Stress Ratio Method to Predict Fracture Pressure Gradient in Southern Iraqi Deep Wells

This research presents a method for calculating stress ratio to predict fracture pressure gradient. It also, describes a correlation and list ideas about this correlation. Using the data collected from four wells, which are the deepest in southern Iraqi oil fields (3000 to 6000) m and belonged to four oil fields. These wells are passing through the following formations: Y, Su, G, N, Sa, Al, M, Ad, and B. A correlation method was applied to calculate fracture pressure gradient immediately in terms of both overburden and pore pressure gradient with an accurate results. Based on the results of our previous research , the data were used to calculate and plot the effective stresses. Many equations relating horizontal effective stress and vertical effective stress are obtained for each well and used to calculate fracture pressure gradient. Similar equations are found for group of formations that calculate fracture pressure gradient and to find the most accurate correlation among them. Journal of Petroleum Research & Studies


Introduction
Rock at depth is subjected to stresses resulting from the weight of overlying strata and from locked in stresses of tectonic origin (see fig. 1) [2]. When an opening is excavated in this rock, the stress field is locally disrupted and a new set of stresses are induced in the rock surrounding the opening. Knowledge of the magnitudes and directions of these insitu and induced stresses is an essential component of underground excavation design since, in many cases, the strength of the rock is exceeded and the resulting instability can have serious consequences on the behavior of the excavations. The instantaneous shut in pressure (ISIP) [3] recorded during or after a fracturing job provides a good approximation to the minimum principal insitu total stress component σ Hmin   With the assumption of constant overburden pressure gradient (G ov =1 psi/ft). Then K i is plotted as a function of depth.
The stress ratio was correlated with depth but constant overburden pressure gradient was not, so the stress ratio became: . Where: Rearranging the above equation, the author plotted Poisson's ratio against depth using measured data.
Nevertheless, Eaton's procedure as stated by Breekels and Eekelen, 1982 [3] is regarded to be unnecessary and somewhat dangerous complication because it might create the wrong impression that the effective stress ratio can be accurately determined by measuring Poisson's ratio σ on a core.
All the previous illustrated procedures are based on finding a correlation between horizontal to vertical effective stress ratio and depth. But soon it was concluded that this procedure generated a very poor correlations, which can be attributed to variation in the depth of the top of the abnormal pore pressure zone and the rate of change of

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the pore pressure. To minimize these factors Brennan and Annis, 1984 [7] made a correlation between effective horizontal stress gradient versus effective vertical stress gradient. By this plot, the depth problem was eliminated and pore pressure effects minimized.

Theory of proposed method
Formation fracture gradient predictions have been given a considerable attention over the past years. The model developed by Hubbert and willis, 1957 [2] has provided the foundation of the majority of the proposed method. In the proposed method, overburden pressure has been either assumed as 1.0 psi\ft. or more correctly, evaluated from velocity data, sonic logs, or density log. Pore pressure gradient has either been assumed as normal pressured (0.44 psi\ft) or, in the case of abnormal pressures, evaluated from resistivity (conductivity) logs, and sonic measurement. So, accurate calculation of pore and overburden pressure gradient can be obtained. The effective stress ratio (K) is usually developed as an empirical function of depth. The effective stress ratio is calculated using equation (6): A correlation between horizontal to vertical effective stress ratio and depth has been developed. But soon it was concluded that this procedure generated very poor correlation, which can be attributed to variation in the depth of abnormal pore pressure zone and the rate of change of the pore pressure. To minimize these factors, EHSG versus EVSG was plotted. By this plot the depth problem was eliminated and pore pressure effects minimized.

Results and conclusions of proposed method
Entering the collected data for the studied wells in equation (9) The above two equations (14) & (15) were used to calculate FPG using overburden pressure gradient (from bulk density log) and pore pressure gradient (using drilling and log data). The results were illustrated in Tables (1-4) for the studied wells.
Using the AAPE (absolute average percent error), the degree of accuracy for the two attempts for calculating FPG were illustrated in In well (D), well equation gives best AAPE than pore pressure behavior equations due to missing in G formation and down ward.
As a conclusion, these correlations using the measured data give best AAPE among all other methods to estimate FPG.