Numerical modeling of asphaltene precipitation in petroleum reservoirs is important in relation to possible precipitation around the wellbore in the producing well. Production from some reservoirs results in asphaltene precipitation in the wellbore region, leading to productivity loss and need for cleanup. Fluid injection even when there is asphaltene precipitation may not lead to injectivity loss. There are desirable processes in which precipitation of asphaltenes can lead to "in situ" upgrading of heavy oil recovery. Reservoir compositional models that are currently in use rely on cubic equations of state for asphaltene precipitation. The cubic equations, despite their relative reliability in describing reservoir fluids' phase behavior, become unreliable in asphaltene-rich phase description. A number of noncubic equations of state have been introduced to overcome the shortcomings of cubic equations. The cubic-plus-association equation of state (CPA-EOS) is perhaps the method of choice in representing asphaltenes in compositional modeling. When the hydrocarbon fluids do not contain asphaltenes, CPA-EOS reduces to the standard cubic equation. In this work, we implement CPA-EOS in compositional modeling and introduce a simple technique to speed up considerably the root finding of the CPA-EOS. Our efficient algorithm reduces significantly the additional computational cost from the incorporation of the CPA-EOS. We also derive the basic equations for the total compressibility and total partial molar volume in our implementation of the CPA-EOS compositional modeling. We present three numerical examples for CO2 injection in 2D and 3D domains saturated with Weyburn oil and show results of asphaltene-rich phase saturation among other predictions. This work introduces a general framework for widespread use of CPA-EOS in compositional modeling in three-phase flows of gas, light liquid, and asphaltene-rich phases.