A Well Test for In-Situ Determination of Relative Permeability Curves

Abstract

fax 01-972-952-9435. AbstractWe propose a novel well-test for in situ estimation of relative permeabilities under two-phase (oil-water) flow conditions. The test consists of three periods, (i) injection of water into an oil reservoir operating above bubble point pressure, (ii) a falloff test and (iii) a producing period. The producing period is critical as it yields production data that reflects changes in sandface mobility and thus is highly sensitive to the parameters used to model relative permeability curves, whereas, our results indicate that injection/falloff pressure data by themselves are not as reliable for defining relative permeability curves. We have developed optimization code based on the LevenbergMarquardt algorithm and coupled it with a commercial reservoir simulator to obtain a procedure for data analysis where the reservoir simulator is used as the forward model. By matching data by minimization of a weighted least squares objective function, we generate estimates of absolute permeability, relative permeabilities and the well skin factor. We show the method can be applied with either power law models or B-splines. We introduce a variable transformation that can be used to ensure that the estimated relative permeabilities are monotonic and concave up when B-splines are used.

A Well Test for In-Situ Determination of Relative Permeability Curves

“…However, it has been verified with detailed calculations (Chen 2007) that during the injection and falloff periods, the change in saturation caused by capillary pressure has a negligible effect on the wellbore pressure solution for the examples presented here, as well as for other examples with reasonable test times and a reasonable injection rate. However, Chen (2007) has shown that during the flowback period, capillary pressure affects the total mobility distribution at the sandface in a short time interval around the time when "oil breakthrough" occurs (i.e., during the period when the oil rate increases rapidly). More importantly, during this time period, the difference between the solution without capillary pressure and the one which includes capillary pressure is not always negligible from the viewpoint of data analysis.…”

“…However, even when capillarity effects are nonnegligible during the flowback period, we can apply nonlinear regression using a reservoir simulator as the forward model to solve for wellbore pressure. In this case, we are able to obtain estimates of both capillary pressure and relative permeability curves (Chen 2007). It is conceivable that gravity can have a large enough effect on the saturation distribution generated by neglecting gravity so that the pressure solution presented in this work is not sufficiently accurate for analysis purposes.…”

“…A-5 hold. As with the monotonicity condition, we can make a transformation to a new coordinate system to ensure that the control points are convex (Eydinov et al 2005;Chen et al 2005).…”

Relative Permeability Estimation from Displacement Experiments Using EnKF Method

“…The non-parametric model is far more general and flexible as there is no assumption regarding the shape of the relative permeability curves. For example, the B-spline model has been used in various studies to represent the relative permeability curves (Watson et al, 1988;Yang and Watson, 1991;Kulkarni and Datta-Gupta, 2000;Okano et al, 2005;Chen et al, 2008;Eydinov et al, 2009).…”

Analytical Solution for Injection-Falloff-Production Test

“…Either a power law model or B-splines can be used to model the relative permeability curves 17,18 , but here we focus on the power law model. All other rock and fluid properties are assumed to be known.…”