Numerical Simulations Of The Combined Effects Of Wellbore Damage And Partial Penetration

Abstract

Abstract There is considerable disagreement in the literature concerning the interpretation of wellbore damage (the skin effect) in partially completed wells. The skin factor is composed of two components, one of which is indicative of actual formation damage and the other of which results from an additional pressure drop due to the partial completion. The skin factor measured in a buildup test does not reflect the simple sum of these two components. Rather, the effect of the actual damage is accentuated by the partial completion. A method is presented to aid in the interpretation of well tests which yields estimates for both contributions to the skin factor. Analysis techniques are derived for steady-state flow and these are corroborated for transient flow by using simulated well test results. The simulations also provide a basis for comparing the various correlations for determining the skin factor due to partial penetration. The importance of the ratio of vertical to horizontal permeability is considered in the analysis. An example illustrates the application of the method. Introduction An altered zone of reduced permeability surrounding a wellbore is quantified in terms of the skin factor, s. This factor is related to the excess steady-state pressure drop1,2 in a flowing well as:Equation 1 The flow efficiency, E, is expressed in terms of Î"ps and the total drawdownÎ"pw, as:Equation 2 The skin factor has been related3 to an altered zone near the wellbore (Figure 1). If a zone of reduced permeability, ka, extends a distance, ra, into the formation, then the skin factor, s, is:Equation 3 where rw is the wellbore radius and k is the bulk formation permeability. It is the skin factor described by Equation 3 that is a measaure of the true formation damage caused by drilling and completion practices and other factors. This type of flow impediment is the target of acid treatment and other workover procedures. Thus, in order to evaluate completion practices and to recommend workover procedures, it is necessary to accurately determine the 'true' skin factor due to formation damage. In subsequent discussion this skin due to true damage will be designated as sd. The value of sd can be somewhat difficult to measure directly. A well is often completed over only a portion of the producing formation (Figure 2). This leads to a flow construction which is detected as an additional pressure drop or skin effect. Several authors4,5,6,7,8 have developed analytical descriptions of the skin factor, sp, due to partial penetration in an otherwise undamaged reservoir. In particular, Nisle9 has developed a formulation for simulating well tests within an infinite acting reservoir with a partial completion. The concept of a skin factor is not introduced.