Flow towards a guarded sampling probe: Modelling of a 2D flow cell

Analytic and numerical methods are used to predict fluid flow in a thin rectangular sheet of porous material when fluid is extracted through a port at the midpoint of one of the edges of the sheet. The aim is to model (in 2 dimensions) flow towards a sampling probe used to extract reservoir fluids from the rock surrounding a newly-drilled well. Such samples are usually contaminated with drilling fluid filtrate that saturates the rock adjacent to the wellbore, but a guarded probe can eliminate this contamination. Complex variable techniques are used to determine the flow of incompressible fluids when the interface between the two fluids is sharp, and filtrate and original pore fluid have identical viscosities. Results are compared against the predictions of a numerical reservoir simulator, and agreement is reasonable once numerical dispersion has been accounted for. Numerical results are also obtained for the case when the viscosities of the two fluids differ. The results give confidence in the use of 3-dimensional numerical computations to predict flow towards a guarded probe in a real wellbore, and thereby to optimize the design of such probes.