Field data used for parameter determination and performance prediction problems includes significant biased and unbiased errors. Mathematical models used for these problems have model errors due to the simplified assumptions. Input parameters also have errors. These errors together may cause serious errors in search parameters and performance prediction. However most of the pressure tests, his tory matching techniques and loggings were developed disregarding the error sensitivity analysis although they involve parameter determination and performance prediction. In order to solve these problems, new error sensitivity indicators are proposed in this paper applying a statistical theorem to the condition numbers developed for the linear algebra. These error sensitivity indicators may he useful when one wants to judge (1) the number and the range of input data to minimize error of search parameters and performance predictions; (2) the necessary accuracy of data, input parameters and mathematical models; (3) the ill-conditioned or the well-conditioned system used for parameter determination; (4) the accuracy of search parameters and performance prediction.
The finite element method has now become recognized as a general method of wide applicability to engineering and physical science problems. As a result of the broad applicability and the systematic generality, the method has gained wide acceptance by civil engineers and architectural engineers for designing the rock structures and soil foundations. Usually these engineers have reduced the rock and soil to simple linear elastic or plastic materials. However, since their behavior is so complicated that the simplification significantly decreases the accuracy of simulation models. Meanwhile experimental studies on rocks and soils have been conducted since the early 20th century. Numerous data of the effect of temperature, pore pressure, stress state and time upon rock and soil behavior have been published. The fundamental theories for interpretation of these data owe to Prager and Drucker. In 1960th, various simple non-linear constitutive equations were proposed based upon their theories. Although these simplified non-linearity was good for analytical use, the development of the sophisticated numerical discretization techniques have not necessarily required simplified constitutive equations. In 1970th were proposed two methods which have more generality and flexibility to fit non-linear stress strain curves. One of which is the cap model with two loading surfaces moving along the hydrostat. And the other is the modified kinematic hardening model with a loading surface shifting and changing its shape. In this paper latter model is applied to a finite element simulator. As an example of its practical application, the fracture gradient around a wellbore was studied.