Log-based prediction of pore pressure and its relationship to compressional velocity, shear velocity and Poisson’s ratio in gas reservoirs; Case study from selected gas wells in Iran

: A precise identification of pore fluid pressure (PP) is of great significance, specifically, in terms of drilling safety and reservoir management. Despite numerous work have been carried out for prediction of PP in oil reservoirs, but there still exists a tangible lack of such work in gas hosting rocks. The present study aims to discuss and evaluate the application of a number of existing methods for prediction of PP in two selected giant carbonate gas reservoirs in south Iran. For this purpose, PP was first estimated based on the available conventional log data and later compared with the PP suggested by Reservoir Formation Test (RFT) and other bore data. At the end, it has been revealed that while PP prediction is highly dependent on the type of litho logy in carbonates, the effect of fluid type is negligible. Moreover, the velocity correlations work more efficiently for the pure limestone/dolomite reservoirs compared with the mixed ones.


Introduction
Pore Pressure (PP), that is the pressure inside pore spaces of a rock, is known as one of the key parameters that must be well studied and predicted in order to optimize the formation evaluation and drilling programs [1][2][3].Equivalent depth methods [4], the ratio method [5], Eaton's method [6], resistivity method with depth-dependent Normal Compaction Trendline (NCT), sonic method with depth-dependent and effective stress method [7] are examples of methods commonly used to determine the PP. It has been shown that PP is foreseeable from variation in specific rock physics properties, such as, sonic velocity and electronic resistivity [8]. However, despite of extensive efforts in development of several approaches for PP prediction but difficulties and uncertainties in carbonate formations persist mainly due to their significant multi-scale heterogeneities [9].
In fact, the conventional PP prediction methods may not be reliable to be used for carbonate rocks mainly because their porosity is highly affected bypost-diagenesis chemical and cementation processes [10].Subsequently, the dominance of lithification by diagenesis over the one developed by compaction is the reason why acoustic velocity in carbonates show no clear correlation with increasing depth [11].
As mentioned by [2], the PP prediction process based on elastic wave data must follow three main steps including data acquisition and analysis, linking the elastic wave attributes to either effective stress (PE) or PP through a proper geophysical model, and finally estimation of the PE or PP.
The present research aims to apply elastic moduli PErelation to predict the PP in two selected carbonate gas reservoirs.

Methodology
Data were collected from two giant carbonate gas reservoirs, here named as AA and BB, located in south-Iran. Table 1 presents further details from the target reservoirs.  (1) Moreover, compressional and shear velocities (Vp& Vs) were estimated based on a number of well-known existing correlations developed by [12] and [13] as explained below.

Castagna et al. (1993) correlation
The V p values resulted from Eq.1 were used to estimate the Vs according to the following equations as suggested by [12]for dolomite (Eq. 2) and limestone (Eq. 3): It should be noted that both of the [12] and [13] equations were specifically developed for carbonate reservoirs and attention must be paid in case of siliciclastic or mixed carbonate-siliciclastic reservoir rocks.

Effective pressure modeling
The above-mentioned estimated velocities were then used to determine the Poisson's ratio. It worth mentioning that Poisson's ratio can be estimated based on static and/or dynamic methods [14]. In the former method, rock specimen is affected by uniaxial or tri-axial load until the failure occurs and the recorded stress, lateral and axial deformations will be used to determine the Poisson's ratio. In dynamic method the Poisson's ratio will determined based on the measured Vp and Vsand using the following equations as suggested by: Where  is the Poisson's ratio.
Next, the overburden pressure (σv) was estimated based on the depth, density and sonic log data and using the following equation as suggested by [2]: Where g is the gravity acceleration is in [ (9) Where P p is the pore pressure, is the vertical stress and is the Biot constant that is defined as the ratio of fluid volume gained (or lost) in a material element to the volume change of that elementand is considered 0.7 for carbonate rocks [16]. The estimated effective pressures were plotted against the Poisson's ratio (derived from different velocity correlations) and V p /V s . Note that, as suggested by [17],effective stress is exponentially related to the Poisson's ratio and V p /V s according to Eq. 10: Where eff  is the effective stress, a and b are constants, and x is either Poisson's ratio or Vp/Vs.Eq.10 is specially handful to estimate the effective stress in case no RFT data is available.
The estimated Poisson's ratio and V p / V s were imported into the model as input data, the effective pressure was modeled, and subsequently, pore pressure was predicted based on the Terzaghi's equation with a Biot coefficient of 0.7 The results of PP predictions were further compared to the real PP values extracted from available RFT data and the errors were determined from the following equation: Where PP RFT is the RFT reported pore pressure and PP mod is the model predicted pore pressure.

Results and discussion
Based on the available bore reports, well A can be divided into two parts including an upper dominantly dolomite and a lower dominantly limestone sections, and Well B includes a mixed limestone and dolomite section.  In addition, due to lack of RFT report, static pressure data were collectedin nine points along the Well B ( Figure 2). It must be mentioned that since log and pore pressure data wereavailable from the depth of 2370 to 2525 meters and 0 to 2487 meters, respectively, it was only possible to apply the [17] model and determine the effective pressure in four points along the overlapped section. Figure 3 through Figure 6 present the results of V p and V s based on the DT log data and correlations developed by [12] and [13].     6.Variation of V s , estimated from [13] and [12] equations, along the Well B.

3.2
Effective pressure prediction based on dynamic Poisson's ratio As listed in Table 2, the effective pressure was correlated to dynamic Poisson's ratio in Well A at ten selected points extracted from available RFT data.

Effective pressure prediction based on V p /V s
As shown in Table 4 and 5, the effective pressure also was modeled based on the V p /V s ratio that is significant to sense the effect of fluid type on PP prediction especially in Well A as a two phase (oil and gas) producer well. In general, Vs is more affected by the highly porous fabric of the low-velocity carbonates than V p [13] while [18] mentioned that pore-filled fluid type affect the dynamic Poisson's ratio.

Error of PP predictions
The results of error estimations are presented in Table 2, Table 3, Figure 11 and Figure 12.

Conclusions
During the present study, elastic moduli effective stress (PE)-relation method was revealed to be efficient for Pore Pressure (PP) prediction in carbonates mainly due to the lack of relationship between porosity and compaction in this type of rocks. However, the effect of lithology and fluid type must be accounted for, especially, in selection of a proper velocity estimation correlation. Moreover, dynamic elastic moduli parameters were estimated based on dynamic data instead of static parameters which are generally more realistic and lower than the corresponding dynamic data due to the effect of pore pressure, cementation, stressstrain rate and amplitude. The dynamic Poisson's ratio is specifically recommended to be applied in case of gas reservoirs while it has been revealed that Biot's coefficient of 0.7 can be effectively used in Terzaghi's effective stress law for the case of carbonate reservoirs.
The Castagna model works effectively for the case of well A with a dominant lithology of limestone in the lower part overlaid by a dominantly dolomite section. In addition, the Anselmati model could predict properly as well in upper part of well A and the whole section of well B.
At the end, the methods discussed in this study have some main advantages, such as, they are purely based on mechanics and so not restricted to the mechanisms of abnormal PP and as a result the process of calculation is not complicated.
We are thankful to the South Zagros Oil and Gas Production Company (SZOGPC) and Shiraz University for all their support.