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Fracture is a nonconstanly rock movement that usually seen as a separation in rock feature locally made and has natural sequence. Most of geological formations on top of earth crust crack at some parts of it. The fracture represents mechanical failure of rock stability because of geological pressure such as plate tectonics, lithostatic pressure exchange, thermal pressure, high pressure fluids, drilling activity, and even fluids movement, because fluids has a role as burden in the overburden rock. Even though, petroleum reservoar rocks can be found in most of depth, in deeper depth, the overburden pressure is enough to deform sedimentary rock plastically. It cannot hold on from shear pressure for a long period and flows until balanced state.

[[Fracture]] is a non constant rock movement that usually seen as a separation in rock feature locally made and has natural sequence. Most of geological formations on top of earth [[crust]] crack at some parts of it. The fracture represents mechanical failure of rock stability because of geological pressure such as plate tectonics, lithostatic pressure exchange, thermal pressure, high pressure fluids, drilling activity, and even fluids movement, because fluids has a role as burden in the overburden rock. Even though, petroleum reservoar rocks can be found in most of depth, in deeper depth, the overburden pressure is enough to deform sedimentary rock plastically. It cannot hold on from shear pressure for a long period and flows until balanced state.

Fracture can appear as a long micro rock separation in micrometer or continental fault until thousands of kilometers. It can be limited by a rock formation or a layer of rock, a fracture is a nonconstanly straight or curve line because brittle deformation process in earth crust. The plane is a weak part of rock’s feature from pressure exchange on earth crust because of fracture from one or more different ways, depends on pressure direction and type of rock. A fracture contain 2 uncommon rock’s surface, and contact each other. Volume between surfaces is called by fracture gap.

Fracture can appear as a long micro rock separation in micrometer or continental fault until thousands of kilometers. It can be limited by a rock formation or a layer of rock, a fracture is a nonconstanly straight or curve line because brittle [[deformation]] process in earth crust. The plane is a weak part of rock’s feature from pressure exchange on earth crust because of fracture from one or more different ways, depends on pressure direction and type of rock. A fracture contain 2 uncommon rock’s surface, and contact each other. Volume between surfaces is called by fracture gap.

Naturally, rock is fractured can be categorized into 3 type geologically, based on porosity system :

Naturally, rock is fractured can be categorized into 3 type geologically, based on porosity system :

==Fractured reservoir permeability==

==Fractured reservoir permeability==

The existence of two systems (matrix and fracture), permeability can be defined as matrix permeability, fracture permeability and system permeability between fracture and matrix.

The existence of two systems (matrix and [[fracture]]), permeability can be defined as matrix permeability, fracture permeability and system permeability between fracture and matrix.

Primary definition of permeability is fracture permeability can be interpretated as single fracture permeability or fracture system permeability or sometime fracture permeability of total fracture volume of rock. So permeability will be defined more detail.

Primary definition of permeability is fracture permeability can be interpretated as single fracture permeability or fracture system permeability or sometime fracture permeability of total fracture volume of rock. So permeability will be defined more detail.

Evaluation of relative permeability has generate formula.

Evaluation of relative permeability has generate formula.

Capillary pressure, desaturation curve is expected with formula,

[[Capillary pressure]], desaturation curve is expected with formula,

:<math>\frac{1}{P_c^2} = \text{B S*oe}</math>

:<math>\frac{1}{P_c^2} = \text{B S*oe}</math>

Where B is constanta and S*oe is effective saturation in oil (percentage of volume in effective porous for run off the fluids). Relative permeability is expressed to function of saturation,

Where B is constant and S*oe is effective saturation in oil (percentage of volume in effective porous for run off the fluids). Relative permeability is expressed to function of saturation,

:<math>K_{ro} = \text{S*}_o^4</math>

:<math>K_{ro} = \text{S*}_o^4</math>

:<math>K_{rg} = (1 - \text{S*}_o)^2 [1 - (\text{S*}_o)^2]</math>

:<math>K_{rg} = (1 - \text{S*}_o)^2 [1 - (\text{S*}_o)^2]</math>

Velocity, in pressure with low reduction ΔP/Δt very important for replace relative permeability curve in porous limestone with Kg/Ko value specifically.  

Velocity, in pressure with low reduction ΔP/Δt very important for replace relative permeability curve in porous limestone with Kg/Ko value specifically.  

Relative permeability from fracture and porous generate secondary porosity of limestone that has been tested with simplified model which has been developed by Erlich, 1971. It contains isolated porous in matrix, and connected porous with one or two direction cracks. Porous and fracture that connected is expressed with probability f, that indicates degree between porous connection with fracture. Value variation f from 0 – 1 is ilustrated in image below. The example of relation between fracture and porous, shows comparative size in matrix with probability fracture factor f = 0,5. Residual saturation of oil has been evaluated by Erlich model with dimension of 12 x 12 with random process based on probability realtion between porous and fracture. In this case, there are 312 fracture location possibilities. If some of the fracture filled with oil and water, transmigration process can be simulated. For water and oil transmigration, residual saturation of oil is used as parameter function f. Product of this simulation has been compard with core data and adjusment, shows no execption in core with huge secondary porosity, where transmigration cannot be mixed and value of residual saturation is producted separately. This model on fracture-matrix part known as pseudo-function so it is possible to make a better closure to transmigration evaluation.

Relative permeability from [[fracture]] and porous generate secondary porosity of limestone that has been tested with simplified model which has been developed by Erlich, 1971. It contains isolated porous in matrix, and connected porous with one or two direction cracks. Porous and fracture that connected is expressed with probability f, that indicates degree between porous connection with fracture. Value variation f from 0 – 1 is ilustrated in image below. The example of relation between fracture and porous, shows comparative size in matrix with probability fracture factor f = 0,5. Residual saturation of oil has been evaluated by Erlich model with dimension of 12 x 12 with random process based on probability realtion between porous and fracture. In this case, there are 312 fracture location possibilities. If some of the fracture filled with oil and water, transmigration process can be simulated. For water and oil transmigration, residual saturation of oil is used as parameter function f. Product of this simulation has been compard with core data and adjusment, shows no execption in core with huge secondary porosity, where transmigration cannot be mixed and value of residual saturation is producted separately. This model on fracture-matrix part known as pseudo-function so it is possible to make a better closure to transmigration evaluation.

Relative permeability in fracture-matrix system or fracture-crack-matrix system can be tested with core in laboratory with conventional method. This procedure more successfu as primary direction determinant from visible fracture. This closure can be done with using unconformity rock method so can make pseudo- relative permeability curve.

Relative permeability in fracture-matrix system or fracture-crack-matrix system can be tested with core in laboratory with conventional method. This procedure more successfu as primary direction determinant from visible fracture. This closure can be done with using unconformity rock method so can make pseudo- relative permeability curve.

Flow condition is illustrated in image below, where trickle flow (first image) may the bazaar phase from bubble to follow one wall; bubble flow (second image) where bubble flow both fractured walls so there is bouyancy force; string flow (third image) fluids that appear constantly and wet phase follows fractured wall.

Flow condition is illustrated in image below, where trickle flow (first image) may the bazaar phase from bubble to follow one wall; bubble flow (second image) where bubble flow both fractured walls so there is bouyancy force; string flow (third image) fluids that appear constantly and wet phase follows fractured wall.

Physical parameter of fluids and rock that effects flow in the fractured media are density, viscosity, surface tension, bazaar properties, fracture length, fractured wall roughness, and tilt degree. First thing that must be known is 2 phases flow in relative permeability which can be seen in simplified model Romm, 1966., that produce 10 until 20 paralel fracture. Saturation is counted with electric resistance value and evaluated permeability of velocity flow of fluids, water, and kerogen. The result will show linear tred of diagram Kf vs saturation. It also determine the limit value of 2 phase from unreducted fracture flow become a result of a fracture. Relation between fractures can be modified each flow characteristics perfectly.

Physical parameter of fluids and rock that effects flow in the fractured media are density, viscosity, surface tension, bazaar properties, fracture length, fractured wall roughness, and tilt degree. First thing that must be known is 2 phases flow in relative permeability which can be seen in simplified model Romm, 1966., that produce 10 until 20 paralel fracture. Saturation is counted with electric resistance value and evaluated permeability of velocity flow of fluids, water, and [[kerogen]]. The result will show linear tred of diagram Kf vs saturation. It also determine the limit value of 2 phase from unreducted fracture flow become a result of a fracture. Relation between fractures can be modified each flow characteristics perfectly.

Other experiments conducted by du Prey, 1973, which resulted in two models where fluid is injected from one and more holes. Relative permeability derived from the value of Q_o and Q_w through the equation:

Other experiments conducted by du Prey, 1973, which resulted in two models where fluid is injected from one and more holes. Relative permeability derived from the value of Q_o and Q_w through the equation:

:<math>K_{rw} = \frac{12 Q_w \mu_w L_f}{a b^3 \Delta P_w}</math>

:<math>K_{rw} = \frac{12 Q_w \mu_w L_f}{a b^3 \Delta P_w}</math>

Because of the pressure ΔP_o and ΔP_w can’t be measured if the fluid is moving, so that the problem should be avoided by maintaining a phase that doesn’t move and forget about the possibility of them, moving as the effects of segregation fluid. In this case, instead of a decrease in pressure, gravity  

Because of the pressure ΔP_o and ΔP_w can’t be measured if the fluid is moving, so that the problem should be avoided by maintaining a phase that doesn’t move and forget about the possibility of them, moving as the effects of segregation fluid. In this case, instead of a decrease in pressure, [[gravity ]]

:<math>\Delta \gamma \times g \times \sin{\alpha}</math>  

:<math>\Delta \gamma \times g \times \sin{\alpha}</math>  

plays a role. Saturation is given in varying conditions of flow by counting the length of time or the time of trial.

plays a role. Saturation is given in varying conditions of flow by counting the length of time or the time of trial.

#*<math>dLD = \frac{1}{9.44 \times 10^{-3}exp(FII) - 9.3 \times 10^{-3}}</math>

#*<math>dLD = \frac{1}{9.44 \times 10^{-3}exp(FII) - 9.3 \times 10^{-3}}</math>

Where:

Where:

:dLU = lateral distance to the fault plane for block up, feet  

:dLU = [[lateral]] distance to the fault plane for block up, feet  

:dLD = lateral distance to the fault plane for block down, feet  

:dLD = lateral distance to the fault plane for block down, feet  

:FII = fracture intensity index, fraction

:FII = fracture intensity index, fraction

===Solution A===

===Solution A===

By using the existing formula, fracture intensity index is:

By using the existing formula, [[fracture]] intensity index is:

:<math>\text{FII} = \frac{ \frac{1}{R_{xo}} - \frac{1}{R_t}}{ \frac{1}{R_{mf}} - \frac{1}{R_w}} = \frac{ \frac{1}{9.7} - \frac{1}{95}}{ \frac{1}{0.17} - \frac{1}{0.19}} = 0.15</math>

:<math>\text{FII} = \frac{ \frac{1}{R_{xo}} - \frac{1}{R_t}}{ \frac{1}{R_{mf}} - \frac{1}{R_w}} = \frac{ \frac{1}{9.7} - \frac{1}{95}}{ \frac{1}{0.17} - \frac{1}{0.19}} = 0.15</math>

The distance to the closest fault estimated from the correlation of the blocks up and can be estimated using the equation:

The distance to the closest fault estimated from the correlation of the blocks up and can be estimated using the equation:

:<math>k = \frac{\displaystyle \sum_{i=1}^n \left ( \frac{1}{S_{vpi}^4} \right )}{\displaystyle \sum_{i=1}^n \left ( \frac{K_{Ti}}{\phi_i S_{vpi}^2} \right )}</math>

:<math>k = \frac{\displaystyle \sum_{i=1}^n \left ( \frac{1}{S_{vpi}^4} \right )}{\displaystyle \sum_{i=1}^n \left ( \frac{K_{Ti}}{\phi_i S_{vpi}^2} \right )}</math>

Where

Where

:<math>Equation</math>

:<math>K_T = 6f_{sp} \tau </math>

In the case of formations that contain little number of holes per unit pore volume, as in a reservoir with high storage capacity in the rock matrix, and the storage capacity is very low in the hole, n1>>n2, the equation can be stated as follows:

In the case of formations that contain little number of holes per unit pore volume, as in a reservoir with high storage capacity in the rock matrix, and the storage capacity is very low in the hole, n₁>>n₂, the equation can be stated as follows:

:<math>Equation</math>

:<math>k = \frac{\phi_1}{2S_{pv1}^2} = \frac{\phi_1 r_{c1}^2}{8}</math>

Where subscript 1 for the primary pore space that accommodates almost all fluids. In the case of n2 >> n1, for example, on rocks with fluid accommodated in secondary porosity such as cracks and holes. The above equation would be:

Where subscript 1 for the primary pore space that accommodates almost all fluids. In the case of n2 >> n1, for example, on rocks with fluid accommodated in secondary porosity such as cracks and holes. The above equation would be:

:<math>Equation</math>

:<math>k = \frac{\phi_2}{2S_{pv2}^2} = \frac{\phi2 r_{c2}^2}{8}</math>

Where subscript 2 for secondary pore space. So in the case of n1>>n2 and n2>>n1, dual porosity system can be estimated from a single pore system. n1 approximately equal to n2, because it can not determine the value of n1 and n2, so it can be approached to take the geometric mean of the two capillary system, for example:

Where subscript 2 for secondary pore space. So in the case of n1>>n2 and n2>>n1, dual porosity system can be estimated from a single pore system. n1 approximately equal to n2, because it can not determine the value of n1 and n2, so it can be approached to take the geometric mean of the two capillary system, for example:

:<math>Equation</math>

:<math>k = \sqrt{\left ( \frac{\phi_1 r_{c1}^2}{8} \right ) \left ( \frac{\phi_2 r_{c2}^2}{8} \right )} = \frac{r_{c1} r_{c2}}{8} \sqrt{\phi_1 \phi_2}</math>

Using the average value of rc1 and rc2, and the average value of φ1 and φ2, the equation similar to the Kozeny equation.

Using the average value of rc1 and rc2, and the average value of φ1 and φ2, the equation similar to the Kozeny equation.

Fracture provides a capacity to store and permeability and fluid flow is controlled by the properties of the fracture. The equation for velocity of volumetric flow, combined with Darcy's law, creating basic approaches to estimate the fracture permeability.

Fracture provides a capacity to store and permeability and fluid flow is controlled by the properties of the fracture. The equation for velocity of volumetric flow, combined with Darcy's law, creating basic approaches to estimate the fracture permeability.

Determined a block of rock that cracking naturally with fractures, as shown in [[:File:UGM_Porosity_Fig_10.png|Figure 10]].

Determined a block of rock that [[cracking]] naturally with fractures, as shown in [[:File:UGM_Porosity_Fig_10.png|Figure 10]].

Assumed fracture is a box, smooth and doesn’t contain any mineral, Hagen- Poiseiulle equation is:

Assumed fracture is a box, smooth and doesn’t contain any mineral, Hagen- Poiseiulle equation is:

:<math>Equation</math>

:<math>q = \frac{nh_f w_f^3}{12} \frac{\Delta P}{\mu L}</math>

Darcy's law is:

Darcy's law is:

:<math>Equation</math>

:<math>q = kA \frac{\Delta P}{\mu L}</math>

The equation obtained two calculations and troublesolving of permeability results:

The equation obtained two calculations and troublesolving of permeability results:

:<math>Equation</math>

:<math>k = \frac{nh_f w_f^3}{12A}</math>

Difficulties were obtained using the above equation is the number of fractures, fracture height, and width of fracture should be sought. Thus defined as:

Difficulties were obtained using the above equation is the number of fractures, fracture height, and width of fracture should be sought. Thus defined as:

:<math>Equation</math>

:<math>\phi = \frac{V_p}{V_b} = \frac{nh_f w_f L}{AL}</math>

And

And

:<math>Equation</math>

:<math>A = \frac{nh_f w_f}{\phi}</math>

So it can be substituted:

So it can be substituted:

:<math>Equation</math>

:<math>k = \frac{\phi w_f^2}{12}</math>

Previous equation k = φr2/8, where the capillary radius r and constant 8 exchanged withfracturewidthwf and12.The equation is usually used to calculate fracture permeability. Fracture porosity in percent and fracture width in micrometers (m), so the equation becomes:

Previous equation  

:<math>Equation</math>

:<math>k = \frac{\phi r^2}{8} </math>

where the capillary radius r and constant 8 exchanged with fracture width wf and 12. The equation is usually used to calculate fracture permeability. Fracture porosity in percent and fracture width in micrometers (m), so the equation becomes:

:<math>k_f = 8.33 x 10^{-4} w_f \phi_f</math>

Where kf in darcy.

Where kf in darcy.

Previous equation can be used to calculate wf if porosity and permeability are known from well log or well testing :

Previous equation can be used to calculate wf if porosity and permeability are known from well log or well testing :

:<math>Equation</math>

:<math>w_f = \sqrt{12 \frac{k}{\phi}}</math>

So that, when viewed the relationship between the dimensions of fractures and fracture permeability, will be shown in  [[:File:UGM_Porosity_Fig_11png|Figure 11]] (Nelson, 2001). So that, when viewed the relationship between the dimensions of fractures and fracture porosity, will be shown in [[:File:UGM_Porosity_Fig_12.png|Figure 12]] (Nelson, 2001).

So that, when viewed the relationship between the dimensions of fractures and fracture permeability, will be shown in  [[:File:UGM_Porosity_Fig_11png|Figure 11]] (Nelson, 2001). So that, when viewed the relationship between the dimensions of fractures and fracture porosity, will be shown in [[:File:UGM_Porosity_Fig_12.png|Figure 12]] (Nelson, 2001).