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Abstract

Spontaneous countercurrent imbibition is one of the essential parameters in the study of formation damage effect in hydrocarbon reservoirs when the drilling fluid is contacted with the drilled formation. Formation damage is considered as one of the harmful phenomena which would seriously affect the efficiency of drilling performances. In this paper, a numerical model was proposed to analyze the main parameters which have profoundly impacted the formation damage. Based on the following parameters of porosity, permeability, water saturation, oil viscosity, pressure drop, contact time, and capillary pressure which were performed in the proposed model, the dominant influence of each parameter was evaluated in more detail. Regarding the high expenditures of scanning electron microscopy and CT scan in petroleum industries, the proposed analytical model would be beneficial instead of spending vast expenditures of experimental evaluation. Subsequently, to provide the accuracy of the model, a set of experimental CT scan data were used to validate the proposed model, and according to the results of this study, it is evident that the proposed model results are in a good agreement with the laboratory data.

Keywords

Formation damage imbibition numerical model drilling fluid CT scan laboratory data

Introduction

Importance of energy as a strategic factor has been caused that attention by governments and people to it increase day to day. In this regard, correct policy and planning are two of the most important factors for achieving good results. Actually, governments should have a comprehensive look at all issues for obtaining high-security percent for their inhabitants especially in the energy field (Razmjoo and Davarpanah, 2019; Razmjoo et al., 2019a; Razmjoo et al., 2019b; Davarpanah et al., 2019b). Underbalanced drilling is contributed as the designation of lower drilling fluid hydrostatic head rather than the pressure of the drilling formation to provide the formation stability during the drilling operations (Davarpanah et al., 2018a; Ghosh et al., 2019; Hamon and Vidal, 1986; Kashchiev and Firoozabadi, 2002). Therefore, it would be considered as one of the efficient drilling techniques to control the formation damage (Davarpanah, 2018; Davarpanah and Mirshekari, 2019; Kroepsch et al., 2019; Willis et al., 2018, 2019). Moreover, the pressure of overbalanced and underbalanced drilling is defined as $\begin{array}{l} Overbalanced Drilling (OBD) : P_{reservoir} < P_{bottom hole} = P_{hydrostatic} + P_{friction} {+P}_{choke} \\ UBD: P_{reservoir} > P_{bottom hole} = P_{hydrostatic} + P_{friction} + P_{choke} \end{array}$ (1)

Conventional and underbalanced drilling operations are schematically depicted in Figure 1 ((a) for conventional drilling and (b) for underbalanced drilling).

Figure 1.

Conventional and underbalanced drilling operations.

Due to the geological properties of hydrocarbon reservoirs which are constituted with the stability of formation rock, it is not possible to drill all the reservoirs in the underbalanced circumstances (Moghadasi et al., 2010; Pashin et al., 2018; Perrin and Benson, 2010; Pooladi-Darvish and Firoozabadi, 1998). Therefore, predicting and selecting the best drilling scenario for the drilling performances would be one of the main challenges of petroleum industries that should be addressed significantly (Ardila Jaimes et al., 2018; Bello et al., 2018; Davarpanah et al., 2019a; Kakoli et al., 2016; Raza, 2015).

Formation damage of the hydrocarbon reservoirs is mainly happened by completion, drilling performances, and production operation, which has caused to productivity reduction of the oil and gas development. Thereby, this phenomenon has caused the efficiency and safety of the drilling operations (Davarpanah et al., 2019c; Russell et al., 2018; Yuan and Wood, 2018a, 2018b; Zhao et al., 2019). Countercurrent imbibition issue is considered as one of the principal factors in drilling operations to enter the penetrated drilling mud to the formation due to the existed capillary pressure. However, this phenomenon has led to produce hydrocarbons; it might be caused to pore throat blocking and permeability reduction (Hatiboglu and Babadagli, 2004; Iffly et al., 1972; Kashchiev and Firoozabadi, 2002; Morrow and Mason, 2001). According to the experimental investigation which was done by Cuiec for some sandstone water-wet samples, water was entered to the samples from the bottom of the cores regarding the dominant directional imbibition. Thereby, oil was moved upward, and more volume of oil would be produced due to the capillary pressure reduction and velocity reduction (Davarpanah et al., 2018b; Ebadati et al., 2018, 2019). Amanullah (2003) proposed an experimental investigation of filter cake erosional characteristics to control the formation damage effect (Amanullah, 2003). Civan (2015) proposed some experimental core analysis such as mercury intrusion, X-ray diffraction, and scanning electron microscopy (SEM) to provide a deep understanding of sensitive minerals occurrence and the characteristics of the formation.

Moreover, different types of drilling fluids which are contained of saline water, freshwater, and alkali water were used to core analysis complementation (Civan, 2015). Kang et al. (2014) proposed a comprehensive evaluation of formation damage which was induced by drilling fluid loss in the fractured and tight gas reservoirs by the utilization of dynamic evaluation method (Kang et al., 2014). According to the Ma et al. (2016) investigation, alkali fluid damage mechanisms in the low permeable reservoirs were extensively discussed by the administration of core flow experimental analysis (Ma et al., 2016).

Hydrocarbons reservoirs are divided into two types: conventional and unconventional reservoirs. Unconventional reservoirs are considered as those reservoirs that are characterized as the heterogeneous, pore throat scale, and continuous accumulation of hydrocarbons which are extremely difficult to drill regarding the rough and unpredictable behavior of this reservoir. Thereby improving the characterization of these reservoirs would be of importance to virtually eliminate the considerable influence of formation damage effects. High-resolution technologies have been taken into consideration to measure unconventional reservoirs characterizations. These techniques are CT, Nano CT that are based on the micron computed tomography and focused ion beam–scanning electron microscopy (FIB-SEM). One of the main parameters which should be considered on the recovery efficiency enhancement of unconventional hydrocarbons reservoirs is the mineralogical heterogeneity characterization regarding the profound impact of minerals distribution.

Moreover, compaction, deposition, and modification performances have primarily affected by the characterization of pore throats (Du et al., 2018a, 2019). A new experimental investigation which is named umbrella deconstruction has been used to measure the pore heterogeneity in microscopic scale for unconventional hydrocarbon reservoirs. The following parameters were estimated according to the FE-SEM; cement content, porosity, and reservoir fractal dimension are such the essential parameters. Hence, this method would be of significance to estimate the unconventional reservoir characteristics in microscopic scale which would be a beneficial tool for estimating formation damage effect (Du, 2019; Du et al., 2018b).

Although formation damage prediction and how to control its effect in hydrocarbons are widely reported in the literature and is considered as one of the main challenges of petroleum industries, in this study, a numerical model was proposed to consider different crucial parameters which have severely affected the formation damage. Therefore, a sensitivity analysis which is based on the following parameters was performed in the model to investigate the considerable influence of each parameter on the saturation of filtrated mud. These parameters are porosity, permeability, water saturation, oil viscosity, pressure drop, contact time, and capillary pressure. Due to high expenditures of CT scan and SEM laboratory investigation to check the formation damage effect in petroleum industries, the proposed analytical model would be beneficial instead of spending vast expenditures of experimental evaluation. To provide the accuracy of the model, a set of experimental CT scan data were used to validate the proposed model and according to the results of this study, it is evident that the proposed model results are in a good agreement with the laboratory data.

Governing equations

As drilling mud has entered to the core and oil has exited from the core, it is necessary to provide a simultaneous solution for the equilibrium equation of mass balance for two phases. To simplify the governing equations, the fluid flow is considered in a one-dimensional direction. Equilibrium equation of mass balance equations is defined as $- - \frac{\partial}{\partial x} (\frac{u_{x}}{B_{x}}) = \frac{\partial}{\partial t} (\frac{φ S_{x}}{B_{x}})$ (2)where φ is the cross-sectional porosity, fraction; S is the saturation profile, dimensionless; u is velocity, ft/s, and x is expressed for each phase (oil and drilling mud). By applying the velocity equation, equation (1) was changed as follows $\frac{\partial}{\partial x} (K λ_{x} \frac{\partial P_{x}}{\partial x}) = \frac{\partial}{\partial t} (\frac{φ S_{x}}{B_{x}})$ (3)

As equation (2) is challenging to solve, it is necessary to add boundary conditions. $S_{o} = 1 - S_{wc}$ and $P_{m} = P_{i} - P_{c} (S_{wc})$ were considered as the boundary conditions. Due to the complexity of equation (2), the finite element method is administered in this paper to numerically solve this equation. Therefore, equation (2) is changed as follows $\frac{\partial}{\partial x} {(K λ_{x} \frac{\partial P_{x}}{\partial x})}_{i} ≅ T_{x, i + \frac{1}{2}} (P_{x, i + 1} - P_{x, i}) + T_{x, i - \frac{1}{2}} (P_{x, i - 1} - P_{x, i})$ (4)

where $T_{x, i \pm \frac{1}{2}} = \frac{λ_{x, i \pm \frac{1}{2}} K_{i \pm \frac{1}{2}}}{Δ x^{2}}$ (5)

And $K_{i \pm \frac{1}{2}}$ is defined as $K_{i \pm \frac{1}{2}} = \frac{2 K_{i \pm 1} K_{i}}{K_{i \pm 1} + K_{i}}$ (6)

Thereby, equilibrium mass balance for oil and drilling mud is defined as $T_{m, i + \frac{1}{2}} (P_{o, i + 1} - P_{o, i}) + T_{m, i - \frac{1}{2}} (P_{o, i - 1} - P_{o, i}) - T_{m, i + \frac{1}{2}} (P_{c, i + 1} - P_{c, i}) - T_{m, i - \frac{1}{2}} (P_{c, i - 1} - P_{c, i}) = C_{pom, i} (P_{o, i} - P_{o, i}^{t}) + C_{smm, i} (S_{m, i} - S_{m, i}^{t})$ (7)

Therefore $\frac{\partial}{\partial x} {(K λ_{α} \frac{\partial P_{α}}{\partial x})}_{1} ≅ \frac{{(K λ_{α})}_{1 + \frac{1}{2}} (\frac{P_{α, 2} - P_{α, 1}}{Δ x}) + {(K λ_{α})}_{1 - \frac{1}{2}} (\frac{8 P_{α, \frac{1}{2}} - 9 P_{α, 1} + P_{α, 2}}{3 Δ x})}{Δ x}$ (8)

And for block N $\frac{\partial}{\partial x} {(K λ_{α} \frac{\partial P_{α}}{\partial x})}_{N} ≅ \frac{{(K λ_{α})}_{N - \frac{1}{2}} (\frac{P_{α, N - 1} - P_{α, N}}{Δ x}) - {(K λ_{α})}_{N + \frac{1}{2}} (\frac{8 P_{α, N + \frac{1}{2}} - 9 P_{α, N} + P_{α, N - 1}}{3 Δ x})}{Δ x}$ (9)

Results and discussion

The following parameters were used in the modeling to provide the best reliability with the field data; φ = 0.16; dimensionless, K = 2.7; mD, $μ_{o}$ = 1.4; cP, $μ_{m}$ = 1; cP.

Sensitivity analysis

Contact time

To provide a comparative analysis of different parameters which significantly influenced the saturation of filtrated mud, the following crucial parameters were taken into consideration. One of the parameters that were considered in the proposed model is the penetration time of 0.5, 1, 1.5, 2, and 2.5 hours after the drilling mud and formation contact. As it is evident in Figure 2, in the earlier times of drilling mud and formation contact, the saturation of filtrated mud has dropped slightly (t = 0.5 hours). Due to the increase of formation and drilling mud contact time, the saturation of filtrated mud has been decreased dramatically, and it has been reached the plateau in with the sharper increase. Therefore, when the formation and drilling mud is in the contact in longer times, the formation pore throats and cracks have occupied fast and would cause more serious formation damage rather than their contact in shorter periods.

Figure 2.

Saturation of filtrated mud versus dimensionless length at different times.

Pressure drop

Another significant parameter which was considered in this model is the pressure drop impact on the saturation of filtrated mud. Thereby, different pressure drops of 2, 5, 10, 15, and 20 psi were considered in the model to measure the saturation of filtrated mud. As can be seen in Figure 3, the lower pressure drops would cause a higher saturation of filtrated mud in the formation, and its decrease pattern has the fastest rate rather than other pressure drop changes. The reason for this phenomenon is related to the direct relation of pressure drop rise and resistivity forces, which has caused the drilling mud penetration reduction in the formation. Thereby, lower pressure drops have provided more filtrated mud penetration, and subsequently, the formation damage has increased accordingly.

Figure 3.

Saturation of filtrated mud versus dimensionless length at different pressure drops.

Oil viscosity

Regarding the dependency of the fluid viscosity to the present phases in the formation, this parameter and its influence should be taken into consideration in this model. To do this, different viscosities of 0.5, 1, 1.5, 2, and 2.5 cP were assumed in the modeling performances after the 2 hours contact of drilling mud and formation. The impact of oil viscosity on the saturation of filtrated mud is schematically plotted in Figure 4. As it is evident from Figure 4, higher oil viscosities have led to the lower filtrated mud saturation in the formation when it is contacted with the drilling mud, and subsequently, lower oil viscosities have provided more formation damage.

Figure 4.

Oil viscosity impact on the saturation of filtrated mud.

Capillary pressure coefficient

Wettability differences between the drilling mud and formation would be considered as another crucial parameter in drilling operations which should be taken into consideration in the measurement of capillary forces. Hence, to discuss the profound impact of wettability and capillary forces on the saturation of filtrated mud, a laboratory coefficient is derived from modeling these effects concisely. The effect of different values of this coefficient on the saturation of filtrated mud is depicted in Figure 5. According to the results of this analytical model, higher amounts of capillary forces have caused to higher imbibition forces and thereby the rate of penetrated drilling mud through the formation has increased dramatically. Consequently, higher capillary forces, which is the sign of more values of coefficient b, have provided more mud filtrated saturation, and the formation damage has been increased significantly in the formation during underbalanced drilling operations.

Figure 5.

Capillary pressure coefficient impact on the saturation of filtrated mud.

Water saturation

Initial water saturation was considered as one of the most important parameters when the formation is in contact with the drilling mud. Moreover, this water saturation has a dominant influence on mobility, relative density, and the penetration of drilling mud to the formation. Regarding the increase of water saturation in the formation, the saturation of filtrated mud has risen with more slope than lower water saturation. This phenomenon is elaborated as the invasion of more filtrated mud penetration to the formation. Therefore, higher water saturation would cause a higher saturation of filtrated mud in the formation, and the formation damage has increased. It is plotted in Figure 6.

Figure 6.

Water saturation impact on the saturation of filtrated mud.

Permeability

Permeability is defined as the transfer conductivity of the fluid into the formation. As permeability is one of the reservoir characteristics, its changes were considered in the modeling analysis to provide a more reliable estimation with realistic circumstances. Furthermore, permeability is directly related to the average pore diameters of the formation and affected the saturation of filtrated mud significantly. Higher values of permeability regarding the higher pore volume diameter has caused, the lower forces to penetrate the drilling mud into the formation, and therefore the saturation of filtrated mud has decreased slightly, and the formation damage has the lowest amount. The considerable influence of this parameter is schematically depicted in Figure 7.

Figure 7.

Permeability impact on the saturation of filtrated mud.

Porosity

Porosity is defined as the pore size distribution of the porous medium and one of the most critical parameters in the reservoir characteristics estimation. Different values of porosity in the modeling and investigating its impact on the saturation of filtrated mud were considered. As can be seen in Figure 8, higher porous layers have caused to lower values of filtrated mud saturation. This issue is of elaborated to the reduction of capillary forces to penetrate drilling mud to the formation.

Figure 8.

Porosity impact on the saturation of filtrated mud.

Validation of the model

As every mathematical and analytical model needed to be validated by laboratory or field data, in this paper, a set of CT scan laboratory analysis which was done by Khakshour (2010) after 1.5 hours was taken into consideration to compare the modeling results. As it is evident in Figure 9, the results of modeling are in a good agreement with the laboratory investigations for different cores. The validation of both methods is schematically depicted in Figure 9.

Figure 9.

Validation of the model by CT scan experimental data.

Conclusion

As petroleum industries have encountered numerous challenges in drilling operational performances, formation damage was one of the principal issues which should be taken into consideration. A sensitivity analysis, which is based on the following parameters were performed in the model to investigate the considerable influence of each parameter on the saturation of filtrated mud. These parameters are porosity, permeability, water saturation, oil viscosity, pressure drop, contact time, and capillary pressure. Due to high expenditures of CT scan and SEM laboratory investigation to check the formation damage effect in petroleum industries, the proposed analytical model would be beneficial instead of spending vast expenditures of experimental evaluation. As every mathematical and analytical model needed to be validated by laboratory or field data, in this paper, a set of CT scan laboratory analysis which was done by Khakshour (2010) after 1.5 hours was taken into consideration to compare the modeling results. As it is evident in, the results of modeling are in a good agreement with the laboratory investigations for different cores. The main conclusions of this paper are as the following illustrations;

Due to the increase of formation and drilling mud contact time, the saturation of filtrated mud has been decreased dramatically, and it has been reached the plateau in with the sharper increase.

The lower pressure drops would cause a higher saturation of filtrated mud in the formation, and its decrease pattern has the fastest rate rather than other pressure drop changes. The reason for this phenomenon is related to the direct relation of pressure drop rise and resistivity forces, which has caused the drilling mud penetration reduction in the formation.

Higher oil viscosities have led to the lower filtrated mud saturation in the formation when it is contacted with the drilling mud, and subsequently, lower oil viscosities have provided more formation damage.

Higher values of capillary forces have caused to higher imbibition forces, and thereby the rate of penetrated drilling mud through the formation has increased dramatically. Consequently, higher capillary forces, which are the sign of more values of coefficient b, has provided more mud filtrated saturation, and the formation damage has been increased significantly in the formation during underbalanced drilling operations.

Regarding the increase of water saturation in the formation, the saturation of filtrated mud has risen with more slope than lower water saturation. This phenomenon is elaborated as the invasion of more filtrated mud penetration to the formation.

Higher values of permeability regarding the higher pore volume diameter has caused, the lower forces to penetrate the drilling mud into the formation, and therefore the saturation of filtrated mud has decreased slightly, and the formation damage has the lowest amount.

Higher porous layers have caused to lower values of filtrated mud saturation. This issue is of elaborated to the reduction of capillary forces to penetrate drilling mud to the formation.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author(s) received no financial support for the research,authorship,and/or publication of this article.

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