For this reason, computer modeling of economically viable reservoirs is often carried out. Geologists , geophysicists and reservoir engineers work together to build a model which allows simulation of the flow of fluids in the reservoir, leading to an improved estimate of the recoverable resources. Reserves are only the part of those recoverable resources that will be developed through identified and approved development projects. Because the evaluation of "Reserves" has a direct impact on the company or the asset value, it usually follows a strict set of rules or guidelines even though loopholes are commonly used by companies to inflate their own share price.

Government may also have their own systems, making it more complicated for investors to compare one company with another. To obtain the contents of the oil reservoir, it is usually necessary to drill into the Earth's crust, although surface oil seeps exist in some parts of the world, such as the La Brea tar pits in California , and numerous seeps in Trinidad. A virgin reservoir may be under sufficient pressure to push hydrocarbons to surface. As the fluids are produced, the pressure will often decline, and production will falter.

The reservoir may respond to the withdrawal of fluid in a way that tends to maintain the pressure. Artificial drive methods may be necessary. This mechanism also known as depletion drive depends on the associated gas of the oil. The virgin reservoir may be entirely liquid, but will be expected to have gaseous hydrocarbons in solution due to the pressure. As the reservoir depletes, the pressure falls below the bubble point , and the gas comes out of solution to form a gas cap at the top.

This gas cap pushes down on the liquid helping to maintain pressure. This occurs when the natural gas is in a cap below the oil. When the well is drilled the lowered pressure above means that the oil expands. As the pressure is reduced it reaches bubble point and subsequently the gas bubbles drive the oil to the surface. The bubbles then reach critical saturation and flow together as a single gas phase.

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Beyond this point and below this pressure the gas phase flows out more rapidly than the oil because of its lowered viscosity. More free gas is produced and eventually the energy source is depleted. In some cases depending on the geology the gas may migrate to the top of the oil and form a secondary gas cap. Some energy may be supplied by water, gas in water, or compressed rock.

These are usually minor contributions with respect to hydrocarbon expansion. By properly managing the production rates, greater benefits can be had from solution-gas drives. Secondary recovery involves the injection of gas or water to maintain reservoir pressure. In reservoirs already having a gas cap the virgin pressure is already below bubble point , the gas cap expands with the depletion of the reservoir, pushing down on the liquid sections applying extra pressure.

This is present in the reservoir if there is more gas than can be dissolved in the reservoir. The gas will often migrate to the crest of the structure. It is compressed on top of the oil reserve, as the oil is produced the cap helps to push the oil out. Over time the gas cap moves down and infiltrates the oil and eventually the well will begin to produce more and more gas until it produces only gas. It is best to manage the gas cap effectively; that is, placing the oil wells such that the gas cap will not reach them until the maximum amount of oil is produced.

Also a high production rate may cause the gas to migrate downward into the production interval.

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In this case over time the reservoir pressure depletion is not as steep as in the case of solution based gas drive. In this case the oil rate will not decline as steeply but will depend also on the placement of the well with respect to the gas cap. As with other drive mechanisms, water or gas injection can be used to maintain reservoir pressure. When a gas cap is coupled with water influx the recovery mechanism can be highly efficient. Water usually salty may be present below the hydrocarbons. Water, as with all liquids, is compressible to a small degree.

As the hydrocarbons are depleted, the reduction in pressure in the reservoir allows the water to expand slightly. Although this unit expansion is minute, if the aquifer is large enough this will translate into a large increase in volume, which will push up on the hydrocarbons, maintaining pressure. With a water-drive reservoir the decline in reservoir pressure is very slight; in some cases the reservoir pressure may remain unchanged. The oil rate will remain fairly stable until the water reaches the well.

In time, the water cut will increase and the well will be watered out. The water may be present in an aquifer but rarely one replenished with surface water. This water gradually replaces the volume of oil and gas that is produced out of the well, given that the production rate is equivalent to the aquifer activity. That is, the aquifer is being replenished from some natural water influx. If the water begins to be produced along with the oil, the recovery rate may become uneconomical owing to the higher lifting and water disposal costs.

If the natural drives are insufficient, as they very often are, then the pressure can be artificially maintained by injecting water into the aquifer or gas into the gas cap. The force of gravity will cause the oil to move downward of the gas and upward of the water. DOI: An, C. Bhide, R.

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American Rock Mechanics Association. Blanton, T. Boyle, E. Cao, Y. Durlofsky, L. Gale, J. Natural fractures in shale: a review and new observations. AAPG Bull, 98 11 , pp.

Natural fractures in the Barnett Shale and their importance for hydraulic fracture treatments. AAPG Bull. Jenkins, C. AAPG Bull ; 93 11 : e Kim, J. McLennan, J. Mi, L. The impact of diffusion type on multiscale discrete fracture model numerical simulation for shale gas. In general, the wellbore passes through one fracture grid, so. Because the governing equations cannot be calculated directly, we must choose some methods to discretize and linearize their time term and space terms.

We do not give the details of the derivation in this paper, but we will introduce a new method to understand the relationship between the coefficient matrix and the EDFM connection list, which can help beginners study EDFM effectively. If the well produces under constant pressure,. After assembling discrete equations of all matrix cells and fracture cells, we can obtain a system of linear equations to calculate 20 where A represents the coefficient matrix a large sparse matrix , represents the vector of unknown pressure difference between two iteration steps, which is assembled from an unknown matrix and the fracture pressure difference and in the EDFM, and b represents a constant vector.

From Equation 21, we can see that the coefficient matrix is sparse and the locations of nonzero elements in the matrix are symmetric. However, when the upstream method is employed for the flux term, the coefficient matrix is not symmetric. To be specific, the volume factor B at the interface of two cells is related to the larger pressure of the two cells and will contribute to the coefficient matrix. Based on the physical meaning, this matrix can be divided into four parts. Algebraic equations for the i th cell are represented by the i th row in the coefficient matrix.

The a i , j element, which is the element of the i th row and j th column in the coefficient matrix, represents the relationship between cell i and cell j , and the cell can be a matrix cell or a fracture cell. Therefore, if a i , j is not equal to zero, there is a connection between cell i and cell j. The location of a i , j in different parts of the matrix also means different connections.

If cell i is connected to cell j , then cell j will also be connected to cell i , which makes both a i , j and a j , i nonzero. This makes the locations of nonzero elements symmetric in the matrix. Besides, a cell only connects to a few cells, which gives the matrix only a few nonzero elements per line, so the matrix is sparse. Based on the above discussion of the connection list and matrix properties, we created a method to assemble this matrix. First, we sort the grid number of the matrix, fracture, and well cells in a natural order. Second, we construct the connection list, which means, for every single cell, find out which grids it is connected to and record the types of these connections.

Then, we calculate the transmissibility and other factors that are required for the element in the matrix. Finally, according to the connection list, we assemble the coefficient matrix. In this way, we built the relationships among the EDFM connectivity list, the physical meaning, and the location of the nonzero elements in the matrix. It then becomes very simple to understand and assemble the matrix.

Therefore, we only need to construct the upper left part of the coefficient matrix in Equation It is very simple. Based on a comparison of random fracture generation methods, we used the most flexible method to randomly generate fractures. It is very easy to change the generation of fractures according to realistic distributions. The EDFM uses equal time steps of 1 day. This is because, for the DFM, there are refined grids around wells and fractures, and there are only four fractures and one horizontal well in this simple scenario. However, the advantage of the EDFM is that it can handle a scenario with a large number of complex fractures without refined grids around each fractures, just like the scenarios as shown in Section 5.

There is only a slight difference in the early stage, which is probably due to the simplification for interporosity flow for the EDFM. The EDFM assumes that the fluid in the matrix perpendicularly flows to the fracture.

## Simulation of tight fluid flow with the consideration of capillarity and stress-change effect

This simplification method for the pressure ignores the variation of pressure within the cells. Sensitivity analysis is a quantitative method to study the effect of parameter variation on the model results. It can identify the key reservoir and fracture parameters and provide important guidance for designing the development program.

In our work, based on two tight oil reservoir scenarios, we conducted several simulation studies.

## The reservoir engineering aspects of fractured formations

A 3D model was adopted for the fracture height, and the other parameters used a 2D model. In the 3D model, except for the formation thickness of m, which is divided into 10 grids in the z direction, the simulated parameters were the same as in the 2D model. We studied the effect of the number of hydraulic fractures 4, 6, 8, 12, and The result was the same as our qualitative understanding. Production is positively correlated with the number of fractures.

Beyond 8, the effect of fracture number on productivity is reduced. Therefore, there is no need to design too many hydraulic fractures. Any number slightly greater than that at which the inflection point occurs is enough. Thus, longer hydraulic fractures should be designed as much as economically possible. As the time increases, the difference gradually becomes smaller.

However, as for hydraulic fractures, there is always something proppant, raised part of a rock face, etc. So, in practice, the conductivity of the fracture will not be very low. However, the size of the SRV remains almost the same. Therefore, the difference in COP is not large, and hydraulic fracture conductivity does not have much impact on production. We also studied the effect of the length of the horizontal well m, m, m, and m. After that, the longer the horizontal well is, the higher the production becomes.

A length of m had the biggest decline in daily production. This occurs because, during the development of a tight reservoir, the reservoir pressure decreases and the pore channels become smaller, resulting in an increase in flow resistance, a decrease in matrix permeability, and ultimately a decrease in production. We used a 3D model to analyze the sensitivity of hydraulic fracture height. The 3D model is basically the same as the 2D model, except that there are multiple layers in the z direction to account for the influence of gravity and the flow between longitudinal layers.

To save calculation time, we set the time step to 2 days. However, during the later production period, daily oil production is almost the same. We determined that due to the different sizes of the SRVs, there is a large difference in the initial production.