Most of the districts use TY Pickett or Capital Appraisal. They have a few others but mainly those two. Unless you are a petroleum engineer or have the knowledge to estimate the reserves I would leave that aspect alone. What you can do and have a high probability of succeeding is evaluate the actual price used for gas and oil the appraisal company is using. All you would have to do is calculate the average price per month on a well by well basis. Add them all up and divide by 12. That gives you the average price for the product for the year and then the appraisal company usually uses your price with proof.
The process the appraiser goes through is sometimes not as thorough for pricing as it should be. Sometimes all they do is get a data drop for the entire county and calculate the average price that way. So if you are receiving a higher price you benefit from the lower priced areas in the county. If your prices are lower than the average you are going to pay more than you should. All at the same time the districts are going to receive the same amount of money no matter what. If no one disputes their bill it should be nearly if not the exact same as sent out in the estimate. When people start contesting and proving that their production is not receiving as high of price they will get a reduction in value and the tax percentages will go up.