 Sor. That tracer A (primary) reacts in situ to form tracer B (product) at a rate given by....................(2)whereRH= hydrolysis reaction rate, in moles of A per vol-day;CA= concentration of A, in mol/volume; andkH= hydrolysis rate constant (days1) in the aqueous phase. Tracers are dispersed in the radial flow with an effective dispersion coefficient (Da), given by....................(3)where= dispersivity (ft).The material balance for tracer A is the partial differential equation:....................(4)Similar equations apply for product tracer B and the material-balance tracers.SWCT test simulation requires the numerical solution of these equations for A, B, and the material-balance tracer. The equations first are converted to finite-differenced form, based on the perfectly mixed cell model.[1]The simulation program then solves the finite-differenced equations for the concentrations of the tracers in a radial series of cells over the test time interval.Simulation program inputsInput to the simulation program consists of: Known parameters, which are:qas a function of time (injection, shut-in, production), injected concentration of tracer A (CA) and concentration of tracer B (CB) as a function of time;rw,h,;KAandKB. Unknown (estimated) parameters, which are:kH,Sor, and the radial dimension of the cells (R). Note: according to the theory of the perfectly mixed cell model for small time intervals, R= 2.