SIMULATION VERIFIES ADVANTAGES OF MULTIPLE FRACS IN HORIZONTAL WELL

Richard F. Walker, Erwin Ehrl, Mahmoud Arasteh
Mobil Erdgas-Erdol GmbH
Celle, Germany

Simulation studies indicate that the emerging technology of multiple fractured horizontal wells (MFHW) is a strong candidate for economic development of tight gas reserves in Germany.

Mobil Erdgas Erdol GmbH (MEEG) conducted the feasibility study for the exploitation of low-permeability gas sands in the Sohlingen field in northwest Germany (Fig. 1).

In this area, MEEG has identified the presence of large quantities of gas reserves and resources.

MEEG defines reserves as hydrocarbons that can be economically developed with existing technology at current market prices, and resources as hydrocarbon quantities that are not currently economic with existing prices and technology.

The objective of the simulation was to determine an economic method to develop these reserves and resources.

Mobil, as operator, began developing Sohlingen field in 1982. Partners in the field are BEB Erdgas und Erdol GmbH, RWE-DEA AG, and Wintershall AG.

Table 1 shows typical reservoir parameters for the Rotliegend main sand at Sohlingen. Mobil has drilled and completed three vertical wells in the main sand of this field. Cumulative production has reached 19 bcf (Fig. 2).

These wells were conventionally stimulated with hydraulic fracturing. The fracs increased productivity significantly, but better methods still were needed to develop the gas resources.

Because a production forecast is critical for determining if multiple fractures in horizontal wells are economic, MEEG pursued several alternatives for estimating future production. Two of these are discussed in this article.

The first method is using Hyfrac, Mobil's PC program for hydraulic fracture design and analysis. The model can design a fracture stimulation for a user-specified number of hydraulic fractures and provide a production forecast for that scenario, including scoping economics. This program, of course, is limited to an idealized reservoir with constant properties.

MEEG was also interested in investigating the significance of certain effects that were beyond the capabilities of Hyfrac. These included the interference between the fracs, and the effects of different drainage areas on ultimate production.

To address these concerns requires numerical simulation. MEEG developed a numerical simulation to create a forecast for a horizontal well with multiple hydraulic fractures using Mobil's multipurpose reservoir simulator, Pegasus. This simulator incorporates the horizontal well equations of Babu-Odeh. When making fore casts for complex scenarios such as horizontal wells with multiple fracs, one should understand the assumptions of the method used, and be sure these assumptions are appropriate for the problem being addressed.

HYFRAC FORECAST

Mobil's PC program Hyfrac was used to determine the best combination of horizontal well length, frac parameters, and associated production forecasts for various numbers of hydraulic fractures.

Needed first to run the program were frac input design parameters for the reservoir. Representative data were secured by modeling an existing vertical well in the same field, which had been stimulated with a single vertical frac. MEEG developed a matrix of combinations of parameters through iterative calculations. After selecting the best match using production data as a benchmark, the match was verified by traditional type curves. This match defined critical reservoir parameters such as permeability, and also provided empirical efficiency values for variables governing frac design. 4

Next, the history-matched data from the fractured vertical well were extended to the design of a horizontal well with multiple fractures in the same field. Numerous scenarios with different numbers of fracs and various lengths were investigated. For the sake of simplicity, this article will discuss only one scenario, as follows:

A horizontal well has six vertical fractures perpendicular to its axis.
The well is symmetrically centered in a 240-acre square drainage area.
Each frac is infinitely conductive, that is, gas influx along the length of the frac into the well bore experiences only negligible pressure drop.
The fracs are spaced equally along the horizontal section of the well (Fig. 3).

Notice that the edge of the square drainage area is positioned at a distance from the outer fracs that is equal to half the spacing between the fracs. This results in a condition of symmetry, with identical drainage areas for each frac.

This symmetry assumption also dictates the interference effect among the multiple fracs. In such a drainage area configuration, each frac is surrounded by a stationary no flow boundary (Fig. 4). The production forecast, Fig. 5a, was developed with this approach.

The early constant rate portion of the curve reflects the specified initial producing rate. During the later time, rate decline occurs when a specified minimum flowing bottom hole pressure constraint is reached.

SIMULATOR VALIDATION

The PC program had determined the economically optimum number and length of fracs. But because MEEG was interested in pursuing some less idealized effects, it had to validate the use of a numerical simulator to model wells that were stimulated with a massive hydraulic fracture.

MEEG's practice had been more oriented toward analytical and type curve solutions for hydraulic fracture productivity calculations. 3 Because MEEG had not done a great deal of numerical simulation of wells stimulated with hydraulic fractures, this validation was considered essential.

In this validation, the production history was modeled for an existing vertical well that had been stimulated with a single hydraulic fracture. This was the same well that had been evaluated with Hyfrac.

The Pegasus simulator contains no specific analytical functions to represent hydraulically fractured well. Therefore, a hydraulically fractured well model was developed by assigning appropriate permeability values and cell dimensions to a rectangular simulation grid.

The variation in cell dimensions and permeabilities around the frac was, of course, extreme.

The reservoir's 0.009-md effective permeability contrasted sharply - with the permeability of the frac cells measured in Darcies. And the small width of the frac cell contrasted to "normal" sizes of simulation cells. MEEG solved these problems primarily by combining the buffering cells surrounding the fractures with carefully controlled time steps.

MULTIPLE FRAC SIMULATION

After successfully developing a numerical simulation technique to model a hydraulically fractured well, the next problem was to model multiple fractures.

One of the first points addressed was the pressure drop along the horizontal length of the well bore. 5 With the planned tubular configuration and at the given producing rates, the pressure drop was not significant.

Another point was to properly address the pressure drop of radial flow into the well bore. This pressure drop can be significant in fractures with finite conductivity.

MEEG's multiple fracture investigation dealt only with infinite conductivity fractures and when the pressure drop into the well bore is negligible.

The symmetrical arrangement of fractures within the drainage area is shown in Fig. 4. These were modeled using a single representative area with appropriate distances to drainage area boundaries. Fig. 3b shows the simulation production forecast of the six frac symmetrical case compared to that of the Hyfrac model. Cumulative production vs. time for both is identical for early times because in both models production began with a constant initial production rate. A slight difference is noticeable later during rate decline.

This difference was accepted as reasonable and attributed to the different assumptions in the two methods. Because Pegasus is a numerical simulator, its computational approach is different from Hyfrac's, and it incorporates the effects of more Variables (e.g., formation compressibility). A similar difference was also noticed in the comparison of the sin-le frac cases.

This symmetry assumption seemed perhaps a bit restrictive because of the rarity of homogeneous reservoirs with equally spaced wells. In a low-permeability reservoir with a larger peripheral area surrounding the fracs, should one expect any significant increase in productivity? Put in another way, Would the first well in a large area benefit from untapped portions of the reservoir farther away? MEEG investigated this "shape factor", effect for the scenario with a non-symmetrical drainage pattern as shown in Fig. 6. Specifically, MEEG wished to:

Improve the definition of the interference between the multiple fractures during the transient flow period for this less idealized drainage configuration.
Quantify any additional productivity from a reservoir boundary that is not constrained at a distance of half the frac spacing.

To answer these questions, MEEG created a new model that simulated six identical fractures with a similar horizontal well length and fracture spacing, but with a larger reservoir areal extent (Fig. 6).

The height (y direction) of the reservoir was doubled, and the width (x direction) was tripled. The well remained within the original 240 acres, although MEEG extended the outer fracs to the edge of the 240 acre beyond the artificial "d/2" limit of Fig. 3.

Notice that the degree of symmetry is reduced, because the outer fracs have a larger area available to them. Thus, the simulation was slightly more complex but the approach was otherwise identical.

Initially the results were as expected. The larger reservoir recovers more reserves in later time (Fig. 7a).

Closer inspection revealed the presence of an interesting phenomenon. Fig, 7b shows the well's production rate as a function of time. Note the early time plateau period with the well producing at a constant rate and then the beginning of rate decline. This is the composite production from all six of the fracs.

Fig. 7c shows the same data for the three representative half fracs. The "greedy" outer fracs with fracture conductivities identical to the inner fracs, take more than their proportional share of the total production, even during the period of constant (total well) production rate. Fig. 8 shows the same data for all six fracs, with the inequality increasing with time.

For the symmetrical case each frac's production rate can easily be calculated by dividing the total well rate of the time of interest by the number of fracs. This is not true in this case. Here, the drainage pattern is two groups of opposing concentric "U-shapes," opening outward toward the less depleted areas of the reservoir (Fig. 9).

This schematic represents the drainage area for each frac at one specific time in the producing life of the well. The pattern shifts continually. The no flow boundaries between the fractures are dynamic as opposed to the stationary boundaries of the symmetrical case.

This drainage pattern is remarkably similar to that generated by multiple gas wells producing with a constant pressure boundary created b), an aquifer.8 The impact of this disproportionate sharing of the production beyond technical interest is still under consideration.

It brings up questions such as:

Should inner fracs be increased in length or capacity to equally share in the production?
Is the proppant production tendency of the outer fracs significantly increased?

MEEG has investigated these questions, but addressing them here is beyond the scope of this article.

To our knowledge, this dynamic drainage area phenomenon has not been addressed in the literature. Addressing this behavior analytically or With type curves will be difficult, and future pursuit will likely require numerical simulation.

REFERENCES

Babu, D.K., and Odeh, A.S., "Productivity of a Horizontal well," SPEJ, Nov. 1989, pp. 417-21.
Agarwal, R.G., Carter, R.D., and Pollock, C.B., "Evaluation and Performance Prediction of Low Permeability Gas Wells Stimulated by Massive Hydraulic Fracturing," JPT, March 1979, pp. 362-72.
Economides, M.J., and Nolte, K.G., Reservoir Stimulation, Prentice Hall, 1989, pp. 11-1 to 11-18.
Nolte, K.G., and Economides, M.J., "Fracture Design and Validation With Uncertainty and Model Limitations," JPT, September 1991, pp. 1147-55
Novy, R.A.. "Pressure Drops in Horizontal wells: When Can TheN. Be Ignored?," SPE Piper No, 24941.
Soliman, Hunt, J.L., and El Rabaa, A.M., "Fracturing Aspects of Horizontal Wells," JPT, August 1990, pp. 967-68.
Matthews, C.S., and Russell, D.G., Pressure Buildup and Flow, Tests in Wells, SPE Monograph Series, 1967, pp. 109-112.
Ramey, H.J., Jumar, A., and Gulati, M.S. Gas Well Test Analysis Under Water-Drive Conditions, American Gas Association at Stanford University, 1973, pp. 98-102, 179-180, and 195.