Experimental Study on Gas Slippage of Tight Gas Sands in Kirthar Fold Belt Sindh, Pakistan

The laboratory experiments on samples from Kirthar fold belt of lower Indus basin Sindh Pakistan were carried out to investigate the effect of gas slippage under varying conditions of pore pressures and overburden stress. The samples were dried in an oven at temperature of 600C and were randomly selected for measurement of permeability and porosity. Permeability was measured using nitrogen gas, while the porosity measurements were made using helium gas expansion porosimeter. The bulk volume was determined by measuring sample diameter and length with caliper. The permeability results suggest that gas slippage increases as if low pore pressures are used, which leads to higher measured permeability than intrinsic permeability of samples. An attempt was also made to estimate the permeability using existing correlations and found that there is large scatter in predicted permeability and measured data. This large amount of scatter in the predicted permeability values concludes that unless absolutely necessary, such correlations should not be used where accurate absolute permeability values are needed. Moreover, the permeability and porosity were plotted together to develop a relation between two properties; the power law fitting of the data well explains the relation between permeability and effective porosity.

T ight rock formations are important in many ways either to produce the gas, oil, to meet the energy needs or to store the CO 2 and nuclear wastes into underground earth, as these rocks exhibits extremely low permeability [1,2]. Hence, it is essential to characterise the flow of gas within such tight rock formation having very small pore throats and the rocks having compacted pore structure, dense pore network, and flow pathways are very small, so the mean free path of the molecules of gas changes considerably compared totheirpore-throat radius. It also have been reported that if mean free path of the gas molecules is higher in the magnitude of order two of the diameter of pore throats there will be possibility of molecules slippage on the pore surfaces. Hence, this deviates from obeying Darcy's law and the resulting value of permeability will be higher [4].
The gas permeability measurements are generally made using low pore pressures i.e. 100 psi and lower confining stress of about 400 psi. Hence, the permeability measurements conducted at low pore pressures need to be corrected to take into account of gas slippage effects to obtain accurate permeability values.Although, in a low permeability porous medium, the pores with their diameter equal to mean free path of the gas molecules further enhances the gas flow within pore walls i.e. the slippage flow of gas molecules resulting in increased rate of flow of the gas as well as the apparent permeability [5]. Permeability of tight rocks could be measured either by steady-state measurement methods [6] or by pressure pulsetransient method [7,8]. Steady-state measurements are extensively used to measure the gas slippage effects apart from permeability of porous rocks. Several authors conducted steady-state flow experiments at constant confining pressure and constant net confining pressures [6,9,10]. Steady state experiments on low permeability samples however are expensive and time consuming. Further that pulse-decay method for permeability measurement of tight rocks is based on unsteady-state flow mechanism [1], which is less expensive and less time consuming. However, in petroleum industry single permeability measurement is conducted at a low gas pore pressures, and then corrected for Klinkenberg effect to get the gas slippage factor values. Gas slippage factor values are then used to relate with permeability or with porosity and permeability [11,12] and furthermore the rock is a group of cylindrical pores, and their permeability is directly related to pore radius such as, k " ∝r 4 , hence slippage radius obtained from slippage parameters could be related with permeability asr slip ∝(k " /φ) 1/2 and or b∝(K " /φ − 0.5 ) [13]. The slippage (b) factor in the above equation could be influenced by the type of gasused during the measurements; hence the correlations need to be modified for the individual gas used [14]. However, [10]  The pulse-decay permeability experiments are performed using high pore pressures gas, usually more than 2000 psi [15]. Permeability measured using higher pore pressures will result in lower gas slippage effect [15], however, it is still recommended to perform the Klinkenberg corrections to achieve the slippage corrected absolute gas permeability data [15]. Though, the core laboratories use theoretical [5] or empirical relationships between permeability and slippage to correct data collected at low pressures [4]. Which is not appropriate to account for accuracy rather it would be far better to measure the permeability and obtain slippage corrected permeability in the laboratory. It is perceived that the model of Klinkenberg and its extensions might yet underestimate the role of gas slippage in permeability test data collected by petroleum industry as part of a routine core analysis especially for tight porous media [5][6][7][8][9][10][11][12][13][14][15][16]. Hence, to check the validity of such assumption a comprehensive study has been conducted and results are reported in the following sections.

GAS FLOW MECHANISM
The Klinkenbergslip flow model [17] is linearly associated with the measured gas permeability with the inverse of the mean pressure (1/Pm) and the Klinkenberg b-factor.
The following equation has been formulated based on the pore pressure correction: Where k g is the apparent gas permeability, k l is the and it is recommended that at least four or more data points are required as shown in Fig. 1. It is also theoretically possible to get pore radius from b-factor values using following Equation (2) of (Klinkenberg [17]): Where c is dimensionless parameter that depends on the geometry but is in the order of one (Klinkenberg [17]).
The b factor is constant with pore pressure (Klinkenberg [17]), in that the λ is expressed as in Loeb [34].
Where μ is the gas viscosity, R the gas constant, T absolute temperature, and M the molar mass of the gas.
The gas slippage-factor entirely depends upon the size of the pore; hence, the different rocks have different value of gas slippage factor, which varies with type of rock. The b-factor has remained focus of various investigators within the oil and gas industry to derive a relation with permeability to estimate effective liquid permeability K L [12,13,16,18,19]. Therefore, there are a number of correlations (i.e. empirical and theoretical) are available in literature those relate slip factor to porosity, permeability and tortuosity [7,11,20]. A summary of the existing slippage factor correlations have beenprovided in Table 1.

Different flow regimes could be related with different
Knudsen numbers, these are associated to the Knudsen number values [4,5], such as the continuum flow, slip flow, transitional flow and free molecular flow.A relation of Knudsen number as a function of pressure with varying pore sizes ranging from 5mm to 1 nm. The slippage due to gas molecules occurs in the condition when, gas molecule's mean free path results in similar to pore throat radius (0.001<Kn<0.1). In these conditions the molecules of gas gets slipped on the inner surfaces of the pores resulting in higher apparently permeability than the absolute permeability liquid permeability measured using a liquid as a pore fluid [7].

GEOLOGY OF KIRTHAR FOLD BELT
The samples collection location as specified in Fig. 2 and is represented as Kirthar Fold Belt which is located in (West Pakistan Fold Belt) [22]. This location provided a good reservoir formation and is realized to have good potential of hydrocarbon reserves as well as having good trapping mechanism [23][24].

Pab formation in Kirthar Fold
Belt is a sedimentary rock; this comprises the thick marine siliciclasticpab formations and is ranging from 50-450m.
Kirthar fold belt pab sedimentary formation is composed of sandstone rocks, which are interbedded with marl and mudstones associated with other rock formations of limestones [25]. The color of these sands is yellow, grey, light brown and greenish [23]. This Kirthar fold belt rock formation comprises the medium to coarse gained, moderately sorted, and is well rounded to sub rounded.
In this Marl present is very thin bedded and is light grey in color and is finely laminated Mudstone is bioturbated and is brownish reported two depositional systems. One is shallow marine and other one is fluviodeltaic to deep marine turbidities [23-24-25].

SAMPLE PREPARATION AND EXPERIMENTAL SET-UP
Cylindrical plugs of ~35 mm diameter and 62 mm length were completely cleaned by a Soxhlet extractor apparatus in the laboratory using a mixture of methanol-toluene and dichloromethane. The samples were dried by placing them in oven at 60°C for two days prior to measurements.
After that the samples were randomly selected and  where μ is the gas viscosity, L s is the sample length, Q a is the flow rate at ambient pressure P a , A s is the cross sectional area of the sample, and P 1 and P 2 are the pressures at the upstream and downstream side of the sample respectively. Transient permeability tests were conducted; and permeability measurements were made at stress up to 70 MPa confining pressure and 55 MPa to prevent the leakage of the permeant (Fig. 3).  (Fig. 4).

CHARACTERISTICS OF GAS FLOW IN TIGHT GAS SANDS
The experimental methodology was used for tight rock sample's gas permeability measurement under different confining stresses and different pore pressure conditions.

Experimental Study on Gas Slippage of Tight Gas Sands in Kirthar Fold Belt Sindh, Pakistan
Mehran

INFLUENCE OF PORE PRESSURE ON GAS SLIPPAGE EFFECT
The Equation (3) describes that if there is increase in mean free path of the gas molecules (λ) due to the reduced pore pressure of gas which will result in increased gas slippage effects leading to higher gas permeability (measured) than true permeability of the samples.
Moreover, if the mean free path of molecules of gas decreases the gas pore pressure rises and the slippage affects get in reduced values. The permeability data obtained using laboratory facility was plotted against the inverse of mean pore pressure of gas and are shown in Fig. 7 (a-b) for samples KFB1 and KFB2. These results show that there is good relationship between gas permeability and inverse of mean pore pressure and obey the Darcy's law. However, it was seen that the measured permeability to gas increases at the same overburden stress, by raising the inverse of mean pore pressure (1/pm). It is often seen that if gas pore pressure is lower i.e. below <100 psi, the molecules mean free path will be larger compared to higher pore pressure i.e. >500psi, so in case of low pore pressure the measured gas permeability will be high. Hence, the Klinkenberg effect shows major role in these low permeability reservoirs and is essential to quantify, and could not be ignored.
The slip-free permeability and slippage (b) factor values can be determined using Equation (1) function of porosity is plotted Fig. 8(a-b). The relation of permeability porosity follows a power law regression fitting and is: Where 0 ∞ g K , is the slip-free permeability measured at ambient stress conditions in m Darcy, φ is the porosity at initial conditions, and n is the regression coefficient. The present study data fitted with regression co-efficient is reported in Tables 3-4. After fitting the data with several different correlations as exponential and power law regression coefficient we found that the power fitting was reasonably good compared to Civan et. al. [20]. Our results are consistent with the finding of other authors [20].

RELATIONSHIP BETWEEN ABSOLUTE GAS PERMEABILITY AND SLIPPAGE FACTOR
It is generally known that for low permeability samples the slippage factor values becomes larger; this means that it is essential to do corrections for low permeability samples otherwise errors could be expected in permeability and the extent of these errors likely become larger as permeability decreases. The results obtained within present study shows that it is essential to either measure b-values for each sample separately. Otherwise it is recommended that alternatively, high gas pore pressures (>1000 psi) should be used so that the Klinkenberg correction becomes negligible for tight gas sandstone reservoirs [5]. Fig. 4 shows the gas slippage b-values measured during the present study and compared to that data presented about Mesaverdetight sands [10]. Three key findings of the data obtained from results are, (i) the b-factor values are related to absolute permeability using the Equation (7): Whereb is in psi and k ab in m Darcy. There appears to be no systematic difference between b-values between tight gas samples from our study and that of Byrnes [10] and (iii) there is around half order of magnitude scatter in measured b-values.
Various correlations are present within the literature (Table 1) to relate the gas slip factor with permeability [7-12-21]. We tested these relationships, for comparing with our data to see the validity of model predictions (Fig. 9). It was found that in Fig. 9

CONCLUSIONS
The study was conducted to assess the gas flow characteristics in tight gas sandstones. The tight rock samples permeability, porosity measurements were made under varying pore pressures and over burden stress conditions. The impact of gas slippage on measured permeability of tight sands of Kirthar formations is discussed.The main conclusions drawn from the work is as follows: (i) The experimental results displays that the plot of gas flow rate and pressures squared difference follows the no-linear trend, this deviation in between gas flow and pressure difference squared provides the nonlinear flow behavior.
(ii) It was also observed from experimental results that gas slippage has a significant effect on tight rocks permeability. As the pore pressure was low, the mean free path of the gas molecules were high and in that situation the slippage effect of gas molecules were considerably high which resulted in high permeability than true permeability of the tight rock samples.
(iii) A relation between permeability and effective porosity was developed and the data fitted with the power law described a good relation.
(iv) The permeability and gas slippage factor correlation was developed based the measured and estimated data, it was found that it is essential to either measure b-values for each sample separately; or otherwise it is recommended to use high gas pore pressures (>1000 psi) so that the Klinkenberg correction becomes negligible for tight gas sandstone reservoirs.
(v) By employing a constant overburden stress and using small pore pressure, the Klinkenberg slippage effect was noticeable. As the pore pressure further decreased to certain value, the impact of gas slippage increased by around 40%.
Hence, it is essential to take account of the Klinkenberg slippage effect on absolute permeability of tight rocks if the pore pressure is low in such reservoirs and the reservoirs which are sensitive to stress.