There are a few factors that determine the size of orifice for natural gas. I worked for a commercial meat locker we had a large smokehouse that was fired with natural gas. And this link will take you to a chart that gives orifice based on a particular gas pressure.
http://www.joppaglass.com/burner/lowp_chrt.html
Problem is basically one of modifying the burner for burning of natural vs bottled gas. The bottled gas is far richer than nat gas. Being a "natural" product that is produced by gas or oil wells, nat gas has a high amount of CO2 (which basically dilutes the combustible constituents) and, therefore, more of the natural gas product must be burned than the bottled gas you are now using in order to get the same amount of heat or BTUs. The procedure for doing this is to increase the size of the orifice at the base of your burner assembly. The size of the orifice is dependent upon the pressure of the gas (a constant for home applications), the BTU rating of the gasseous fuel you are burning (your gas company will know the BTU rating of what they are putting in their distribution system) and the BTU rating of your burner. There are charts that will give you orifice size for nat gas based upon burner size (BTU rating of the burner). This info can be had from either your local BBQ shop or your local gas company. Since you will be going to a larger size orifice, you will have the option of either carefully drilling out your present orifice with the proper size drill or of buying a new orifice of the proper size. Unless you feel capable of carefully drilling the old orifice, just buy a new one of the proper size. Without a drill press, sometimes the drill can get away from you and you will get an irregular, ragged hole of uncertain size.
The orifice is a small brass fitting of approx 1/4 or 3/8" diameter. A new orifice can usually be bought for around a dollar or so. If you decide to just buy a new orifice, you will need to locate and remove the old one and take it with you to the BBQ store. There are several styles of orifices, depending upon BBQ burner manufacturer. You will need the old one to know the proper style for the new one.After conversion of the orifice and change-over to natural gas, you will need to adjust your air intake of your burner to get a proper combustion mixture. This will amount to loosening a screw and rotating an air intake assembly for proper colmbustion. Note the color of the flame before you change fuel or orifice size. Proper adjustment is to open the air intake so as to just get a blue flame at full gas input. My best suggestion here is to have someone who knows this procedure to do the adjustment. Often your gas company will send a service man to check proper adjustment of any of your gas appliances.
You will receive lots of discouragement from everyone you will talk with about a conversion. Your BBQ shop will want to sell you a new BBQ (which will be identical to a propane model with exception of orifice size and mixture adjustment!). If you are in doubt of any step, seek professional help from either a BBQ shop or your gas company. You certainly do not want to get into the situation where you have a lot of unburned nat gas that collects and burns off suddenly (called an explosion). A lot of personal and property damage could result.