Textile composites offer an excellent alternative to metallic alloys in the aerospace engineering, due to their high stiffness and strength, lightweight and excellent fatigue resistance. For example, CFM international (SAFRAN & GE) has developed, in their new engine LEAP-X, the fan blades using an advanced 3D woven carbon composite. In order to achieve computational feasibility and efficiency, traditional computational analyses of 3D woven composites involve the use of homogenization, usually under the assumption of periodicity instead of conducting full field computational analyses. By doing so, a modeling error is induced due to the difference between the homogenized model and the heterogeneous one. The key goal of this work is to demonstrate the use of a posteriori modeling error estimation techniques as in [1] and [2] for 3D woven composites assuming linear elasticity. As a result, a new promising algorithm referred to as Patch Wise Moving RVE (PWMRVE) is developed to first estimate the modeling error and second to detect areas where refining the material model is necessary in order to steer an adaptive process reducing then the modeling error. Hence, this method couples a fine material description in some regions of the domain and a coarse, less accurate macroscopic model in other regions. Therefore, in a comparison with a full field computation, this process could reduce the computational cost considerably without any major influence on the accuracy of the analysis. The PWMRVE algorithm is implemented in the finite element code Z-set [3], and was demonstrated using several numerical examples.