New Method to Estimate Damaged Formation Permeability With Well Testing

摘要

Most composite solutions used in modern well test interpretationuse the "step-permeability" model where the altered formationsare divided into two or more concentric zones, each withconstant permeability. Depending on the causes of alteration orvariation, this model can deviate significantly from the realcondition. A formation can be altered because of stressredistribution, drilling damage, solids co-production, mineralprecipitates, and drilling mud invasion, each factor more likely togenerate spatially-varying permeabilities rather than constant kzones. Experimental data confirm that a continuous permeabilitymodel is more realistic than the step permeability model.A new semi-analytical solution with smooth radius-dependentpermeability has been developed to analyze well test results fromsuch altered formations. The altered formation is approximatedas a concentric two-zone composite model: an exterior intactzone that retains the original unaltered permeability, and aninterior zone where the permeability values have been alteredand change as a function of radius. The permeability in thisnear-well zone can change continuously to the originalpermeability or to a different value at the boundary with theexterior zone, where there is a step-change in permeability. Thechoice of an increase or decrease of permeability with radiuswithin the altered zone depends on the nature of the actualalteration. The permeability can also be simulated as a step-wisefunction if appropriate parameters are used; in such situations,the model collapses to conventional step-wise composite models.Other parameters such as formation porosity and compressibilityof each zone can also be different, but they are assumed constantfor this derivation. The new solution is derived in Laplace space, Most composite solutions used in modern well test interpretationuse the "step-permeability" model where the altered formationsare divided into two or more concentric zones, each withconstant permeability. Depending on the causes of alteration orvariation, this model can deviate significantly from the realcondition. A formation can be altered because of stressredistribution, drilling damage, solids co-production, mineralprecipitates, and drilling mud invasion, each factor more likely togenerate spatially-varying permeabilities rather than constant kzones. Experimental data confirm that a continuous permeabilitymodel is more realistic than the step permeability model.A new semi-analytical solution with smooth radius-dependentpermeability has been developed to analyze well test results fromsuch altered formations. The altered formation is approximatedas a concentric two-zone composite model: an exterior intactzone that retains the original unaltered permeability, and aninterior zone where the permeability values have been alteredand change as a function of radius. The permeability in thisnear-well zone can change continuously to the originalpermeability or to a different value at the boundary with theexterior zone, where there is a step-change in permeability. Thechoice of an increase or decrease of permeability with radiuswithin the altered zone depends on the nature of the actualalteration. The permeability can also be simulated as a step-wisefunction if appropriate parameters are used; in such situations,the model collapses to conventional step-wise composite models.Other parameters such as formation porosity and compressibilityof each zone can also be different, but they are assumed constantfor this derivation. The new solution is derived in Laplace space,Most composite solutions used in modern well test interpretationuse the "step-permeability" model where the altered formationsare divided into two or more concentric zones, each withconstant permeability. Depending on the causes of alteration orvariation, this model can deviate significantly from the realcondition. A formation can be altered because of stressredistribution, drilling damage, solids co-production, mineralprecipitates, and drilling mud invasion, each factor more likely togenerate spatially-varying permeabilities rather than constant kzones. Experimental data confirm that a continuous permeabilitymodel is more realistic than the step permeability model.A new semi-analytical solution with smooth radius-dependentpermeability has been developed to analyze well test results fromsuch altered formations. The altered formation is approximatedas a concentric two-zone composite model: an exterior intactzone that retains the original unaltered permeability, and aninterior zone where the permeability values have been alteredand change as a function of radius. The permeability in thisnear-well zone can change continuously to the originalpermeability or to a different value at the boundary with theexterior zone, where there is a step-change in permeability. Thechoice of an increase or decrease of permeability with radiuswithin the altered zone depends on the nature of the actualalteration. The permeability can also be simulated as a step-wisefunction if appropriate parameters are used; in such situations,the model collapses to conventional step-wise composite models.Other parameters such as formation porosity and compressibilityof each zone can also be different, but they are assumed constantfor this derivation. The new solution is derived in Laplace space,and numerical Laplace inversion is used.